About depth of field

A recent flurry of palaver on another site made me think it might be time to give my periodic set of lectures on the topic of depth of field.

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What is depth of field, anyway?

The distance called depth of field is the answer to this question:


How can we quantify "that degree" of blurring?

As an actual optical phenomenon, the effect of the blurring is that a point on a subject will not form, in the image on the sensor, a point, but rather a circular "blur figure" (a circle of confusion). A measure of the degree of blurring is the diameter of that blur figure (circle of confusion diameter). If we want to quantify blurring "not over a certain degree", one way is to express that as a limit on the allowable diameter of the blur figure (circle of confusion diameter limit which I call COCDL), on the sensor.


Without our adopting a COCDL, there is no such thing as a depth of field. The COCDL is not calculable from any parameters of the camera setup - it is our own limit, just as we might adopt a limit for how large an error a surveyor can make before we deem him "unqualified".

Choosing the COCDL

Now, on what basis might we adopt a COCDL? In traditional photographic work, a common premise was that the COCDL should be the diameter of a blur figure that would make the blur just clearly visible to the human eye. So a common basis was to make the COCDL correspond to perhaps twice the human eye resolution.


So wait a minute - the COCDL is defined on the image as generated on the sensor, and we don't look at the image there. In traditional photography, for small format cameras, we always look at a print made form the negative. The print size might be variable multiple of the actual image size, and we might view it from different distances.

To take that confusion out of the picture, we think in terms of an arbitrary print size, seen at an arbitrary distance.

It turns out the twice the angular spacing the eye can resolve at the arbitrary distance we assume for viewing is about 1/1400 of the diagonal size of that arbitrary print size.

Then, chasing this back to the sensor, it suggests we should choose a COCDL that is 1/1400 of the diagonal size of the image on the sensor.

And depth of field figures quoted for a certain camera setup without benefit of further explanation are often based on that choice of COCDL, or another fraction but defined on the same basis.

Another approach

There are some that say we should choose the COCDL so that the depth of field will be determined as the range of distances over which subjects range will be imaged with no perceptible degradation of sharpness due to imperfect focus. That means choose the COCDL as perhaps, twice the pixel pitch (on the sensor) of the camera.

Which if these is "right"? There is no "right". This whole concept is based on our choosing what we will consider "perceptible" blurring. And how we want to define that that may well depend on the use that is to be made of our image.


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In the next section, I will discuss that burning question, "how does sensor size affect depth of field."

[continued]

Doug Kerr said:

............
It turns out the twice the angular spacing the eye can resolve at the arbitrary distance we assume for viewing is about 1/1400 of the diagonal size of that arbitrary print size.

Click to expand...

• twice the angular spacing the eye can resolve (x) is
  
• angular spacing the eye can resolve (x) is

I am confused with the syntax.

Asher

[Part 2]

The effect of sensor size on DoF

We often hear it asked, "what is the effect on DoF of a difference in sensor size".

That's pretty vague. Perhaps it would be better to ask, "If camera B has a larger sensor than camera A, everything else being equal, which will have the greater deth of field?"

But to do that, we must adopt and announce what we mean by "everything else being equal".

Here is definition we might adopt:

a. Focal length such that the field of view is the same in both setups. (Aha!)

b. Camera focused at the same distance. (Of course.)

c. Same f-number. (Of course.)

d. The adopted COCDL is a consistent fraction of the image diagonal size. (Aha!)

If you don't like those aspects of a definition, then choose some others. But you are on your own on the calculations, and the result!

Now, suppose in particular, we are comparing two cameras, with "B" having an image size 2x that of "A" (hard to believe, but I don't want to be hauling around a lot of numbers like "1.6".)

Then:

1. Under rule a, we must use a lens of twice the focal length on B as on A.

2. Under rule c, our COCDL is twice for B what it is for A.

Now, with regard to point 2, that means that we are more tolerant of blur in B than in A (in B we will not consider the blur limit to be exceeded until the diameter of the blur figure is twice as much as for A. Thus this consideration alone would lead to a greater depth of field for B than A.


