VWDOF user manual
toothwalker.org/optics/vwdof.html
Calculator version 2.1, April 2005
Document version 2.1.1, February 2009
© P.A. van Walree 2002–present
VWDOF user manual
2. Units
By default, VWDOF adopts the Système International
d’Unités (SI) and uses the metric system. However, it
is possible to switch to the English system of inches,
feet, and other deprecated units of length, via the
OPTIONS/UNITS dialogue window. The full range of
units that can be encountered with VWDOF is as
follows:
Metric
mu
mm
m
km
1. Introduction
This document describes VWDOF, a versatile depthof-field (DOF) calculator. In addition to the DOF it
calculates quantities like the field of view, effective
aperture, depth of focus, the amount of background
blur, etc. The document is not intended as an introduction to depth of field. It assumes some familiarity
with the concept of depth of field and mainly functions
as a sort of manual for the calculator. More
information on the concept of DOF can be found at
http://toothwalker.org/optics/dof.html
micrometer
millimeter
meter
kilometer
English
in
inch
ft
foot
yd
yard
mi
mile
0.000001 m
0.001 m
1000 m
0.0254 m
0.3048 m
0.9144 m
1609.344 m
The OPTIONS/UNITS dialogue window allows individual
unit choices for each input or output parameter.
VWDOF attempts to format the output fields such that
the order of magnitude is reflected by the prefix and
not by the number itself. For instance, 0.00174 m is
formatted as 1.74 mm. If you don’t like a mixture of
VWDOF user manual
mu, mm, m, and km in the calculated values, you can
force an output in meters at the bottom of the dialogue
window. The above value would then be displayed as
0.00174 m. Likewise, the output of English units can
be forced in feet. To get a feeling about the units and
conversions, you could play with the HELP/UNIT
-30
are set
CONVERSION utility. Numbers smaller than 10
30
to zero and numbers larger than 10 are written as
“Inf” (infinity). This should be no limitation even for
astronomers.
3. Precision
At default, VWDOF rounds off the calculated values to
three significant digits. Via the OPTIONS/PRECISION
dialogue it is possible to increase the precision up to
six digits, but this is useful only for academic
excursions. For any normal photographic application
three digits are more than sufficient. There are many
reasons for this. One of them is that the true lens focal
length may differ up to 5% from its nominal value and
that it is not uncommon for a lens aperture to deviate
by 0.1 or 0.2 stops from the set F-number. So why
bother with a high precision at the output with this
degree of uncertainty at the input? Further, a
hyperfocal distance of 59.6238 m has little practical
importance given the fact that it’s hard enough to
focus at either 59 m or 60 m, let alone to notice a
difference in the image if one could.
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strictly only required for the field of view and the object
width and height. The reason is that the circle of
confusion (COC) value intimately connects with the
format, so whenever the COC is required for a
calculation the format shows up as well.
A flexible feature of VWDOF is that either the object
distance, the image magnification or the lens
extension can be placed among the input fields. In
this manner a certain magnification or extension can
be inserted directly, instead of finding it via a trial-anderror procedure by adjustment of the object distance.
OPTIONS/FIELDS OF INTEREST.
4. Fields of interest
VWDOF can employ a total of seven input fields and
fifteen output fields. This may lead to a slightly
overwhelming array of numbers, especially in
combination with a large number of scenarios. The
OPTIONS/FIELDS OF INTEREST dialogue window enables
a selection of fields. The fewer fields are selected, the
smaller and more surveyable the VWDOF window
becomes. The input fields are coupled to the output
fields in the sense that those input fields that are not
required to calculate the selected output quantities are
omitted. An exception is made for the format, which is
present with most output quantities although it is
Finally, there are choices for the POI (point of
interest). The input value can be taken as the distance
relative to the object or to the lens and the output can
be either the blur disk diameter or the ratio of the blur
disk diameter to the COC. The former quantity has the
unit of length, the latter is dimensionless.
VWDOF user manual
NB: When the pupil factor is not selected its value
always equals one for the calculations.
