Talk:Hyperfocal distance

Question of Definition
Q: Can anyone provide a source for the second definition? I've never heard of it before, and what's more, the difference is NOT subtle, especially as you get tighter apertures and longer lenses. Thanks! Girolamo Savonarola 22:39, 27 April 2006 (UTC)

A: Yes, both definitions are common throughout twentieth-century books on photography and optics. For example, the Manual of Photography, formerly the Ilford Manual of Photography, used the second definition in several editions through Sidney Ray's chapter in the 1978 seventh edition. See these: By the way, in his 1979 book The Photographic Lens, Ray uses both versions, and makes an interesting observation that simplifies DOF calculations to a simple discrete set of easy-to-remember overlapping focus ranges: "When a lens is focused on infinity, the value of Dn is the 'hyperfocal distance' H. When the lens is focused on distance H, the depth of field extends from infinity to H/2.; and when focused on H/3 extends from H/2 to H/4 and so on.  This concept simplifies the depth of field equations considerably." This same observation is in Mortimer (1938), Sinclair (1913), and Piper (1901). Sinclair credits Piper with the idea; Piper calls it "consecutive depths of field" and shows how to easily test the idea. Girolamo, I see you've added this observation yourself; it only makes sense to the extent that you accept that the two definitions are approximately equivalent, or if you measure distance from one F.L. in front of the front principal plane.
 * Ralph E. Jacobson, The Manual of Photography, seventh edition, London: Focal House, 1978; see chapter "The Geometry of Image Formation" by Sidney F. Ray, pp. 80–83.
 * Alan Horder, The Manual of Photography, sixth edition, London: Focal House, 1971.
 * Alan Horder, The Ilford Manual of Photography, fifth edition, Essex: Ilford Ltd, 1958.
 * James Mitchell, The Ilford Manual of Photography, fourth edition, London: Ilford Ltd., 1949.


 * C. Welborne Piper, A First Book of the Lens: An Elementary Treatise on the Action and Use of the Photographic Lens, London: Hazell, Watson, and Viney, Ltd., 1901.

More notes about Piper from my historical studies:

Piper may be the first to have published a clear distinction between "Depth of Field" in the modern sense and "Depth of Definition" in the focal plane, and implies that "Depth of Focus" and "Depth of Distance" are sometimes used for the former. He uses the term "Depth Constant" for H, and measures it from the front principal focus (i. e., he counts one focal length less than the distance from the lens to get the simpler formula), and even introduces the modern term, "This is the maximum depth of field possible, and H + f may be styled the distance of maximum depth of field. If we measure this distance extra-focally it is equal to H, and is sometimes called the hyperfocal distance.  The depth constant and the hyperfocal distance are quite distinct, though of the same value." I’m not sure I appreciate the distinction. By Table I in his appendix, he further notes, "If we focus on infinity, the constant is the focal distance of the nearest object in focus. If we focus on an extra-focal distance equal to the constant, we obtain a maximum depth of field from approximately half the constant distance up to infinity.  The constant is then the hyper-focal distance."

I have not found the term hyperfocal before Piper, nor hyper-focal which he also used, but he obviously did not claim to coin this descriptor himself.

Johnson 1909 also uses the second definition very explicitly:

"Thus if a lens which is focused for infinity still gives a sharp image for an object at 6 yards, its depth of field is from infinity to 6 yards, every object beyond 6 yards being in focus. This distance (6 yards) is termed the hyperfocal distance of the lens, and any allowable confusion disc depends on the focal length of the lens and on the stop used. If the limit of confusion of half the disc (i.e. e) be taken as 1/100 in., then the hyperfocal distance H = Fd/e, d being the diameter of the stop, ..." I believe he has a factor-of-two error here in using a COC radius instead of diameter.


 * George Lindsay Johnson, Photographic Optics and Colour Photography, London: Ward & Co., 1909.

The better question might be: when did the first definition first get articulated? Dicklyon 00:23, 28 April 2006 (UTC)

ps. I just noticed that I had already put a lot of this info in the history section. See for example what I said about Kingslake 1951, and the nineteenth-century precursors to hyperfocal distance.


