# Appendix A LDV Measurement System Manual

```Appendix A
LDV Measurement System Manual
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A.1
Introduction
Laser Doppler Velocimetry (LDV) is a non–intrusive method for the measurement of velocity. This technique measures the frequency shift (Doppler shift) in the
light scattered from particles moving through the intersection of two coherent laser
beams. Single probe implementations can measure two of three velocity components
simultaneously. Directional sensitivity of the velocity probe is obtained by frequency
shifting one of the two intersecting beams. The result is a non-intrusive measurement
technique well suited for highly turbulent separated flows. A complete introduction
to LDV can be found in many textbooks on the subject, some of which are given
in the bibliography. Commercial system manuals also contain a treasure of technical
information and should be consulted if available.
A.2
Principles of Operation
LDV relies on the principle that the light scattered from a particle moving
through a coherent laser beam will be frequency shifted in direct proportion to the
particle’s velocity in the direction of the beam. The difficulty of measuring a frequency shift of several megahertz out of the light frequency of several gigahertz is
removed by mixing the shifted frequency light and original frequency light. The result of the mixture of these two coherent signals will contain a component at the
Doppler shift frequency. In practice, the mixing of light signals can be achieved by
intersecting and focusing two coherent laser beams causing the intersection area to exhibit a diffraction pattern. If both laser beams are of exactly the same frequency and
are coherent, the diffraction pattern will be stationary. As a particle moves through
the diffraction pattern the scattered light from the particle will exhibit frequency content proportional to the particle’s velocity perpendicular to the diffraction pattern.
The velocity component measured by such a beam intersection is the resultant of
adding the two beam vectors as shown in Figure A.1. An example diffraction pattern
is shown in Figure A.2 using the optical probe described here with only green light
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1st beam
direction
measured
2nd beam
Figure A.1: Velocity vector measured by a given laser beam pair
(514nm) emanating from the probe.
In its raw form, as just described, the LDV will not be able to measure the
direction of the velocity component perpendicular to the diffraction pattern. To
obtain a direction sensitive signal, one of the two laser beams is frequency shifted
causing the diffraction pattern to move at a constant velocity, directly related to
Figure A.2: Photograph of single 514 nm diffraction pattern
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the frequency shift between the two beams. The frequency contained in the light
scattered from the particle will now be centered about the shift frequency of the two
beams and the velocity direction can be deduced from the frequency.
To measure two velocity components simultaneously, a second pair of beams is
focused onto the same point, however, with the laser beam resultant orthogonal to the
first laser beam pair resultant. In this manner, two independent velocity components
will be measured by the two beam pairs. Similarly, if a third pair of beams were
focused on the same point, the third velocity component could be measured. The
problem with implementing a 3-D LDV system is that in order for the third component
to be measured, the resultant of the two laser beam vectors can not lie in the same
plane as the resultants of the first two laser beam pairs. In practice, this requires
that the third pair of beams not be focused using the same focusing lens as the first
two laser beam pairs as this would guarantee that the resultant of the third pair of
laser beams lies in the same plane as the resultants of the first two pairs of laser
beams. This also means that if the angular alignment of the focusing lens is changed
without changing the measurement location, successive measurements at this same
point allow the third component of mean velocity to be deduced. A close-up of the
diffraction patterns generated by the green and blue beams pairs without frequency
shifting of one of the beams is shown in Figure A.3.
A further distinction in LDV systems is made based on the manner in which the
scattered light is collected. If the light is collected on the opposite side of the laser
beam focusing lens, the system is called a forward scatter system because the light
collected is scattered in the direction of the laser beams. If the light is collected on the
same side as the laser beam focusing lens, usually even using the same lens, the system
is called a back-scatter system. The advantage of forward-scatter systems is that the
amount of light scattered in that direction is greatest. The back-scatter system has
the advantages of requiring less optical access and being more spatially compact with
the penalty that the amount of light scattered back towards the focusing lens is much
smaller than the light scattered away from the focusing lens.
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Figure A.3: Photograph of the 2-D diffraction pattern
A.3
Laser Operation Alignment and Maintenance
LDV performance is strongly influenced by the characteristics of the focused laser
beams. Proper laser alignment and good maintenance practices are key to maintaining
the performance of the LDV system as a whole.
A.3.1
Laser requirements
The LDV requires that the laser beams focused produce a sharp diffraction pattern with bright fringes and good contrast between the bright fringes. To obtain such
a diffraction pattern, the beams must be coherent, of equal intensity and exhibit the
same polarization. Beyond these requirements, detection of the scattered light signal
requires that the focused laser beams have the highest intensity possible, to generate more scattered light. This is especially important in a back-scatter LDV as was
implemented here. Furthermore, the laser must be operated in multi-band mode so
that at least two high intensity laser beams of different wavelengths are generated.
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aperture wheel
shutter
ouput coupler
cavity seal
Figure A.4: Front of the laser head assembly
A.3.2
Basic laser alignment and maintenance
To maintain and align the laser, the instructions contained in the Spectraphysics
2020-05 manual (Spectraphysics, 1984) should be followed closely. The alignment
instructions have been verified with their use all the way through starting with the
relatively simple procedure for walking the mirrors to the more complicated procedure
for aligning the plasma tube and centering the beam on the aperture. However, some
additional information is helpful for the clarification of several of the instructions. It
has also been necessary to develop a ”from scratch” plasma tube alignment procedure.
For the case where all lasing is lost, the Spectraphysics 2020-05 manual, does
not give a re-alignment procedure. However, such a circumstance had to however be
handled and the following is the procedure used to re-align the laser plasma tube,
output coupler and high reflector. The start of the procedure assumes that the laser
head is open with all power disconnected and cavity seals retracted. The procedure
also assumes familiarity with the laser head components and their location. The front
of the laser head is the end containing the output coupler (Figure A.4) whereas the
rear of the laser head is the end containing the high reflector (Figure A.5).
To obtain approximate alignment between the front of the plasma tube and the
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cavity seals
rear reflector
etalon
Figure A.5: Rear of the laser head assembly
aperture, hold a flashlight at the rear of the laser with the high reflector removed
shining the light forward towards the output coupler. Also with the output coupler
removed, observe the light coming out of the plasma tube core and move the plasma
tube front end so that the light is centered on the aperture. Next shine the flashlight
into the front of the laser and center the light coming out of the rear of the plasma
tube with respect to the high-reflector enclosure. The alignment of the plasma tube
here will not be as accurate because it is harder to visually center the light from the
plasma tube with high-reflector enclosure.
At this point, lasing should usually be possible but may require a large amount of
mirror walking in order to optimize laser power output. A further helpful procedure
in laser alignment uses an outside laser source such as a HeNe laser to align the
output coupler and rear reflector. First, with both the output coupler and rearreflector removed, align the laser beam so that it travels through the entire laser
head, through the center of the plasma tube from the rear to the front. Install a
mirror at the front of the laser head and align it so that the beam doubles back on
itself. A reflection from the front plasma tube window should now be visible on the
ceiling. The output coupler should now be installed. After the output coupler is
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installed a second reflected beam will be visible along with the first reflection just
mentioned. Adjust the output coupler controls to align the second beam with the
first using the front laser head output coupler alignment controls. The output coupler
is now aligned very close to its optimal position.
Next, the laser source should be moved to the front of the laser head and be
aimed back through the laser. To align the beam, use the reflection from the output
coupler back towards the source. Now, the high reflector should be installed. To align
the high reflector, align the laser beam that travels back through the plasma tube
with the laser beam origin. The further the distance between the output coupler and
the laser source, the more accurate the alignment of the high reflector. When this
procedure is finished the laser can be started in the usual way and if lasing is not
immediately obtained, the beam search procedure described in the Spectraphysics
2020-05 manual (Spectraphysics, 1984) will allow lasing to occur. Be sure to reinstall
all cavity seals, especially in the front of the laser as the reflection from the front
plasma tube window can be very powerful and is easy to look into accidentally.
A.3.3
Etalon installation and alignment
The following describes the etalon installation. In the current setup, the etalon
is not required because the path length of each of the focused laser beams is kept
constant so that the path difference is well below the coherence length of the laser
without etalon (4 cm). However, a lot of time was invested in determining the proper
use of the etalon and other application will require it. Therefore, these instructions
have been included here. Note that it is extremely difficult to operate the etalon
in single frequency mode and also obtain two reasonably strong and equal intensity
beams of different wavelength. The etalon is best used with a prism installed, in
single wavelength mode when efficiencies of 50% are attainable.
Once laser alignment has been optimized, both in terms of maximum output
and centering with respect to the aperture, the etalon installation can proceed. The
following are the alignment steps recommended based on a trial and error record
of experience with the installation and alignment of the etalon. The etalon is used
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etalon cover
screws
imaging paper
mounting
screws
Figure A.6: Rear of the laser head assembly
to select a single frequency of operation of the laser in order to improve the laser’s
coherence length. The laser’s coherence length is the maximum beam distance over
which the phase relationship remains constant. Without an etalon a typical Argon
ion laser has a coherence length of 4 cm. With an etalon installed the coherence
length can be increased to 20 m. In a fiber optic LDV system implementation, a long
coherence length for the laser beam is an absolute necessity as the distance effectively
traveled by the beam inside the fiber varies not only from fiber to fiber but also for
each of the polarization modes of the fiber. (See Section A.4.2)
In the installation of the etalon, refer to Figure A.6 for part identification and
orientation. Before installing the etalon in the laser, remove it from its enclosure by
twisting the large knurled plastic cover. After removing the spring that presses the
etalon into place gently tap out the etalon. Use a cotton swab to push the etalon
out if tapping is unsuccessful. Once removed from its enclosure, inspect the etalon
carefully for any dust and dirt. Clean the etalon using the usual procedure for delicate
optics, making sure that no residue is left when the etalon is put back in its enclosure.
Once back in the enclosure, insert the spring and then the cover but only start the
cover into its threads. Do not tighten down the cover.
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Before installing the etalon in the laser head, turn the laser on and allow ample
time for warm–up. Make a note of the output power. The laser should be started
and allowed to warm up in the same configuration in which it will be used for measurements. That is, the power–level and aperture should be set at their anticipated
final operating points. Currently, the laser is operated at full open aperture and a
current of 34 A. The etalon can be installed with the laser running but with the shutter closed. If the installation is performed with the laser running, extreme caution
should be used as lethal combinations of voltage and current are present near the
installation location. It is highly recommended that the unfamiliar user shut down
the laser and disconnect power to install the etalon. After the etalon is slid into place,
make sure that the rear plasma tube cavity seal is completely retracted so that the
plasma tube window is visible and that the rear cavity seal in no way impedes the
glimbal movement of the etalon enclosure.
The first step in the etalon alignment is to obtain what is called ”flash”. The
”flash” condition is obtained when the etalon surfaces are exactly perpendicular to
the laser beam direction and do not cause any beam displacement. Consequently
the laser power observed should be near 100% of the value observed before etalon
installation. In order to obtain ”flash” very accurate and small adjustments of the
etalon angular position are required. In the case where no lasing is observed, a beam
search technique similar to that used for the high reflector alignment can be used.
Obtaining some amount of lasing should not be difficult, especially at higher current
driving levels. Once some lasing has been obtained, place a piece of paper under the
rear plasma tube window. Observe the dots on the paper as the glimbal controls
on the etalon enclosure are manipulated. To obtain ”flash”, all the dots have to be
completely lined up. Note again that ”flash” is obtained for one particular alignment
of the etalon and a large amount of patience is helpful in finding it. Any ”flash” level
below 90% of the original power should not be considered flash. It is also important to
realize that the output has several maxima throughout the gimbal adjustment range
and that a given maximum not near 100% of the original power is not necessarily an
indication of a dirty etalon.
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Once ”flash” is obtained, align the table optics for transmission of the non frequency shifted beams into the fiber optic cables, as described below in Section A.4.2.
Place the 40X microscope objective at the laser beam intersection. Project the image
onto a surface at least 10 ft away. Observe the image projected onto the surface.
A sharp diffraction pattern for both the green and blue beam pairs indicates single
frequency operation. At ”flash” the laser is not in single frequency operation and the
diffraction pattern will not be sharp. If the laser were operated in single line mode,
it would be possible to achieve 50-60% of original beam power in single frequency
operation. Further performance decreases must be taken to achieve balanced 488 nm
and 514 nm laser output with single frequency operation for both.