5. Scenarios
OPTIONS/SCENARIOS is used to fix the number of
scenarios (columns) to be calculated . Up to eight
scenarios can be set, but like the fields of interest a
large number could result in a large, overwhelming
VWDOF window. The scenarios dialogue further
offers the possibility to synchronize certain input
fields. For instance, when the F-number is
synchronized all columns inherit the F-number of the
left column.
3
7. Sharpness criterion
Any calculation that involves the depth of field or
depth of focus requires a sharpness criterion. When
we take a picture, only one plane in the object space
is rendered tack sharp, but there is a surrounding
region which will be acceptably sharp. That is to say,
acceptable according to a criterion set by the user.
VWDOF provides three built-in sharpness criteria in
the form of automatically inserted COC values upon
selection of a film format. This COC is based on the
format diagonal and yields nicely rounded values for
the 35-mm format.
OPTIONS/COC CRITERION dialogue.
When the multiple F-stops view is selected, VWDOF
will have eight columns with F-numbers increasing by
one-stop increments. The initial F-number can be
picked in the dialogue window. The multiple F-stops
view does not yield anything that cannot be achieved
otherwise, it just saves you the trouble to manually fill
the columns with an array of F-numbers.
6. Check input
To avoid calculations with input values outside the
valid range of the theory, or to avoid dubious regimes
of lens performance, all input quantities have a lower
and/or upper limit. At input, parameters are subjected
to a validity check. When a value is outside the
accepted range, the number shows red in the input
box. If the calculate button is hit nonetheless, VWDOF
will launch a pop-up warning message that mentions
the allowed range for the illegal input parameter.
Alternatively, the OPTIONS/CHECK INPUT option
provides the choice of letting VWDOF silently replace
illegal input values with the closest value that is
accepted. When this happens the replaced value
shows in blue in the input box, as a sign that the
calculation took place with another value than the one
you typed.
For most other formats the automatic assignment
yields funny figures, but at least they ensure that a
comparison between different formats will be based
on a fair comparison when prints of the same
(diagonal) size are compared. The possibility to
choose between three sharpness criteria
(conventional, demanding and critical) sounds nice,
but every scenario ideally requires an individual
approach. VWDOF does not know the size of a print
or the viewing distance adopted by the observer. If
you arbitrarily pick one of the three criteria you could
underestimate or overestimate the COC needed for
your application. A better approach is to determine the
required COC value C yourself:
C=
V
1000 × Q × M p
VWDOF user manual
Here, V is the viewing distance of the print (or slide
projection, or screen display), M p the print
magnification, i.e. the ratio of the print size to the
format size, and Q a quality parameter that indicates
how carefully the photograph will or can be examined.
Q = 1: conventional
Q = 2: demanding
Q = 3: critical
On the assumption of good viewing conditions and a
normal visual acuity of the human eye of one minute
of arc, Q = 3 corresponds to the smallest COC that
makes sense for a person with normal vision.
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inserted manually via the custom-format fields. Every
format has a height, a width and a reminder string. For
the predefined formats the height and width are fixed,
but it’s possible to replace the reminder string with the
name of your favorite camera. Just to add a personal
touch.
Most of the predefined formats are given with their
nominal height and width. In real terms a small margin
is usually lost. For instance, a slide mount or print
mask will reduce a 24×36 mm image to something like
22×34 mm and the 6×6 cm format is often closer to
56×56 mm than to the nominal 60×60 mm. If the
effective format is known precisely, it could be entered
among the custom fields.
As an example, a high-quality print from a 6×6 cm
negative measuring 30×30 cm (i.e. a 5× print
magnification), and viewed from a distance of 50 cm
in a bright room, would require a COC of
C=
50 cm
1000 × 3 × 5
= 0.033 mm
if we want it to pass a meticulous examination. On the
other hand, a picture displayed at 200×300 pixels
(some 6×9 cm) on a computer screen is more likely to
get away with
C=
50 cm
= 0.20 mm
1000 × 1× 2. 5
Here the quality factor is taken as Q = 1 because the
resolution of a computer screen (72-96 dpi) is lower
than that of high-quality print paper (300 dpi). In this
case the screen resolution is the limiting factor, not
our vision.
