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Author Topic: DOF on crop and FF sensors  (Read 4730 times)

feppe

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DOF on crop and FF sensors
« on: January 10, 2009, 06:03:22 pm »

After years of shooting 35mm and 6x6 Velvia, I reluctantly moved to digital a while back - but am now glad I did. After upgrading my 30D to 450D, Canon released the 5D MkII which I just ordered. I've been quite happy with both crop-sensor cameras I've had, but really looking forward to the IQ, a bright viewfinder and ability to crop more (which I do a lot).

I understand that FF sensor has less DOF than cropped sensor, but was wondering how significant that is. For example, is my 85mm f/1.8 or 135mm f/2L at its widest aperture usable for portraits - or does it go towards the paper-thin DOF you get with MF at wide apertures, along with how critical accurate focusing is? At the other end, what kind of aperture would be necessary to keep tip of the nose to ears sharp?

I've played around with online DOF calculators, but was wondering if anyone has real-world experience.

edit: I just learned the MkII has face detection. I assume this means what it says, and won't be accurate to focus on eyes at wide open apertures?
« Last Edit: January 10, 2009, 06:30:04 pm by feppe »
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Sheldon N

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« Reply #1 on: January 10, 2009, 09:02:05 pm »

Quote from: feppe
After years of shooting 35mm and 6x6 Velvia, I reluctantly moved to digital a while back - but am now glad I did. After upgrading my 30D to 450D, Canon released the 5D MkII which I just ordered. I've been quite happy with both crop-sensor cameras I've had, but really looking forward to the IQ, a bright viewfinder and ability to crop more (which I do a lot).

I understand that FF sensor has less DOF than cropped sensor, but was wondering how significant that is. For example, is my 85mm f/1.8 or 135mm f/2L at its widest aperture usable for portraits - or does it go towards the paper-thin DOF you get with MF at wide apertures, along with how critical accurate focusing is? At the other end, what kind of aperture would be necessary to keep tip of the nose to ears sharp?

I've played around with online DOF calculators, but was wondering if anyone has real-world experience.

edit: I just learned the MkII has face detection. I assume this means what it says, and won't be accurate to focus on eyes at wide open apertures?

I believe that the difference is close to 1 1/3 aperture stops, if you hold lens field of view, subject distance, and final print size equal between 1.6 crop and full frame. For example, these two will have roughly the same DOF.

50mm lens on 450D at f/1.4
80mm lens on 5D at f/2.2

If you want to see the difference in DOF, shoot two pictures at 1 1/3 aperture stops apart, then compare.
« Last Edit: January 10, 2009, 09:03:13 pm by Sheldon N »
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feppe

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« Reply #2 on: January 11, 2009, 04:06:34 am »

Quote from: Sheldon N
I believe that the difference is close to 1 1/3 aperture stops, if you hold lens field of view, subject distance, and final print size equal between 1.6 crop and full frame. For example, these two will have roughly the same DOF.

50mm lens on 450D at f/1.4
80mm lens on 5D at f/2.2

If you want to see the difference in DOF, shoot two pictures at 1 1/3 aperture stops apart, then compare.

That is indeed significant - I'll try that out!

Ken Bennett

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« Reply #3 on: January 11, 2009, 11:03:52 am »

The sensor has nothing to do with depth of field.

Given the same lens at the same subject distance, there is no difference in depth of field. The only difference is that the full-frame camera will capture a wider field of view.

 The difference in Depth of Field comes into play when you *move the camera closer* to account for this increased field of view. Moving the camera closer while using the same lens and aperture will reduce DoF. With the fastest lenses, yes, you will get that razor-thin DoF -- but then, I'm getting that with crop-sensor cameras at short distances, too. Focus is critical with either camera.
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james_elliot

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« Reply #4 on: January 11, 2009, 11:42:51 am »

Quote from: k bennett
The sensor has nothing to do with depth of field.

Given the same lens at the same subject distance, there is no difference in depth of field. The only difference is that the full-frame camera will capture a wider field of view.

