Depth of field question- Crop / Full Frame

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Iliah Borg Forum Pro • Posts: 24,790
Re: Depth of field question- Crop / Full Frame

dsjtecserv wrote:

Iliah Borg wrote:

dsjtecserv wrote:

Bob wrote:

When in doubt, consult The Manual of Photography by Jacobson, Ray, Attridge, etc.

There's an entire chapter devoted to understanding the calculations of depth of field.

I've looked through this in detail.

The only things that affect DOF are:

  • Distance to subject
  • Aperture
  • Focal length
  • Distance to film or sensor from back of lens
  • Lens diameter

Sensor size, directly has no impact. However, indirectly it does because cameras are built around sensors and thus the lens geometry is different. A Nikon 50mm DX lens is indeed smaller than a 50mm FX lens.

So, if you put a full frame 50mm on a crop sensor, the DOF will be unchanged because all the geometetric properties of the lens and distances are the same. But if you use a smaller 50mm made for that crop sensor, then yes, the DOF will be different. This subtle point is missed by people using online DOF calculators and then arguing the point.

Please see page 53 (I think; it is hard to tell on the text-only version I found), which discusses visual acuity and the derivation of the circle of confusion limits. This describes how depth of field is tied to the limit of the ability of humans to discern blur, and how this limit is traced back to the size of blur circles on the recording medium (which may be film or sensor). This notes that images from film of different sizes needs a different degree of enlargement to create a print of standard size, to be viewed under standard conditions. The size of the blur circle on the film that, after enlargement, will be just discernible in the final print is a function of the degree of enlargement, and thus the film size. This is the circle of confusion limit, C, and that is noted to be different for different film sizes.

For a photograph viewed at D^, any subject detail
resolved and recorded optically that is smaller than
0.2 mm in general dimensions may not be perceptible
to the unaided eye. Thus any detail finer than this size
is not required. This leads to a practical definition of
resolution. A limit is set to the diameter of an image
blur circle that is not distinguishable from a true point
(by the unaided eye), and this is called the (minimum
permissible) circle of confusion (C).

Obviously the value of C in the camera image must
be related to subsequent enlargement and correspond-
ingly reduced as enlargement increases...

To summarize, the permissible diameter of the
circle of confusion must be reduced if subsequent
enlargement is to take place. In practice values of C
from 0.025 to 0.033 mm are used for the 24 x 36 mm
format to allow x8 enlargement. Values of 0.06 mm
and 0. 1 mm are used for medium and large formats
respectively.

Depth of field is directly proportional to the
diameter of the circle of confusion, the /-number and
the square of the focused distance, and inversely

proportional to the square of the focal length of the
lens. Subject distance and focal length have the
greatest influence; doubling the value of m increases T
fourfold, while doubling focal length reduces T (at a
fixed distance) by a factor of four.

The circle of confusion, C, is an element of the equations presented by the authors for depth of field, and as described above, one of the factors determining C is the size of the film or other recording medium.

Thus the source you cited clearly supports and documents that depth of field is a function film or sensor size, in addition to the other parameters that affect the image that is recorded. This is clearly evident in calculations, charts and depth of field apps, where it is necessary to either directly specify a circle of confusion, or alternatively specify a sensor format, in order to produce a depth of field calculation.

Dave

I can't find the quote above in the Tenth Edition. It is page 52 in the Ninth Edition, published in year 2000.

I don't own a copy. Google books provides a generous selection of pages, but unfortunately not the ones we need here. So I found a text-only version, which is indeed the Ninth edition. But I doubt that there is any significant difference; these are pretty long-standing principles. Which quote can't you find?

DoF is a function of the sensor size if the full frame is to be included in the final image.

Yes, if the full frame is cropped, then it is a function of the cropped size.

The "Circle of confusion" segment you are quoting makes it abundantly clear the factor is image magnification, not the sensor size per se:

"Obviously the value of C in the camera image must be related to subsequent enlargement and correspondingly reduced as enlargement increases." (Here C is diameter of circle of confusion.)

DoF is a function of both magnification at the image plane, and the "subsequent enlargement" from the original image size to the final size as viewed. That's what the quoted passage says, and it is clear from the context which I also quote that this is a function of film/sensor size. The ratio of film size to final print size is a proxy for the degree of enlargement that the blur circles will undergo in that transition.

Generally speaking, DoF is a function of subject magnification at the image plane of the camera and taking aperture, see https://en.wikipedia.org/wiki/Depth_of_field#DOF_in_terms_of_magnification

Depth of field can indeed be expressed as a function of image magnification, but one cannot neglect the effect of enlargement to final viewing size. This is discussed at length earlier in the article you linked.

I have a Hasselblad with 6x6 and 6x4.5 adapters. From where I stand I can't fill the 6x6 frame, but I'm taking two shots with the same lens and same aperture, one 6x6, the other 6x4.5. I will have the same DoF on both shots, in spite of different "sensor" sizes.

No, not if you enlarge the images to the same print size and viewing distance, etc.

You are not reading.

1. "From where I stand I can't fill the 6x6 frame"

2. "but I'm taking two shots with the same lens and same aperture, one 6x6, the other 6x4.5"

- means I have the same subject size at the camera image plane, and thus the enlargement factors are the same.

While 6 x 6 and 6 x 4.5 are not vastly different, the degree of enlargement needed to produce the same-size print will be a bit different

You can't produce the same size print from 6x6 and 6x4.5 unless you are cropping.

and that will have an effect on the size of the blur circles in the print, and thus on depth of field. That is precisely what is discussed in the Manual of Photography and the Wiki article.

Note that the field of view will not be the same in your example. If you were to normalize the field of view by, for instance, using equivalent focal lengths or changing the distance to the focused subject, then the depth of field result would be different.

I have a Nikon FF camera, and I take two shots, one in FF mode, the other in DX mode, same lens, same position, same taking aperture. The DX shot has the subject filling the frame; the FF one - obviously hasn't. DoF is the same on both shots if I print only the subject and at equal size for both shots.

If you print only the subject, then you will have to crop the full frame image to the same size as the crop sensor. Which is, of course the same thing as having used a smaller, crop sensor in the first place.

Yes. And that is an important case, when one can't fill the frame withe the subject he can switch to a smaller format, and the same lens shot at the same aperture from the same position will now provide the same geometrical DoF as on the equivalent crop from a larger format.

The fact that two images taken with the same sensor size have the same depth of field is not surprising.

It is not about the sensor size. Effective sensor sizes are different in this case.

But that is not what this discussion has been about, up till now anyway.

Dave

All I'm saying the view that DoF is "a function film or sensor size" as you suggested is limited and often misleading.

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