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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.
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.
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.
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.
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.
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.
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)
It would appear that this phenomenon holds only for the approximate formulae for DOF:
If
This does not work for the “exact” formulae
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)
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)
hyperfocal distance is a distance from a lens beyond which all objects can be brought into an "acceptable" focus.
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.
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)
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?...
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)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
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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.
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.
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.
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.
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.
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.
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)
It would appear that this phenomenon holds only for the approximate formulae for DOF:
If
This does not work for the “exact” formulae
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)
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)
hyperfocal distance is a distance from a lens beyond which all objects can be brought into an "acceptable" focus.
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.
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)
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?...
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)