 The difference in Depth of Field comes into play when you *move the camera closer* to account for this increased field of view. Moving the camera closer while using the same lens and aperture will reduce DoF. With the fastest lenses, yes, you will get that razor-thin DoF -- but then, I'm getting that with crop-sensor cameras at short distances, too. Focus is critical with either camera.

That's not completely true. Depth of field also depends on the size of the circle of confusion, which is much smaller on APS-C cameras (higher pixel density).
The general formula for dof is:
dof = df - dn = (2 d c a (d - f) / f) / (1 - (c a / f (d -f)))
with d: focusing distance, f: focal length, a:aperture number, f: focal distance and c:size of the circle of confusion.
If d is much larger than f, there is a simplification:
dof = 2 c a d / f
If a, d and f are the same, the dof is proportional to c. For example, c is around 6.5 microns on a 5D Mark II and 5 microns on a 50D, so you have around 30% less dof on the 50D, which is the opposite of what most people believe.
Of course, as soon as the crop factor is taken into account (and this is the right thing to do of course), things get back to normal, as it introduces a 2.5 (1.6x1.6) factor in favor of the FF format.
Complete computations here.
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Ken Bennett

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« Reply #5 on: January 11, 2009, 02:51:34 pm »

James,

Why is the circle of confusion different for the different cameras? The article you referenced makes the claim that DoF varies linearly with the granularity of the film or the the pixel size of the sensor, but I'm not sure I understand why this makes a difference. The CoC seems to be strictly a function of the lens and aperture, given their equations.



Quote from: james_elliot
Of course, as soon as the crop factor is taken into account (and this is the right thing to do of course), things get back to normal, as it introduces a 2.5 (1.6x1.6) factor in favor of the FF format.


Of course it's the right thing to do.

Thanks.
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james_elliot

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« Reply #6 on: January 11, 2009, 04:07:47 pm »

You are right when you say that the circle of confusion only depends on the lens and the aperture. But this circle of confusion only becomes a problem when its size becomes larger than the pixel size of the sensor: that's when one point of the object creates an image on more than one point of the sensor: this is the definition of blur.

Thanks for the comment. The article is not properly worded, and I will rewrite it to make it more clear on that point. My english is far from being perfect...

Thanks again.

Quote from: k bennett
James,

Why is the circle of confusion different for the different cameras? The article you referenced makes the claim that DoF varies linearly with the granularity of the film or the the pixel size of the sensor, but I'm not sure I understand why this makes a difference. The CoC seems to be strictly a function of the lens and aperture, given their equations.






Of course it's the right thing to do.

Thanks.
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Sheldon N

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« Reply #7 on: January 11, 2009, 04:23:40 pm »

Here's a good article for putting this issue in layman's terms....



http://www.bobatkins.com/photography/techn...digitaldof.html
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spidermike

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« Reply #8 on: January 15, 2009, 01:17:03 pm »

Quote from: james_elliot
You are right when you say that the circle of confusion only depends on the lens and the aperture. But this circle of confusion only becomes a problem when its size becomes larger than the pixel size of the sensor: that's when one point of the object creates an image on more than one point of the sensor: this is the definition of blur.

Can I clarify then that the CoC only differs because the pixel pitch is commonly different in crop and full-frame cameras - so if a FF and crop frame have sensors with similar pixel pitch, kbenntt's description holds true.
Is that correct?
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james_elliot

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« Reply #9 on: January 16, 2009, 02:41:12 am »

Quote from: spidermike
Can I clarify then that the CoC only differs because the pixel pitch is commonly different in crop and full-frame cameras - so if a FF and crop frame have sensors with similar pixel pitch, kbenntt's description holds true.
Is that correct?
Right.
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Ray

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« Reply #10 on: January 16, 2009, 06:30:35 pm »

One should understand that the crop factor number in relation to a larger format is only a rough guide or rule-of-thumb for equalising DoF between the formats.