This works roughly proportionally to the COCDL, and thus roughly proportionally to the image size (sensor size).

Now, to point 1. Because of the optical situation involved (and I will not attempt to describe this in detail here), assuming a certain f-number, for a greater focal length the "incorrectness" in focus distance to cause a certain diameter of the blur figure is less. Thus this consideration alone would lead to a lesser depth of field for B than A.

This works essentially proportionally to the square of the focal length, and thus (because of rule a) to the square of the image size (sensor size).

So, considering both of these considerations, as we move from A to B, we find that consideration 2 gives an increase in the depth of field, and consideration 1 gives a larger decrease in the depth of field (because it varies inversely as the square of the image size).

Thus, the overall effect is that (under the rules stated above), for an increase in sensor size we have a net decrease in depth of field.

And that's how it works.

Best regards,

Doug

Hi, Asher,

Asher Kelman said:

• twice the angular spacing the eye can resolve (x) is
  
• angular spacing the eye can resolve (x) is

I am confused with the syntax.

Click to expand...

Sorry if that was not as clearly stated as should be.

Suppose the angular spacing the eye can resolve is assumed to be v. It turns out that at the arbitrary distance for print viewing that is used in this matter, 2v subtends about 1/1400 of the diagonal size of the print size that is arbitrarily considered.

To be less cryptic, the arbitrary print size contemplated in this is 12 x 8 inches, the arbitrary viewing distance is 16.7 inches (and I forget the rationale for that). The diagonal of the assumed print is about 14.42 inch.

The visual resolution assumed is 1/3000 radian (very nearly one minute of arc). Twice that (1/1500 radian), at a distance of 16.7 inches, subtends a distance of about 0.111 inch. That constitutes 1/1295 of the print diagonal. The custom is to use a slightly smaller distance, 1/1400 of the diagonal.

I hope that helps.

Best regards,

Doug

A great lecture Doug, very well explained imo. Then again, I'm no stranger to this subject myself. Being an engineer is also an advantage. But there will be people out there who have never read scientific texts before. They may skip reading this. To them I want to say: persevere and read this, you will be happy you did.

Hi, Cem,

Cem_Usakligil said:

A great lecture Doug, very well explained imo. Then again, I'm no stranger to this subject myself. Being an engineer is also an advantage. But there will be people out there who have never read scientific texts before. They may skip reading this. To them I want to say: persevere and read this, you will be happy you did.

Click to expand...

Thank you

Best regards,

Doug

It seems that with a digital camera, one could define the COCDL in terms of the pixel size. If there is no blurring across pixels then the image is sharp -- at least as sharp as it can be given the sensor.

Bob Rogers said:

It seems that with a digital camera, one could define the COCDL in terms of the pixel size. If there is no blurring across pixels then the image is sharp -- at least as sharp as it can be given the sensor.

Click to expand...

Yes, this is the "another approach" Doug has explained in his first post. I use the formula 1.5 times the sensel pitch for Bayer sensors to calculate the optimal COCDL. But this is only useful for pixel peeping perfectionists like myself, the real photographers out there do not need to be that conservative when calculating the DoF. Having said that, this formula to calculate COCDL is relevant when one wants to know the maximum aperture value of a lens beyond which diffraction blur will be introduced to the image.The lower the sensel pitch, the lower the maximum aperture value will be.

Cem_Usakligil said:

Yes, this is the "another approach" Doug has explained in his first post. I use the formula 1.5 times the sensel pitch for Bayer sensors to calculate the optimal COCDL. But this is only useful for pixel peeping perfectionists like myself, the real photographers out there do not need to be that conservative when calculating the DoF. Having said that, this formula to calculate COCDL is relevant when one wants to know the maximum aperture value of a lens beyond which diffraction blur will be introduced to the image.The lower the sensel pitch, the lower the maximum aperture value will be.

Click to expand...

