Depth of field and out-of-focus blur performance

In depth of field calculations, we essentially answer this question:

With the camera focused at a certain distance, and with a certain focal length lens, an a certain aperture, over what range of distances may we have objects whose images are not blurred by greater than some degree we establish.

We can of course "solve" this relationship "in other directions"; for example we may ask, "to have objects over a certain range of distances whose images are not blurred by greater than some degree we establish, for a certain focal length, what aperture must we use?

In some cases, we are interested in assuring blurring of background or foreground objects as part of the artistic objectives of the result - the matter of "bokeh".

The equations governing this are the same as for the first interest, but we use them a different way up.

This calculator, in the form of an Excel spreadsheet, can help us project what will happen in this regard:

http://dougkerr.net/pumpkin/articles/OFB_calculatorP.xls

Best regards,

Doug

Doug Kerr said:

In some cases, we are interested in assuring blurring of background or foreground objects as part of the artistic objectives of the result - the matter of "bokeh".

Click to expand...

Hi Doug,

If you don't mind my addition, 'Bokeh' is more a description of the 'quality' of the blur, than the blur itself. One can even distinguish several types based on the origin of their 'quality', as described in this, always excellent, and this information source.

Thanks for the link to your spreadsheet.

Cheers,
Bart

Hi, Bart,

Bart_van_der_Wolf said:

If you don't mind my addition, 'Bokeh' is more a description of the 'quality' of the blur, than the blur itself.

Click to expand...

I think actually it properly refers to the whole matter of intentionally-cultivated blur in photography - its presence, and of course its various properties. We don't speak of the "bokeh" of the blur. We may speak of various aspects of the "nature" of the bokeh.

Note carefully how I introduced the term in my note.

One can even distinguish several types based on the origin of their 'quality', as described in this, always excellent, and this information source.

Click to expand...

Thanks so much for those nice references.

Best regards,

Doug

Hi, Bart,

I had said (regarding "bokeh"):


Upon reflection, I think that indeed we should concentrate the use of the term to refer to" nature" of the blur rather than just the overall concept of blur as an artistic tool in an image.

Thus, we can say, "the out-of-focus blur with this lens has an especially nice bokeh".

Thanks for pointing this out.

Best regards,

Doug

Doug Kerr said:

The equations governing this are the same as for the first interest, but we use them a different way up.

Click to expand...

What you seem to forget is that to come to these equations a particular set of hypothesis were made.

The hypothesis are that optical aberrations and diffraction are negligible. Thus we come to a very simplified formula. The formula also imply that the images of point sources outside of the plane of focus are uniform discs.

But when we want to study the different rendering of out of focus areas between different lenses, the effects are due to the exact factors which the implied hypothesis in the formula presumes to be negligible. One cannot use these simplified equations to study what the equations themselves imply not to exist.

Hi, Jerome,

Jerome Marot said:

What you seem to forget is that to come to these equations a particular set of hypothesis were made.

Click to expand...

Oh, I don't think I forget.

The hypothesis are that optical aberrations and diffraction are negligible.

Click to expand...

Essentially.

However, in the regime in which this calculator is generally used - that is, with an intentionally-substantial circle of confusion diameter - indeed diffraction and probably most aberrations as well will be negligible with respect to the circle of confusion diameter (which is the sole issue here).

Thus we come to a very simplified formula. The formula also imply that the images of point sources outside of the plane of focus are uniform discs..

Click to expand...

The classical depth of field formulas have many simplifications. One is essentially that the disk is essentially Gaussian.

But when we want to study the different rendering of out of focus areas between different lenses, the effects are due to the exact factors which the implied hypothesis in the formula presumes to be negligible. One cannot use these simplified equations to study what the equations themselves imply not to exist.

Click to expand...

Thank you for your outlooks on this matter.

