Laboratory 2 Basic Optical Instruments Physics

Laboratory 2 Basic Optical Instruments Physics
Laboratory 2
Basic Optical Instruments
Physics 4150
September 14, 2016
Purpose:
Similar to last week’s lab, this one consists of three short segments that can be done in any order. You
will construct and characterize a telescope and slide projector, providing an introduction to some of the
problems involved in designing practical optical instruments. You will also construct a pinhole camera or
simple single-lens camera and use it to produce an image on the sensor of a small Firewire-interfaced
video camera. This video camera will be used later in the semester for several purposes. Most of the
required theory for these experiments is described fully in chapters 5 and 6 of of Hecht, or chapter 3 of
Pedrotti3, and will not be repeated here.
Equipment:
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Optical rails with four lens holders.
Bright lamp.
White cards or opal glass screens for viewing real images.
Grids on transparent backing (or other slides) for projection.
Large scale on wall to measure telescope magnification.
2 cm and 10 cm PCX or DCX lenses, 1” diameter.
5-10 cm PCX lenses (2 per setup), 1.5” or larger diameter.
50–70 cm PCX lens, 1.5” or larger diameter.
Bright LED or small light bulb (preferably with a bare filament).
Point Grey Firefly MV camera, either the USB or Firewire version, and a computer with
NI Vision software. Full data on the camera is available on the Physics 4150 web page
under “Resources”.
Mounted pinholes: 100, 200, and 400 microns.
Illuminated objects for image formation by the camera.
Rulers and meter sticks.
I. Pinhole Camera
The classic pinhole camera can be constructed from a cardboard box and a piece of film, which is
subsequently developed in the darkroom. Here we use a modern variant by replacing the film with the
sensor of a CMOS video camera, providing instant views of the resulting image on a computer screen.
The setup is very compact because the sensor is quite small: it has 640 × 480 pixels (or 752 × 480 in a
special video format), each sized 6 m × 6 m. Full information is available in the “Resources” section
of the Physics 4150 web page. A reasonable field of view is obtained if a pinhole is placed a few cm
away from the sensor.
Set up the camera by removing its usual lens, instead attaching a pre-mounted 400 m pinhole to the
C-mount lens adapter of the camera. Use a ruler to determine the distance from the pinhole to the
mounting flange, and combine this with the known distance to the sensor to determine the total sensor-topinhole distance. Place a brightly lit object about 20-50 cm away from the camera, and use the National
Instruments Vision Assistant program to view the resulting image. You will probably have to adjust the
shutter speed and gain of the camera to obtain a properly exposed frame.
Once you have obtained a clear image, save the result for later analysis and printing. Now repeat the
process with a 200 micron pinhole. In principle the image should be sharper, reflecting the fact that the
pinhole size directly determines the size of the image of a point source on the sensor. Does the measured
resolution of your image match what you expect, given the distances to the pinhole and the object? You
can measure the resultion either by using a calibrated scale as the object, or by using your knowledge of
the pixel size, 6 m. You might experience some unexpected results, here, though, because of the effects
of near zone diffraction. This is much more complex than the standard long-range treatment that we
apply elsewhere is this lab, and in most of this course as well.
It might be possible to suppress this
somewhat by using a larger target pattern, further away from the pinhole.
Next, explore the diffraction limit of your camera by substituting a smaller pinhole, 100 mm. Note
that this time the image resolution is worse, not better! Because the image is also quite dim, depending
on the source brightness, you might have to use the “pixel binning” feature of the camera to obtain a
usable image. This feature combines groups of two or four pixels to produce a brighter but lowerresolution image, and in the present instance the resolution is much larger than the pixel size in any case.
Quantitatively, the diffraction limit is easily estimated. We will soon show that for a uniformly
illuminated circular aperture of diameter d, diffraction causes an angular spread of  = 1.22 /d. If the
distance from the pinhole to the image sensor is si, the spot size resulting from diffraction is siThe
overall resolution will be determined by this diffractive spreading if the spot size is larger than the
geometric resolution of the pinhole camera, which is simply d. Equating these quantities, we find that the
camera is diffraction limited if
d  1.22 si  .
Use this result to show that the 100 micron pinhole should indeed yield a diffraction-limited image.
Note that the small sensor size of our camera makes it particularly susceptible to diffractive limitations—
for a large piece of film, the geometric resolution on the image plane would still be d, which corresponds
to a much smaller fraction of the total image size. This is an intrinsic limitation of miniature cameras
with small lenses or apertures. In the present case, it is actually something of an advantage, since it
makes it easy to observe diffraction-limited performance.
Finally, compare the performance of the camera when it is used with a lens rather than a pinhole.
First, try a simple 2 cm DCX lens, then try a lens that’s actually designed for the camera. Note that the
images are much, much brighter and also much better-resolved, but that the depth of field is limited. By
contrast, the resolution of the pinhole camera is essentially independent of the object distance.