8. The film format
Eighteen predefined film formats can be selected via
the OPTIONS/IMAGE FORMATS dialogue. The vast
number of new formats that came with the emergence
of digital cameras are not included, but these can be
9. The edit menu
If you want to use the outcome of a calculation in
another application it is not necessary to copy the
values by hand as VWDOF can copy the columns to
the Windows clipboard. EDIT/COPY LAST copies the
last valid calculation to the clipboard, EDIT/COPY ALL
copies all scenarios. A valid calculation is recognized
by a blue bar below the calculate button, an invalid
calculation by a red bar. The last valid column has a
green bar. The red bar signifies that the Calculate
button was not yet hit or that the calculation is invalid
(illegal input). The presence of one or more red bars
disables one or both copy options.
VWDOF allows five clipboard text formats, where the
difference is in the field separator. Blank spaces or
dots yield horizontally aligned fields, but only when
the clipboard contents are copied into a text
application using a monospace (fixed-pitch) font such
as Courier new. The comma, semicolon or tab might
be useful to insert the calculations into spreadsheet
applications.
A typical copy-and-paste action looks like:
VWDOF user manual
VWDOF 2.0---------input--------------------Format
24x36 mm
24x36 mm
COC
0.0300 mm
0.0300 mm
Focal length
50 mm
100 mm
F-number
8
8
Magnification
1
1
------------------output-------------------Extension
50.0 mm
0.100 m
Field of view
24.4 deg
12.3 deg
Depth of field
0.960 mm
0.960 mm
Or, with the semicolon separator:
Format;24x36 mm;24x36 mm
COC;0.0300 mm;0.0300 mm
Focal length;50 mm;100 mm
F-number;8;8
Magnification;1;1
Extension;50.0 mm;0.100 m
Field of view;24.4 deg;12.3 deg
Depth of field;0.960 mm;0.960 mm
The two lines designating the input and output are
omitted when the comma, semicolon, or tab delimiter
is used.
The EDIT/CLEAR menu entry is perhaps clueless. It just
brings back VWDOF to its state with two columns and
the default fields of interest. It could be useful if this is
what you want, or when strange output results from a
‘forgotten’ setting. EDIT/CLEAR brings all settings to
default, but preserves the (custom) formats and their
reminder strings.
10. The view menu
VIEW/MULTIPLE F-STOPS is a shortcut to the multiple Fstops view in the OPTIONS/SCENARIOS dialogue
window. VIEW/STANDARD brings VWDOF back to its
normal state. The VIEW/WINDOW LAYOUT dialogue box
offers the choice between two font sizes for the
window, the choice between two colors for the output
fields, and the option to show or hide the tooltipstring
(the yellow text boxes that appear when the mouse is
moved over a field).
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11. Input parameters
Five parameters are required to calculate all numbers
in the output fields.
ƒ Format
Eighteen predefined film formats are available, and an
additional eighteen custom formats. The accepted
format dimensions range from 1 mm to 1 m. You can
go to the image formats dialogue box by either
clicking on the format field, or via the OPTIONS/IMAGE
FORMAT menu.
ƒ COC
Being the sharpness criterion, the circle of confusion
is of paramount importance. When a film format is
selected, VWDOF automatically sets a value for the
COC. This value is proportional to the format diagonal
to allow a fair comparison between two formats when
prints of the same (diagonal) size are compared.
Three levels for the general criterion can be chosen in
the OPTIONS/COC CRITERION dialogue. However, you
are free to change the COC value to your liking or
needs. Just type a number in the input field. VWDOF
accepts values between 0.1 µm and 10 mm.
ƒ Focal length
VWDOF accepts focal lengths between a certain
lower limit and a telescopic 100 m. The lower limit
depends on the format and relates to the so-called
fisheye limit. This limit says that any rectilinear lens
will have a poor optical performance when the field of
view exceeds a value of ~ 140 degrees. For that
reason the calculator refuses focal lengths that would
exceed the fisheye limit in combination with the set
format.