 * The overwhelming comprehensiveness is astounding. Look forward to seeing many of your future edits. One small piece of advice - the article would like a lot cleaner with standard Wikipedia-format footnotes. Also, avoid referring to yourself; this includes your personal research. Sources are what we want. Otherwise, wonderful job. Thanks much! Girolamo Savonarola 20:13, 28 April 2006 (UTC)


 * Thanks for the comments. I'd appreciate some help with the references, since I'm pretty new at Wiki syntax.  Feel free to do it right and I'll follow your lead in the future.  As to the comment where I said basically "as far as I know", I didn't see a good alternative under the circumstances.  Your change claims that Piper 1901 is "among the earliest" uses of Hyperfocal, but it's hard to know that for sure without a lot more research.  Is there a good way to say this is what I've found, without making a firm statement as to what is true? And how can your statement be backed up by a source, if the only source is me?  I know this wikipedia is not supposed to be a place to public original research, but where's the line? Dicklyon 20:50, 28 April 2006 (UTC)


 * By the way, I just noticed that your favorite movie technical reference, Camera Assistant, The: A Complete Professional Handbook by Hart acknowledges both definitions on p.205. And a lot of what is says about depth of focus is really not quite right; see my edits there.

extends from H/2 to H/4 and so on. This concept simplifies the depth of field equations considerably." This same observation is in Mortimer (1938), Sinclair (1913), and Piper (1901).  Sinclair credits Piper with the idea; Piper calls it "consecutive depths of field" and shows how to easily test the idea.  Girolamo, I see you've added this observation yourself; it only makes sense to the extent that you accept that the two definitions are approximately equivalent, or if you measure distance from one F.L. in front of the front principal plane.


 * C. Welborne Piper, A First Book of the Lens: An Elementary Treatise on the Action and Use of the Photographic Lens, London: Hazell, Watson, and Viney, Ltd., 1901.

More notes about Piper from my historical studies:

Piper may be the first to have published a clear distinction between "Depth of Field" in the modern sense and "Depth of Definition" in the focal plane, and implies that "Depth of Focus" and "Depth of Distance" are sometimes used for the former. He uses the term "Depth Constant" for H, and measures it from the front principal focus (i. e., he counts one focal length less than the distance from the lens to get the simpler formula), and even introduces the modern term, "This is the maximum depth of field possible, and H + f may be styled the distance of maximum depth of field. If we measure this distance extra-focally it is equal to H, and is sometimes called the hyperfocal distance.  The depth constant and the hyperfocal distance are quite distinct, though of the same value." I’m not sure I appreciate the distinction. By Table I in his appendix, he further notes, "If we focus on infinity, the constant is the focal distance of the nearest object in focus. If we focus on an extra-focal distance equal to the constant, we obtain a maximum depth of field from approximately half the constant distance up to infinity.  The constant is then the hyper-focal distance."

I have not found the term hyperfocal before Piper, nor hyper-focal which he also used, but he obviously did not claim to coin this descriptor himself.

Johnson 1909 also uses the second definition very explicitly:

"Thus if a lens which is focused for infinity still gives a sharp image for an object at 6 yards, its depth of field is from infinity to 6 yards, every object beyond 6 yards being in focus. This distance (6 yards) is termed the hyperfocal distance of the lens, and any allowable confusion disc depends on the focal length of the lens and on the stop used. If the limit of confusion of half the disc (i.e. e) be taken as 1/100 in., then the hyperfocal distance H = Fd/e, d being the diameter of the stop, ..." I believe he has a factor-of-two error here in using a COC radius instead of diameter.


 * George Lindsay Johnson, Photographic Optics and Colour Photography, London: Ward & Co., 1909.

The better question might be: when did the first definition first get articulated? Dicklyon 00:23, 28 April 2006 (UTC)

ps. I just noticed that I had already put a lot of this info in the history section. See for example what I said about Kingslake 1951, and the nineteenth-century precursors to hyperfocal distance.


 * The overwhelming comprehensiveness is astounding. Look forward to seeing many of your future edits. One small piece of advice - the article would like a lot cleaner with standard Wikipedia-format footnotes. Also, avoid referring to yourself; this includes your personal research. Sources are what we want. Otherwise, wonderful job. Thanks much! Girolamo Savonarola 20:13, 28 April 2006 (UTC)


 * Thanks for the comments. I'd appreciate some help with the references, since I'm pretty new at Wiki syntax.  Feel free to do it right and I'll follow your lead in the future.  As to the comment where I said basically "as far as I know", I didn't see a good alternative under the circumstances.  Your change claims that Piper 1901 is "among the earliest" uses of Hyperfocal, but it's hard to know that for sure without a lot more research.  Is there a good way to say this is what I've found, without making a firm statement as to what is true? And how can your statement be backed up by a source, if the only source is me?  I know this wikipedia is not supposed to be a place to public original research, but where's the line? Dicklyon 20:50, 28 April 2006 (UTC)


 * By the way, I just noticed that your favorite movie technical reference, Camera Assistant, The: A Complete Professional Handbook by Hart acknowledges both definitions on p.205. And a lot of what is says about depth of focus is really not quite right; see my edits there.

