Doug Kerr
Well-known member
We often address the question of, if we move from a camera with a certain sensor size to, for example, what happens to the depth of field.
Before I address that, I call attention to the fact that depth of field is not a property that is dictated by the laws of optics alone. If we have some hypothetical camera, with a lens of certain focal length and f-number, the camera focused at a certain distance, there is no unique optical situation at the two planes in "object space" we say are the limits of the depth of field. (No rays cross there, for example, nor is the image magnification for objects there equal to pi and pi minus one, or any such thing.)
Rather, the concept is one of our interpretation of a continuously-varying optical phenomenon: the rendering of a point on an object as a "blur figure" (called a circle of confusion) in the image if the object is not precisely at the distance at which the camera is focused.
The concept of depth of field is that blurring from imperfect focus that is less than a certain amount is "negligible", or "acceptable", and thus the range of distances to an object such that the blurring does not exceed that certain amount is considered the "depth of field".
To determine the depth of field by calculation, or even by observation, we must articulate our criterion of how much blurring is "acceptable" We normally do that by stating a maximum acceptable diameter of the circle of confusion (which I call the circle of confusion diameter limit, or COCDL).
How do we choose the COCDL value to adopt? A traditional way is this. Imagine the image is printed on a print of some arbitrary size, and we view it from some arbitrary distance. We then consider the circles of confusion as they appear on the print. We then say that the blurring is only "noticeable" (that is, not "acceptable") if the diameter of the circle of confusion on the print subtends a greater angle at the eye than the eye's resolution. Then maybe we double that just to make our criterion a little less stringent.
But this only pertains to a certain contrived viewing situation. Is there any generalizable form of that outlook?
Yes. It turns out that if we go through the math (or the maths, if we are in Great Britain), it suggests a certain COCDL as a fraction of the image size (we usually work in terms of its diagonal size).
And in fact the traditional COCDL number used by lens manufacturers is determined on that basis. But keep in mind that it is still as arbitrary as "the best age for a girlfriend is half your age plus ten years") - it doesn't flow from any principles of optics.
So now back to the question, "as we move from a camera with one format size to that with a large sensor size, what happens to the depth of field. Well, that question of course is not meaningful unless we resort to that old notion of "all other things being equal". And of course there again we have to make some arbitrary decisions.
One set of "all other things being equal" that can be useful is this:
• The focal lengths of the lenses will produce the same field of view on each camera.
• The cameras are focused at the same distance.
• The f-numbers of the lenses are the same
• The COCDL we adopt is a consistent fraction of the frame's diagonal dimension.
Then:
The depth of field of the larger-format camera is less than that of the smaller-format camera.
Now suppose that for some reason (hopefully relating to a special interest), we adopt this set of "all other things":
• The focal lengths of the lenses are the same.
• The cameras are focused at the same distance.
• The f-numbers of the lenses are the same
• The COCDL we adopt is a consistent fraction of the frame's diagonal dimension.
Then:
The depth of field of the larger-format camera is greater than that of the smaller-format camera.
Some people suggest that the most useful criterion of "blurring from imperfect focus being negligible" is when that blurring cannot be noticed at all given the resolution of the camera, but that is hard to define. Based on the same notion, they then suggest that perhaps we should consider the blurring from misfocus negligible if the diameter of the circle of confusion can just be resolved by the resolution of the camera. And so forth.
Any of these criteria will result in our adopting a COCDL that is related to the reciprocal of the camera resolution.
Sometimes the geometric resolution (based only on pixel pix) is used as a simpler predicate. The, we would choose a COCDL that was equal to some number of pixel pitches.How many? Well, that's a matter of judgment, like "how many months' salary should we try to keep in the bank".
Now, following that notion, let's again do our smaller and larger format camera comparison, for cameras with the same resolution in terms of picture height (or the same format height in terms of pixels, if we want the simpler criterion). That then suggests the same set of "other things being equal" we had at the beginning:
• The focal lengths of the lenses will produce the same field of view on each camera.
• The cameras are focused at the same distance.
• The f-numbers of the lenses are the same
• The COCDL we adopt is a consistent fraction of the frame's diagonal dimension.
Then, as before:
The depth of field of the larger-format camera is less than that of the smaller-format camera.
Another interesting case under this outlook is where the two cameras have the same pixel pitch. Then, the terms of comparison become:
• The focal lengths of the lenses will produce the same field of view on each camera.
• The cameras are focused at the same distance.
• The f-numbers of the lenses are the same
• The COCDL we adopt is the same.
Then:
The depth of field of the larger-format camera is less than that of the smaller-format camera, and to a greater degree than in the previous case.
***********
In part 2 of this series (after breakfast), I'll talk about what simple models will allow us to intuitively grasp these relationships. (Plot spoiler: not really any.)