From ”flash” adjust the vertical gimbal control to lean the etalon, turning the
control to the right. Stop when both green and blue diffraction patterns are sharp.
At this point, the laser is single frequency operation but the operating frequency
is probably not located near the maxima of the laser gain curves for each of the
laser lines. By turning the knurled etalon enclosure cover, the pressure exerted by
the spring on the etalon increases and changes its length slightly. With the length
change, the resonant frequency of the etalon changes and can be adjusted to be closer
to the gain curve maxima. During the spring pressure adjustment, the output power
should be monitored either at the laser head exit or for one of the two laser lines
of interest. The key is to achieve balance between the 488 nm line and the 514 nm
line without losing single frequency operation and while maximizing beam intensity
to increase the amount of light scattered for measurement. There is no set procedure
for finding the optimal point and trial and error is an essential ingredient in this
procedure.
Once the etalon is aligned, the laser beams should remain non frequency shifted
for several days so that the repeatability of the operating condition can be checked.
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A.4
Laser Doppler Velocimeter Optics
The following sections describe the optical components used in the LDV along
with their purpose and any operating and usage guidelines. The description follows
the path of the laser beams from the laser head all the way to the measurement
volume and back through the receiving optics until finally the light flux is converted
to an electronic signal using a Photo Multiplier Tube (PMT).
A.4.1
Overview
The following paragraph is a basic description of the entire optical system from
a functional perspective, omitting any alignment procedures or other detailed operational information. The multi-band beam from the laser head is redirected by a set of
three mirrors to the top of the table. There the beam is re-collimated to be slightly
converging using a Galilean telescope. The individual laser wavelengths contained in
the multi-band beam are then separated by two successively placed dispersing prisms.
The diverging beams are reflected on the far side of the table by a 1 inch mirror. The
desired laser beams of wavelength 514 nm and 488 nm are picked off successively and
processed further, each beam undergoing the same conditioning on its way to being
coupled into the fiber in two parts, one frequency shifted half and one non frequency
half.
The laser beam is first rotated from its vertical position using a polarization
rotator. Then the beam is split in two by a polarization beam splitter which reflects
the horizontally polarized portion of the beam and transmits the vertically polarized
portion. The horizontally polarized portion is reflected by a second polarization beam
splitter and then coupled into the fiber. The vertically polarized portion is reflected
off of a half inch mirror and then frequency shifted by a Bragg cell. The frequency
shifted beam is reflected off of a second half inch mirror, rejoining the horizontally
polarized portion at the second polarization beam splitter. Both beams travel along
the same fiber.
The frequency shifted and non-frequency shifted beams travel along the same
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fiber independently because the fiber used is polarization maintaining fiber and the
two beams are perpendicularly polarized. The present LDV implementation thus
requires only two light delivery fibers. One fiber is used for the green beams (514 nm)
and one fiber is used for the blue beams (488 nm). The fiber connect to the LDV
probe. At the probe, the fibers connect to a pair of laser collimators which form
approximately 3 mm diameter beams. Inside the probe, the two laser beams are
separated from each other by a polarization beam splitter. The reflected beam hits
a mirror and is redirected to travel in the same direction as the transmitted beam.
Once reflected, the beam passes through a polarization rotator in order to match
the reflected beam’s polarization to the transmitted beam’s polarization. The beam
separation occurs identically for the green and blue laser beam pairs.
At this point four laser beams are traveling parallel to each other toward the large
achromatic focusing lens. The lens focuses all four beams to the same spot, which is
called the measurement volume. As particles pass through the measurement volume,
the scatter light. Some fraction of this light is reflected back towards the focusing
lens. The focusing lens collimates the coherent light from the measurement volume.
The collimated light is then focused onto the end of a 50µm multimode fiber. The
fiber transports the light back to the optics table from the probe. At the end of the
multimode fiber, the scattered light is collimated. The light contains both green and
blue scattered light. A dichroic mirror is used to separate the two colors. The green
light is transmitted whereas the blue light is reflected. The transmitted green light
and reflected blue light are further filtered by narrow band-pass filters. The scattered
light flux of each laser color is then converted to electrical current by the PMT as
described in Section A.5.
A.4.2
Table optics
To accommodate the entire LDV system on a single optical table, able to be
moved from experiment to experiment, the laser head is located on the bottom of an
optical table. Three mirrors are used to redirect the beam vertically to the top of
the table and provide it level travel along the long edge of the optical bread board.
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Figure A.7: Top beam steering, beam collimator and dispersion prisms
1st beam target
Figure A.8: First beam target located near dispersion prisms
Figure A.7 shows the three mirrors and follows the laser beam from the laser head
through the steering mirrors. The two end mirrors, the first and third mirrors are used
in the initial adjustment of the beam location when fiber alignment is begun. The first
mirror is used to center the beam on the first beam target hole located immediately
after the two color separating prisms(see Figure A.8). The third mirror is then used
to center the beam on the second beam target hole near the blue polarization rotator
(see Figure A.9). Finally, the beam alignment can be given an initial fine tuning by
visually optimizing the light coupling into the fibers.
The collimator is used to convert the slightly diverging beam emanating from
the laser to a slightly converging beam. The collimator design is based on a Galilean
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2nd beam target
Figure A.9: Second beam target located near first blue polarization beam splitter
dispersing prisms
collimator
3rd steering mirror
Figure A.10: Top beam steering, beam collimator and dispersion prism assembly
telescope design using a concave and convex lens. The collimator is shown in between
the dispersing prism assembly and the last steering mirror in Figure A.10. The
collimator can either expand the beam or contract the beam. In its present alignment,
the collimator contracts the beam. By adjusting the knurled control on the collimator
the focusing distance can be changed from far positive (slightly converging) to far
negative (slightly diverging). In the present setup, the collimator is set up to focus
the beam at some large positive distance much greater than the total optical path
length of the system (laser head to fiber coupler).
The next component is the color separator which consists of two back to back
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Brewster
prisms
Figure A.11: Top view of Brewster prism assembly
dispersing (Brewster) prisms, shown in Figure A.10 and in a top view in Figure A.11.
The prisms separate the different laser lines by diffraction at the glass surfaces. Two
prisms are used to increase the divergence angle of the laser lines and allow for easier
optical line separation. The optimal orientation of the two prisms is tip to tip as
shown in Figure A.11. In order for the color separator to work most efficiently, the
incident angle of laser beam must be close to the Bragg angle which will minimize
internal reflection losses at the glass–air interface. To set the angle, the platform
the prisms are mounted on is rotated. As the platform is rotated, the laser beams
formed by the different laser lines will move and change separation when observed on
a target. With rotation the beams will move to and away from the collimator end of
the table. As the beams move not only the separation will change but also the shape
of the beams, from circular to elliptical. The optimal separation of the laser lines is
obtained by fixing the rotational position of the prism platform so that the beams are
at their turn–around point, furthest away from the collimator end of the table. At
this point the beams are still circular and the beam separation is acceptable. Further
beam separation will only be achieved at the cost of non-circular beams and increased
reflective losses. Some reflective losses will be incurred regardless and the strongest
of these reflections should be masked to prevent injury.
In order to adequately separate the two laser lines of interest (488 nm and
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Figure A.12: Redirect mirror giving necessary path length for separation
514 nm), a certain path length has to be covered. The beams are therefore reflected
from the far end of the table using a 1 in. broad–band mirror, shown in Figure A.12.
Once reflected the laser beams of interest are picked off using two small half inch
mirrors as shown in Figure A.13. The optics downstream of these mirrors for each of
the laser beams of interest are the same, and the components will be described only
once with the understanding that analogous components are used for the 514 nm and
488 nm laser beams.
All of the optics of the two analogous optical paths are shown in Figures A.14
and A.15. Of the optical components used, several are specific to the laser line
wavelength, that is to say, these components are functionally identical but can not be
substituted for each other. For example, the polarization rotator used for the 488 nm
laser line is designed specifically for that wavelength and should not be used for the
514 nm wavelength. The polarization rotators are marked with their wavelength,
whereas the polarization beam splitters are not. Therefore, care and labeling are
necessary if the optical system is ever disassembled.
The separated laser beam’s polarization is vertical as it has not been modified
from its state at the exit of the laser head. To enable separation of the beam into
equal intensity parts, a polarization rotator is used to change the polarization angle of
the laser beam to near forty–five degrees. Both green and blue polarization rotators
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Green pickoff mirror
Green pickoff mirror
Green polarization
rotator
Figure A.13: Laser beam pick-off mirrors
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blue polarization rotator w/
non-488nm beam block
green Bragg cell
green polarization beam splitters
green polarization rotator
green fiber coupler assembly
Figure A.14: Green beam conditioning components
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blue polarization beam splitters
blue fiber coupler assembly
blue Bragg cell
Figure A.15: Blue beam conditioning components
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are shown in Figure A.14, where part of the blue polarization rotator is masked
to block the beam components at wavelengths other than 488 nm. The beam is
separated into two equal intensity parts by a polarization beam splitter. The beam
splitter transmits the vertically polarized part of the incoming beam and reflects
the horizontally polarized portion at ninety degrees. The transmitted portion of the
beam is reflected by a half inch mirror and then frequency shifted by a Bragg cell, as
described below. The reflected portion travels towards the second polarization beam
splitter.
The LDV system Bragg cells are used to shift the frequency of one of the coherent
beams forming the diffraction pattern by 40 MHz, resulting in a moving diffraction
pattern as discussed above. Depending on the Bragg cell alignment, the Bragg cell
can also be used as a beam splitter. Both the angle of incidence of the laser beam
and the power supplied to the Bragg cell change the behavior of the Bragg cell. For
the LDV application, in the present setup, the goal is to maximize the intensity in
the first order of the Bragg cell diffracted beams.
To align the Bragg cell, first align the laser beam so that it is centered on the
Bragg cell inlet and outlet windows. Once the beam is centered on the Bragg cell
windows, measure the intensity of the beam with the Bragg cell power supply off.
Next, turn on the Bragg cell power supply and set to near full power. The Bragg cell
power supplies are shown in Figure A.16.
When the power is turned on, the original single beam is separated into several
diffraction orders. The zero frequency shift beam can be identified by turning the
power down to zero and noting which of the beams remains. The first order beam
is located right next to the zero frequency shift beam. It is this beam’s intensity
that must be maximized by changing the angular alignment of the Bragg cell and the
Bragg cell power level. Using these controls it should be possible to obtain greater
than 95 % of the originally measured power in the first order diffraction. Experience
has shown that the optimal power level (dial setting) for the 514 nm laser line is about
nine whereas the optimal power level for the 488 nm laser line is closer to 7.5. To
finish the optimization, it is possible to measure the intensity of the zero shift beam
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Figure A.16: Bragg cell drivers
and use the controls to minimize this intensity. This step should be the last step in
the alignment of the Bragg cells because minimization of the zero order beam only
succeeds in maximizing the first order diffraction beam if the alignment is already
close to the maximum. Using the zero order intensity merely allows a more sensitive
detection of the optimal alignment. The Bragg cells are not laser line specific and
could be interchanged if necessary. The polarization angle of the beam is not altered
in the frequency shifting process. Note that a first order beam can be produced on
either side of the zero shift beam. Depending on the orientation of the Bragg cell,
the first order beam is either upshifted or downshifted in frequency. It is important
to make the frequency shift compatible with the measurement setup. The frequency
shift should be such that both measured components are predominantly on the same
side of the shift frequency. This will allow a better selection of the mixing frequency
as described below in Section A.5.1.
The frequency shifted beam and non frequency shifted beam are collocated using a second polarization beam splitter. The originally vertically polarized frequency
shifted beam is again transmitted while the non frequency shifted beam is once again
reflected. The polarization beam splitter is oriented so that the reflected beam prop340
agates in the same direction as the transmitted frequency shifted beam. In order to
facilitate the alignment of the fiber coupler, the two beams are collocated visually as
close as possible before attempting fiber coupler alignment. With the fiber coupler
still removed from its alignment housing, the two beams are collocated using the
following procedure.