Theoretically, a Canon 40D or 50D with 50mm lens at F4 should produce the same DoF as a 5D with 80mm lens at F6.3 (1.6x4=6.4).

However, in practice it doesn't always work out like this. There seem to be other factors involved that are too variable to be included in a simple formula. I have found, for example that focussing on a fairly close subject, say a couple of metres away, requires a full 2 stop difference to equalise DoF between the 50D and 5D. That is, the Canon 24-105 zoom used at 50mm and F4 with the 50D produces the same DoF as the same zoom used at 80mm and F8 with the 5D. If I use the crop factor of 1.6x to adjust F stop, which gives a value of F6.3, I find that the background and foreground are clearly more detailed in the 50D shot.
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james_elliot

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« Reply #11 on: January 17, 2009, 08:40:34 am »

Ray, I think you are mixing things up.

The formula is:
 f(d,c,a,f)=(2*d*c*a*(d-f)/f**2)/(1-(c*a*(d-f)/f**2)**2)
d: distance
c: circle of confusion
a: aperture
f: focal length

1) If you don't take into account the difference of pixel size between  the two cameras (we take 7 micrometers for both of them), then they would have the same depth of field when the 50D is at F10
[attachment=10941:file2.png]

2) If you take into account the pixel size which are very different for these two cameras (around 5e-6 for the 50D and 8e-6 for the 5D), then  they have the same dof at 6.4
[attachment=10942:file1.png]

3) But using pixel size as the value for the circle of confusion is only useful if you are watching the images at 100% magnification on your screen. If you are printing them at the same size, the resolution must also be taken into account, and there is a 1.1 advantage for the 50D. If we now "correct" the coc to have the same perception, the two cameras have the same perceived dof slightly below F8 (F7.6), which is exactly what you see.
[attachment=10943:file3.png]


There is no magic in optical science...

   

Quote from: Ray
One should understand that the crop factor number in relation to a larger format is only a rough guide or rule-of-thumb for equalising DoF between the formats.

Theoretically, a Canon 40D or 50D with 50mm lens at F4 should produce the same DoF as a 5D with 80mm lens at F6.3 (1.6x4=6.4).

However, in practice it doesn't always work out like this. There seem to be other factors involved that are too variable to be included in a simple formula. I have found, for example that focussing on a fairly close subject, say a couple of metres away, requires a full 2 stop difference to equalise DoF between the 50D and 5D. That is, the Canon 24-105 zoom used at 50mm and F4 with the 50D produces the same DoF as the same zoom used at 80mm and F8 with the 5D. If I use the crop factor of 1.6x to adjust F stop, which gives a value of F6.3, I find that the background and foreground are clearly more detailed in the 50D shot.
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Ray

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« Reply #12 on: January 17, 2009, 10:08:17 pm »

Quote from: james_elliot
Ray, I think you are mixing things up.

The formula is:
 f(d,c,a,f)=(2*d*c*a*(d-f)/f**2)/(1-(c*a*(d-f)/f**2)**2)
d: distance
c: circle of confusion
a: aperture
f: focal length

Ah! I see you are using a formula which is not so simple. I didn't read all the posts. My comment was in relation to a crop multiplier applied to focal length and F stop number, which is the simplest and most common method of determining DoF equivalence. But I see you've addressed this lack of precision with a more complicated formula.

However, I wonder how useful your formula is in practice, if one has to guess the distance. I also got the impression from some folks who claim to be experts on such matters, that lens design has a bearing on DoF. That is, two lenses of the same focal length but from different manufacturers, or even two different models of lenses from the same manufacturer, might not exhibit exactly the same DoF at the same f stop. I don't know if this is true or whether the differences might be so small as to be ignored.



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Panopeeper

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« Reply #13 on: January 17, 2009, 10:36:39 pm »

All the concepts and formulas used above are from innumerate dinosaurs.

1. One needs to differentiate betwen the lens and the presentation. The circle of confusion has nothing to do with the lens; it is a purely perceptional issue.

