CCD capture size and FOV formulas

[setvector]

Hello,
I am a 3D animation interactive developer working on a project where a gesigner will be able to place a computer-generated object and place it interactively into a still photo.
In order to do this, I need to generate a value (field of view) that is used in the synthetic 3D scene. This value is derrived from a formula based on film back size and focal length.

I have experimented with several formulas and they all resemble this:
Field of View = 4 * arcsine ( frameSize/( focal length * 4))

However, I seem to be missing something. as I plug in frame sizes for various film backs like the P45 49.1mm x  26.8mm , the resulting view needs to be scaled up or down..similar to a digital multiplier or crop factor? (i'm reading these terms from various internet articles so I may be using the terms wrong). It seems like the formula works for *film* back sizes and needs some sort of additional factor to compensate for image sensor sizes

Does anyone have any knowledge of crop factors or digital multiplers in DSLR backs like the P21, P25, P30, P45 and even other filmbacks like Leaf Aptus, HaselBlad, Canon EOS-1D Mark2?

Much appreciation if anyone can help me. Thanks, eric

[pss]

what you are trying to do is way over my head...but to start you out: the P45 is not 49x26mm (imagesize)..all the manufacturers list the exact imager sizes of their backs on their websites...
the focal length multiplier only helps people coming from film if they want to see what their lenses will be on their digicams or with their MF backs, a lens does not change optically just because you change the imager (or film) size behind it...you just use more (or less) of the circle of illumination (what the lens can project)....
sorry if you already know all this, like i said i was really only able to follow half your post...

[setvector]

what you are trying to do is way over my head...but to start you out: the P45 is not 49x26mm (imagesize)..all the manufacturers list the exact imager sizes of their backs on their websites...
the focal length multiplier only helps people coming from film if they want to see what their lenses will be on their digicams or with their MF backs, a lens does not change optically just because you change the imager (or film) size behind it...you just use more (or less) of the circle of illumination (what the lens can project)....
sorry if you already know all this, like i said i was really only able to follow half your post...
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yeah, i wrote it down in the email incorrectly from my notes. my notes and my tests match those on the website: 49.1 x 36.8 mm
I have 22 different digital film backs, all of various sizes I'm trying to match

[Tomas Johanson]

Do you have the exact focal lenghts of the lenses. A 45mm lens isn´t allways exactly 45mm for example and this will have influence of the field of view in the end.

/Tomas

[rljones]

Eric,

The diagonal angle of view, in degrees, is = 2 * atan(D/2/F)

where D = Diagonal of sensor, mm
          F = Focal length of lens, mm

If you wish to determine the horizontal angle of view, replace D with the horizontal length. Similarly, if you want the vertical angle of view, use the vertical length in place of D.

Example:
35mm  lens with a Leaf 75 (V=36, H=48, and D=60 mm):
AOV (V) = 54°
AOV (H) = 69°
AOV (D) = 81°

As for the multiplier, is determined by the ratio of the diagonal as compared to the 'parent' frame, where the 'parent' frame is 35mm film for a 1D2, 30D, etc, with a D=43 mm. But for MF, such as a 645, the film diagonal is approximately 75 mm. So, for the Leaf 75, with a diagonal of 60 mm, the factor is 75/60 = 1.25. This means a 645 system based 50 mm lens on a Leaf 75 will behave like a 62.5 mm lens. The 50 mm lens on the smaller sensor will thus function as a slightly longer focal length (more telephoto-like).

However, many reference a 35mm film. In that case, the multiplier for a Leaf 75 is 43/60 = 0.717. This means that the same 50 mm lens on a Leaf 75 will behave like a slightly wide-angle 35 mm lens (that is, 50 mm * 0.717 = 35.8 mm).

The same 50 mm lens on a 500CM square format Hasselblad seems even wider (D = 85 mm; 50 mm * 43/85 = 25 mm), but only if you compare the diagonal view, which is what most manufacturers quote for lens angles of view. That is, the horizontal 60 mm length is the same for one side of the 645 and the 6x6 cameras, so the horizontal (landscape orientation) angle of view is the same for either format when using the same lens.

Regards, Robert

[setvector]

Thanks robert for your help,
Do you know what the film-equivelant of a P45?  is it 4x5cm or 6x4.5cm medium format?

-eric

Eric,

The diagonal angle of view, in degrees, is = 2 * atan(D/2/F)

where D = Diagonal of sensor, mm
          F = Focal length of lens, mm

If you wish to determine the horizontal angle of view, replace D with the horizontal length. Similarly, if you want the vertical angle of view, use the vertical length in place of D.