Best regards,

Doug

Doug Kerr said:

However, in the regime in which this calculator is generally used - that is, with an intentionally-substantial circle of confusion diameter - indeed diffraction and probably most aberrations as well will be negligible with respect to the circle of confusion diameter (which is the sole issue here).

Click to expand...

They are not for many cases, hence the various myths about "bokeh". Note that aberrations and hence "bokeh" can be computed by ray tracing programs and that lens designers take this criterium into account.

Doug Kerr said:

The classical depth of field formulas have many simplifications. One is essentially that the disk is essentially Gaussian.

Click to expand...

I don't think that this is the assumption. You may be thinking about angle resolution figures and the Airy criterium. I really think that the assumption is that the disc is essentially uniform.

Dear Jerome,

Jerome Marot said:

I really think that the assumption is that the disc is essentially uniform.

Click to expand...

Actually, my only "assumption" is that the blur figure has what we can reasonably call a "diameter". Nothing I do in any way makes any assumptions about the distribution of luminance across the blur figure, or deals with any ramifications of that. I think that is a red herring.

I would certainly enjoy learning of your outlook on a more rigorous way to estimate a "largeness" metric for the blur figure arising on the focal plane from an object point not in the object space surface of ideal focus, or a proposed definition for that metric itself.

Best regards,

Doug

Doug Kerr said:

I would certainly enjoy learning of your outlook on a more rigorous way to estimate a "largeness" metric for the blur figure arising on the focal plane from an object point not in the object space surface of ideal focus, or a proposed definition for that metric itself.

Click to expand...

That is a surprisingly complicated problem as we would need to take the psychometrics of human vision into account: in a real photograph, we rarely image point sources but real life subjects and we would need to characterize how various out-of-focus subjects can be recognized and found to be pleasing by average people depending on the shape of the blur discs.

What I wanted to point out are the limitations of your formulas. For real lenses, especially very fast ones, it is not unheard of to have two lenses of identical aperture and focal length that give visually different depths of field. That cannot be explained by your formulas, for the reasons I gave.

Interesting concept. I put a few values in for some situations I'm kind of familiar with and the results are a bit surprising.

Ex1: for focus and subject distances of 72 and 84 inches, respectively, a 50mm lens and the given ref. circle, I put in values for aperture of 1.4, 2.8, and 5.6, and found the blur to drop as follows -- 4.63, 2.31, 1.16

I would have thought the blur would be more than twice as much for 2x the aperture.

But then I put in distance of 24 and 2400 inches, with a focal length of 24 and apertures of 2.8 and 16. The blur factors I got were 11.22 and 1.96.

If I'm understanding this, it's saying that even at f1/16 my background is more blurred in the 24 than two closely spaced objects with the 50 at 5.6, and I really would have thought it would be the other way around.

This is really making me want to set up some test targets!

Blur aside, I do find it really interesting how various lenses render the out of focus areas so differently. I wonder how Nikon's two DC lenses fit into this discussion, if at all.

Let me clarify what the calculator I presented does and does not do.

It is predicated on the concept that a point source on an object not located (in object space) on the current surface of perfect focus will create, on the focal plane a "blur figure".

In any real case:

• This blur figure may or may not have essentially a "circular" boundary (see below).

• It may have a wide range of distributions of luminance along any given radial. In some cases, this distribution, regardless of its "interior" nature, will have a fairly-well defined boundary (at which the luminance drops off precipitously).

We assume that, in the case of interest:

• The blur figure is essentially circular and has a radial distribution of luminance such that we can reasonably consider it to have a "boundary", such that we can reasonably ascribe to it a diameter.

We also assume that the nature of the optical system is such that this "diameter" can be reasonably predicted by a simplistic application of paraxial optics, predicated on:

• The focal length of the lens.

• The relative aperture of the lens (expressed as an f-number)

• The distance, P, at which the camera is focused.

We further assume that the relative aperture is such that diffraction effects are inconsequential. And, by our use of the paraxial conceit, we essentially ignore most lens aberrations.