Hi Cem, Bob, and others,

Indeed, 1.5x is exactly what I use as the most critical criterion, and the reason is because it corresponds with the Aperture setting which begins to visually impact the contrast of microdetail, because the diameter of the diffraction pattern starts to exceed that diameter of 1.5x the sensel-pitch.

That also allows to approximate the onset of diffraction limiting by aperture quite easily, just take 1.1x (or 1.108 if you're good at math by head) the sensel-pitch in microns, and you'll get the Aperture that's on the edge of compromise.

Of course that is capture centric reasoning, which makes sense when optimizing technical capture quality, and especially when large format output may be a possible application.

The Circle of Confusion is a useful criterion to plan output requirements with. There, output size and viewing distance also play a role in how large the COCDL is reproduced. In that case also printer resolution (PPI) becomes a useful parameter, because we do not need to exceed the capabilities of the printer. For smaller output sizes that may mean that we can use shots taken with narrower apertures, without quality compromises.

For the printer PPI requirements, and to calculate if we can use more diffraction limiting apertures without much penalties, one can extend the angular resolution that's a the basis of the COCDL as follows.

Rule of thumb for the required PPI for viewing (large format) output at a given distance:
• 1 arc minute at 1 metre equals 87.32 PPI.
• 0.4 arc minutes at 1 metre equals 218.3 PPI.
Divide by the viewing distance in metres to find the required minimum PPI.

For the metrically challenged this would become:
• 1 arc minute at 1 foot equals 286.48 PPI.
• 0.4 arc minutes at 1 foot equals 716.2 PPI.
Divide by the viewing distance in feet to find the required minimum PPI.

The difference between using a 1 minute of arc, or 0.4, is the difference between very good and excellent print quality.

This is before upsampling to the printer driver's native resolution (to avoid low quality printer driver interpolation, and to allow output sharpening at the printer's native output resolution).

That should cover all bases, from creative requirements like having acceptable sharpness at the edges of the DOF zone, to uncompromised capture quality, to perfect output quality.

Cheers,
Bart

Speaking of printer resolution, I have found that the printed statistics aren't very useful. Instead, I create 1 pixel wide lines in alternating colors in Photoshop and print them to discover the actual resolution. The designjet 5000, for instance, has a real resolution of 150 ppi.

Since I've started wearing bi-focals my standards have really declined. I just can't see stuff anymore the way I used to.

Hi, Bob,

Bob Rogers said:

It seems that with a digital camera, one could define the COCDL in terms of the pixel size. If there is no blurring across pixels then the image is sharp -- at least as sharp as it can be given the sensor.

Click to expand...

Indeed.

This outlook is meaningful if our objective is to not have any "important" subject features less sharp, by virtue of imperfect focus, than the ultimate capability of the sensor system.

This might well be true of technical or architectural photography.

But in much photography we will consider as "satisfactory" a rendition of an object with sharpness less than the capability of the sensor system, but still within some "bogey" we adopt.

Remember, the whole purpose of the DoF concept is to give us guidelines for planning the "settings" for a shot. These guidelines must in the light of our actual objectives for the work product.

You may recall the endless discussions in some quarters about the "proper" formula for determining the ideal age of a girlfriend. (The late former director of Comsat Laboratories, a former client of my consulting practice, recommended "half your age plus 10 years".)

Best regards,

Doug

Hi, Bart,

Bart_van_der_Wolf said:

Hi Cem, Bob, and others,

Indeed, 1.5x is exactly what I use as the most critical criterion, and the reason is because it corresponds with the Aperture setting which begins to visually impact the contrast of microdetail, because the diameter of the diffraction pattern starts to exceed that diameter of 1.5x the sensel-pitch.

That also allows to approximate the onset of diffraction limiting by aperture quite easily, just take 1.1x (or 1.108 if you're good at math by head) the sensel-pitch in microns, and you'll get the Aperture that's on the edge of compromise.

Of course that is capture centric reasoning, which makes sense when optimizing technical capture quality, and especially when large format output may be a possible application.