In the current setup, the frequency shifted beam is designed to travel a longer
distance on the optical table so that the overall path length traveled by each beam will
be equal by the time the beams are focused to the measurement volume. The nonfrequency shifted beam travels a longer distance inside the probe equal to 3 in. Both
the 514 nm and 488 nm beam pairs are setup in this fashion. Due to this setup, the
non-frequency shifted beam position and angle cannot be changed without changing
the alignment of the polarization beam splitters which after initial alignment should
be avoided.
To align the polarization beam splitters, use the following procedure, involving
only the non-frequency shifted beam. Mount the first polarization beam splitter such
that the weak reflection off of its face travels back along the original beam. The
reflection can be seen either on the polarization rotator or on the pick-off mirror.
Once perpendicular alignment is achieved, add the second polarization beam splitter
and repeat the procedure to ensure that the non-frequency shifted beam also hits
the second polarization beam splitter at normal incidence. The non-frequency shifted
beam should now have been reversed from its original direction of travel. Locate
the fiber coupler assembly so that the non-frequency shifted beam is as close to the
center of the assembly as possible given the constraints of the optical breadboard.
The coupling assembly should also be located as close as possible and practical to the
last polarization beam splitter.
Each of the mirrors that reflect the vertically polarized beam (the beam marked
for frequency shifting) have to be located so as to provide an additional 3” of travel
compared to the non-frequency shifted beam. Thus, the distance from the center
of the first polarization beam splitter to the first mirror must be equal to 1.5”. The
same is true for the distance between the second mirror and second polarization beam
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splitter. The Bragg cell is mounted between the two mirrors. Before beginning the
beam collocation, ensure that the Bragg cell optimally frequency shifts the laser beam
using the procedure above.
To move the frequency shifted beam horizontally, a translation stage is used
to move the second mirror. To change the beam angle horizontally or vertically, the
second mirror gimbal controls should be used. Vertical movement is more difficult and
involves walking the two mirrors used by the vertically polarized beam, ensuring after
each adjustment of the first mirror, that the Bragg Cell is still aligned optimally. The
resulting process is iterative but since only small adjustments in height are required,
the procedure is not too cumbersome.
The actual collocation of the frequency shifted and non-frequency shifted beam
is accomplished as follows. Observe both beams on a screen a far distance away from
the fiber coupler (> 5 m). Move the frequency shifted beam image on top of the nonfrequency shifted beam image using the gimbal controls of the second mirror. Now
observe the beams as they come out of the second polarization beam splitter. If they
are not collocated at this point move the frequency shifted beam using the horizontal
and vertical displacement procedures as discussed above. Repeat this procedure until
the beams appear collocated both at the polarization beam splitter and the screen.
The two collocated beams are finally coupled into the fiber. The type of fiber
used in LDV and other coherent light applications is polarization maintaining fiber.
Polarization maintaining fiber is designed to allow the transmission of light without
altering its polarization state if the polarization axis of the light is aligned with one of
the two eigen–axes of the fiber. In the present implementation of the LDV, one fiber
is used to transmit both the frequency shifted and the non-frequency shifted beam,
each beam traveling along one of the fiber eigen–axes. Such a configuration makes
the LDV less sensitive to vibration because both beams are always exposed to the
same environmental conditions. Using polarization maintaining fiber thus requires
rotational alignment of the optical fiber with the light beam polarization. Note that
since the input light beams are polarized at ninety degrees with respect to each other,
rotational alignment of the fiber for one beam guarantees rotational alignment of the
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other. The rotational alignment requires repeated optimization of the fiber coupling
because of the slight eccentricity of the alignment housing and fiber coupler mount.
The fiber coupling procedure will be described first followed by a method to check
the rotational alignment of the fiber input end.
To couple the collocated beams into the fiber, proceed as follows, assuming the
two beams have already been visually collocated as described above. In order to
assure that the correct beam is coupled into the fiber of the various diffraction orders
generated by the Bragg cell, the non frequency shifted beam is coupled into the fiber
first. Once the non frequency shifted beam has been coupled into the fiber, the
frequency shifted beam is uncovered while the non frequency shifted beam is blocked.
The frequency shifted beam will be coupled into the fiber to some degree due to
the previously mentioned visual collocation procedure. The fiber coupler assembly
consists of five parts as shown in Figure A.17: the assembly platform (L-shaped
aluminum bracket), the coupler adjustment controls (combination of 2-D translational
stage and a 2-axis tilt platform), the coupler alignment housing, the fiber coupler
mount and the fiber coupler itself.
To couple a light beam into the fiber, proceed as described in this paragraph.
Insert the fiber coupler mount into the alignment housing without the fiber attached.
Use the translation controls of the alignment stages to visually center the beam on
the fiber coupler focusing lens. Observe the light emanating from the fiber coupler
on a screen no more than 12 in removed from the coupler. Center the beam in the
opening visually. Maintain a smooth elliptical shape of the image using the gimbal
alignment controls. Insert the fiber into the coupler, but do not insert it all the way.
Remove the other end of the fiber from the probe and observe the light from the
fiber on a screen. The light will be very faint. Insert the fiber further and further
into its receptacle while continuously attempting to maintain some light coupling
into the fiber. As the fiber is inserted further and further with the key aligned to
the key–way (see Figure A.18), the maxima achieved by alignment will increase. Be
sure to look for single mode coupling not multimode coupling. Single mode coupling
is indicated by a smooth intensity distribution in the light beam coming from the
343
Fiber coupler mount
Fiber coupler
alignment housing
assembly platform
2-axis tilt platform
2-D translation stage
Figure A.17: Fiber coupler assembly
344
PM fiber key-way
Figure A.18: Polarization maintaining fiber key–way
fiber. Multimode coupling is indicated by a speckled light output. If single mode
coupling is not achieved prior to full fiber insertion, finding the operating point for
single mode coupling is exceedingly difficult. Once the fiber is fully inserted and
the fiber attachment screw is tightened down, the coupling is optimized using all
the controls, repeating adjustment of all controls because the adjustments are not
independent. The maximum coupling efficiency able to be achieved using the present
setup is around 33 %.
Once coupling has been optimized for the non frequency shifted beam, block
that beam and uncover the frequency shifted beam. Optimize the coupling for the
frequency shifted beam using all of the fiber coupler alignment controls. Make a
note of the controls which yield the highest increase in coupling efficiency. Once the
coupling has been optimized, uncover the non frequency shifted beam and check its
coupling. Very likely coupling will have deteriorated from its initial setting. Once
again optimize the coupling efficiency of the non frequency shifted beam. Finally,
optimize the coupling efficiency of the frequency shifted beam without using the
fiber coupler alignment controls. Adjust the beam controls that will yield the most
345
improvement in coupling first. These should have been noted during the procedure
just described. The procedure for translating the beam and changing its angular
alignment was described above. The coupling efficiencies of each of the beams should
be similar.
The rotational alignment of the fiber is achieved using the procedure outlined in
this paragraph. The rotational alignment is achieved by maximizing the extinction
ratio of the light coming out of the fiber. The extinction ratio must be measured
without any polarization optics in place in the probe. The extinction ratio is defined
as the ratio of the maximum to minimum light intensity observed as a linear polarizer
is rotated. Place the polarizer at the exit of the fiber collimator and rotate to find the
maximum intensity by measuring the light transmitted through the polarizer. Make
a note of the intensity and repeat to find the minimum intensity. Once the minimum
intensity is found, slightly shake and move the fiber and observe the output. Make
a note of the maximum in the oscillations in intensity. Take the logarithm of the
ratio of the maximum over the minimum measured power and multiply by 10. The
ratio should be about 20 for good rotational alignment. The oscillations induced by
shaking and moving the fiber should not cause the intensity to change by more than
approximately 30 % when the fiber is correctly rotated. The rotational alignment of
the fiber is facilitated by the knowledge that the fiber key is aligned with one of the
polarization eigen–axes. As the fiber is rotated from its initial position, the coupling
efficiency suffers and re-alignment will be necessary. Use small adjustments to ensure
that the beam coupling is not lost completely.
At this point the input ends of the 488 nm and 514 nm laser line fibers are aligned
for optimized coupling and are rotated to match the eigen-axes with the input light
beam polarization. The following section describes the optical components of the
LDV probe and the procedures to align its components for proper LDV operation.
A.4.3
Probe optics
the task, translated all of the optics including the laser to scan a range of locations.
346
collection lens
(multi-mode fiber
coupling lens)
green polarization
rotator
blue polarization
beam splitter
blue beam
collimator
focusing lens
green beam
collimator
multimode fiber
alignment and coupling
green polarization
beam splitter
green polarization
rotator
Figure A.19: LDV probe with components labeled
The advent of the use of fibers in LDV allows most of the optics including the laser
head to remain stationary and a much smaller probe containing few optical components is translated to obtain measurements in the locations of interest. A labeled
photograph of the LDV probe is shown in Figure A.19.
For the present implementation the probe contains fiber collimators to reform the
laser beams as the light escapes the fiber. The probe also contains two polarization
beam splitters which split the two beams that traveled along the same fiber into
the frequency shifted and non frequency shifted beam. After the polarization beam
splitters, one of which is used for the 488 nm line and the other for the 514 nm line,
there are four beams inside the probe, two 488 nm beams and two 514 nm beams.
The beams split off by the polarization beam splitters are redirected in the same
direction as the frequency shifted beams using two mirrors. After being redirected by
347
the mirrors the beams pass through a polarization rotator whose role it is to make
both 488 nm beams and both 514 nm beams have the same polarization. All four
light beams are then focused using a large achromatic lens. The light scattered from
the measurement volume is collected by the same focusing lens and then focused down
onto a multimode fiber using a two inch achromatic lens. The multimode fiber serves
as an aperture filter for the scattered light and ensures that the light measured on
the other end of the multimode fiber originates from the measurement volume center.
Thus the optics for the green and blue beams are once again exactly analogous
and the discussion about the beam alignment applies to both beam pairs, green and
blue. In the discussion it is assumed that since the beams must be realigned, the
probe is also disassembled. Disassembled here means that the polarization beam
splitters are removed from their mounts and that the focusing lens is also removed
from the mounting platform. The probe should be located on an optical table for
the alignment procedure, locked in a position that will allow the straightness of beam
travel to be checked, e.g. parallel to a row of mounting holes on an optical table. The
longer the table, the more precise the initial alignment of the beams. The procedure
assumes that all other alignment procedures have been completed and especially that
the fiber correctly aligned rotationally at the input end.
The first alignment procedure to be accomplished is the correct rotational alignment of the fiber collimator. The vertical, horizontal and angular alignment of the
fiber collimator follows the rotational alignment because rotation of the collimator
requires the mounting/adjustment screws to be relatively loose. Approximate rotational alignment can once again be obtained by recognizing that the key of the fiber is
aligned with one of the fiber eigen–axes. The key should be horizontal for the green
collimator and vertical for the blue collimator for the current setup. A change of
90 degrees in the rotational alignment will switch which of the two beams traveling
in the fiber will be transmitted by the first polarization beam splitter and which will
be reflected. The orientation of the collimator must take into account the constant
path length requirement and the direction of frequency shifting.
To align the collimator, block the frequency shifted beam before it enters the fiber.
348
With the fiber key approximately aligned, place a linear polarizer at the collimator
exit. For correct rotational alignment and a vertically aligned linear polarizer axis,
the green beam intensity should be a maximum and blue beam intensity should be a
minimum. The ratio between max and min should be close to the measured extinction
ratio of the fiber, as discussed above in Section A.4.2. Alignment should be performed
when the polarizer alignment (vertical or horizontal) is close to an intensity minimum
because the intensity minimum is more sensitive to adjustments than the intensity
maximum. Thus the blue beam collimator should be aligned with the polarizer aligned
vertically and the green beam collimator should be aligned with the polarizer aligned
horizontally.
Once the collimators are rotationally aligned, the position and angular alignment
of the collimator should be fixed. To accomplish this, check that the beam travels
through the center of the hole in the collimator mounting platform. Knowing the
dimensions of the collimator mounting platform and the fact the beams should lie
on a circle of 3 inches diameter, the straightness of beam travel can be checked
by measuring the beam vertical and horizontal position with respect to the table at
several locations. Position adjustments are accomplished by pushing on the collimator
which is held to the collimator mounting platform by a cover and separated from the
platform by an O-ring. Angular adjustments are performed by tightening the four
collimator cover mounting screws, shown in Figure A.20. At the end of alignment the
collimator cover mounting screws should be relatively tight so that the collimator is
securely held in place but yet not as tight as possible to allow future tweaking of the
alignment.