The hope is that by making such an estimate of the "diameter" of the blur figure for a proposed "photographic" setup, we will have insight into one aspect of the overall matter of the blur of objects not at the focus distance (specifically, "how big is the blur figure").

There are of course many other aspects of the rendering of out-of-focus object in which we are typically, and understandably, interested (including the rendering of "extended" objects). I'm sorry, but the calculation I discuss here does not read on those.

For those who feel that:

• An estimate of how big is the blur figure is not a useful property in planning a pictographic shot, or

• An estimate based on the assumptions I have outlined above is so faulty as to be useless,

then, as far as my ability to assist the process is concerned, you are just shít out of luck.

Best regards,

Doug
Just a telephone engineer
Tip on the top, ring on the right

So if I wanted to do experiments to see this stuff in action, it might be good to print a couple black dots on white pages for targets, right? And then set them up at the chosen distances?

It's a neat concept -- it never occurred to me that the size of a blur could be calculated, but based on the prior discussion of dof it is plainly obvious!

Hi, Bob,

Bob Rogers said:

So if I wanted to do experiments to see this stuff in action, it might be good to print a couple black dots on white pages for targets, right? And then set them up at the chosen distances?

Click to expand...

Sure.

It's a neat concept -- it never occurred to me that the size of a blur could be calculated, but based on the prior discussion of dof it is plainly obvious!

Click to expand...

Exactly. It's the same question, just asked "the other way to".

Best regards,

Doug

I found two photographs that illustrate the effect I was thinking about. They are not a scientific test, simply a way to show the effect of some aberrations. I chose the two pictures to give similar depth of field (as seen on the flowers, the centre dandelion is where I focussed the lenses), but the rendering of the out of focus parts are obviously very different.

Hi, Jerome,

Jerome Marot said:

I found two photographs that illustrate the effect I was thinking about. They are not a scientific test, simply a way to show the effect of some aberrations. I chose the two pictures to give similar depth of field (as seen on the flowers, the centre dandelion is where I focussed the lenses), but the rendering of the out of focus parts are obviously very different.

Click to expand...

Thanks you so much for these two very nice examples. Both the D700 and the A900 did a very nice job.

I am not sure what you mean that the two images had a similar depth of field. Depth of field is only defined based on some criterion of "acceptable" blurring.

If we take the approach that the acceptable blurring is a blur figure whose diameter is a fixed fraction of the image dimensions, then I am unable to conclude by calculation that these two images had the same depth of field.

Perhaps you mean that the two would have comparable "geometric" out-of-focus blur performance (by "geometric" I mean only in terms of the predicted diameter of the blur figure for some particular object distance), not the same thing as depth of field performance.

And in fact my calculations suggest that such is the case.

And visually, the two images seem to illustrate, for any given object, essentially the same blur figure diameter.

And they nevertheless exhibit a different blur circle luminance distribution (one factor that can significantly affect the "nature" of the blur).

Still, I'm not sure that I would say that the overall visual blur effect is significantly different between the two images. If I for example concentrate on the dandelion just partially visible at the upper left corner of the frame (substantially affected by misfocus but not blurred into a blob). I don't see much difference.

Thanks again for these nice demonstration images.

Best regards,

Doug

We should not forget that the idea behind the theory is that we are trying to make images for other people to look at. And the blur, or the absence of any detectable blur, is a means that we use to express ourselves: as photographers, we use blur to signal that something is less important than something else (which is sharp) or to send part of the scene into oblivion.

Basically, we have 3 choices:
-make it look sharp to the viewer
-make it look blurred, but still recognizable
-make it look so blurred than it cannot be recognized.

So blur is one of the tools that photography has (and that painting did not have before photography started to be used, check it out...).

Of utmost importance to us as photographer is the "blurred, but still recognizable" item. "Still recognizable" is not only a function of the blur quality, but also a function of how humans actually recognize things for what they are.