The Circle of Confusion (I think you mean COCDL) is a useful criterion to plan output requirements with. There, output size and viewing distance also play a role in how large the COCDL (I think you mean circle of confusion) is reproduced.

Best regards,

Doug

Click to expand...

Hi, Cem,

Cem_Usakligil said:

Yes, this is the "another approach" Doug has explained in his first post. I use the formula 1.5 times the sensel pitch for Bayer sensors to calculate the optimal (Ooh!) COCDL.

Click to expand...

I think you mean the COCDL you like to use!

Maybe 0.75 times your age plus 5 years.

Best regards,

Doug

Hi, Bart,

Bart_van_der_Wolf said:

Hi Cem, Bob, and others,

Indeed, 1.5x is exactly what I use as the most critical criterion, and the reason is because it corresponds with the Aperture setting which begins to visually impact the contrast of microdetail, because the diameter of the diffraction pattern starts to exceed that diameter of 1.5x the sensel-pitch.

That also allows to approximate the onset of diffraction limiting by aperture quite easily, just take 1.1x (or 1.108 if you're good at math by head) the sensel-pitch in microns, and you'll get the Aperture that's on the edge of compromise.

Of course that is capture centric reasoning, which makes sense when optimizing technical capture quality, and especially when large format output may be a possible application.

The Circle of Confusion is a useful criterion to plan output requirements with. There, output size and viewing distance also play a role in how large the COCDL is reproduced. In that case also printer resolution (PPI) becomes a useful parameter, because we do not need to exceed the capabilities of the printer. For smaller output sizes that may mean that we can use shots taken with narrower apertures, without quality compromises.

For the printer PPI requirements, and to calculate if we can use more diffraction limiting apertures without much penalties, one can extend the angular resolution that's a the basis of the COCDL as follows.

Rule of thumb for the required PPI for viewing (large format) output at a given distance:
• 1 arc minute at 1 metre equals 87.32 PPI.
• 0.4 arc minutes at 1 metre equals 218.3 PPI.
Divide by the viewing distance in metres to find the required minimum PPI.

For the metrically challenged this would become:
• 1 arc minute at 1 foot equals 286.48 PPI.
• 0.4 arc minutes at 1 foot equals 716.2 PPI.
Divide by the viewing distance in feet to find the required minimum PPI.

The difference between using a 1 minute of arc, or 0.4, is the difference between very good and excellent print quality.

This is before upsampling to the printer driver's native resolution (to avoid low quality printer driver interpolation, and to allow output sharpening at the printer's native output resolution).

That should cover all bases, from creative requirements like having acceptable sharpness at the edges of the DOF zone, to compromised capture quality, to perfect output quality.

Click to expand...

Very nice discussion. Thanks so much.

Best regards,

Doug

Doug Kerr said:

Hi, Cem,


I think you mean the COCDL you like to use!

Maybe 0.75 times your age plus 5 years.

Best regards,

Doug

Click to expand...

Hi Doug,

I actually meant the optimal COCDL. If the diameter of the airy disk is smaller than this value, then the image doesn't get any better but if it is larger, a loss of microcontrast is introduced. It is not just an arbitrary value I've chosen to my liking.

Let me help get the discussion into a more interesting turn: the calculations above assume that the image of a point light source becomes a uniform lit disc when not in the locus of sharpness (it also assumes this locus to be a plane, but that is less important).

Hi, Cem,

Cem_Usakligil said:

Hi Doug,

I actually meant the optimal COCDL. If the diameter of the airy disk is smaller than this value, then the image doesn't get any better but if it is larger, a loss of microcontrast is introduced. It is not just an arbitrary value I've chosen to my liking.

Click to expand...

What is to your liking is that we should consider the distance range within which we would confine our "important" subjects to be such that their sharpness is not degraded by imprecise focus. That is after all what the calculated DoF number is for!

What other use do we make of that number that we, having first adopted a COCDL, calculate as the DoF?

Best regards,

Doug

Doug Kerr said:

What is to your liking is that we should consider the distance range within which we would confine our "important" subjects to be such that their sharpness is not degraded by imprecise focus. That is after all what the calculated DoF number is for!