ƒ Pupil factor
The pupil factor P (also known as the pupil
magnification) is a measure of the symmetry of the
lens design. It can be ignored for faraway subjects (an
image magnification of ~ 0.1 or smaller) but it
becomes important in the macro regime. The pupil
magnification is defined as
VWDOF user manual
P=
exit pupil diameter
entrance pupil diameter
and may be evaluated by the pupil sizes specified in
the information sheet for your lens. If this information
is not available, you may estimate P by inspection of
the lens. Close down the lens by a few stops and
estimate the size of the diaphragm opening when you
look into the lens from the front (entrance pupil) and
from the rear (exit pupil). The ratio of the diameters is
more important than their absolute values. More often
than not, a wideangle lens for an SLR camera
(retrofocus design) will have P > 1 and a telephoto
lens P < 1. Wideangle lenses for rangefinder cameras
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dialogue. For some purposes it is preferred to indicate
the POI location relative to the lens. For instance, if a
lens is focussed at infinity the POI blur of a nearby
point can only be evaluated by specifying it relative to
the lens. POI re lens uses the same distance scale as
the object distance. Thus, an input value for POI re
lens that is identical to the subject distance yields a
blur disk of zero diameter as the POI is in the plane of
sharp focus.
The accepted values for the POI are between the
focal length f (to be precise: a distance f in front of the
front principal plane) to infinity. Theoretically it can be
closer to H, but with most lenses that would place the
POI inside the glass and make it an academic matter.
are nearly symmetrical with P ≈ 1. Be careful with
zoom lenses or lenses that employ “floating elements”
because the pupil sizes (and hence P ) may depend
on the focal length or object distance.
The pupil magnification affects the effective aperture,
the near and far points, the front and rear DOF, the
depths of field and focus, the POI blur and the field of
view. For all these quantities the influence of P is only
significant at close focus. The accepted range for P is
between 0.1 and 10.
ƒ F-number
Among other things, the F-number (often referred to
as the aperture) is instrumental in the control of the
depth of field. VWDOF accepts F-numbers from 0.5 to
128. Use the true F-number and not the effective
aperture that is sometimes used for exposure
compensation at close range. If you set a lens at F/8,
the true F-number is 8 regardless of the focussing
distance.
ƒ POI re lens and POI re subject
The POI (Point of Interest) is an advanced feature that
allows to calculate the blur size for an arbitrary point in
object space. The position of this point can be entered
relative to the subject or relative to the lens. To
determine how unsharp a point at a certain distance in
front of or behind the subject is rendered, select POI
re subject in the OPTIONS/FIELDS OF INTEREST
12. Intermediary parameters
Either one of the object distance, the image
magnification or the lens extension can be chosen as
an input parameter. The other two quantities (if
selected) will be among the output fields.
ƒ Object distance
The distance to the object that is in sharp focus. The
close limit depends on the focal length. VWDOF
allows image magnifications from 100×lifesize to zero,
corresponding to object distances from 1.01 times the
focal length to infinity. Type “Inf” to put an object at
infinity. It is important to realize that the DOF
equations rely on object distances measured from the
lens (or more precisely, the front principal plane)
whereas the distance scale imprinted on lenses
traditionally gives the values relative to the film plane.
For faraway objects the difference can be ignored, but
not for close-up photography. If you don’t know where
the front principal plane is you can perhaps find it in
the lens specifications – some manufacturers provide
this information. If the information is not available you
can circumvent the problem by specifying the image
magnification or lens extension instead of the object
distance. For macrophotography, these parameters
are often more useful than the object distance
anyway.
VWDOF user manual
ƒ Magnification
The image magnification is the ratio of the size of the
image to the real size of the subject in object space. A
stamp that has the same size on the negative as in
real life has a magnification M = 1 . Macro lenses that
achieve this magnification will have the designation
1:1. Likewise, a photograph where the image is half
the size of the original has M = 0.5 (1:2), which
implies that 1 cm on the film corresponds to 2 cm of
the real object. At infinity focus M = 0 . VWDOF allows
image magnifications from 100 to zero.
ƒ Extension
The lens extension can be useful as an input
parameter when bellows or extension rings are used.
Notice that the extension is the sum of the added
extension and the extension of the lens itself. When
the lens is set at infinity, the extension is just the
length of the bellows or the ring(s), but if the lens
focussing ring is used to fine-tune the focus the lens
own extension must be added to the added extension.
13. Output parameters
ƒ Field of view
This field gives the full diagonal angle of view. Note
that this angle depends on the object distance and
narrows when a lens is used at close range. Lens
manufacturers tend to specify the angle of view with
the lens used at infinity. If you want to check this
infinity angle, type a very large number (or better:
“Inf”) for the object distance.
