DX vs FX and DOF, perspective and AOV

[ToddnTN1]

Another thread got me to thinking:

Is it possible to get the exact same depth of field, perspective and angle of view from a DX and FX camera by changing the focal length of the lens and the distance to the subject?

For example to get result "X" you would need to use an FX camera with an 85mm lens at a distance of 15 feet from the subject.


To get the same result "X" you could use a DX camera with a 60mm lens at a distance of 12 feet.

All those numbers are made up. Would it be possible to come up with a formula to achieve what I am talking about?

 

[astroNikon]

on another thread one of the posters gave this webpage. it has several different calculators to calculate out a bunch of your questions. No formulas though.
Digital Camera Sensor Sizes: How it Influences Your Photography

 

[Ysarex84 78]

Simple answer: No.

Perspective is a function of only one thing: camera placement relative to subject. Move the camera and you change the perspective. So to get the same perspective from two different cameras they must be used from the same place.

Joe

 

[JTPhotography]

I agree with Ysarex. I think it would be possible to achieve an equal depth of field, but the perspective can't be equal because you are using a different focal length and changing the distance between camera and subject.

 

[iolair]

As above ... you can get a "equivalent result" but not an identical result. The perspective will be slightly different. The closer the subject is to the camera, the larger the parts of the subject that are closer to the camera will appear, the smaller parts further from the camera.

Shoot from 2ft away and you'll give your subject a huge nose (assuming they're facing the camera) compared to from 20ft away.

12ft vs 15ft is not such a difference, but it will still be there. Obviously there is a point where the differences will be barely noticeable though.

 

[Murray Bloom]

The answer to your question is no. Even with the same framing, proportional focal length, the same f-stop, etc., the smaller sensor will always provide increased depth of field, usually by 1-2 f-stops. It's an optical anomaly due mostly to the fact that, although everything else remains proportional, the subject does not. It's the same physical size, regardless of everything else. Therefore the two images, while they may be composed exactly the same, will have different depths of field.

 

[Helen B]

The formula you are looking for is quite simple. You use the 'crop factor' on the focal length and the f-number, while keeping the distance the same. Say you have a crop factor of 1.5. Then a 20 mm lens at an f-number of 2 on the 'crop' camera will produce the same angle of view and DoF as a 30 mm (1.5 x 20) lens at an f-number of 3 (1.5 x 2) on a full-frame camera with the cameras (entrance pupils, to be exact) in the same position. (Assumes same aspect ratio)

Notice that the entrance pupil diameter is the same in both cases (10 mm).

 

[Gavjenks]

(Also need to change shutter speed or ISO or flash power by the crop factor, to get the same exposure)

 

[Helen B]

(Also need to change shutter speed or ISO or flash power by the crop factor, to get the same exposure)

Well, maybe the crop factor squared.

 

[Gavjenks]

Also should be pointed out: the Brenizer method.

Obviously you can't always do the things Helen mentioned, because you might not HAVE sufficiently wider, faster glass to mimic a larger sensor. Especially if what you want to mimic is something like medium format, which APS-C sensors might have a crop factor to of 3 or more. Or large format (APS-C has a crop factor of 5.5 or more to this)

So to compensate instead, a thing that people sometimes do is to take a bunch of pictures in a small area and stitch them together as a panorama. By moving your camera small amounts and taking many of the same shot (without refocusing!), you're essentially giving yourself a bigger sensor, with both field of view and DOF. It's not perfect, because when you turn your camera, the sensor pivots a bit (a better but usually prohibitively impractical method would be shifting with a tilt shift lens instead). Also, obviously you can't capture any moving subjects this way, because they will be at different points in space from one picture to the next.

So you sort of have to go back to poses more reminiscent of the dawn of photography, where people have stable, easy-to-hold positions, and hair that may not be blowing freely in the wind, etc. But in exchange you can punch way above your apparent weight in sensor size.

A site that explains it in painstaking detail:
The Brenizer Method Explained With Directions | San Francisco Bay Area Editorial Story-telling Wedding Photography