Click to expand...

Hi Doug,

That's essentially correct if we calculate the DOF, and use a certain COCDL to calculate it.

However, that's not what Cem was explaining why he sometimes uses a different COCDL i.e. 1.5x sensel pitch.

There is no such thing as a single COCDL, because ultimately the result has to be looked at in a certain output size, and from a certain distance. When we downsample the image to an 800 pixel dimension, and look at it from 1 to 2 feet distance, almost everything will be as sharp as the display resolution allows.

When mentioning 1.5x sensel pitch as a COC criterion, one uses that to a.) allow to make an estimate of DOF, e.g. for focus stacking decisions, but b.) also to understand that stopping down further will not produce better focused DOF, only a deeper more blurred DOF zone (especially in the plane of optimal focus). That is particularly important for those who may require large format output, where the pixels are likely to be magnified.

In other words, when using an aperture that's narrower than is deemed optimal from a diffraction point of view, we are (one may hope) knowingly sacrificing technical quality and trading it for a creative effect. That effect may be justified from the creative point of view, but can perhaps also be achieved by using a technique (such as focus stacking) that doesn't compromise the per pixel quality.

Ultimately, a creative use of DOF as calculated with a COCDL parameter should incorporate the final viewing conditions (size and distance).

Perhaps more important from a creative point of view, is the ratio of blur between the main subject and the foreground or background features. For that purpose one must calculate the COC at different distances relative to the focus distance.

A very useful tool for planning such scenarios ahead of time is the VWDOF calculator (Windows platform only). It allows to be configured with several scenarios side by side, and include or exclude relevant output values, amongst others a "Point of interest blur" (e.g. foreground), and "Infinity blur". That allows, after resizing for output, to calculate the resolution at those DOF zone points, and at the optimal focus plane.

Another useful DOF tool is the "Barnack" DOF calculator (also Windows platform), which (amongst others) allows to graphically show a 2 sensel lower resolution limit in addition to the foreground and background limits.

Cheers,
Bart

My point is this:

Why do we want to calculate a value of Dof?

We calculate DoF in order to know, when planning a shot, either:

• For a certain f-number (and assuming a certain focus distance), over what range of distances can we have subjects such that they will be imaged with blurring, due to them not being at the focus distance, not over a certain degree of blurring, or

• For subjects over a certain range of distance (around a certain focus distance), what f-number must we use such that these subjects will be imaged with blurring, due to them not being at the focus distance, not over a certain degree of blurring

We instruct the DoF equation (or a calculator using the Dof equations) as to that "certain degree of blurring" by feeding it a COCDL value.

Case A

Now, if the certain degree of blurring we have in mind is "blurring that does not significantly degrade the perfect-focus resolution of the camera", then we can choose a value of COCDL that is comparable to the perfect-focus resolution of the camera, which comes in large degree from the pixel pitch (with proper respect to brother Kell), and should ideally take into effect such phenomena as diffraction.

Cem and Bart have discussed ways we might do this.

Case B

If instead the certain degree of blurring we have in mind is "blurring that is not visibly manifest to the viewer of the delivered image in a certain assumed viewing situation", then we can choose a value of COCDL that perhaps corresponds to 1/1500 radian in the "viewing situation of interest", transformed back to distance on the focal plane.

Case B1

If the viewing situation we have in mind is a print 8.5 times the linear dimensions of the sensor (e.g., for a "full-frame 35-mm sensor", about 12" x 8"), to be viewed at a distance of 24 inches, then that will yield a certain value of COCDL (about 0.048 mm).

This will almost certainly be a more liberal amount of blurring to the viewer than in case A. For a certain focus distance and f-number, that would lead to our concluding that we can safely have the subjects for that "shot" over a greater range of distance than in that case.

Case B2

If the viewing situation we have in mind is a poster 85 times the linear dimensions of the sensor (e.g., for a "full-frame 35-mm sensor", about 120" x 80"), to be viewed at a distance of 50 feet, then that will yield a certain value of COCDL (about 0.119 mm).

