The Ultimate Depth of Field Skinny

[Jeff Donald]

Arguably more is written about Depth of Field (DoF) on the DV Info net than any other subject. This is my attempt to provide the ultimate discourse and treatment on this subject. All misconceptions, hearsay, rumors and innuendo will be laid to rest. My motivation for doing this is to avoid future disagreements and confusion among our community. By posting all the variables and examples in one place, novices and old hands can benefit and apply the newly gained knowledge in the field. Dre...., Good Dog and myself argued over confusion with the english language, semantics etc. Dre....is the retired Chief Technical Officer and VP for Research and Development for Barco. Good Dog has 20+ years in the photography field (cinema, video, etc). I have a BS in Physics and I've taught Photography for 22 years (not full time). We should combine our considerable experience, knowledge and expertise for the benefit of the community. So, with that all out of the way, let's get started.

I will start with the formula for DoF as it appears in the "American Cinematographers Manual" 8th edition pages 698, 699.

Hyperfocal Distance

H= F^2 / (f)(Cc)
F=focal length of lens
f=f-stop number
Cc=circle of confusion

Depth of Field

Near limit
(H)(S) / H+(S-F)

Far limit
(H)(S) / H-(S-F)

Where:
H=HYperfocal distance
S=Distance from camera to object
F=Focal length of lens

What is Depth of Field?

The distance range between between the nearest and farthest objects that appear to be in acceptably sharp focus in the image plane. Depth of field involves one image plane and the area between two target planes (in front of the lens).

What is Hyperfocal Distance?

The nearest object distance in sharp focus when the lens is focused on infinity. It varies with each F Number. When the lens is focused on that distance, everything from 1/2, the distance to the camera to infinity will be in sharp.

Depth of Field (DoF) is dependent upon the following variations:
a. The focal length of the lens.

b. The diaphragm opening (effective aperture).

c. The distance from the lens to the object that is focused on.

d. The distance from which the image is viewed.

e. The viewer's personal standard of the permissible degree of sharpness (or unsharpness).

Other variables in the formula remaining constant, it follows that:

a. The shorter the focal length of the lens, the greater the DOF.

b. The smaller the diaphragm opening (larger F Number), the greater the DOF.

c. The greater the distance to the object being focused on, the greater DOF.

d. The greater the distance from which the image is viewed, the great the "apparent" DOF.

e. An often used standard of acceptable sharpness is the reproduction in the image of a small point in the object plane by means of a "Circle of Confusion" or disc not greater than 1/100 of an inch. This is often expressed as 1/1000 of the focal length. Sometimes a figure of 1/300 of an inch or 1/3000 of the focal length is used.

At this point in the discussion the image size will not remain constant. If you change the focal length, in the above example, the subject (target size) will get larger or smaller depending on the change in focal length.

How do I apply this in the real world?

Much of what is written above is common practice for many of us. I want more depth of field so I increase my F Number to F11 or F22 or even higher. If I want less depth of field I lower the F Number and /or add Neutral Density filters and polarizer to reduce the light, thereby forcing the F Number lower (less depth of field).

Move the camera closer for less depth of field, further away for more. But if you zoom the lens at the same time (to maintain a constant subject size) the depth of field will stay the same. If the target size remains the same, by moving the camera all you have done is change perspective. In the real world (News Anchor at desk) the size of the head needs to remain the same size. As you move closer, to decrease DoF, image size increases, you decrease the focal length to maintain the same head size. The two variables (distance to subject and focal length) cancel themselves out (Law of Reciprocity).

What's all this I hear about 1/3 inch chips having more DoF than 16mm or 35mm film?

Just as the subject size (Target Size) can vary in the above paragraph, so can the size of the CCD or film stock. If the Target Size (News Anchors Head) in front of the lens is to remain the same size when we change chip sizes, DoF will change. Why, what happens when we change chip (format) sizes? If the focal length of the lens stays the same (100mm lens on 1/3 inch CCD, 100mm lens on 35mm film) Target Size (anchors head) will increase 7.2 times (chip is 7.2 times smaller). To maintain the same Target Size, lens to subject distance must be 7.2X greater or reduce the focal length 7.2X By either increasing the lens to subject distance or reducing the focal length, the DoF is increased. If all formula variables stay the same and the Target Size (CCD) behind the lens changes, DoF will not change. If the Target Size changes in front of the lens (change focal length or change camera to Target distance) DoF will Change.