II. Astronomical Telescope
Use a lens with a focal length of about 50–70 cm together with a 10 cm lens to construct an
astronomical telescope on one of the optical benches. You will probably want to start by aiming it
towards a bright outdoor scene or a brightly lit object, although later you will want to re-aim it at the large
scale on the wall in order to measure the magnification. Initially, place your lenses at the optimal distance
calculated when both the object and the image are at infinity. Since the entrance pupil and aperture stop
are both determined by the rim of the objective lens, the exit pupil is just the image of the objective lens
formed by the ocular. Estimate the position of the exit pupil. Now put your eye there, and bring the
telescope into sharp focus by sliding the ocular lens back and forth slighty.
Find the position of the exit pupil more accurately. You can do this approximately by finding the
position where the field of view is largest (probably limited by the diameter of the ocular). An even
better way is to put a screen after the eyepiece approximately where the eye normally goes, then move it
back and forth until you see focused image of the objective lens and its mount. Then measure the
position and diameter of the exit pupil. Is its size well-chosen for the pupil of the eye, with a diameter of
about 5 mm in a darkened room?
Now we will try a measurement that’s very useful, but does not work for everyone. Use your
dominant eye (usually the right eye) to look through the telescope. Next use your other eye to look
directly at the large scale on the wall at the same time. Refocus the telescope if necessary so the image is
at infinity, and you can see the magnified and inverted image of the scale through one eye superposed
over the directly viewed scale seen by the other, both in sharp focus. It may take a little practice to be
able to see both views at once, since the brain wants desperately to reject one or the other when it
processes the image. For some people with one strongly dominant eye, this may prove impossible. If you
can see both images, compare the imaged and direct scales to determine the angular magnification
directly. Also measure the spacing between the two lenses of the telescope.
Finally, estimate the angular field of view by measuring the range of the scale that is in clear focus,
calibrating the scale itself with a meter stick, and dividing by the distance to the scale.
Compare all of your results with calculated values, using the labeled values for the focal lengths and
diameters of the lenses (don't forget to record them!) Remember that for a telescope, the exit pupil
diameter is given by the entrance pupil diameter divided by the angular magnification. It may seem
difficult at first to estimate the expected angular field of view, but this is really quite simple if the size of
the ocular lens determines the limits of the visible field. The maximum range of angles you can view at
your eye is then determined by the angular size of the ocular lens at the position of the exit pupil. Since
you already know the angular magnification of the telescope, you can now calculate the maximum
observable angular range for objects viewed by the telescope. If this isn't obvious, make a quick sketch.
III. Slide Projector
A projector is a good system with which to get some practical experience with the proper sizing of
optics and apertures, since the whole purpose of the instrument is to provide an intense and clear image.
Start by using a 5–10 cm lens to image a slide or small transparency on a white viewing screen or the
wall, with a bare-filament light bulb or a bright LED as the light source. A distinct improvement can be
made by introducing an aperture stop between the bulb and the system, so the bundle of light rays from
the bulb just fills the lens--this eliminates much of the extraneous light from the screen.
A much larger improvement comes from the introduction of an appropriately designed condenser lens
to collect light from the bulb and direct it optimally. In many commercial projectors, a parabolic reflector
behind the bulb is also used, but we will omit this for simplicity. Try using a second 5–10 cm lens,
placed to produce a focused image of the light source at the position of the projection or “field” lens.
Notice that the light source can't be imaged by the condenser too near the slide, since the illumination of
the slide would then be very nonuniform, and even worse, a rather distinct image of the light bulb
filament would then be imaged onto the projection screen. It is still helpful to use an additional stop to
block stray light, setting it so the condenser lens is just barely filled with light. Alternatively, the
condenser lens can be mounted on a large black plate to serve the same purpose. The size and focal
length of the condenser lens of course determine how large a slide can be projected.
With a properly positioned condenser lens you should be able to dramatically increase the intensity of
your projector while maintaining uniform illumination over the field of view. Incidentally, the yellowish
edges of the field of view come from chromatic aberrations in the condenser; if you want, you can try to
eliminate them by substituting a cemented two-element achromat for the simple lens. Observe the
illuminated area as a function of distance downstream, and measure the position and size of the entrance
pupil, exit pupil, the illuminated field in the final projected image, and the magnification of the slide by
the projector. Compare with calculated values for your geometry.
You have undoubtedly noticed that this projector suffers from rather severe aberrations, at least if the
condenser is moved so as to give a wide angular field—if a grid is used as the image source, severe
“pincushion distortion” is observed, and it’s impossible to sharply focus the center of the image at the
same time as the outer edges. To see what can be done about these aberrations with clever lens design,
try replacing your 50 mm lens with the Kodak projection lens available in the lab. The improvement
should be dramatic. Even though all of the internal lenses within the large projection lens are themselves
spherical, their design has been carefully optimized to nearly eliminate the optical imperfections.
Fig. 1. Suggested projector arrangement with efficient light usage.
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