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Depth of field and out-of-focus blur

Doug Kerr

Well-known member
In another thread, Jerome Marot reminds us that an advantage of a larger sensor, beyond image quality issues, largely related to noise performance, is that it facilitates our separating a subject from background (or even foreground) objects by intentionally making those objects out-of-focus (exploiting bokeh).

This increased ability is often spoken of as "better depth of field control". But in fact, to be rigorous, the issue here is not depth of field (DoF) but rather its closely-related counterpart, out-of-focus blur (OFB).

The distinction becomes significant when we try to quantify one or the other, even qualitatively.

In the matter of depth of field, we ask this question: With the camera focused at a certain distance, over what range of object distances will the object be imaged with blurring, due to imperfect focus, not greater than a certain arbitrary criterion we choose? In effect, we say that any lesser blurring is considered "negligible".

In the matter of our-of-focus blur, we ask this question: With the camera focused at a certain distance, then for an object at some certain other distance, how much will its image be blurred due to imperfect focus?

These are of course in a sense two sides of the same coin. In particular, if, for example, we increase the aperture of our camera (keeping everything else the same), then:

• The depth of field becomes less.

• The out-of-focus blur, for any given out-of-focus object distance becomes greater.

Note that the matter of depth of field depends on our choice of a criterion as to how much blurring is considered "negligible", expressed as the circle of confusion diameter limit (COCDL)*. The matter of out-of-focus blur does not depend on any such arbitrary criterion.

* Often, but misleadingly, called the "circle of confusion".​

Now, how does the sensor size get involved in each of these matters? I will not look into the underlying optical model, but will concentrate on practical results (but as revealed by the formulas for calculating the metrics of interest in each case).

In each case, we will assume that the images from camera S. with a smaller sensor, and camera L, with a larger sensor, are viewed with a consistent overall subtended angle; that is, for example, as prints of the same size viewed from the same distance.

Depth of field

As we move from the situation of camera S to that of camera L, we will keep constant:

• The aperture (as an f-number).

• The distance at which the camera is focused.

• The field of view given by the focal length of the lens to be used. Thus the focal length must be increased with sensor size.

• The allowable defocusing as seen on the "print". Thus the COCDL (which is defined on the image) must be increased, owing to the decreased image-to-print magnification.

Then these two things happen:

A. As a result of the increase in focal length, the depth of field decreases.

B. As a result of the increase of the COCDL, the depth of field increases.

But the decrease due to consideration A goes as about the inverse of the square of the focal length (for representative values of all the factors), while the increase due to consideration B is about linear with the change in COCDL. The result is that A overcomes B and thus the actual depth of field decreases for the larger sensor camera (on the order of inversely with sensor size).

Out of focus blur

As we move from the situation of camera S to that of camera L, we will keep constant:

• The aperture (as an f-number).

• The distance at which the camera is focused.

• The distance to some given out-of-focus object.

• The field of view given by the focal length of the lens to be used. Thus the focal length must be increased with sensor size.

Note that the concept of a "limit on the defocusing that will be considered negligible", as quantified through our choice of a COCDL, is not involved here. However much defocusing we get, we get, and our interest is in "how much will that be".

Then these two things happen:

A. As a result of the increase in focal length, the degree of defocusing on the out-of-focus object (as quantified by the actual diameter of the circle of confusion that is created on the image from a point on the object) increases.

B. As a result of the decrease in image-to-print magnification, the degree of defocusing seen on the object, for any given degree of defocusing on the image, decreases.

But the increase due to consideration A goes as about the square of the focal length, while the decrease due to consideration B is exactly linear with the change in magnification. The result is that A overcomes B and thus the actual degree of blurring increases for the larger sensor camera (on the order of linearly with sensor size).

A practical issue of considerable interest in connection with out-of-focus blur is, "to attain a certain degree of blur, how is the aperture I must use affected by sensor size?"

For some arbitrary (but reasonable) values of the factors involved, if on camera S we are able to get a certain degree of blurring, as observed on the print, on an object at a certain distance with an aperture of f/2.0, then on camera L, with a sensor of twice the linear dimensions, we are able to get that same degree of blurring, as observed on a print of the same size viewed from the same distance, with an aperture of about f/4.0.

The bottom line

A bottom line on all this is:

• A larger sensor makes it more difficult for a photographer shooting, say, landscapes or building interiors to achieve a desirable depth of field.

• A larger sensor makes it easier for a photographer shooting, for example, portraits to attain a desirable degree of out-of-focus blur.

Best regards,

Doug
 

Jerome Marot

Well-known member
A bottom line on all this is:

• A larger sensor makes it more difficult for a photographer shooting, say, landscapes or building interiors to achieve a desirable depth of field.

• A larger sensor makes it easier for a photographer shooting, for example, portraits to attain a desirable degree of out-of-focus blur.

While the "bottom line" is reasonably close to what happens in practice, you made a few untold assumptions which do not necessarily happen for all sensor sizes. One of these untold assumptions is that the print size does not change. This is rarely true in practice: photographers who spend money on high resolution cameras often like to print in large sizes.

Another untold assumption is that you suppose the Gauss conditions are met. This is not true for fast lenses, which are exactly what we use for limiting depth of field.
 

Doug Kerr

Well-known member
Hi, Jerome,

While the "bottom line" is reasonably close to what happens in practice, you made a few untold assumptions which do not necessarily happen for all sensor sizes. One of these untold assumptions is that the print size does not change.

It was in fact "told":

In each case, we will assume that the images from camera S. with a smaller sensor, and camera L, with a larger sensor, are viewed with a consistent overall subtended angle; that is, for example, as prints of the same size viewed from the same distance.

This is rarely true in practice: photographers who spend money on high resolution cameras often like to print in large sizes.

Sure.

Another untold assumption is that you suppose the Gauss conditions are met. This is not true for fast lenses, which are exactly what we use for limiting depth of field.

Sure.

Thanks.

Best regards,

Doug
 
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