Q: Why no photographic examples? The equations might super accurate for boffins, but an actual image using hyperfocal distance would be useful for anyone else. —Preceding unsigned comment added by 122.57.158.218 (talk) 22:14, 8 May 2011 (UTC)

A: It's a very hard concept to illustrate in a photo on a screen. What would you use as the CoC? How would you clue in the veiwer what CoC you consider to represent sharp enough? Dicklyon (talk) 23:06, 8 May 2011 (UTC)

Consecutive depths of field
It would appear that this phenomenon holds only for the approximate formulae for DOF:


 * $$D_{\mathrm N} \approx \frac {H s} {H + s}$$


 * $$D_{\mathrm F} \approx \frac {H s} {H - s}$$

If $$s = H/a,$$


 * $$D_{\mathrm N} \approx \frac {H (H/a)} {H + H/a} = \frac {H} {a + 1}$$


 * $$D_{\mathrm F} \approx \frac {H (H/a)} {H - H/a} = \frac {H} {a - 1}$$

This does not work for the &ldquo;exact&rdquo; formulae


 * $$D_{\mathrm N} = \frac {H s}{H + ( s - f )}$$


 * $$D_{\mathrm F} = \frac {H s}{H - ( s - f )},$$

so it would seem to break down as the subject distance approaches the lens focal length.

Does Piper shed any light on this? JeffConrad 02:51, 29 August 2006 (UTC)


 * No, I think he was just working in the approximate regime. I'll look it up again tomorrow; he's at work.  You can read the rest of my notes from Piper in my DOF draft paper: . Dicklyon 02:58, 29 August 2006 (UTC)


 * Sorry, new here, I really need more information on the Mathematical phenomenon "Piper (1901) calls this phenomenon "consecutive depths of field" and shows how to test the idea easily". there is no citation, I've searched thoroughly for his work, and I need to see how he tested the idea urgently. If this is the wrong place to ask this can you tell me? in that case message me Hans.thm@gmail.com thanks. — Preceding unsigned comment added by 182.18.209.5 (talk) 09:05, 21 April 2013 (UTC)

Help for the layman
This is a fine article, but it's focused primarily on the optics of hyperfocal distance, complete with heavy-duty math. In film school, I was taught that at the hyperfocal distance setting the lens would deliver acceptable sharpness from half the hyperfocal distance to infinity. Many lenses then had the hyperfocal distance marked on the focus ring. More generally, can we do anything to make some of this article more accessible to the curious layman/photographer?Jim Stinson (talk) 00:21, 19 May 2014 (UTC)


 * Very old comment but ten years later, I must concur - this article is still a bit of a mess from the practical photographer's perspective. Not to suggest this is the only audience that should be served here, but I think we can safely assume they are a sizable share of the readership. The most glaring issue I see is the definition in the intro:
 * As @Jim Stinson notes, the formulae and practical application indicate that the hyperfocal distance actually represents the center of a range which will be in acceptable focus, with the far end at infinity. While the lens should be focused at this distance to achieve the "hyperfocal distance", the nearest distance which will be in "acceptable" focus is represented by the near end of that range. If that is in fact always 1/2 the hyperfocal distance I'm not sure, I'll defer to the math aficionados who seem to have a strong presence on this article. Walkersam (talk) 20:17, 13 March 2024 (UTC)
 * As @Jim Stinson notes, the formulae and practical application indicate that the hyperfocal distance actually represents the center of a range which will be in acceptable focus, with the far end at infinity. While the lens should be focused at this distance to achieve the "hyperfocal distance", the nearest distance which will be in "acceptable" focus is represented by the near end of that range. If that is in fact always 1/2 the hyperfocal distance I'm not sure, I'll defer to the math aficionados who seem to have a strong presence on this article. Walkersam (talk) 20:17, 13 March 2024 (UTC)

Accuracy and Usefulness of the Diagrams
I was away from home and needed to see the formula for hyperfocal distance without deriving it. The formulae here are correct, but the diagrams do not support the derivations. You can find a mathematically accurate derivation for depth of field with these definitions for the hyperfocal distance in Prais, Michael G., Photographic Exposure Calculations and Camera Operation, (North Charleston, South Carolina: BookSurge Publishing, ISBN 978-1-4392-0641-6 ) 2008, pp 285-297.