That defines a more liberal amount of blurring to the viewer than in case B1. For a certain focus distance and f-number, that would lead to our concluding that we can safely have the subjects for that "shot" over a greater range of distance than in that case.

******

Which of these COCDL values is is "optimal"? Well, if by optimal, we mean "just barely retaining for us the inherent resolution of the camera", then it is the COCDL value per case A.

If by optimal we mean "just barely yielding blurring that the viewer cannot notice in viewing situation B1", then it is then it is the COCDL value per case B1.

If by optimal we mean "just barely yielding blurring that the viewer cannot notice in viewing situation B2", then it is then it is the COCDL value per case B2.

It is easy to be seduced by choice A in that only it is independent of the viewing situation. It gives the universally-"foolproof" result


But in any case, in using such language as "optimal COCDL", we must be mindful of the question, "for what do we wish to use the calculated the depth of field"?

Best regards,

Doug

Hi Doug,

Inspired by this thread, I've done the inevitable ...

I've made an on-line DOF calculator that uses most of the insights shared in your thread, and perhaps adds a few.

Thanks for sparking this effort, and I hope you can agree with my approach. Your feedback would be appreciated, as usual.

Since the discussion may involve specifics about the tool, I've created a separate thread here.

Specific discussion about Doug's topic, is best done in this thread here.

Cheers,
Bart

During my review of the excellent photographic planner developed by Bart van der Wolf, I had to review how the "resolution of the human eye" is expressed, and I now have have a clearer view of how we should do that.

I will discuss that, and then proceed to describe the "traditional" premise for choosing a COCDL (circle of confusion diameter limit, a pivotal parameter in depth of field calculations) in that vein.


Lines and cycles

Part of the problem is the 2:1 ambiguity we have when we express resolutions in terms of "lines" In some cases, lines are equivalent to the "cycles" we consider in such work the use of the Modulation Transfer Function. In other cases, lines correspond to rows of pixels, or raster TV scan lines.

So here, I will only work in cycles.

Human vision and the Snellen chart

I will consider the resolution of the human eye "with normal vision", by which I mean vision that is rated as 20/20 in US customary units (6/6 in SI units) as determined with the Snellen eye chart.

The special glyphs ("optotypes") used on the Snellen chart are based on a coarse pixel grid, with the glyphs five pixels in height. The normal testing distance is 20 feet, at which distance the pixel pitch of the "20/20" row is one minute of arc (1/60 degree). Thus the period of a cycle is 1/30 degree.

It is assumed that if the subject can just clearly read the "20/20" row then his eye resolution is in fact "30 cycles per degree".

Choosing a value for COCDL

The traditional concept of depth of field determination is that we will consider "negligible" blurring as that which does not compromise the perceived sharpness of objects on a viewed print from the sharpness that is potentially available with "20/20" human vision, for a certain arbitrary viewing situation.

The arbitrary viewing situation that was adopted by the workers in this field is one that would, if the camera had used a 50-mm focal length lens, would produce "life-size" viewing of the print. That is, in this viewing situation, the angular size of objects on the print, as seen by the viewer, would be the same angular size they would have in direct viewing of the scene from the camera position.

If we assume an image size of 36 mm × 24 mm ("the "full-frame 35-mm frame" size), then one viewing situation that would meet that criterion would be a print 12" x 8" in size, viewed from a distance of 16.7 inches.

Our basic concept is that if the circle of confusion (the circular blur figure produced on the image, and thus on the print, from a point in the scene because of imperfect focus) has a diameter of 1/2 cycle of the eye resolution (imagine a blur figure just the diameter of one pixel on a Snellen optotype), then any larger blur figure would degrade perceived image sharpness.

So this basic COCDL would have a subtended angular diameter of 1/60 degree. At our viewing distance of 16.7", that would be a diameter on the print of 0.00486 inches, or very nearly 1/3000 of the print diagonal dimension.