In the same configuration, insert the polarization beam splitters into their mounts.
The correct alignment of the polarization beam splitter is achieved when both the
green and blue frequency shifted laser beams are transmitted (not reflected) and the
non frequency shifted beams are reflected in the direction of their redirection mirrors.
Ensure using methods described above in Section A.4.2 that the polarization beam
splitter is aligned perpendicular to the laser beam. For initial alignment also check
that the polarization beam splitters are mounted aligned with the vertical given by
349
green collimator
blue collimator
green collimator cover
green collimator cover
mounting screws
Figure A.20: Probe collimator mounting platform
the collimator mounting plate. Uncover the non-frequency shifted beams if that has
not already been done. At this point, four beams should be traveling away from the
collimator mounting platform. The distance between the two green beams should always be 3 inches and the same is true for the distance between the blue beams. Since
the frequency shifted beam location has already been adjusted, the other beams must
now be aligned. Angular movement is accomplished easily using the mirror gimbal
controls. Displacement of the beams is more cumbersome and involves walking the
mirror together with the corresponding polarization beam splitter.
Once all four beams are aligned to travel in parallel, the polarization of the non
frequency shifted beams must be changed to match that of the frequency shifted
beams. The adjustment is accomplished by the proper rotational alignment of the
two polarization rotators mounted in the probe. First, place a linear polarizer in
front of the frequency shifted beam and adjust the polarizer for minimum light transmission. Then, without changing the orientation of the polarizer, place it in front
of the non frequency shifted beam. Remove the polarization rotator cover, shown
350
green polarization rotator mount
blue polarization
rotator
blue polarization rotator cover
Figure A.21: Probe polarization rotator mounts
in Figure A.21, and adjust the angle of the polarization rotator until a minimum in
intensity is achieved. At this point both green beams and both blue beams have the
same polarization.
At this point, the focusing lens mounted on its platform is attached to the probe.
To check that all four beams are focused to the same spot, a 40x microscope objective
is required. The image of the microscope objective should be observed on a screen at
least 12 inches away from the objective. It is not possible to check beam alignment at
the exact focal point of the lens. Instead, current practice uses the green beam pair
as the alignment standard. The only adjustment required for green beam crossing
is vertical. Using the microscope objective, follow one of the green beams near the
focal point until the second green beam comes into view. The two beams will likely
351
miss each other, but the working focal point of the lens in our current setup is defined
to be the location at which the beams are only separated vertically. Adjust the non
frequency shifted beam angular alignment inside the probe to make the green beams
intersect here. The blue beams should also be in view at this point. Blocking the non
frequency shifted blue beam, adjust the angular alignment of the blue beam collimator
so that the frequency shifted beam intersects the green beams at their intersection
point. Now, unblock the non frequency shifted beam and adjust its angular alignment
using the mirror controls to also intersect at the same location. All four beams are
now optimally aligned for data collection. If one of the beams in each of beam pairs
were not frequency shifted, a diffraction grid could now be observed on the screen,
if that screen is placed several meters from the microscope objective. Because the
beams are frequency shifted however, the diffraction pattern is not stationary and
cannot be made out in the image.
The last optical alignment for the probe is the alignment of the scattered light
coupling optics. The 2 inch scattered light focusing lens located inside the probe cannot be aligned very precisely. Its location is fixed by an accurately located mounting
hole and accurately machined lens holder and post. The only available adjustment is
the angle of the lens with the plane of the focusing lens. The two should be aligned
as parallel as possible. The light focused by the lens is collected by a fiber which is
mounted to five degree of freedom compact translation stage. The stage assembly is
shown in Figure A.22. To align the assembly, the blue fiber is disconnected at the
input end and the output end of the multimode fiber is connected in its place. Since
the optical system under investigation here only involves linear optics, focusing the
light coming from the multimode fiber to the green beam crossing will ensure that
the light from the four beam crossing is also focused into the multimode fiber. Some
training is required to identify the focused beam image from a multimode fiber. Since
the fiber employed is not a multimode fiber, the image will be somewhat speckled.
Away from this axial location, the image either becomes blurred or much larger in
size. Three pictures of the multimode fiber spot are shown in Figure A.23. The first
picture is taken with the objective placed too close to the lens. The image shows the
352
speckled nature of the spot. The second image shows the spot in focus. The size of
the speckled spot has decreased and the density of light is greater. The focus is at
this maximum point of light density. The third image is taken with the objective too
far from the lens. Some of light has begun to spiral away from the center. The goal of
the alignment is to have the multimode fiber focused spot located at the same exact
location as the green beam crossing. To obtain the desired alignment an iterative
procedure is required. The iterative procedure is required because the translation
stage adjustments are not entirely independent (poor design). Special care and patience is required for these adjustments especially because it is highly desirable to
have a rigid mount at the end of alignment. The mount becomes rigid by tightening
the lock-down screws and unfortunately the very tightening of these screws can cause
alignment to be lost.
At the end of the alignment procedure, the multimode fiber should be disconnected from the blue fiber coupler and the blue fiber should be reconnected. Some
realignment for optimal coupling will probably at this point also be required. Once
coupling for the blue beams is optimized, with the microscope objective still in place,
the scattered light from the green and blue beams can be observed coming out of the
multimode fiber.
It should also be mentioned that a fiber alignment monitoring system was added
to the probe. The system takes the form of a large photodiode that measures the
intensity of one of the errant beam reflections off the focusing lens. The reflection is
always in the same place and so represents an ideal opportunity for monitoring the
light power in the fiber on a relative basis. The photodiode is shown in Figure A.24.
The circuit used to bias the diode and obtain a voltage signal proportional to light
flux is shown in Figure A.25. The circuit is related to the PMT amplifier circuit
discussed below in Section A.5.1.
A.4.4
The receiver optics process the scattered light collected at the probe and coupled
into the multimode fiber. Figure A.26 shows the receiver optics. A collimator is used
353
multimode fiber
gimbal mount
Z-translation
lockdown screws
Y-translation
X-translation
Z
Y
X
Figure A.22: Probe collection fiber translation stage
before focus
at focus
past focus
Figure A.23: Collection fiber image series
354
Monitoring system
photodiode
Figure A.24: Fiber alignment monitor photodiode
-12V
1uF
8200
Vin
OP27G
Vout
1uF
12V
Figure A.25: Photodiode amplifier circuit
355
green PMT housing
blue band-pass filter
green band-pass filter
blue PMT housing
dichroic mirror
fiber collimator
multimode fiber
to form a beam from the scattered light which contains both green (514 nm) and
blue (488 nm) light. The green and blue light is initially separated by a dichroic
mirror which reflects most of the blue light (80%) and transmits most of the green
light (80%). Both reflected and transmitted light is further decontaminated by a
narrow band pass filter at 488 nm and 514 nm respectively. After the light is filtered,
it is absorbed by a PMT which converts the light flux into electrical current. The
PMT circuit is described in detail in Section A.5 which discusses the processing of
the electronic signal.
356
A.5
Laser Doppler Velocimeter Electronics
The next sections deal with the electronics that process the scattered light collected by the optics. The PMT converts the light to electronic current. From there
the current must be converted to voltage. The voltage is then filtered amplified and
collected by rapid D/A conversion. The D/A conversion cannot be continuous and
must be triggered by the presence of a Doppler burst. The detection circuitry will
also be described here. The analysis of the digital signal collected will be discussed
in Section A.6. Note that the signal path does not differ for the green or blue signals
so that the discussion is left general without referring to each signal separately unless
necessary.
A.5.1
Photomultiplier signal conditioning
The PMT converts the scattered light flux into electrical current. The current
is produced by a photosensitive cathode which emits electrons in proportion to the
incident light flux. The cathode emitted electrons impact ten successive dynode
stages, each of which emits electrons in proportion to the incident electron flux.
The result of this large amplification of the initially cathode emitted electrons is a
measurable current.
The current is converted to voltage by a transimpedance amplifier. Ordinary
applications would only require a load resistor but employing a transimpedance amplifier allows the current to voltage conversion process to be accomplished more efficiently (larger voltage for given current) and the output impedance of the amplifier
can be designed to match the downstream device impedances, thereby avoiding signal loss and distortion. The transimpedance amplifier circuit diagram is shown in
Figure A.27. Note that the construction of the circuit had to be done using extremely short leads to enable the circuit to perform well even at frequencies around
50 MHz. Impedance matching at these frequencies is especially important and therefore the transimpedance amplifier was designed with an industry standard 50Ω output
impedance.
357
-5V
1uF
1000
Vin
LM6181
50
1uF
Vout
5V
Figure A.27: Transimpedance Amplifier Circuit
The electronic signal leaving the PMT is filtered at the exit by a high-pass filter
whose cut-on frequency is 25 MHz. The filter eliminates any low frequency noise that
could not possibly carry a signal. One of the consequences of this is that the resulting
signal no longer contains any time average information. After being high-pass filtered
the signal is connected to the instrumentation box, shown in Figure A.28 inside of
which it enters the mixer. The mixer is a circuit element that effectively multiplies
two electronic signals. When two periodic signals of different frequency are multiplied,
the resulting signal contains the sum and difference of the two original frequencies.
The second signal into the mixer is an amplified and split RF generator signal.
The RF generator, shown in Figure A.29, is used to provide a constant frequency
reference so that rather than having to measure frequencies around 40 MHz, the
velocity information is extracted from a signal around 10 MHz which is much easier
to acquire using an A/D conversion process. Furthermore, the accuracy of frequency
identification increases dramatically if the same number of samples are used to identify
a frequency of around 10 MHz compared to a frequency around 40 MHz. The mixing
frequency choice requires some discussion. If 40 MHz were chosen as the mixing
frequency then all of the advantages of frequency shifting would be lost. The mixing
frequency should be chosen to be either higher than or lower than all anticipated
358
Figure A.28: Instrumentation box
doppler shifted burst frequencies. For the present setup, a typical mixing frequency
is 38 MHz. The Bragg cells were aligned so that forward flow and clockwise rotation
of the swirl velocity will cause a positive shift in the light frequency (i.e. shifting the
frequency beyond 40 MHz). The 2 MHz difference between the shift frequency and
the mixing frequency allows for 2 MHz worth of reverse flow (about 3.4 m/sec - see
Section A.6).
The RF generator signal needs to be split between the mixer for the green and
Figure A.29: RF generator
359
blue signals. The signal is split using a power splitter device which allows the two
signals to be split without distortion. Simply connecting the signal in parallel would
cause an impedance miss-match and would result in signal distortion. Since the
power provided by the RF generator is insufficient to drive both mixers, an amplifier
is used to amplify the RF generator signal before it is split and connected to the
mixers. The signal level leaving the RF generator must be chosen so as to not cause
saturation in the amplifier and not exceed the input limits of the splitter and the
mixer. For further information on these devices, please refer to the manufacturer
website: www.minicircuits.com.
The output of the mixer is low-pass filtered with a cut-off frequency of 30 MHz,
effectively isolating the frequency difference portion of the multiplied signals. The
resulting signal is then sent to the trigger identification circuit, discussed in Section A.5.2.
A.5.2
Doppler identification and trigger circuits
The filtered signal from the mixer now contains the information desired at a
practical frequency. The signal now enters a circuit designed to amplify the signal
and determine whether or not it contains a Doppler burst worthy of data collection.
The circuit is shown in Figure A.30 and the diagram for one of the trigger circuits
(the green and blue circuits are identical) is given in Figure A.31. The trigger logic
circuitry shown in Figure A.30 is described below and illustrated in Figure A.32.
The first portion of the circuit is a simple amplifier with gain of approximately
100. The output of the amplifier is connected to another stage of the circuit and to
the back of the instrumentation box. From there the signal is connected to the data
acquisition board. The second stage of the circuit essentially consists of a half-wave
rectifier that also additionally amplifies the signal. The next element consisting of
a resistor and capacitor combination, follows the peaks in the rectified signal in a
delayed fashion. A single sharp peak will be filtered out by this R-C circuit. The
time constant was designed so that the repeated peaks of a Doppler burst will allow
the output of the R-C circuit to reach the Doppler burst signal peak.