Bring me back to the real world. What does all this mean to me? The real world is that under most conditions (TV set, product shots, speaker at podium) the subject must stay the same size. It stays the same size because of rules of composition, head room for subject, or the Art director says the box will be so big. The Art Director also wants less DoF. So you move the camera closer. Now the AD says the box is too big. So you zoom the lens wider to make the box smaller. Then the AD says hey, you got too much DoF again. By moving closer and zooming wider you cancelled out the change in DoF. Law of Reciprocity. The only effective way to reduce DoF and maintain the Target Size is to lower the F Number (F2.8, F2.0). In a well lit scene you will need to use ND filters.

I want to play with DoF and I don't have one of those cool Palms. How about a link?

http://www.dof.pcraft.com/dof.cgi

So, what is next? This is it. You may need to read it several times to really grasp it. I'm still having trouble, HELP. Reread both sets of A to E points above. Remember, in the A to E examples the Target Size will change. In the real world, Target Size usually stays the same.

Questions that may come up and I'll answer if anyone is interested, would concern Circle of Confusion (Cc) and proper viewing distance of a TV monitor. Cc is a formula variable that I did not discuss. Viewing distance affects "apparent" DoF.


Jeff Donald

[Chris Hurd]

Holy cow Jeff, this is so well done, many thanks. Perhaps we can add it to the website, along with your other lens articles, here in the very near future? This is great stuff, as always!

[Bill Ravens]

Well done, Jeff. Thanx.

[Chris Simmons]

THANK YOU!

It is very very helpful....

[Jeff Donald]

Thank you for the kind words. Dre..... emailed me a couple more interesting links http://www.shuttercity.com/DOF.cfm and http://www.bealecorner.com/trv900/dof.html The second link contains some generalizations that could be confusing. However, it covers some interesting material in regards to diffraction and small chip cameras. Diffraction could be my next topic like this if people are interested.

Jeff

[Barry Goyette]

Jeff

Thanks for posting your info on depth of field, I think it's of great help to both the neophyte and the more experienced among us to have this information. When you first posted the ACM data, I noticed that there is one factor missing that surprised me. In some ways, it is similar to (D) distance from which the image is viewed, but I think it is distinct, so I'll add it here

F) Freguency or resolution of the output medium.

I first noticed this back in college when playing with an obscure kodak special order film that later became known as technical pan. Using a homemade soup one was able to produce a negative that was virtually grainless...and one of the first things I noticed was that it had almost no depth of field (even at f16), especially when compared to the same image on triX (for non photographers, a much grainier film). In essence, all things being the same, the film itself actually affected the depth of field.

This effect can also be seen when one compares a photographic print with the same size image rendered with a 65 line litho screen (newsprint). The newsprint will show substantially more depth of field than the original higher resolution print.

As we move into the cinematography realm, this effect could in theory be seen in varying amounts between film stocks, although the result would probably be too subtle to notice. But in the digital realm it should be visible when switching between monitors of different resolution, given the input resolution is sufficient to cover the highest res monitor....One would probably see a difference between a SD monitor and an HD monitor if given the same HD signal. More dramatic would be to have 35mm film projected side by side with the same image on an SD monitor (at the same size).

While this effect is certainly more subtle (and less important) than issues of focal length and subject distance...it is probably on par with, or even more noticeable than "viewing distance".

Thanks again for the time and energy you put into this thread and the forum as a whole.

Cheers.

Barry

[Jeff Donald]

What your getting into is several factors that relate in one way or another to Circle of Confusion (E). Factors affecting Cc are human visual acuity, sharpness at DoF limits, diffraction, lens aberrations and film properties (and in the case of film, film flatness). Several of these factors can be measured with MTF (Modular Transfer Function).

MTF is not the same as grain. Grain is analogous to noise in video terms. MTF is more like bandwidth in video. The greater the bandwidth the greater the resolution. Resolution being the ability to distinguish line pairs per length (usually mm). Kodak has devised the Print Grain Index http://www.kodak.com/cluster/global/en/professional/support/techPubs/e58/e58.shtml Certainly grain and perceived sharpness go hand in hand.