At this point, I suppose that you'll understand that the problem is slightly more complex than we would like it to be. How humans recognize things is a complex problem. And don't dismiss the problem as a purely aesthetics problem; it is very much an engineering problem as well: the jpeg compression which allows us to see these images on the web is based on how humans recognize things. And indeed, quite interestingly, jpeg compression will change the rendering of out of focus areas of photographs. You don't see the performance of the two lenses here, you only see a jpeg interpretation of it. The originals are a bit different.

So what can we do as photographers? Or what can the optical engineer designing lenses do for us? A rule of thumb which works in most cases is that the blur figure of a point source has a somewhat gaussian distribution. This is what was attempted with the lenses above, with considerable more success for the second lens (and plenty of limitations, due to the optical system involved). Another rule of thumb is that we should try to avoid changing the color of out of focus subjects (neither of the lenses here are optimized for that).

Now for the interesting question: what would make it easier or more difficult to achieve these two criteria?

Hi, Jerome,

All well said.

Thanks.

Best regards,

Doug

Jerome Marot said:

A rule of thumb which works in most cases is that the blur figure of a point source has a somewhat gaussian distribution. This is what was attempted with the lenses above, with considerable more success for the second lens (and plenty of limitations, due to the optical system involved). Another rule of thumb is that we should try to avoid changing the color of out of focus subjects (neither of the lenses here are optimized for that).

Now for the interesting question: what would make it easier or more difficult to achieve these two criteria?

Click to expand...

I see that nobody is interested in answering the question or discussing the matter further. Maybe I should not have raised these problems.

Hi, Jerome,

Jerome Marot said:

A rule of thumb which works in most cases is that the blur figure of a point source has a somewhat gaussian distribution.

Click to expand...

Do you mean:

• The theoretical model of an ideal lens would predict a Gaussian blur figure?

• Most actual lenses product a blur figure that approximates a Gaussian distribution?

• Lenses whose blur figures approach a Gaussian distribution typically produce what is considered a "desirable" æsthetic effect for significantly out-of-focus objects?

Best regards,

Doug

There is a nice treatment of some of the issues in this paper:

http://www.zeiss.com/c12567a8003b8b6f/embedtitelintern/cln_35_bokeh_en/$file/cln35_bokeh_en.pdf

Best regards,

Doug

Doug Kerr said:

Hi, Jerome,



Do you mean:

• The theoretical model of an ideal lens would predict a Gaussian blur figure?

• Most actual lenses product a blur figure that approximates a Gaussian distribution?

• Lenses whose blur figures approach a Gaussian distribution typically produce what is considered a "desirable" æsthetic effect for significantly out-of-focus objects?

Best regards,

Doug

Click to expand...

I meant to say that lenses whose blur figures approach a Gaussian distribution and which do not produce colored aberrations typically produce what is considered a "desirable" aesthetic effect for objects which are out-of-focus but still recognizable.

The question is: how can we make it easier to design such lenses? The answer is quite simple.

Hi, Jerome,

Jerome Marot said:

I meant to say that lenses whose blur figures approach a Gaussian distribution and which do not produce colored aberrations typically produce what is considered a "desirable" aesthetic effect for objects which are out-of-focus but still recognizable.

The question is: how can we make it easier to design such lenses? The answer is quite simple.

Click to expand...

Thanks.

Best regards,

Doug

Very useful discussion.

However, I wonder how useful all this theoretical discussions are in real life photography. Of course, it is useful to know, in general terms, how a car works. Some know much more detail..but that does not necessarily make one a better driver...maybe a more informed driver!!

I know of forums where there is endless talk about sensor design, bayer arrays, lens design etc. From my point of view, this is interesting for gear heads but not necessarily for photographers ( assuming some basic knowledge and experience has been gained by the photog ).