360
blue trigger circuit
green trigger circuit
logic circuitry
Figure A.30: Trigger circuit
From logic
To logic
5600Ω
560Ω
(2) 2N2222
120Ω
Vin
+LM
- 6181
47Ω
47Ω
560Ω
47Ω
47Ω OPA
+ 642
Vamp
2nF
- LM
+ 311
1kΩ
1kΩ
50pF
470kΩ
6.8kΩ
10kΩ
Figure A.31: Trigger circuit diagram
361
+5V
5kΩ
8
7
6
2
1
4
3
LM
555
Vtrig
5
1µF
The next circuit element consists of a comparator whose output is logic high
unless the R-C circuit level is above the current trigger level. The trigger level is set
using a potentiometer, as shown in Figure A.31. The higher the resistance, the higher
the trigger level. As soon as the output from the comparator drops below two thirds
of its steady state value, a counter–timer circuit is activated that sends out a digital
trigger pulse. The width of the pulse determined by another potentiometer setting.
The higher the potentiometer setting, the longer the pulse width. The trigger pulse
width is important in forming the coincidence window, as discussed below. The pulse
is interpreted by the logic circuitry and, independent of the logic circuitry, the digital
trigger pulse activates the transistor causing the R-C voltage to be held to ground
for the duration of the pulse. The voltage of the R-C circuit is thus reset, although
the voltage does not quite go to zero because there is a finite voltage drop across
the transistor of about 0.1 V. A second transistor is shown in Figure A.31. This
transistor is connected to the output trigger of the logic circuitry so that whether or
not a Doppler burst occurred in the circuit under consideration, if a data acquisition
trigger is produced by the logic circuitry, this pulse also resets the R-C circuit voltage.
The logic circuit that is used to control under what conditions the data acquisition
is triggered is illustrated in Figure A.32. Note that all AND ports are located on the
same IC chip. The 555 cirucit indicated is similar to those shown in Figure A.31 and
a potentiometer again allows the trigger pulse width to be determined. The pulse
width for the data acquisition trigger essentially works as an absolute limit on the
repeat frequency of triggers. The longer the pulse width the longer the minimum time
between recorded Doppler bursts. The circuitry supports three trigger types: green,
blue and coincidence. The trigger types are controlled by the output from the digital
port of the National Instruments data acquisition board (PCI-6034E). The digital
port also controls the trigger enable function of the circuit. In order to synchronize
both the rapid A/D and pulse timing operation, both of these operations are armed
before the trigger enable and trigger type bits are set on the digital port. Only if
the trigger enable bit is high, will trigger pulses actually pass through to the data
acquisition system. Note that, if neither the green trigger or blue trigger bits are
362
Trigger Dacq on Blue
Trigger Dacq on Green
Blue Trigger
AND
Green Trigger
AND
AND
NOR
555
Trigger Enable
AND
Data Acquisition (Dacq)
Trigger
Figure A.32: Trigger logic circuit diagram
set to high, the system outlined in Figure A.32, will turn into a coincidence trigger
automatically (i.e. only 2 digital bits are necessary to control the three trigger types).
A.5.3
Doppler data acquisition
In order to complete the picture of the electronics involved with the LDV, the
data acquisition trigger issued by the Burst trigger circuitry must be followed to the
actual collection of data. There are two elements to the data acquisition. The first
is high speed analog to digital (A/D) conversion of the Doppler burst. The second is
the recording of the time of collection of the Doppler bursts so that a time resolved
picture of the flow field can be obtained.
363
High speed A/D conversion is accomplished using a Gage model CompuScope 2125.
The board is configured with 4 Ms (mega samples) of on-board memory. The board
is set up to run in what is called multiple record mode which allows the board to
support extremely high trigger repeat frequencies. The board fills up the on-board
memory with blocks of data, the length of which is usually 256 samples. The data
acquisition rate is 25 MHz for most cases. Collecting both components of velocity
therefore allows for 8065 blocks of data, corresponding to a potential 8065 velocity
data points. Based on the 4 Ms of on-board memory a number of 8192 blocks of
data is expected. The reason for the discrepancy has to do with the Embedded Bits
feature of the board which helps make the bounds of each data block more precise.
See GaGe (1999) for more information. Each trigger thus causes the board to collect
a block of data. If both green and blue velocity components are being measured, two
blocks of data are collected simultaneously.
The same rising edge trigger that causes the A/D block to be collected, also
activates the counter timer part of the PCI-6034E board. The PCI-6034E is set up
to measure the period (in clock ticks) between adjacent rising edge triggers. Each
trigger also resets the counter so that the period measurement can begin anew. The
very first trigger received causes a nonsense value for the period to be recorded since
there is no previous trigger to measure a period against. Subsequent triggers reset the
clock and write the clock value prior to reset into memory. The clock speed chosen is
20 MHz so that the period measurement has a resolution of 0.05µs. The individually
measured periods can then be added together to form a time vector with the first
Doppler burst located at time zero.
A.6
Laser Doppler Velocimeter Signal Processing
The interpretation of the collected blocks of data in terms of velocity requires
detailed discussion. The method of information extraction and the proper determination of the quality of the information is critical to the accuracy and speed of the
LDV. A proper method for calculating LDV velocity statistics will also be discussed.
364
Finally, an overview of the software designed to control the LDV is given followed by
a description of the binary and LabVIEW data file formats.
A.6.1
Frequency identification and burst quality
Each of the data blocks collected is analyzed for its frequency content. Two different methods of frequency identification were considered. The first is the standard
FFT (Fast Fourier Transform) (Press et al., 1992) and the second is a parametric
autoregressive model (Marple, 1987). The FFT is further processed to obtain an estimate of the power spectral density. Regardless of the estimate for the power spectral
density, an interpolation was performed on the peak to further refine the frequency
estimate. For both algorithms the form of the interpolation is that described by Matovic and Tropea (1991), fitting a parabola to the logarithms of the values in the
immediate vicinity of the frequency peak. The authors actually recommend an interpolation algorithm based on the cos2 curve but report that the algorithm is subject to
instability. Thus the algorithm chosen has a small performance penalty but is overall
more stable. The three values defining the parabola are the frequency peak itself the
and the power estimates immediately before and following the peak. The peak estimate is then obtained from the maximum in the parabola. Figure A.33 compares the
two methods in a histogram of errors. Errors were calculated for random velocities
distributed over the entire possible measurement range. The Doppler bursts were
simulated by multiplying a gaussian exponential function by a sine function. The
simulated Doppler bursts include the effects of 8-bit discretization to correctly simulate the GaGe CompuScope board. The simulated bursts also include added noise.
For Figure A.33, the signal to noise ratio is about 0.5 corresponding to -6 dB. The
figure shows that both estimates perform very similarly. The method implemented in
the LDV system is however the autoregressive method because it offers advantages in
accuracy over the FFT method when actual data is used. Figure A.34 shows a comparison of accuracy similar to Figure A.33, except that real Doppler data was used.
The standard for the calculation is the autoregressive estimate (100% accuracy). Note
that for this set of data the FFT method is clearly inferior, causing artificial scatter
365
40
FFT
AR-model
Percent of data
30
20
10
0
-15
-10
-5
0
5
Percent Error
10
15
Figure A.33: Comparison between FFT and autoregressive frequency identification
for simulated data
in the data. This was observed consistently, especially at lower signal to noise ratios.
Beyond obtaining an estimate of the Doppler frequency, the data must also be
processed to obtain a measure of the significance of the peak. The signal to noise ratio
(SNR) of the estimate will be used as indication of how significant the frequency peak
100
FFT
AR-model 20
AR-model 15
AR-model 10
Percent of data
80
60
40
20
0
0
2
4
6
Percent Error
8
10
Figure A.34: Comparison between FFT and autoregressive frequency identification
for actual data
366
in the collected data was. Very low signal to noise ratios may indicate that there is no
Doppler frequency information at all. As the trigger level is lowered, this becomes a
possibility where a burst of noise can cause the circuit to issue a trigger even though
there is no significant Doppler information present. A lower signal to noise ratio may
also cause significant error in the peak frequency estimation. After processing some
data points, whose SNR is lower than some threshold value, will be discarded because
of the likelihood that the frequency estimate contains large errors.
The SNR of the frequency estimate here is determined by the ratio between the
frequency peak value and the the average power spectrum value. The logarithm of the
ratio then forms the displayed value for SNR. The value thus calculated is different
from that more commonly used. Strictly speaking, the SNR should be calculated
as the ratio of the area under the peak of the power spectrum over the rest of the
area under the entire power spectrum. The SNR estimate used here is related to the
customary one but is computed more easily.
A.6.2
Conversion to velocity
In order to obtain a physical velocity from the measured doppler frequency estimate, both optical and electronic system parameters must be known. Equation A.1
shows how the fringe spacing is calculated for a given beam separation and focusing
lens focal length. Table A.1 gives the values of the optical parameters in the current LDV configuration as well as the calculated fringe spacing for both 488 nm and
514 nm laser beams. The fringe spacing is then used in conjunction with Equation A.2
to determine the velocity, including directional sign. Equation A.2 clearly shows how
the mixing frequency changes the velocity measurement range of the LDV for a given
sampling rate. For a sample rate of 25 MHz, the maximum frequency that can be
resolved is 12.5 MHz. The minimum frequency is of course close to 0. The range of
measurement is thus the sampling frequency divided by two and by the fringe spacing.
The measurement range can be shifted by changing the mixing frequency as clearly
shown by Equation A.2. The selection of the mixing frequency must be matched with
anticipated experimental conditions.
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Table A.1: Optical parameters required for frequency to velocity conversion
Beam separation (mm)
76.2
Lens focal length (mm)
250
Beam diameter (mm)
2.2
Light wavelength (nm) 488 / 514
Fringe spacing (µm)
1.62 / 1.71
df =
vd =
A.6.3
λ
db
2 sin arctan 2f
l
(A.1)
fd + fm − fs
df
(A.2)
LDV velocity statistics
Developing statistics of velocity from LDV measurements is not straightforward
because the sampling intervals are uneven. Furthermore, a bias in the velocity statistics exists due to the fact that seed particles are uniformly distributed in a measurement medium. The bias is often explained using the conveyor belt analogy. The seed
particles are evenly spaced on the conveyor belt but the belt moves at various speeds.
The number of particles passing through a given location is thus not constant in time.
At times of higher velocity, a higher rate of particles passes a given location than at
times of lower velocity. A simple particle or data point weighted average thus results
in a bias toward higher velocities.
The most efficient, straightforward way to combat this effect is to calculate true
time averages, that is performing an integration such as that given in Equation A.3
and dividing by the measurement period. Similar expressions can be developed for
RMS and even higher order statistics of the velocity field.
1
x̄ =
T
Z
0
368
T
xdt
(A.3)
The evaluation of the power spectrum of the unevenly sampled data also requires
some discussion. However, this is treated in Section 3.2.4 of Chapter 3.
A.6.4
Software description
The present section is divided into three parts, successively becoming more and
more low level in programming. The routines visible to the user are described first
followed by LabVIEW subroutines. Finally, C-code that interfaces with LabVIEW is
discussed.
A.6.4.1
LDVinstCTRL
The routines described here are all visible to the user and demand some form
of user input or action. The main program that controls all other LDV processes is
called LDVinstCTRL. The LDVinstCTRL front panel is shown in Figure A.35. The
user can move the probe, set the PMT excitation voltage, check fiber alignment, set
the LDV data acquisition parameters and call several different subprograms.
VI, the actual program is initiated by pressing on the white arrow at the top left of
the screen. A dialog window will come up asking the user to power up the stepper
motors. At this point the program has sent an inhibit signal to the stepper motor
controller to allow for the power to the motors to be turned on without inadvertent
stepping. After the motors have been powered up, the OK button on the dialog
should be clicked. The inhibit signal is reset and normal operation of the control
program can begin.
