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Old Saturday 19th November 2011, 18:31   #1
locustella
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Digiscoping - how to calculate the depth of field ?

This is strictly theoretical question, knowing the depth of field is not needed for anything practical.
But how to calculate it ?

Example 1:
f = 24 mm (focal length of the camera lens)
N = 2.8 (F - number in the camera lens)
s = 50 m (object distance)
m = 60 (scope magnification)
d = 80 mm (entrance pupil diameter for the scope)
c = 0.029 mm (the circle of confusion for 35 mm film)
P = 1 (Pupil Factor, but of what ? It strongly affects the depth of field in the macrophotography)

Example 2:
the same data, but N = 22 (aperture limited by the aperture of the lens, not exit pupil of the scope)

Maybe using these data:
f' = 24 mm x 60 mm = 1440 mm (effective focal length)
s = 50 m
N' = 1440 mm / 80 mm = 18 (Example 1)
or
N' = 22 (Example 2) (like for the camera lens alone because the exit pupil of the scope: 80 mm / 60 = 1.33 mm is bigger then the entrance pupil of the camera lens: 24 mm / 22 = 1.09 mm)
???

And the depth of field would be:

DOF = 2 * N * c * [s - (P-1)/P*f]*(s-f) / {f^2 - [N*c*(s-f)/f]^2}
DOF ≈ 2*N*c*s*(s-f)/f^2 (approx and without P)

^2 means raised to power 2, formulas based on:
http://toothwalker.org/optics/dofderivation.html
http://www.largeformatphotography.in...DoFinDepth.pdf

Example 1
DOF = 2 * 18 * 0.000029 * [50 - (1-1)/1*1.440]*(50-1.440) / {1.440^2 - [18*0.000029*(50-1.440)/1.440]^2} = 1.22 m
DOF ≈ 2 * 18 * 0.000029 * 50 * (50-1.440) / 1.440^2 ≈ 1.22 m

Example 1
DOF = 2 * 22 * 0.000029 * [50 - (1-1)/1*1.440]*(50-1.440) / {1.440^2 - [22*0.000029*(50-1.440)/1.440]^2} = 1.49 m
DOF ≈ 2 * 22 * 0.000029 * 50 * (50-1.440) / 1.440^2 ≈ 1.49 m

This way of calculating the F - number is perhaps good in terms of luminance (and exposure time), but is it correct for the depth of field (the angular blur) ? This is a little suspicious ... I think that it may be wrong.
Maybe knowing the image (or object) distance of the camera lens alone is needed ?
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Old Saturday 19th November 2011, 18:57   #2
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Hi,
Interesting, thanks for sharing yout thoughts but I believe the DOF is shallower than this. Circle of confusion is much smaller than 0.35 mm

DOF Master can be used for lenses up to 1200 mm FL, and at F/22 the DOF should be around +/- 0.35m



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Old Saturday 19th November 2011, 19:40   #3
locustella
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Quote:
Originally Posted by Tord View Post
I believe the DOF is shallower than this. Circle of confusion is much smaller than 0.35 mm
Thank you for your answer. Perhaps it is shalower, or not.
But for circle of confusion c = 0.029 mm DOF master shows the same result like obtained from the equatioms above.

This circle of confusion was calculated for 35 mm film. For 22.2×14.8 mm sensor the classical circle of confusion is 0.01779 mm. And then for N = 22 DOF = 91.65 cm.
If you use diameter of one pixel taken from that sensor (12.2 MP) as the circle of confusion (5.19 μm = 0.00519 mm), DOF = 26.74 cm, for two pixel circle of confusion (0.01038 mm) DOF = 53.48 cm.

And the question was - can we use 1440 or 1200 mm and f#22 to calculate the depth of field of the camera lens - scope combination ? I mean parameters for the combination of a camera lens and scope (effective focal length and such "effective" F-number) ?
Maybe 28 mm, f#22 and the object distance for the camera lens should be used and equation especially designed for digiscoping, different than that classical one ? Maybe we need entrance or rather exit pupil, different than 24 mm / 22 = 1.09 mm ?
Can we really treat such combo as normal tele lens 1440 mm with the aperture 22 ?

Last edited by locustella : Saturday 19th November 2011 at 20:03.
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Old Saturday 19th November 2011, 23:40   #4
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The relevant values for the calculation are fl=1440 and F18.

If you stopped down the lens so that the cameral lens iris is smaller than the eyepiece exit pupil, then yes you would use F22. There is no practical value for you to do this though other than having "fun with numbers".

Last edited by RJM : Sunday 20th November 2011 at 00:19.
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Old Sunday 20th November 2011, 00:28   #5
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That would be good. Thank you for your answer. But I believe that in 67%.
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Old Sunday 20th November 2011, 00:57   #6
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It is what it is. If you have doubts about the correct values to use then testing is the best confirmation.

For our digiscoping purposes there are basically two rules:

1. EFFECTIVE focal length and distance to target are the main determinants to DoF no matter if using a dslr or compact when using the same sized scope; and

2. Larger 80mm class scopes have shallower DoF than smaller 60mm class scopes.

Last edited by RJM : Sunday 20th November 2011 at 00:59.
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Old Tuesday 1st January 2013, 17:38   #7
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How about next situation
Nikon V1 + Nikon FT 1 adapter + V1/t2 adapetr + Swarovski TSL APO adapter + Swarovski ATX 25-60x85 scope

If the bird are about 200 meters distance, how much are depth of field.
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