Here is one dof calculator, I used to employ. Not now. I just lined up empty cans of pepsi/coke at various distances from each other; put my camera on a tripod; changed the aperture and found what this science was all about. I moved the tripod a further distance, away or towards the cans, changed the aperture again and got some other results. Then I changed the focal lengths and did the same exercise again.

I could have easily looked up:

in/out of focus areas

I know my lenses inside out..their behaviors. I do not use too many lenses

To Bokeh now..Japanese refer to this as boke. In any case I would define bokeh as:

" the character of out of focus areas, not simply how far out of focus they are. "

Some lenses are good, some passable, some downright atrocious. The choice of what is good or bad depends on the individual; but generally people tend to agree on good and terrible bokeh.

As in life, compromises have to be made. In camera, sensor and lens designs. The photog, too, makes compromises; the instant a certain fl, aperture, speed, iso and distance from the subject has been determined.

For me, this is second nature, without the need for all the science involved.

Although I appreciate and am in awe of those who know of such mathematical intricacies. Imagine where we would be without the concept of ' zero '.

And these circles of confusion are so much more complex. To illustrate ( posted previously )


And the drink is on me:

Hi, Fahim,

fahim mohammed said:

To Bokeh now..Japanese refer to this as boke.

Click to expand...

Well, in romaji, yes. 暈け in kanji/hiragana or ボケ in katakana

Iin this context, actually ボケ味 (in romaji, boke-aji ).

Your points are all well taken. Thanks.

We used to use nail polish bottles rather than Coke cans!

Best regards,

Doug

fahim mohammed said:

I wonder how useful all this theoretical discussions are in real life photography. Of course, it is useful to know, in general terms, how a car works. Some know much more detail..but that does not necessarily make one a better driver...maybe a more informed driver!!

Click to expand...

It does not make one a better driver to be able to design an engine or a car suspension. Conversely, it does not make one a better photographer to know how lenses are designed. You are right on that point.

But if I wand to buy a car, I try to find out data about its dimensions, about the engine, fuel consumption, etc... Understanding what were the considerations for the designers of that car allows me to determine more quickly whether it is likely to fit my needs or not. The idea is to be able to predict from whatever limited data is available online whether a given car is likely to fit my needs or not. Then I can go to a few car shops and check things like the boot or the position of the driver, etc... or rent a few models to feel how they handle. I can't try all the models on the market, so I need a pre-selection.

The same is true for lenses. Better lenses or better bokeh will not allow me to be a better photographer. Nevertheless, I would like to know beforehand what lens to use and at which aperture so as to get the effect I like in my photograph. I could, probably, rent a complete collection of lenses in my mount of choice and try them a various distances and apertures, but this would take a lot of time. Or I can try to find out why some lenses produce better bokeh and preselect on these criteria.

I don't drive enough to consider myself a good driver, but I am quite pleased with my car. I am also quite pleased with my camera and lenses.

Jerome, but I do not need to know the mathematics or mechanical engineering to buy a car.

I need only to know ( amongst other things ) if I could afford it for the purpose I want to use it for. How economical is it to drive, service costs, after sales support.

I would test drive a car. Feels ok to me. Checks all my boxes. I buy it.

Same with cams, lenses, house/s, food, clothes. I do not get involved in organic chemistry to buy food.
I don't know if it would make it more palatable. Things I need to know are usually written on the packaging.

Cams/lenses..just try them. And, of course, a camera that gives acceptable results ( for me ) is all I need to know.

Could not care less if it is concave/convex/hybrid/with/without anything/everything/something. Show me the beef. If it good, if I like it, I buy it. Texan horn or Angus.

Tell me how to improve my vision, my photography. I do not want to design cams/lenses. I want to use them. Use those that are created by those much more qualified than me in cam and lens design and development..

All the maths is not going to improve my photography. A trip to the Louvre would.

Another beautiful day here in paradise. No rain, lovely fluffy clouds.

Best regards,

Doug

Same here. A little cooler now.

Best.