Now, transporting this to the focal plane, where the COCDL in actual dimension units (mm) apples, this "basic" COCDL would also be about 1/3000 of the image diagonal dimension.

But the founding wizards decided that this COCDL was unreasonably "stringent". In effect they said, "it is unreasonable to plan our photography to assure that the image sharpness is never worse, for the subjects of interest, than the sharpness potential of the eye." So they decided that the norm for COCDL should be a blur figure twice that diameter: about 1/1500 the frame diagonal. Some workers chose to use 1/1400 instead.

From this (the 1/1400) comes the widely-cited COCDL for a full-frame 35-mm format cameras of 0.031 mm.

Best regards,

Doug

Let me now circle back to the beginning. I pointed out that there are two quite different approaches commonly used to determine the COCDL that one would use in calculating depth of field.

One (just discussed in detail) suggests a COCDL value such that the resulting blurring of subject features within the calculated depth of field would not degrade the sharpness of the image beyond a certain degree compared to the sharpness limit of a "20/20" human eye (for viewing the image on a print of a certain size at a certain distance, corresponding to "life size" viewing if the shot had been made with a 50-mm lens.

The other suggests a COCDL such that the resulting blurring of subject features within the calculated depth of field would not degrade the sharpness of the image beyond a certain degree compared to the sharpness limit of the sensor system itself.

Which is more "correct"? There is no correct COCDL value; there is no "correct" result for depth of field. It is not at all like determining what diameter pin will just ft into a certain-sized diamond shaped hole in a metal baseplate. It is much more like trying to decide what range of age should one consider in the hunt for a girlfriend.

Depth of field calculation is intended to help guide the planning of a photographic shot. The "most useful" basic for determining the COCDL used in that process depends on the use that will be made of the image. And it is very tricky for us to deal with that. So we usually go with the scheme proposed by the designer of our calculation tool.

Best regards,

Doug

Doug Kerr said:

Human vision and the Snellen chart

I will consider the resolution of the human eye "with normal vision", by which I mean vision that is rated as 20/20 in US customary units (6/6 in SI units) as determined with the Snellen eye chart.

The special glyphs ("optotypes") used on the Snellen chart are based on a coarse pixel grid, with the glyphs five pixels in height. The normal testing distance is 20 feet, at which distance the pixel pitch of the "20/20" row is one minute of arc (1/60 degree). Thus the period of a cycle is 1/30 degree.

It is assumed that if the subject can just clearly read the "20/20" row then his eye resolution is in fact "30 cycles per degree".

Click to expand...

Hi Doug,

Here is an interesting link that goes a bit deeper into this particular human vision aspect of the broader Depth of Field situation.

Choosing a value for COCDL

The traditional concept of depth of field determination is that we will consider "negligible" blurring as that which does not compromise the perceived sharpness of objects on a viewed print from the sharpness that is potentially available with "20/20" human vision, for a certain arbitrary viewing situation.

The arbitrary viewing situation that was adopted by the workers in this field is one that would, if the camera had used a 50-mm focal length lens, would produce "life-size" viewing of the print. That is, in this viewing situation, the angular size of objects on the print, as seen by the viewer, would be the same angular size they would have in direct viewing of the scene from the camera position.

If we assume an image size of 36 mm × 24 mm ("the "full-frame 35-mm frame" size), then one viewing situation that would meet that criterion would be a print 12" x 8" in size, viewed from a distance of 16.7 inches.

Click to expand...

That is also close to a viewing distance that's similar to the image diagonal (14.4 inches). That's why it is often mentioned that the 'normal' focal length for a camera system is approx. equal to the diagonal of the capture medium (film or sensor array).

Now, transporting this to the focal plane, where the COCDL in actual dimension units (mm) apples, this "basic" COCDL would also be about 1/3000 of the image diagonal dimension.

But the founding wizards decided that this COCDL was unreasonably "stringent". In effect they said, "it is unreasonable to plan our photography to assure that the image sharpness is never worse, for the subjects of interest, than the sharpness potential of the eye." So they decided that the norm for COCDL should be a blur figure twice that diameter: about 1/1500 the frame diagonal. Some workers chose to use 1/1400 instead.