2. The lens creates a circle of uncertainty, which needs to be measured against the pixel pitch.

3. The formula of calculating the circle of uncertainty is worthless; it is derived from a lens construction, which is nonexistent in the modern cameras, except in the viewfinder. The actual distance to calculate with is not the focal length but something not declared in any published specifications.

Thus the entire discussion is nothing but reading tea leaves.
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Ray

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« Reply #14 on: January 17, 2009, 10:43:31 pm »

Quote from: james_elliot
3) But using pixel size as the value for the circle of confusion is only useful if you are watching the images at 100% magnification on your screen. If you are printing them at the same size, the resolution must also be taken into account, and there is a 1.1 advantage for the 50D. If we now "correct" the coc to have the same perception, the two cameras have the same perceived dof slightly below F8 (F7.6), which is exactly what you see.
[attachment=10943:file3.png]

Yes, it's clear that not only print size can have an effect on the perception of DoF, but viewing distance from the print can have an even greater effect. Viewing images at 100% on one's monitor can be useful to find out if there is any difference at all. If there's no observable difference at 100%, or very little, then for most practical purposes it means the images are the same, even though there might be some slight difference noticeable at 200% or 400%.

What I wonder about is the usefulness of considering pixel or sensel size without also considering lens resolution at the plane of focus. What are your thoughts on this?
« Last Edit: January 18, 2009, 01:11:48 am by Ray »
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AJSJones

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« Reply #15 on: January 18, 2009, 01:30:58 am »

Quote from: james_elliot
You are right when you say that the circle of confusion only depends on the lens and the aperture. But this circle of confusion only becomes a problem when its size becomes larger than the pixel size of the sensor: that's when one point of the object creates an image on more than one point of the sensor: this is the definition of blur.
Sensor (or captor) resolution limited DoF is the one that is altered by the resolution of the medium.  Surely this requires that the image be viewed under conditions where the eye can perceive the blur you describe above?  This in turn might require a 300 ppi print viewed from 10 inches (or some version of human acuity limit).  At this point, the image has been magnified geometrically by a different amount depending on guess what, the pixel pitch.  If the image has been presented, say in a non-huge print, where the eye resolves as discreet points image components that were recorded by more than one pixel, then using a pixel as the CoC isn't right.  If everyone "prints to the max" then using pixel pitch as CoC will be "right".  DoF as a term or concept has been affected by digital but it is still a perceptual issue based on what appears to be in focus when the image is viewed.  Your DoF could be called the "minimum possible DoF" and, as such, would not require standardized print size and viewing distance etc.  Definitely a paradigm shift.  Sort of like how resolution used to mean the fineness of the details that could be resolved (with no reference to the size of the sheet of film), but has now come to mean how many pixels are captured (where bigger area of the same medium becomes higher "resolution")
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Daniel Browning

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« Reply #16 on: January 18, 2009, 04:16:44 am »

Quote from: k bennett
The sensor has nothing to do with depth of field.

Agreed. As long as we're discussing just the depth of field projected by the lens, we can ignore the CoC effects of everything else, such as capture resolution, post processing, display medium, viewing conditions, acuity of vision, etc.

Quote from: k bennett
Given the same lens at the same subject distance, there is no difference in depth of field. The only difference is that the full-frame camera will capture a wider field of view.

Agreed again, given the same caveat.

Quote
The difference in Depth of Field comes into play when you *move the camera closer* to account for this increased field of view. Moving the camera closer while using the same lens and aperture will reduce DoF.

Agreed. That's one method (AKA "move in without zooming"). The other method is to use longer lenses ("zoom in without moving").

Quote
With the fastest lenses, yes, you will get that razor-thin DoF -- but then, I'm getting that with crop-sensor cameras at short distances, too.

For any given composition (angle of view and perspective), the lens with the largest physical aperture (not f/number) will project the thinnest DOF onto the sensor. In the case of comparing APS-C and 35mm systems, for most AOV (Angle Of View) circumstances, the 35mm has larger physical aperture available. At super telephoto, though, the apertures are equal.