In the early '80's I did a great deal of B & W photography with Agfa Pan 4x5 sheet film (ISO 25). It was exposed around F22 (diffraction limited) with Rodenstock APO lenses. Processing was done in Rodinal at 25:1 (if memory serves me) and virtually grainless negatives were obtained. My negatives show normal DoF and virtually grainless 8x10 prints. The answer to your lack of DoF may be in 35mm film flatness.

Jeff

[Aaron Koolen]

Jeff, I get that the Circle of Confusion is basically a fudge factor used to represent a number of traits of the equipment and media used to capture the image, but do you have any information on a break down of the CoC and the maths to go along with relavent, various factors?

Your information was excellent and got me to looking around for more into on DoF. Then just for fun and to cement things in my head a bit more, I ended up writing a small utility (PC Windows only at mo, until I learn java and stick it on a web page:) ) for calculating Depth of field, given certain inputs. There are quite a few utils like this around but my one shows a 2d, side on, view of Lens, object and far and near depth of field and is basically a "slider fest" where you drag ftop, distance, focal length sliders willy nilly and watch the DoF change, you can then select another camera (I have info for Gl2, Xl1s, 16x manual Xl1s, 3x Wide angle and a few others in there) and actually get to "See" what it means and how different the different cameras are. It was interesting to see the proof (Short of having the camera and adapter myself) that with the 3x Wide angle adapter on, the depth of field increases a lot. ANd in some settings the Gl2 had shallower far Depth of Field than the xl1s with standard lens as certain settings.

Anyway, I'll stick the utility up on a page soon (once I find one) for people to download and play with (And validate my maths ;) ), and I'm working on a Java version so that any platform with Java support will be able to use it.


Thanks again Jeff, great info.
Aaron


[edit] I'm still a bit lost on this Viewing Distance thing you're all talking about. I don't see how looking at a projected image from a different distance can alter DoF?

[Jeff Donald]

Aaron,

I'm glad the information proved helpful. The utility your designing sounds really cool. It'll be much more fun than the charts you plug numbers into. I hope you get it all worked out.

Circle of confusion is a whole topic in itself. I'll tackle this in the next couple of weeks. I have another long post due in another forum, first. The easiest way to think of viewing distance is the image on a billboard. When viewed up close, the image is clearly lacking apparent sharpness and appears to be low resolution (lacks detail). It looks out of focus. But when viewed from the proper distance the scene appears in focus. Take a small print, like an 8x10, and view it held just inches from your face. The image, again will not appear to have good sharpness and resolution. It looks out of focus. Now put the picture on the wall and stand back 5 or 6 feet and view the same print. Remarkable difference. All you did was change viewing distance.

Jeff

[Bill Ravens]

In theory, a perfect lens brings all incident light rays to an infinitely small point of light at the focal point. Since we all know theory is subject to the imperfections of a real physical world, lens polishing imperfections, inclusions, etc, we never really see an infinite point at the focal point. What we see is kind of a blurry circle. As kids, I'm sure most of us held a piece of paper under a lens aimed at the sun to try to set the paper on fire. Did you notice that you had to move the paper back and forth ever so little to try to find the smallest spot? Did you also notice that there was also a range in which the spot seemed to not change? This is an experiential definition of the circle of confusion and depth of field.

[Rob Lohman]

I'd love to see your program Aaron. If you want anyone to take
a look (I can't test your numbers, but I can test user interface
and such) please send it to visuar@iname.com. Thanks.

[Jeff Donald]

Aaron,

I missed the first part of your reply. Do you still need the math and figures for Cc? Some of it is just personal standards (you say the image is sharp, I say it is not or vice versa) but common figures used today are 1/300 and 1/500 of an inch. Anything smaller than your choosen standard, the human eye will perceive as a point (sharply focused) and anything larger is a circle that is perceived as unsharp.

Jeff

[Aaron Koolen]

Hi Jeff, I was just wondering if there is some way to break down the CoC rather than have a single "subjective" value? It's probably not a big deal but if I have more inputs into the CoC calculation I might be able to make my little utility a bit more accurate, and above all it will help me understand how this CoC is worked out.

Cheers
Aaron

[Bill Ravens]

CoC is a function of several things, some quantifiable, some not. The part that is not quantifiable is the eye to eye variations in what is perceived as out of focus.

Which Xl1 lens has the best depth of field