Click to expand...

I also assume that a reason may have been a practical one, because at the time images were not printed as large.

The DOF markers on most lenses are roughly based on a 5x7" print size, which was already quite a bit larger than what normal consumer prints were produced at. A common consumer print size for a photo album in Europe was around 6x9 cm, decades later 9x12cm, and a postcard size of 10x15 cm was considered luxurious. A 13x18cm (~5x7 in) print was an enlargement for a picture frame, and an 18x24cm (close to an 8x10 in) was for a formal (wedding) portrait.

Cheers,
Bart

Hi, Bart,

Bart_van_der_Wolf said:

Here is an interesting link that goes a bit deeper into this particular human vision aspect of the broader Depth of Field situation.

Click to expand...

A very interesting and valuable paper. Thanks so much.

Best regards,

Doug

If in fact our objective in planning a shot is that all the "designated" subject features will be imaged with a resolution comparable to the resolution of the sensor system, which is typically about (in cycles per mm) 0. 75 x that suggested by the sensel pitch (largely a manifestation of the Kell factor), what COCDL should we use to plan the shot?

Note that if we chose a COCDL that corresponds to a maximum blurring due to imperfect focus that is comparable to the "resolution" of the sensor itself, this does not not constitute "no degradation" in image sharpness as a result of imperfect focus. If we convolve two spread functions implying equal "resolution" (one for the sensor, the other for the inexactly-focused optical system) the result is not that same resolution, but rather a lesser one.


The only situation in which the impact of inexact focus does not have any effect on the delivered resolution is for "perfect focus". We would confine our "designated" subject features to that neighborhood by using a COCDL of zero to compute our DoF (which would of course yield a DoF of zero).

So our choice of a COCDL is still arbitrary.

Best regards,

Doug

Doug Kerr said:

So our choice of a COCDL is still arbitrary.

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Hi Doug,

No problem with that.

However I do also consider that a camera like the D800E (without fully implemented Optical Low-pass Filter, OLPF), and even the D800 with such an OLPF, allows to resolve my sinusoidal grating test chart right up to the Nyquist frequency of the sensor (admittedly with almost zero MTF response).

I'd call that, the sensel pitch, a practical measure for ultimate quality COCDL, the limit.

Cheers,
Bart

Hi, Bart,

The bottom line is this.

If we are planning a shot in which the important subject features have distances in the range of 8 through 10 feet, and we choose focus distance, focal length and aperture such that, using the sensel pitch as the COCDL, the DoF range calculates to be 8 through 10 feet, then we can expect an image in which the object features at distances of 8, 9, and 10 feet are of essentially indistinguishable sharpness.

Have we "left anything on the table"?

Hey, insurance costs!

Best regards,

Doug

Just as a coincidence (?), Ctein has just published an article titled The Practical Side of Depth of Field in the Online Photographer.

Hi, Cem,

Cem_Usakligil said:

Just as a coincidence (?), Ctein has just published an article titled The Practical Side of Depth of Field in the Online Photographer.

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I might be able to use my influence to have this reprinted in The Small Farmer's Journal.

Best regards,

Doug

Doug Kerr said:

The bottom line is this.

If we are planning a shot in which the important subject features have distances in the range of 8 through 10 feet, and we choose focus distance, focal length and aperture such that, using the sensel pitch as the COCDL, the DoF range calculates to be 8 through 10 feet, then we can expect an image in which the object features at distances of 8, 9, and 10 feet are of essentially indistinguishable sharpness.

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Yes, that's correct for a digital camera, assuming the sensel pitch is set as the COCDL. The sensor array will put a hard (sensel aperture) limit on the maximum sharpness at the focus plane. Film on the other hand would potentially show higher sharpness at the focus plane but an equal amount of blur at the given COCDL boundaries of the DOF zone.

Have we "left anything on the table"?

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That seems to cover it, as far as I am concerned.

Cheers,
Bart