To calculate the physical aperture, divide the focal length by the f/number. For example, given the same composition (AOV/perspective), 50mm f/2.0 has the same depth of field as 400mm f/16, and 50/2 and 400/16 both equal 25mm.


That's why "aperture and composition" is my preferred way to explain DOF which scales among all sensor sizes. Another way is "magnification ratio and f/number". Longer focal lengths and closer focus distances increase magnification, which makes DOF thinner.

Quote from: james_elliot
That's not completely true. Depth of field also depends on the size of the circle of confusion, which is much smaller on APS-C cameras (higher pixel density).

Correct. This is what I meant above by capture resolution. It's helpful sometimes, though, to do as Mr. Bennett did above and assume that all formats to have the same resolution, processing, display size, viewing conditions, etc. just for the purpose of discussion. A more comprehensive
  • discussion includes the effects of things like varied capture resolution, like you did.
Quote from: k bennett
Why is the circle of confusion different for the different cameras?

I'll add a little something here. APS-C must be enlarged (magnified) more than FF 35mm to be displayed at the same size. This scales in perfect balance with the f/number on FF35 for a given composition. So if both cameras have the same aperture and composition (as in the case of much wildlife photography), the one with higher resolution is capable of thinner DOF.

So, the simplest way to think about DOF, IMHO, is to break it into two things: A. DOF projected by the lens and B. DOF seen by the viewer.

A. DOF projected by the lens. Two simple but comprehensive
  • definitions:

A1. Aperture determines DOF for a given composition.
A2. Magnification ratio and f/number determines DOF.

I prefer A1 ("aperture for a given composition") because composition (angle of view, perspective, and focus distance) is central to photography, and I think making it central to the discussion of DOF is most enlightening. (Allowing perspective or angle of view to vary with sensor size is not nearly as useful, IMHO.)

Both of those definitions let you abstract out the effect of sensor sizes, focal lengths. A1 lets you abstract out f/number. A2 lets you abstract out perspective and AOV.

B. DOF seen by the viewer.
Of course you have to start with "A. DOF projected by the lens", but there are many effects that occur after the light passes through the exit pupil. You can get very close by just assuming the CoC is determined only by the lesser of the capture resolution and display resolution. But to be accurate requires the consideration of subject size, pixel density, lens MTF, demosiac algorithm, sharpening, other PP, display size, resolution, viewing distance, environment lighting, eyesight, etc.

Aperture rules.

  • I'm left out bellows factor on purpose; this post is long enough as it is.
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james_elliot

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« Reply #17 on: January 18, 2009, 04:44:46 am »

Quote
Sensor (or captor) resolution limited DoF is the one that is altered by the resolution of the medium. Surely this requires that the image be viewed under conditions where the eye can perceive the blur you describe above? This in turn might require a 300 ppi print viewed from 10 inches (or some version of human acuity limit). At this point, the image has been magnified geometrically by a different amount depending on guess what, the pixel pitch. If the image has been presented, say in a non-huge print, where the eye resolves as discreet points image components that were recorded by more than one pixel, then using a pixel as the CoC isn't right. If everyone "prints to the max" then using pixel pitch as CoC will be "right". DoF as a term or concept has been affected by digital but it is still a perceptual issue based on what appears to be in focus when the image is viewed. Your DoF could be called the "minimum possible DoF" and, as such, would not require standardized print size and viewing distance etc. Definitely a paradigm shift. Sort of like how resolution used to mean the fineness of the details that could be resolved (with no reference to the size of the sheet of film), but has now come to mean how many pixels are captured (where bigger area of the same medium becomes higher "resolution")

Yes absolutely.

 Using pixel pitch and comparing it to the CoC is just a maximal limit to use, to know when you camera sensor is going to be affected by the cone of light rays which are not in perfect focus on the sensor plane. It is indeed somewhat of a paradigm shift.