The field of view also depends on the pupil
magnification. The reason is that the field of view
originates from the center of the lens entrance pupil,
whereas the object distance is measured from the
front principal plane. For asymmetrical lenses (P ≠ 1)
the entrance pupil and front principal plane are
separated. Lenses with identical focal lengths but
different pupil magnifications, when used at the same
image magnification (the subject framed in the same
7
way) will have different fields of view. That is to say,
the perspectives are different and one picture will
show more of the background than the other.
ƒ Object width and height
The width and height of the plane placed in sharp
focus, in case you want to know the dimensions of an
object that fills the frame. Landscape orientation is
assumed.
ƒ Effective aperture
When a lens is used at close focus, the collected light
is spread over a larger circle than at infinity focus.
Consequently, the light intensity per unit area
decreases and exposure compensation is necessary.
TTL metering automatically takes the effect into
account, but a handheld meter does not. The effective
aperture (or better: effective F-number) gives a
value for the F-number that should be used to
evaluate the exposure, instead of the true F-number
set on the lens.
ƒ Hyperfocal distance
Depending on the focal length, the F-number and the
COC, the hyperfocal distance H gives the object
distance at which maximum depth of field can be
achieved. A lens focused at H yields a sharp image
from H/2 up to ∞.
ƒ Near point
The near point is the point closest to the camera that
meets the COC criterion. Anything in front of the near
point is considered out of focus.
ƒ Far point
The far point is the point furthest from the camera that
meets the COC criterion. Anything beyond the far
point is considered out of focus.
ƒ Front DOF
The depth of field in front of the object. It is simply the
difference between the object distance and the near
point.
VWDOF user manual
ƒ Rear DOF
The depth of field behind the object. It is the
difference between the far point and the object
distance.
ƒ Depth of field
The total DOF, also known as the depth of field, is the
sum of the front DOF and the rear DOF.
ƒ Depth of focus
The depth of focus may be regarded as the depth of
field in image space. It gives the margin around the
focal plane (i.e. the plane of exact focus, where the
film is supposed to be) where the image blur is
smaller than the prescribed COC. Precisely half of the
depth of focus is in front of the focal plane, and half of
it in rear. Since a film can usually not curl backwards,
owing to the presence of the pressure plate, the depth
of focus should be divided by 2 in the context of film
flatness issues. For example, if the depth of focus
amounts to 0.34 mm the film flatness should be 0.17
mm or better to avoid image degradation.
ƒ Infinity blur
This field gives the amount of blur imposed upon a
distant background. It is the diameter of the circle of
confusion, measured on the film, for an object point at
infinity. Control of the background blur is of considerable importance and can make the difference
between a subject that “sticks to the background” or a
subject that “stands out” against a nicely blurred
background. Notice that a large amount of
background blur is not necessarily the same as a
small DOF. The infinity blur is a special case of the
POI blur; if you’re only interested in the rendering of a
faraway background the infinity blur is easier to use..
ƒ POI blur disk / relative POI blur
The POI blur can be used to determine the blur disk
diameter for an arbitrary point in object space. The
position of this point is specified with the input
parameters. The OPTIONS/FIELDS OF INTEREST
dialogue gives the choice between two output options:
the blur disk diameter (POI blur disk) or the ratio of the
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blur disk diameter to the COC. The former gives the
diameter of the blur disk on the film/sensor, the latter
is a dimensionless quantity. For example, a COC of
0.030 mm and a POI blur disk of 0.060 mm yield a
relative POI blur of 2, indicating that the blur of the
selected point exceeds the sharpness criterion by a
factor of two. When the point of reference is placed at
infinity, the “POI blur disk” yields the same value as
the infinity blur.
14. Feedback
Bug reports or suggestions for improvements are
welcome. Send your comments by e-mail to the
current address found at toothwalker.org/about.html.
When you report a bug, be sure to include a screen
shot or a clipboard dump that shows the misbehavior.
15. Terms of usage
VWDOF is freeware and may be freely distributed.