The top left and middle of the front panel show the controls to move the probe
along all three axes. This part of the front panel also allows the swirl angle to be
changed. To move the probe or change the swirl angle, select the desired axis of movement (X,Y,Z or swirl) to the left of the front panel under ”Axis”. Enter the change in
position including sign into the ”Distance to move” box. The program will calculate
whether or not the movement can be accomplished exactly. The minimum round
369
Figure A.35: LDVinstCTRL front panel
370
number of inches that can be resolved is 0.0025 inches. The minimum rotational step
is 1.8 degrees. If the movement cannot be accomplished exactly, the actual movement
box font will change to red and the box marked Error will contain the percent error
between the desired and actual movement. Sometimes roundoff error is sufficient to
make the font for the actual movement to turn red. The error in this case is seen to
be very low however and it is OK to proceed with the distance entered. To initiate
motor movement, the ”Move” button is pressed (clicked). Control of the program
will pass to the subroutine StepDir.vi described below in Section A.6.4.8. During
the movement, the screen will be non-responsive to user actions. When movement
is done, control returns to the front panel and the new probe location is saved to
”Coordinates.dat”. In this way, even if the system halts or the program is otherwise
aborted, the probe location is recorded on disk and the axes will not have to be re–
zeroed. The current axis positions are indicated below the ”Actual Movement” box.
Selecting an axis and pressing the ”Reset” button will cause the current location to
become the origin of the selected axis.
To the right of the front panel, at the top, the PMT desired and actual voltage
is displayed. The control voltage is sent through a D/A channel to the PMT power
supply. The monitor output from the PMT is connected to the PMT-M1 monitor
input on the instrumentation box. The input is measured using an A/D channel. The
measured value is reported in ”Actual PMT 1 V”. Below the ”Actual PMT 1 V”
indicator is the indicator that allows monitoring of the fiber alignment as discussed
above in Section A.4.3.
Some LDV data acquisition characteristics can be controlled from the LDVinstCTRL front panel. These include the Doppler sample rate, the length of the burst
collected and the number of bursts collected. Note that due to hardware restrictions,
only combinations of burst length and number of bursts that will fill up the entire on
board memory (4Ms) are allowed. The most common configuration is for 8065 bursts
of length 256. Other LDV parameters controlled from the panel include the trigger
mode (whether triggering on green bursts, blue bursts or only under coincidence), the
mixing frequency which is approximately the same from day to day but should always
371
be changed to the number exactly measured with the frequency counter, the number
of data blocks (blocks of 8065 bursts) to be collected and the SNR threshold for green
and blue Doppler bursts above which the velocity data points must lie. Further, it
is possible to ”Start” or ”Stop” the burst collection automatically depending on the
setting of these buttons on the front panel. When the ”Start” button is depressed,
the burst collection will begin immediately upon entering the measurement subroutine (Unsteady-Velocity). When the ”Stop” button is depressed the subroutine will
exit immediately following completion of data interpretation. The LDVinstCTRL
front panel also allows A/D channels and an A/D sample frequency to be specified.
In Unsteady-Velocity, the A/D channels will be collected at the same time as the
Doppler bursts at the specified frequency. If the sampling frequency is specified to be
zero, then no A/D data collection will be performed.
Below the LDV data acquisition characteristics, a current flow rate indicator is
located between user specified flow limit controls. The indicator displays the flow
rate currently measured on the A/D channel, scaled to have units of SCFM. To the
left and right of the indicator are the low and high limits between which the flow rate
is desired to be held during data collection. If the measured flow rate falls outside
these limits, data collection in Unsteady-Velocity will be prevented.
To the right of the LDV data acquisition characteristics, four different subprograms can be called up. Pressing the ”Single Data” button will cause the program to
call Unsteady-Velocity (see Section A.6.4.2) to collect the specified data at the current
location only. Pressing the ”Grid Data” button will bring up the MeasGrid program
to setup a 2D scan of spatial locations (see Section A.6.4.3. Pressing the ”O-Scope”
button will bring up a window that allows the raw voltage collected from the high
speed data acquisition card to be viewed directly (see Section A.6.4.4. The program
is used in troubleshooting the system, making sure light is hitting each PMT. The
PMT voltage can be monitored directly by disconnecting the corresponding BNC
connectors on the front panel and connecting the cable to the BNC cables leaving the
rear of the instrumentation box connected to the high speed data acquisition board.
Pressing the fourth button ”Display Data” will call up the program used to review
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mean and RMS velocity results (see Section A.6.4.5).
Below the flow rate indicators, lies a cluster of important probe locations. These
values are specific to the translation stage setup and experimental setup (see Appendix C). Alignment locations refer to a location where the beam alignment can
be checked using the microscope objective. The axis limits depend on the coordinate
system used. The most practical (for experiments) reference for these coordinates are
the limits of the translation stages. The program will not allow movement past these
coordinates.
A.6.4.2
The program Unsteady-Velocity is called from both the main LDVinstCTRL
program as well as MeasGrid. The front panel for Unsteady-Velocity is shown in
Figure A.36. The program performs the actual velocity data collection and if desired
pressure data collection. In an automated collection process, the data collection can
be set to begin immediately and the program can also be set to exit automatically. If
Unsteady-Velocity is called with both ”Start” and ”Stop” buttons pressed in, the program will start and exit automatically. Manual operation will allow the user to control
the data acquisition parameters displayed on the Unsteady-Velocity front panel before
acquisition begins. The acquisition process is started by pressing the ”Start” button.
The controls available for the LDV data acquisition on the Unsteady-Velocity front
panel mirror those available in LDVinstCTRL. There are however additional controls.
The shift frequency as well as the fringe spacings can be separately controlled from
the Unsteady-Velocity front panel. Unless optical elements are changed, these values
should not be changed.
The program panel contains two charts. The top chart displays the calculated
and validated velocity data whereas the bottom chart shows the distribution of signal
to noise ratio in time. For the signals displayed in the top chart. The top chart
can display either velocity component or both at the same time depending on the
setting of the data selector located to the left of the ”Save Data” button. The data
selector defaults to ”Both” meaning that both measured velocity components will be
373
374
shown. Pressing the ”Save Data” button allows the user to save either the green or
blue velocity component to a text file containing both time and velocity columns.
To the right of the ”Save Data” button is the ”Re-Calc” button which causes the
program to run the data validation and statistics calculations again. Data validation
can be changed in two ways. The first is by lowering the signal to noise threshold
for validated data. The second way is to change the ”Dev-Stop” value. The ”DevStop” value is used to eliminate all data points located outside a certain number of
standard deviations from the mean. These controls are located in above the data
selector, ”Save Data” and ”Re-Calc” buttons.
A row of indicators is shown above the data validation parameters. The ”backlog”
indicator shows how many Doppler burst periods the counter buffer contains beyond
the last number of burst periods read. The ”number read” indicates the number
of burst periods that have been read. The counter increases continually as Doppler
bursts are collected. The ”ErrorOut” indicator reports any errors associated with the
high speed data acquisition. If there are no errors, its value is zero. If the number of
bursts requested exceeds the number of bursts the board is able to collect at a time,
”ErrorOut” shows the number of bursts actually collected. The ”Block #” indicator
represents the data block that is currently being collected. The counter will increase
towards the total number of data blocks requested.
Two columns of velocity component specific data statistics are displayed below
the data selector row. Each column contains for each velocity component, the number
of valid data points, the mean signal to noise ratio, the mean velocity, the RMS
velocity and the mean sampling rate. For coincident trigger data collection, the two
columns will show the same mean sampling rate and number of valid data points.
The velocity data can be examined in more detail using the programs called up by
the buttons located below the component statistics. Pressing the ”Show Histogram”
button will bring up a window that will display a histogram of the quantity selected
to the right of the ”Show Histogram” button. ”Frequency” will show a histogram
of velocity. If the data selector is set to ”Both”, the histogram will contain both
component data sets. Selecting ”Time intervals” will show a histogram of the time
375
intervals between Doppler bursts. Selecting ”SNR” will show a histogram of the signal
noise ratio calculated for the current data set.
Below the ”Show Histogram” button, the ”Show Spectrum” button allows the
user to bring up a window that displays calculated power spectra and cross spectra.
The selector to the right of the button determines the data set on which the spectra
are calculated. If either ”Blue” or ”Green” is selected only the power spectrum will
be calculated. If ”Both” is selected, each components power spectrum is calculated
along with the cross-spectrum and transfer function between the two components.
Further information on the spectrum window can be found in Section A.6.4.6.
The flow rate measured before the current data block is indicated between the
two charts. To the left and right of the flow rate indicator are the limits between
which the flow rate must fall for data collection to proceed. To the right of the high
flow rate limit is a control that allows scrolling through each data block collected.
The default setting of ”Display Block” is -1 which shows all collected data blocks
superimposed on each other. To the right of the ”Display Block” control are two
switches that allow the user to pause data collection between two data blocks and to
abort the current data block collection respectively. The status window indicates the
task currently being performed by the program.
Pressing the ”Stop” button will cause Unsteady-velocity to return control to its
calling program which is either LDVinstCTRL or the MeasGrid program described
in the next section. If the program is called with the ”Stop” button pressed in, the
program exits as soon as all processing is completed.
A.6.4.3
MeasGrid
The MeasGrid program is called from the main LDV control program LDVinstCTRL (Section A.6.4.1) and is used to perform spatial scans of the measurement
domain. The front panel of MeasGrid is shown in Figure A.37. The program is set
up to perform two dimensional traverses in measurement space. Correspondingly the
program requires inputs for the two axes along which the traverse will take place.
”1st Direction” is the outer translation direction, the direction along which the probe
376
Figure A.37: MeasGrid front panel
will translate after completing a scan of the ”2nd Direction”. Although the nomenclature seems reversed, the labels refer to the fact that programmatically, the ”1st
Direction” is the first or outer loop and the ”2nd Direction” is the second or inner
loop in the iteration over the total number of points to be collected. Once an axis
(direction) is selected the current position is indicated under ”Current 1st/2nd Axis
Position”. The spatial increment along that axis and its maximum extent are entered
under ”Axis Resolution” and ”Final Position” respectively. To perform a single axis
scan set the first axis final position to be the axis current position and ensure that
the increment for the axis is a positive number. The probe will only execute the scan
along the second axis.
The front panel of MeasGrid also once again shows the LDV data acquisition parameters. The parameters may be changed and will be passed to Unsteady-Velocity
each time MeasGrid calls for another data point. Additionally, the currently measured
377
flow rate and the flow rate limits are displayed and will also be passed to UnsteadyVelocity. ”Mean Flow” reports the mean flow rate measured for all the data blocks
collected at the previous point. The ”Show Fiber Monitor” button brings up a large
indicator that shows the currently measured voltage for the fiber monitor. The indicator is oversized so that alignment checks and adjustments can be performed during
a test without moving the probe from its current location or having to attach the
light power meter. The indicator is sized to be visible from the first beam steering
mirror at the exit of the laser.
Just collected data (at the end of a scan) or any previously collected data set
can be displayed by pressing the ”Display Data” button. The DisplayData window
will be called up and the mean statistics of the measured flow field can be reviewed
(see Section A.6.4.5). Pressing the ”Pause” button will interrupt data collection and
allow for realignment of the fiber optics in the middle of a test for example. Pressing
the ”Abort/Exit” button during a data sequence will completely stop all program
execution and should only be used in emergencies. Pressing the ”Abort” button or
the red stop button in the LabVIEW tool bar has the same effect and in order to
continue, LabVIEW must be exited completely and restarted. The ”Abort/Exit”
button can be pressed safely before data collection is initiated or at the end of data
collection and processing. At these times, the window will close and control will
The button ”Start Data Collection” is used to begin the data collection sequence.
Before Unsteady-Velocity is called for the first time, a file dialog window prompts the
user for the data file name to be used. The filename entered will be used to hold the
LabVIEW type data file. The filename, appended with ”TIM” is used to save the
binary data file. Both data files are saved after each point is taken so that aborting
a test part way through will not result in significant data loss. The file types and
formats are described below in Section A.6.5.
Progress of the programmed scan can be monitored by checking the ”Points Left”
indicator. The program also measures how long each data point takes and based on
an average for all the collected data points forecasts the time to complete the scan
378
in minutes. The value is reported in the ”Time left” indicator. Additionally, the
completion times for previous data points can be reviewed by scrolling through the
”Point Times” list.
A.6.4.4
Oscilloscope
The oscilloscope program has many of the same controls as a traditional digital
oscilloscope. The oscilloscope program front panel is shown in Figure A.38. Trigger
levels and sources can be specified. Data from one of the channels or both channels
can be collected and displayed. The input impedance and range can be selected. The
length of each data record can also be set using a front panel input. The oscilloscope
is started by pressing the ”ReStart” button. If parameters are changed, pressing the
”ReStart” button will incorporate the new parameters in the collection process. If
the trigger level selected is too high and data collection does not start, the ”Abort”
button can be used to abandon the current data collection process and begin anew
using the ”ReStart” button. Pressing the ”Exit” button will cause the program to
return control to LDVinstCTRL.