 * Diagram 1 simply shows the position in image space of the arrow in subject space.
 * Placing an ellipse that is twice the height of the image of the arrow in subject space does not provide any connection to a circle of confusion.
 * The statement "Here, objects at infinity with a circle of confusion ..." is incorrect because subjects (arrows) at infinity would appear in image space at the image focal length.
 * Further, objects do not have a circle of confusion: The diameter of the circle of confusion is a property of the camera (lens, aperture, sensor, and their motion).
 * Note that it is inappropriate to use "circle of confusion" as a value or measurement: "Circles" are figures. It is the "diameter of a circle (of confusion)" that is the value that should appear in equations. (Equations show the relationships between values--not figures.)
 * Diagram 2 simply shows the position in image space of the arrow in subject space a little closer to camera (further from infinity).
 * Placing an ellipse at the image focal distance does not signify anything.
 * In both diagrams H is simply a distance in subject space: There is nothing significant about it that would allow you to say that it is the hyperfocal distance.
 * In both equations you have made the restrictive and unnecessary assumption that the arrow in subject space is half the height of the aperture.
 * These derivations fail to provide a functional definition for (the diameter of) the circle of confusion. The diameter must be connected to a (Nyquist) spatial frequency.
 * The definition of the hyperfocal distance is a convenience that comes out of the derivation of the near and far extents of the field of focus and their difference, the depth of the field of focus. That derivation depends upon where those extents are in focus compared to the point of focus of a subject between them and on a definition of the diameter of a circle of confusion, which is a simple function of the resolution of the camera.
 * The diameter of the circle of confusion (diameter of confusion, for short) is the minimum distance over which detail in the subject can be resolved at the point of focus. Comparing the spread of the subject in focus at points nearer to and farther from the lens is what produces the field of focus equations.
 * The far extent of the field of focus is given by an equation with a denominator (f^2/Adc) - (us - f), where dc is the diameter of confusion. When this denominator becomes zero, let's say at and beyond us = uh (by our definition, the "hyperfocal distance"), the far extent of the field of focus and the depth of field become infinite (that is, an extremely large number). So, (f^2/Adc) - (uh - f) = 0 can be rewritten with the hyperfocal distance as uh = (f^2/Adc) - f.
 * The calculation of the near and far extents of the field of focus depends on the similar triangles created by lines from the edges (maximum extent) of the aperture passing through the point in image space at which a alternate subject nearer to or farther from the lens than the actual subject is in focus and passing through the diameter of confusion of the camera at the point in image space at which the actual subject is in focus. (That's a mouthful that is easier to recognize with the diagrams in the book referenced above.)
 * While one can do the derivation for points in focus on the lens axis, this includes an unnecessary assumption, and the more general situation produces diagrams that are probably more helpful to the viewer.

You would be better served to point to the accurate formula of the hyperfocal distance uh (as you do), to say that using h = f^2/Adc = Daf/dc simplifies the depth of field equation to uf - un = 2hus(us - f)/[h^2 - (us - f)^2], to say that in most situations, the focal length is much, much smaller than (negligible to) the subject distance and the hyperfocal distance, so that the depth of field equation reduces in approximation to uf - un ~ 2hus^2/(h^2 - us^2) and the hyperfocal distance reduces in approximation to uh ~ h = f^2/Adc. The derivation and explanation of all this can be found in the referenced book.

us = subject distance un = near extent of the field of focus uf = far extent of the field of focus uf - un = depth of (the) field (of focus) uh = hyperfocal distance h = approximate hyperfocal distance Da = aperture diameter A = aperture number (f/Da) f = focal length dc = diameter of confusion

Please let me know should you have any questions or comments. Thanks.

Mgprais (talk) 23:21, 28 June 2015 (UTC)

Hyperfocal distance for dummies.
I would like to add a section with a diagram explaining how and why photo- and cinematographers can easily understand and utilize the concept. This article is beautifully done, but could frighten away innumerate readers.Jim Stinson (talk) 23:53, 1 September 2016 (UTC)Anyone Anyone?, anyone?, Buhler?...

Definition of brown ellipse
Is it really right in derivation of hyperfocal distance formula (2.) to have the brown ellipse drawn with a center coinciding with the optical axis? Check raytracing to lower part of aperture. What do you think? Any suggestions? 195.37.236.14 (talk) 15:42, 1 July 2022 (UTC)