Example:
35mm  lens with a Leaf 75 (V=36, H=48, and D=60 mm):
AOV (V) = 54°
AOV (H) = 69°
AOV (D) = 81°

As for the multiplier, is determined by the ratio of the diagonal as compared to the 'parent' frame, where the 'parent' frame is 35mm film for a 1D2, 30D, etc, with a D=43 mm. But for MF, such as a 645, the film diagonal is approximately 75 mm. So, for the Leaf 75, with a diagonal of 60 mm, the factor is 75/60 = 1.25. This means a 645 system based 50 mm lens on a Leaf 75 will behave like a 62.5 mm lens. The 50 mm lens on the smaller sensor will thus function as a slightly longer focal length (more telephoto-like).

However, many reference a 35mm film. In that case, the multiplier for a Leaf 75 is 43/60 = 0.717. This means that the same 50 mm lens on a Leaf 75 will behave like a slightly wide-angle 35 mm lens (that is, 50 mm * 0.717 = 35.8 mm).

The same 50 mm lens on a 500CM square format Hasselblad seems even wider (D = 85 mm; 50 mm * 43/85 = 25 mm), but only if you compare the diagonal view, which is what most manufacturers quote for lens angles of view. That is, the horizontal 60 mm length is the same for one side of the 645 and the 6x6 cameras, so the horizontal (landscape orientation) angle of view is the same for either format when using the same lens.

Regards, Robert
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[rljones]

Eric,

Film equivalent? I can take this two ways: size or quality.

Physically, the P45 has the same dimensions as the Leaf 75 mentioned in the above post. Just plug in those numbers for the P45.

A quality-wise comparison is a tough one to answer. This topic is debated here and in other forums, as well as discussed in many of Michael's essays. As far as my opinion, I think that the Leaf 75 and P45 are in the same quality league as 4x5 film (and that high end 35mm sized digital cameras are of equivalent quality as medium format film).

Regards, Robert

[Eric Zepeda]

P45 active sensor is 49.1 x 36.8mm, so closer to 5x4cm than 6x4.5, yielding a crop factor of somwhere around 1.22x for 645 format? Math whizzes invited to reply...I'm going to a shoot.

[rljones]

This sensor differences you quote from 36 x 48 mm used in the calculations has a trivial impact on the results. D becomes 61.4 mm rather than 60 mm, and the AOV(D) = 82° instead of 81° for the 35 mm lens used in the original example above.

Even the Leaf 65, which is 34 x 44 mm, has a D of 55.6 mm and an AOV(D) = 77° for the same 35 mm lens. This is not such a huge difference in coverage from the Leaf 75, considering that the street price for the Leaf 65 is almost half that of the only slightly larger Leaf 75.

As for the magnification differences you quote, they are again dependent upon your 'parent' reference: 35mm film or 6x6. BTW, the 6x6 film frame is actually about 55-56 mm, not an ideal 60 mm, just as the typical 645 film frame is more like 41 x 55 mm (give or take fractions of a mm), not an ideal 45 x 60 mm.

-Robert

P45 active sensor is 49.1 x 36.8mm, so closer to 5x4cm than 6x4.5, yielding a crop factor of somwhere around 1.22x for 645 format? Math whizzes invited to reply...I'm going to a shoot.
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[Doug Kerr]

Greetings,

Hello,
I am a 3D animation interactive developer working on a project where a gesigner will be able to place a computer-generated object and place it interactively into a still photo.
In order to do this, I need to generate a value (field of view) that is used in the synthetic 3D scene. This value is derrived from a formula based on film back size and focal length.

I have experimented with several formulas and they all resemble this:
Field of View = 4 * arcsine ( frameSize/( focal length * 4))

Well, the basic formula (subject to some provisos) is:

A = 2 arctan (d/2f)

where A is the field of view, as an angle (in your choice of direction: vertical, horizontal, or diagonal), d is the corresponding dimension of the frame, and f is of course the focal length (d and f in the same units).

That all assumes focus at a distance that is substantial compared to the focal length.

However, I seem to be missing something. as I plug in frame sizes for various film backs like the P45 49.1mm x  26.8mm , the resulting view needs to be scaled up or down..similar to a digital multiplier or crop factor? (i'm reading these terms from various internet articles so I may be using the terms wrong). It seems like the formula works for *film* back sizes and needs some sort of additional factor to compensate for image sensor sizes

Nothing of that sort is involved if the applicable quantities are put into the formula.

Note that the focal length is the focal length, not some "equivalent" focal length.

The problem is presumably with your formula, which is incorrect. (Sorry!)

Does anyone have any knowledge of crop factors or digital multiplers in DSLR backs like the P21, P25, P30, P45 and even other filmbacks like Leaf Aptus, HaselBlad, Canon EOS-1D Mark2?

Do you want these in order to compare the behavior of various things on those backs with things as they would work on a full-frame 35-mm camera? Or do you want to compare the behavior of things on those backs with the behavior of an 8x10 camera? Or what?

You are really best off not to fool with those notions, and describe the behavior of various things on those backs in terms of their behavior with those backs.

No relative format size factor (by whataver name) is needed for any actual optical calculations. (The laws of optics have no idea what format size some people have adopted as "the real thing". Gauss and Newton had never used a full-frame 35-mm camera.)