A.6.4.5
DisplayData
The DisplayData program window allows the review of previously or just collected
data. The DisplayData front panel is shown in Figure A.39. The program has access
to mean and RMS velocities of both components. The mean sampling rate for the
trigger component at each data point. The overall mean and RMS flow rate for a
test can be examined. The ”Choose variable for graph” and ”Choose 2nd variable
for graph” selectors allow two different quantities to be plotted at the same time on
the chart. The chart includes a legend whose entries reflect the selected quantities
for plotting.
Pressing the ”LoadData” button will bring up a file dialog window for the selection of the data file. If DisplayData is called at the end of a 2-D scan, the collected
The selector located under the second graph variable selector changes the spatial
379
Figure A.38: Oscilloscope front panel
380
Figure A.39: DisplayData front panel
381
coordinate units from ”inch” to ”mm” or vice–versa. The selector to the right of
the unit selector is used to determine which of the two axes scanned will be used as
the x-axis of the chart. For a scan that was collected with the streamwise direction
selected as the first axis and the radial direction as the second axis, setting the axis
selector to ”2nd” will show radial profiles of velocity at different axial (streamwise)
locations. The streamwise location of the radial profile is determined by the slide
control below the x-axis selector. To change the streamwise location, drag the slide
by pressing and leaving pressed the left mouse button. As the slide is moved, different
profiles will be shown on the chart corresponding to that streamwise location. The
exact location of the profile is displayed below the slide control.
Pressing the ”3D Graph” button will bring up a window with a 3-D graph. The
z-axis of the graph will contain the first chart variable selected. The other two axes
are the two coordinate directions of the 2-D scan. Pressing the ”Exit” button will
cause the program to exit and if called from another program return control to that
program.
382
A.6.4.6
PSDavg - Spectrum window
The spectrum window shows the results of the calculation of velocity power
spectra, cross spectrum and transfer function. The front panel of the program is
shown in Figure A.40. A measure of coherence can also be calculated. Cross spectrum,
transfer function and coherence are only calculated if the data selector in UnsteadyVelocity is set to ”Both”. Additionally, it is only possible to get reasonable data for
these functions if the data was collected in coincident mode. The program has inputs
for starting and ending frequency as well as frequency resolution and block length.
Once these inputs are set, the calculation of the quantities is initiated by pressing the
”Calculate” button. The calculation proceeds according to the procedure described
in Section 3.2.4 of Chapter 3. The results are displayed in the four charts. The results
can also be reviewed by scrolling through the arrays below the charts. Results and
velocity inputs can be be viewed element by element. Pressing the ”Exit” button will
cause control to return back to Unsteady-Velocity.
A.6.4.7
Histogram display
The histogram display, Figure A.41, shows the histogram of the data displayed in
the top chart of Unsteady-Velocity window if the histogram data selector in UnsteadyVelocity is set to ”Frequency”. The histogram window can also display histograms of
time between data points and signal to noise ratio. The only input available is the
number of bins to use in the histogram calculation. The chart does not separate the
blue and green components if both components are displayed in Unsteady-Velocity.
See Section A.6.4.2 for more information. Pressing the ”Stop” button will cause
control to return back to Unsteady-Velocity.
A.6.4.8
LabVIEW subroutines
The following is a list of subroutines that are used in the programs described
above. Only custom written subroutines are described, i.e. the subroutines not
supplied with LabVIEW. The underlined names followed by the file extension ”.vi”
383
Figure A.40: Spectrum display front panel
384
Figure A.41: Histogram display front panel
are the files where these programs can be found. Some of the files listed are not
subroutines but are supplementary stand-alone programs that accomplish a specific
task not able to be handled by LDVinstCTRL. These programs are indicate by using
bold lettering.
• BlockCfft
calculates an average Fourier transform by using Cfft repeatedly,
each time using a certain length of data points. Each set can be chosen to
overlap with the previous set. All the sets are averaged at the end to give one
smoothed version of the FFT.
• Cfft
calculates the Fourier transform of the input signals at the desired fre-
quency. using a C subroutine (Cfft).
• DisplayData3DSurface
is a subroutine to DisplayData and is used to show a
3D plot of the 2D scan data collected.
• DivideArrays
is used to separate the results of each of the velocity components
385
from the single long arrays obtained from lview cs board.
• FilterandProcess
enforces the signal to noise ratio minimum on each data
point and then calls SigCalc to eliminate all points outside the ”dev-stop” limits.
• Integerize
is used in OrganizeGridData to determine whether or not two
coordinates are identical. Simple comparison may give erroneous results due to
numerical roundoff. This routine represents the coordinate by an integer that
is 10000 times the original number. This means that unless the round off error
is in the fourth decimal point two coordinates that are equal will be correctly
identified.
• LDVstats
is used to calculate the time mean and rms values of a velocity time
record.
• lview cs board
is the front panel for the C subroutine gage com board which
controls the high speed data acquisition process. The same routine is used for all
tasks, including configuration, arming, collection and interpretation. Different
options are passed to the subroutine to distinguish the tasks.
• MicDataOnly
collects a specified amount of binary A/D data to file from
the specified channels, at the specified rate. The routine was used to collect
raw microphone data. The routine works with the NI 6034E board.
• OrganizeGridData
is the routine that uses the raw LabVIEW data file as
input and organizes it so that results from a 2D scan are arranged in order in
a 2D array, rather than one sequential record.
• PMT FLOW VI
is used to collect the voltages from the Data Translation A/D
card, representing the PMT monitor voltage, the fiber monitor voltage and the
flow meter voltage. The routine also converts the quantities to the proper scale
if known. Both PMT voltage and flow rate are converted to actual PMT volts
and SCFM respectively.
386
• SigCalc
is the front panel for the C subroutines in Filter sig that calculates
the mean and rms of a data set and eliminates all values outside the dev-stop
limits.
is used to cycle the stepper motor over many iterations to ensure
• StepTester
that no steps are being missed by the motor. Missed steps would cause a slow
drift in the start of the cycle position.
• std dev elim
is the LabVIEW code version of SigCalc. It was replaced to
speed up processing of data.
• StepDir
executes all stepper motor movements. Inputs are the motor to
move, the direction and the number of steps. The program coordinates the
digital outputs of the Data Translation and National Instruments boards so
that accurate motor movement is assured. (See Appendix C)
• TotalTime
calculates the total amount of time elapsed while data was being
taken. The total time is used to determine the mean sampling rate for a given
set of data blocks.
• Trig Contrl Digital
is used to control the trigger type and to enable the data
collection. The routine is called once both the burst time operation and the
actual burst collection operation have been armed so that the firs trigger read
by each card is the same.
• WriteMatlabDataFile
is the front panel for the C subroutine WriteData that
writes the binary ”TIM” file as described in Section A.6.5.
• WriteMicsDataFile
is the front panel for the C subroutine WriteMicsData
that writes the binary microphone output data to file.
A.6.4.9
C codes
The following is a list of C files and the functions these files contain. Each listed
function also contains a basic description of its purpose. The functions are listed in
387
the order in which they occur in the file. Some of the functions are not called in the
process of analyzing the collected Doppler bursts. These functions are remnants of
other explored methods of analysis.
calculates the DFT of the given input time records, at the given fre-
• Cfft
quencies. The routine removes the mean of the data before calculating the
DFT.
• Filter Sig
– SigCalc
get mean and rms from MeanCalc and GetSig and then condi-
tionally eliminates all data beyond a certain number of standard deviations
from the mean (dev-stop).
– MeanCalc
calculates the time integration based mean of the data time
record.
– GetSig
• WriteData
calculates the time integration based rms of the data time record.
writes the binary ”TIM” data file for processing by other programs
such as MATLAB.
• WriteMicsData
writes binary 16-bit data to file. The use here was mostly
to write out microphone data but the routine can be used for any binary A/D
data writing.
• gagea2d indiv func
• board config
– gage com board
main function determining the desired task and calling
the appropriate function.
– distrib data
organizes the collected data so that the two arrays returned
to the calling LabVIEW routine represent the raw voltages of the two
channels. If only one channel was collected, the second array is filled with
the number 1.2.
388
– interp data
calls the Doppler frequency identification functions. For
latest iteration, only get fest is called because the auto-regressive estimate
for the PSD is used to determine the Doppler frequency. For the FFT
implementation, the FFT calculation functions are also declared for use in
interp data.
• Estimators
– maxloc
returns the index of the input array’s maximum value.
– meancalc
– stdcalc
returns the mean of the input array.
returns the standard deviation of the input array given the array’s
mean value.
– parainter
based on the index of the maximum estloc in the array psd,
the function returns a parabolic estimate for the actual peak location. The
interpolation is performed on the logarithm of the psd values.
– resample
resamples the array by reordering the elements from 1 2 3 4 to
1 3 2 4. The sample rate has thereby effectively been halved and the data
record length effectively doubled.
– fftest
returns an estimate of the fractional index at which the frequency
peak occurred. The number has to be scaled by the sampling rate in order
to obtain the actual frequency.
– remmean
removes the mean from the input data array.
– autocorr
frequency estimator based on a one bit autocorrelation. The
estimator was eliminated because processing time was excessive. Could
possibly compete with autoregressive speed.
– get fest
get Doppler frequency estimate using the already calculated FFT
based power spectrum or get the frequency using an autoregressive estimate. The autoregressive analysis is the currently recommended method.
• PSDfunction
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– get window
calculates a Hanning window of the specified length for use
in FFT analysis.
– four 1
calculates the Fourier transform or inverse Fourier transform.
The routine is taken from Press et al. (1992).
– twofft
calculates the Fourier transform of two real input vectors simul-
taneously. The routine is the most computationally efficient way to obtain
the FFT of a series of data sets. The routine is taken from Press et al.
(1992). The only change is that two arrays are filled with the power spectra
of the two real input signals.
– realft
calculates the Fourier transform of a single real input vector in
the most efficient manner possible. The routine is taken from Press et al.
(1992) with the exception that it has been rewritten to return the power
spectrum of the input vector.
– truefft
calculates the Fourier transform of a single real input vector. The
routine is unmodified from Press et al. (1992).
– pkloc
finds the peak in the input array and is designed to keep track
of the sum under the peak found. The routine currently simply finds the
maximum and then performs an interpolation similar to parainter to find
the fractional index of the estimated peak location. The output still has
to be scaled by the sampling frequency to obtain an actual frequency.
The routine also calculates the signal to noise ratio based on the ratio of
the peak value of the power spectrum and the mean value of the power
spectrum.
– arpsd
calculates the power spectrum at the given number of evenly
spaced points, using the already calculated autoregressive coefficients. Code
follows Marple (1987).
– modcovar
calculates the coefficients of an autoregressive representation
of the spectrum. Code follows Marple (1987).
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A.6.5
Data file formats
There are several ways to save data from the LDV. For single data points, blue
and green velocity data can be exported to text files as described in Section A.6.4.
The files in this case consist of the velocity and time data for the selected velocity
component in two columns. For data points collected using the MeasGrid subroutine,
two data files are saved. The first data file has LabVIEW format and contains all of
the results including flow rates, mean sampling rates, mean and RMS velocities etc.,
except the time resolved velocity data points. The format is designed for use with
the DisplayData subroutine and stand alone program. If a data set was aborted, the
file format of the LabVIEW file is not compatible with DisplayData. If the binary
”Tim” data file is not available, the data file can be read using custom code similar
to that in OrganizeData, discussed in Section A.6.4.8. The DisplayData program is a
subroutine of MeasGrid and LDVinstCTRL but can also be used on its own, loading
the data explicitly as discussed in Section A.6.4.
The LabVIEW data file is not designed to be exported to any other software
platform. The other data file generated has the same name as the LabVIEW data
file, except that ”TIM” has been appended to the file name. The ”TIM” file is a
binary data file that contains the same information as the LabVIEW data file but
also contains all of the validated velocity data points and their time tags. Table A.2
illustrates how the data from the ”TIM” file should be read in. The table describes
the data written for one point. Successive points in a spatial scan are appended in
the file.