16. Acknowledgment
I am very grateful to my good friend muchan, who
translated my original Matlab code into C++ in order to
keep the file size of the program within bounds. He
added numerous useful features as well.
17. Examples of use
ƒ Bellows
A 50-mm lens mounted on bellows is given a 10-cm
extension. What is the image magnification?
VWDOF 2.0---------input---Focal length
50 mm
Extension
100 mm
------------------output--Magnification
2.00
The object is projected on the film at twice its lifesize.
ƒ
Full moon
6
The moon has a diameter of 3.476×10 m and its
6
distance to the earth is 384×10 m. At what size will
the moon be imaged when a 600-mm lens is used?
VWDOF 2.0---------input-----Focal length
600 mm
Object dist
384E6 m
------------------output----Magnification
1.56E-09
Then, 1.56E-9 × 3.476×106 m = 5.4 mm.
ƒ Butterfly
The insect is photographed at unit magnification with
two different macro lenses. An inspection reveals that
the 60-mm lens is symmetrical with a pupil
magnification of 1, whereas the 100-mm lens is
somewhat asymmetrical with P = 0.7.
VWDOF 2.0---------input----------------Format
24x36 mm
24x36 mm
COC
0.030 mm
0.030 mm
Focal length
60 mm
100 mm
Pupil factor
1.0
0.7
F-number
16
16
Magnification
1
1
------------------output---------------Object dist
0.120 m
0.200 m
Field of view
20.4 deg
10.2 deg
Hyperfocal dist
7.56 m
20.9 m
Depth of field
1.92 mm
2.33 mm
Front DOF
0.952 mm
1.16 mm
Rear DOF
0.968 mm
1.17 mm
Infinity blur
3.75 mm
6.25 mm
The calculation shows that the 100-mm lens provides
a longer object (working) distance. Thus, the butterfly
is less likely to be chased off. Another advantage
might be that the telephoto lens yields 20% more
DOF, which increases the chance of getting the wings
all sharp. Finally, the (absolute) blur size of a faraway
background is larger, which, together with the smaller
FOV, may result in a less distracting background. The
ratio of front:rear DOF is close to one in both cases. In
this example the depths of field are not influenced by
the focal lengths, but solely determined by the image
magnification and the lens (a)symmetry in the form of
the pupil magnification.
ƒ Rhinoceros
Suppose we use the same lenses of the butterfly
example, but now to photograph a rhinoceros. The
image magnification must be considerably smaller if
the entire animal is to be depicted. Let’s take M=0.01.
An object width of 3.60 m and a height of 2.40 m
should be enough.
VWDOF 2.0---------input----------------Format
24x36 mm
24x36 mm
COC
0.030 mm
0.030 mm
Focal length
60 mm
100 mm
Pupil factor
1.0
0.7
F-number
16
16
Magnification
0.01
0.01
------------------output---------------Object dist
6.06 m
10.1 m
Field of view
39.3 deg
24.1 deg
Object width
3.60 m
3.60 m
Object height
2.40 m
2.40 m
Hyperfocal dist
7.56 m
20.9 m
Front DOF
2.69 m
3.29 m
Rear DOF
24.2 m
9.36 m
Depth of field
26.9 m
12.7 m
Infinity blur
37.5 mu
62.5 mu
Several changes are noticed with respect to the
butterfly case. For starters, the fields of view are
larger because of the increased object distance.
Further, the depth of field is now larger for the 60-mm
lens because the pupil magnification is of no
significance at such a small magnification. Instead,
the rhinoceros is not far from the hyperfocal distance
of the 60-mm lens, whose DOF thus rapidly increases
towards the rear. Unlike the butterfly case, the lens
focal lengths now influence the DOF. The infinity blurs
are 100 times as small as in the butterfly example.
They are still larger than the permissible COC value,
which is another way of saying that the depth of field
does not stretch away to infinity.
VWDOF user manual 10
ƒ Small versus large format
Suppose we take a picture with two different cameras.
A small (digital) one with a sensor size of 0.4×0.5” and
a large-format camera using 4×5” film, and equipped
with a 100-mm lens. The ratio of the format
dimensions amounts to 10. If we focus at infinity, the
smaller format needs a lens with a focal length that is
ten times as small to yield the same angle of view.