Best regards,
Doug
Before I address that, I call attention to the fact that depth of field is not a property that is dictated by the laws of optics alone. If we have some hypothetical camera, with a lens of certain focal length and f-number, the camera focused at a certain distance, there is no unique optical situation at the two planes in "object space" we say are the limits of the depth of field. (No rays cross there, for example, nor is the image magnification for objects there equal to pi and pi minus one, or any such thing.)
Rather, the concept is one of our interpretation of a continuously-varying optical phenomenon: the rendering of a point on an object as a "blur figure" (called a circle of confusion) in the image if the object is not precisely at the distance at which the camera is focused.
The concept of depth of field is that blurring from imperfect focus that is less than a certain amount is "negligible", or "acceptable", and thus the range of distances to an object such that the blurring does not exceed that certain amount is considered the "depth of field".
To determine the depth of field by calculation, or even by observation, we must articulate our criterion of how much blurring is "acceptable" We normally do that by stating a maximum acceptable diameter of the circle of confusion (which I call the circle of confusion diameter limit, or COCDL).
Note that this is just commonly called the "circle of confusion", but that is very confusing. The circle of confusion is a circle, not a diameter; it has a diameter; and we are not speaking of either of those, but rather a limit we place on the diameter. Calling that the "circle of confusion" is like calling the minimum allowable diameter of a lifting rope the "lifting rope".
How do we choose the COCDL value to adopt? A traditional way is this. Imagine the image is printed on a print of some arbitrary size, and we view it from some arbitrary distance. We then consider the circles of confusion as they appear on the print. We then say that the blurring is only "noticeable" (that is, not "acceptable") if the diameter of the circle of confusion on the print subtends a greater angle at the eye than the eye's resolution. Then maybe we double that just to make our criterion a little less stringent.
But this only pertains to a certain contrived viewing situation. Is there any generalizable form of that outlook?
Yes. It turns out that if we go through the math (or the maths, if we are in Great Britain), it suggests a certain COCDL as a fraction of the image size (we usually work in terms of its diagonal size).
And in fact the traditional COCDL number used by lens manufacturers is determined on that basis. But keep in mind that it is still as arbitrary as "the best age for a girlfriend is half your age plus ten years") - it doesn't flow from any principles of optics.
So now back to the question, "as we move from a camera with one format size to that with a large sensor size, what happens to the depth of field. Well, that question of course is not meaningful unless we resort to that old notion of "all other things being equal". And of course there again we have to make some arbitrary decisions.
One set of "all other things being equal" that can be useful is this:
• The focal lengths of the lenses will produce the same field of view on each camera.
• The cameras are focused at the same distance.
• The f-numbers of the lenses are the same
• The COCDL we adopt is a consistent fraction of the frame's diagonal dimension.
Then:
The depth of field of the larger-format camera is less than that of the smaller-format camera.
Now suppose that for some reason (hopefully relating to a special interest), we adopt this set of "all other things":
• The focal lengths of the lenses are the same.
• The cameras are focused at the same distance.
• The f-numbers of the lenses are the same
• The COCDL we adopt is a consistent fraction of the frame's diagonal dimension.
Then:
The depth of field of the larger-format camera is greater than that of the smaller-format camera.
Some people suggest that the most useful criterion of "blurring from imperfect focus being negligible" is when that blurring cannot be noticed at all given the resolution of the camera, but that is hard to define. Based on the same notion, they then suggest that perhaps we should consider the blurring from misfocus negligible if the diameter of the circle of confusion can just be resolved by the resolution of the camera. And so forth.
Any of these criteria will result in our adopting a COCDL that is related to the reciprocal of the camera resolution.
Sometimes the geometric resolution (based only on pixel pix) is used as a simpler predicate. The, we would choose a COCDL that was equal to some number of pixel pitches.How many? Well, that's a matter of judgment, like "how many months' salary should we try to keep in the bank".
Now, following that notion, let's again do our smaller and larger format camera comparison, for cameras with the same resolution in terms of picture height (or the same format height in terms of pixels, if we want the simpler criterion). That then suggests the same set of "other things being equal" we had at the beginning:
• The focal lengths of the lenses will produce the same field of view on each camera.
• The cameras are focused at the same distance.
• The f-numbers of the lenses are the same
• The COCDL we adopt is a consistent fraction of the frame's diagonal dimension.
Then, as before:
The depth of field of the larger-format camera is less than that of the smaller-format camera.
Another interesting case under this outlook is where the two cameras have the same pixel pitch. Then, the terms of comparison become:
• The focal lengths of the lenses will produce the same field of view on each camera.
• The cameras are focused at the same distance.
• The f-numbers of the lenses are the same
• The COCDL we adopt is the same.
Then:
The depth of field of the larger-format camera is less than that of the smaller-format camera, and to a greater degree than in the previous case.
***********
In part 2 of this series (after breakfast), I'll talk about what simple models will allow us to intuitively grasp these relationships. (Plot spoiler: not really any.)
Best regards,
Doug