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Table A.2: Structure of the ”TIM” binary data file
Description
Format
1st coordinate in 2-D scan
Double
2nd coordinate in 2-D scan
Double
average flow rate for data point
Single
average velocity measured for green component
Double
average velocity measured in blue component
Double
RMS velocity measured in green component
Double
RMS velocity measured in blue direction
Double
average signal to noise ratio for green component
Double
average signal to noise ratio for blue component
Double
length of date string to be read (len)
32-bit Int
date string representing time and date the data was taken
(len)Char
length of green component time data vector (lentg)
32-bit Int
green component time vector
(lentg) Double
green component velocities
(lentg) Double
length of blue component time data vector (lentb)
32-bit Int
blue component time vector
(lentb) Double
blue component velocities
(lentb) Double
number of points collected
32-bit Int
green component signal to noise ratio threshold used
Double
blue component signal to noise ratio threshold used
Double
burst collection frequency in MHz
32-bit Int
burst sample length
32-bit Int
trigger type used (0=CI,1=G,2=B)
32-bit Int
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A.7
Day to day operating instructions
The following should serve as a working copy of the operating instruction used
in the startup and operation of the LDV. The instructions include the startup of the
laser.
A.7.1
Laser startup and instrument startup
1. Remove any dust covers from LDV optics
2. Start the air purge system
3. Start the cooling water,setting the pressure to between 30 and 50 psi.
4. Turn on the power to the laser at the fuse panel or line power switch. (Do not
press the ”ON” switch though !!)
5. Place beam guards so that both the green beam and blue beam are blocked
from reaching the fiber coupler.
6. Turn the key on the laser to the ”ON” position and press the ”ON” button.
7. Wait for the laser to lase and make sure beam guards are properly placed.
8. Record the date and time the laser was started and its operating condition in
Amps (Read from font panel gauge).
9. Wait for the laser to warm up. This time is determined by checking the power
on the laser. For the typical operating condition of 33 A, the power should
reach 1.0 W before any alignment procedures are started. The time for warmup
under these conditions is generally around 2 hrs.
10. Start the Bragg cell drivers and the RF generator to allow these instruments to
warm up as well.
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11. Start the program LDVinstCRTL, and turn on instrument box and stepper
motor power supplies to move the probe to a location where convenient access
for alignment is possible.
A.7.2
Fiber optic coupling
1. Place the blue beam guard behind the second beam target. Use the mirror
closest to the laser head to move the blue beam onto the center of the target.
2. Observe the beam on the first beam target and make sure the beam is close to
centered on it. If it is not, use the first mirror controls to center it and then the
third mirror’s controls to center the beam on the second beam target.
3. Set up the probe for fiber alignment using the left cover and the attached power
meter mounting arm. Insert the power meter probe with optical post into the
post holder on the power meter mounting arm. Leave the power probe below
the focusing lens.
4. Move the blue beam guard such that only the non-frequency shifted beam is
allowed to hit the fiber coupler.
5. Observe the beam exiting the probe and use the first mirror’s controls to visually
optimize the light coupling.
6. Move the power meter probe to measure the intensity of the blue beam exiting
the focusing lens. Locate the power meter probe by maximizing the output on
the display of the power meter.
7. Use the first mirror controls to maximize the output measured by the power
meter
8. Use the first and third mirror controls to check if walking the beam improves
coupling. The target value of intensity for the standard operating condition of
33 A is 60 mW for the blue beams.
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9. After optimizing the output at the laser head, move to the fiber coupler controls
and use these to further increase the output from the fiber, if possible.
10. Move the beam guard such that the non-frequency shifted beam is blocked from
reaching the fiber coupler.
11. Move the power meter probe to measure the frequency shifted beam power.
12. Use the mirror controls for the frequency shifted beam and the translation stage
to optimize the power output.
13. Slightly perturb the alignment of the Bragg cell to see if a gain in intensity can
14. If a gain was obtained in the previous step, repeat the alignment process.
15. At this point, both blue beams should contain close to the same power. If the
frequency shifted beam has more than 5% lower power than the non-frequency
shifted beam, walk the frequency shifted beam mirrors to translate the beam
up or down, while ensuring the Bragg cell alignment remains optimized.
16. Place the blue beam guard to prevent all blue light from hitting the fiber coupler.
17. Place the green beam guard to let the non-frequency shifted beam hit the fiber
coupler, while still blocking the frequency shifted beam.
18. Align the power meter probe to measure the power of the green beam coming
from the focusing lens.
19. Use the fiber coupler alignment controls to optimize the fiber power for the
non-frequency shifted beam.
20. Follow the same procedure as for the blue frequency shifted beam to align the
green frequency shifted beam.
21. Remove probe side cover.
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A.7.3
Probe alignment
1. Move the probe to a location that makes the measurement volume accessible
for the microscope objective.
2. With the beam guard still blocking the entire blue laser beam, place the microscope objective at the intersection of the green beams.
3. At the intersection, the images of the two green beams should overlap completely. If they do not, adjust the alignment of the non-frequency shifted beam
inside the probe by adjusting the mirror that redirects the beam.
4. Leaving microscope objective in place, block the entire green beam using the
beam guard. Remove the beam guard blocking the blue laser beam.
5. Observe the blue images of the blue laser beams. Since the objective has not
been moved, the blue beam images should also overlap completely. Use the
redirect mirror of the non-frequency shifted beam to get the images to overlap.
6. Remove the beam guard from the green laser beam and observe all four beam
images. If all of the images overlap, probe alignment is complete.
7. Use the blue collimator cover mounting screws to adjust the position of the
blue beam images in case all four beams do not overlap. After adjusting the
collimator cover, recheck that the blue beam images overlap.
A.7.4
Measurement setup
1. Start LDVinstCTRL if it is not already running.
2. Switch on the +/- 12V power supply to turn on the fiber alignment monitor
and the PMT’s.
3. Observe the value of the fiber alignment monitor, so that a reference for good
alignment is known.
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4. Disconnect the mixing frequency BNC connector from the RF driver and connect instead the BNC connected to the frequency counter.
5. Wait for the reading on the frequency counter to stabilize and then enter the
value in the mixing frequency entry on the front panel of LDVinstCTRL.
6. Move the probe to one of the measurement locations of interest.
7. Set the number of blocks to collect to 1 and select ”Single Data”.
8. Run ”Single Data” as often as necessary to establish an appropriate trigger
level.
A.7.5
Measurements
Further details on the measurement procedure used in the experiments can be
found in Chapter 3. Throughout the measurements a SNR cut-off of 1.50 and a
standard deviation cut-off of 3.50 was used and these settings should not have to be
changed. In general, the lower the trigger level, the higher the data rate but also the
lower the total number of good points per record.
A.8
Improvements in the LDV design
The following items describe improvements to the LDV system and their associated cost, effort and reward.
• Doppler trigger circuit overhaul: The factor most responsible for limiting LDV
performance are the trigger circuits. The concepts contained in these circuits
work well but leave a lot to be desired in terms of speed. The result is that a
velocity ceiling exists at around 20 m/sec. The high speed current feedback opamp should be used in the first two stages of both circuits. These stages should
be designed with lower gain so as to not limit the bandwidth of the op-amp
excessively. The lost signal strength should be made up by installing amplifiers
397
immediately downstream of the transimpedance amplifier. No redesign should
be necessary and the time associated with this change is equal to the time
required to replace the op-amps and some of the gain-determining resistors.
Cost is very low since the op-amps can be obtained by sample order. The
minimum useful signal level at the input to the Schmidt trigger circuit is the
voltage drop of the transistors which is 0.1 V. Design should be performed for
a Schmidt trigger input signal level of 1 V (i.e. from current conditions, input
can fall by 50%). The reward for this effort would be a tripling of the available
velocity range.
• The transimpedance amplifiers installed inside the PMT’s work well but have
relatively low gain. Performance improvements can be achieved by replacing
these transimpedance amplifiers with commercially available amplifiers. Cost
for this is relatively high (several hundred dollars) but the increase in performance in future LDV applications may make the investment worthwhile.
• Additional amplifiers could be added prior to the mixer to improve mixer performance and increase the signal level into the Doppler trigger circuit. Care
should be taken not to exceed the input levels of the mixer however. An RF
amplifier from Minicircuits costs approximately 100 dollars.
• A second RF generator is recommended for greater versatility in the relative
measurement ranges of the two velocity components. Currently both components are mixed with the same frequency which is not always practical. An RF
generator costs approximately 150 dollars (MCM Electronics).
• A big handicap for the LDV system is that the maximum number of doppler
bursts collected in succession is limited by the on-board memory of the GaGe
board. Two alternative exist here. The first is to have the board serviced and
add memory to it. The second is to replace the board all together with a new
PCI bus board. On the PCI bus, the data transfer to memory is rapid enough to
keep pace with most Doppler collection processes so that very long continuous
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Table A.3: Specialized vendors and products: Electronics
Minicircuits
Jameco
Marlin P. Jones
MCM Electronics
Analog Devices
National Semiconductor
Newark Electronics
Ph: 718-934-4500 Web: Minicircuits.com
RF amplifiers, RF mixers, RF filters
Ph: 1-800-831-4242
Web: Jameco.com
IC chips, RG174 connectors,
rack mount boxes
Ph: 1-800-652-6733
Web: mpja.com
power supplies, circuit boards,
BNC connectors
Ph: 1-800-543-4330
Web: mcm.com
RF generators
Ph: 1-800-262-5643
Web: analog.com
fast op-amps (get free samples)
Ph: 1-800-272-9959
Web: national.com
fast op-amps (get free samples)
Ph: 1-800-463-9275
Web: newark.com
high voltage connectors
data sets could theoretically be collected. Any dynamic measurements require
such data sets and circumventing the ISA bus will save a lot of testing time (approximately 30% reduction). Cost here is high probably exceeding 1000 dollars
even for the memory expansion.
A.9
List of specialized vendors
The tables in this section list vendors that have been useful in obtaining components for the LDV system. As always, it pays to check several sources for lowest cost.
At least one component of the LDV system was purchased from these vendors. The
tables are divided by category: electronics (A.3),optics (A.4), optoelectronics (A.5),
data acquisition (A.6), hardware (A.7).
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Table A.4: Specialized vendors and products: Optics
Optosigma
Newport
JML Optical
Thorlabs
Coherent (Ealing)
Edmund Optics
Omega Optical
Oz-Optics
Evergreen Laser
Ph: 949-851-5881
Web: optosigma.com
translation tables,tilt platforms,
polarization beam splitters
Ph: 1-800-222-6440
Web: newport.com
lenses, mirrors
Ph: 585-342-9482
Web: jmloptical.com
lenses
Ph: 973-579-7227
Web: thorlabs.com
rotary stages, mirror mounts,half wave plates
Ph: 1-800-295-3220 Web: ealingcatalog.com
optical posts, post holders,
prism mounts, beam splitters,prisms
Ph: 1-800-363-1992 Web: edmundoptics.com
microscope objectives, lenses, optical windows
Ph: 1-866-488-1064 Web: omegafilters.com
optical filters, dichroic mirrors
Ph: 613-831-0981
Web: ozoptics.com
fiber optics: cables, couplers, collimators
Ph: 860-349-1797 Web: evergreenlaser.com
laser maintenance
Table A.5: Specialized vendors and products: Optoelectronics
Hamamatsu
IntraAction
Ph: 1-800-524-0504 Web: hamamatsu.com
photo-multiplier tubes (PMTs)
Ph: 708-547-6644 Web: IntraAction.com
Bragg cell driver and modulators
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Table A.6: Specialized vendors and products: Data acquisition
National Instruments
Gage-Applied
Cyber Research
Ph: 1-800-258-7019
Web: ni.com
multi-function data acquisition
Ph: 1-800-567-4243 Web: gage-applied.com
high speed data acquisition cards
Ph: 1-800-341-2525 Web: cyberresearch.com
terminal boards
Table A.7: Specialized vendors and products: Hardware
C and H supply
Servo systems
TechnoIsel
Pilot fasteners
Ph: 301-663-1812 Web: CandHsupplyco.com
stepper motors, power supplies
Ph: 1-800-922-1103
Web: servosystems.com
stepper motor drivers
Ph: 516-328-3970
Web: Techno-Isel.com
stage components
Ph: 540-382-2365
Web: none
all kinds of screws, nuts, bolts, washers
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