VWDOF 2.0---------input---------------Format
0.4x0.5"
4x5"
COC
0.0113 mm
0.113 mm
Focal length
10 mm
100 mm
F-number
5.6
5.6
Object dist
Inf
Inf
------------------output--------------Field of view
78.2 deg
78.2 deg
Hyperfocal dist
1.59 m
15.9 m
Near point
1.58 m
15.8 m
Far point
Inf
Inf
Depth of focus
0.127 mm
1.27 mm
Moreover, if prints of the same size are compared, the
digital image needs a print magnification that is 10
times as large. Therefore, the COC needs to be 10
times as small in order to compare the two formats on
basis of the same viewing sharpness criterion. From
the above clipboard dump we notice that the factor of
10 reappears at the output of the calculator. The
hyperfocal distance is smaller for the smaller format,
and the depth of field larger. Although the DOF has a
value of ∞ in both cases, the near point is much closer
for the small camera. Finally, the depth of focus is 10
times as small for the smaller format. So although its
depth of field is larger, the smaller camera is more
vulnerable to camera misalignment and focussing
errors.
ƒ Wiremesh
A photograph of a building is taken through a
wiremesh with a 50/1.4 lens at full aperture. The lens
is held close to the wiremesh and the distance
between the wires and the lens front principal plane
happens to be 50 mm. To what degree will the
wiremesh be blurred?
VWDOF 2.0---------input--Focal length
50 mm
F-number
1.4
Object dist
100 m
POI re lens
50 mm
------------------output-POI blur disk
35.7 mm
Every point of the wiremesh is smeared out over a
disk with a diameter of 3.6 cm, which is large enough
to render the wires invisible in the image.
18. The equations
For the sake of completeness the equations used by
VWDOF are given. There are many ways to represent
the DOF equations; the below formulae may look
different from those encountered elsewhere, but
usually it’s just a matter of algebraic rearrangement.
The below equations are exact within the theory of
Gaussian optics. When a computer does the work
there is no reason to use simpler, approximated
equations with a restricted applicability. All too often
such approximations start to lead their own life in
which the original restrictions are forgotten.
ƒ
Input parameters
Format height
L1
Format width
L2
Circle of confusion
C
Focal length
f
Pupil magnification
P
F-number
N
POI re lens
w
POI re object
u
ƒ Intermediary parameters
Object distance
v
Image magnification
M
Lens extension
e
VWDOF user manual 11
ƒ
Dummy parameters
Lens aperture
D =f /N
Image distance
b=
fv
v −f
POI image distance
z=
fw
w −f
z=
f (v + u )
v +u −f
ƒ
Near point
(P − 1)(v − f ) C f + P D f v
P C (v − f ) + PD f
Far point
(P − 1)(v − f ) C f − P D f v
P C (v − f ) − PD f
Front DOF
C ( v − f )[f + P (v − f ) ]
P C (v − f ) + PD f
(POI re lens)
(POI re object)
Calculated quantities
Rear DOF
When the object distance is given:
b
v
Magnification
M=
Extension
e=Mf
Total DOF
When the magnification is given:
Object distance
f
v =f +
M
Extension
e=Mf
f ⎞
⎛
v = f ⎜1 + ⎟
e
⎝
⎠
M=
Magnification
e
f
⎛
⎞
⎟
2f (1 + M / P ) ⎟
⎝
⎠
Field of view
α = 2 × atan ⎜⎜
Object height
L1 ×
v
b
Object width
L2 ×
v
b
⎛
⎝
Effective aperture N ⎜1 +
Hyperfocal distance
L21 + L22
M⎞
⎟
P⎠
f ⎞
⎛
H = f ⎜1 +
⎟
NC
⎝
⎠
v <H
∞
v ≥H
2 f C D ( v − f ) [(P − 1) f − P v ]
P C 2 (v − f )2 − P D2 f 2
Depth of focus
M⎞
⎛
2 N C ⎜1 + ⎟
P⎠
⎝
Infinity blur
k
POI blur disk
k POI =
When the extension is given:
Object distance
C ( f − v )[f + P (v − f ) ]
P C (v − f ) − PD f
∞
=
fM
N
PD | z − b |
z + (P − 1) f
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