If we begin to take into account some perceptual considerations, things change.
If we want to consider the perceptual (human) limit, the usual computation is the following (it has been used since 50 years to compute for example the dof scale on lenses):

At the center of the retina, there is a small spot (3mm) called the fovea which is responsible for most of the properties of human vision, including color vision and resolution power (the rest of the retina is mainly dedicated to motion detection and black and white vision). There are around 300 "detectors" on the 3mm diameter of the fovea, thus one detector every 10 microns, which is someting like the "size of the photosite" of the eye.

The eye has a  focal distance of around 25mm. Thus, at 25 cms, the size s of an object exactly covering one detector would be:
s= 0.25 x (10.10-6)/(25.10-3) = 100 microns
Thus the resolution power of the eye is 100 microns at 25cms.

Thus, if we enlarge a 36x24 film by 3 to get a 105x72 print and view it at a 25cms distance, we have a maximum permissible circle of confusion which is the third of 100 microns and thus the famous 33 microns result for 36x24 film. All scales on lenses were computed with this 33 microns value and the formula I gave in a previous post.

These values remain correct when viewing larger prints because the viewing distance is generally larger than 25 cms. For screen projections, for a 2m wide screen, the usual viewing distance is 5 meters. At 5 meters, the eye resolution is 2 mm. The 36x24 positive is magnified approximatively 60 times to become a 2m x 1.5m screen with a circle of confusion of 33 microns x 60= 2mm! Everything fits.

So the admissible circle of confusion depends of course on the size of the print and on the viewing distance, but the pixel pitch gives a "maximal limit".

This is also an indication of the maximal useful density of pixels on the sensor when we know that the print will be watched from a "standard" distance: for a foveon sensor on an APS-C, one pixel each 22 (=33/36x24) microns would be enough. It's more complex with Bayer arrays (something I didn't discuss earlier to keep things simple), because there is usually an AA filter which mostly distributes one ray on two adjacent pixels of the array to prevent moir effects, thus giving a useful size of around 11 microns for the pixel pitch on APS-C: that was the original value targeted by digital camera manufacturers. The Canon D30 had exactly a pixel pitch of 10 microns.
Everything fits again...

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james_elliot

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« Reply #18 on: January 18, 2009, 05:25:12 am »

Quote from: Panopeeper
All the concepts and formulas used above are from innumerate dinosaurs.

1. One needs to differentiate betwen the lens and the presentation. The circle of confusion has nothing to do with the lens; it is a purely perceptional issue.

2. The lens creates a circle of uncertainty, which needs to be measured against the pixel pitch.

3. The formula of calculating the circle of uncertainty is worthless; it is derived from a lens construction, which is nonexistent in the modern cameras, except in the viewfinder. The actual distance to calculate with is not the focal length but something not declared in any published specifications.

Thus the entire discussion is nothing but reading tea leaves.

I am sorry but the correct word used in my textbooks is "circle of confusion" and not circle of uncertainty, and the definition is "an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source". The usual synonyms are "disk of confusion", "circle of indistinctness", or "blur circle". I presume "circle of uncertainty" might be found but I never found it and would like to have a reference.

The perceptual issue you are speaking of is (at least in my textbooks) called the "maximum permissible circle of confusion". Of course, I am french and I might be mistaken, but I also read optical textbooks in english, and it looks like the person who wrote the article on the english wikipedia had been reading the same ones.

The formula is not worthless: it is a first degree approximation and gives an idea of the result. Of course, this would not apply to some special lenses (such as, for example, macro lenses at very short range).

Exact results would require to know the exact optical formula of the lens and to run a simulation inside specialized softwares such as oslo-edu. This is of course impossible, but if you are curious (and brave) enough to try it on simple known lens designs, you will see that the old "one equivalent lens" approximation is not that bad on the whole.


You post reminds me of one of my student who told me that it was useless to compute the complexity of an algorithm because the current design of microprocessors was now so complex that it was impossible to know how long it would exactly take to run the program as the sequential execution model is mainly obsolete with so many pipes and execution units.
That's right, but there is a difference between one hour and one day, even if there is a 10% or even 20% or 30% error.
Engineering science has always been about making approximations.
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