tvdpid
Member
You're right. But there is a difference between math and applied math. A year ago, I started to collect "things without batteries", like side rules, a leica iiig, an adiphot lightmeter...etc. I recently bought a small russian circular slide rule. You can call it a guessing disc if you want
. It slips easily in my pocket. It perfectly suits to do the Merklinger Math ... yesss ... .
David Hughes
David Hughes
A year ago, I started to collect "things without batteries", like side rules, a leica iiig, an adiphot lightmeter...etc. I recently bought a small russian circular slide rule. You can call it a guessing disc if you want
Well, I dunno about Merklinger maths but I still think you need to choose all tools carefully and so I'm happy to take a circular slide rule with me on holiday to do the currency conversions; very easy with a bit of sticky tape with an arrow on it marking the exchange rate but that's about the limit except for rough percentages. I guess it's a matter of the accuracy you want.
I also like the "no batteries required" and the fact that I can see if I've had the equivalent of finger trouble at a glance. And they don't suffer from sudden death like electronic things do. And you don't have to stand in the sunlight to use then but still...
Regards, David
PS Odd that here we abbreviate 'mathematics' to 'maths' and yet you use 'math' despite seeming to have other varieties, which we usually (well, in the '50's) called "pure" and "applied" maths.
tvdpid
Member
I think it's a Dutchification by my side ... although I am not Dutch
Maybe one writes "maths" just to exaggerate its difficulty ...
Roger Hicks
Veteran
Dear Richard,
His mathematics are however of the variety that involves light inextensible string, spheres of uniform density moving in a vacuum, and the like. As soon as you start to consider enlargement sizes and viewing distances, never mind visual acuity, his arguments rapidly lose the tiny amount of value they ever had.
Cheers,
R.
tvdpid
Member
Roger Hicks
Veteran
Dear Tom,
Put a picture on the wall. Any picture, any size, any distance.
Look at it from different distances.
(A poster in the street provides an excellent example).
See also Post 37, which refers to a direct admission that a lot of what matters has been ignored.
Cheers,
R.
mrmeadows
Established
@tvdpid
Merklinger first describes how lenses work, how circles-of-confusion arise and how those circles affect DOF. Then he presents a second way of thinking about the situation and these same factors. In his first chapters, he regards a lens as making a negative, and he shows how to compute the characteristics of that image. In the second way in later chapters, he imagines the lens as PROJECTING a negative into object space and analyses the projected image. That projected negative is taken to have the same circles-of-confusion that are associated with the lens settings in the first way. That is the focal length, f-stop and focused distance are the same. So the projection of that negative will magnify the circles-of-confusion into the projected scene, and these magnified circles-of-confusions become Merklinger's disks-of-confusion, and he proceeds to calculate and interpret them. When he describes this second way, it is not correct to interpret that he "completely leaves the theories and ideas about any circle of confusion." Metaphorically speaking, he is considering the "other side of the coin." He imagines running the light backwards, and he hopes that doing so will be a useful alternative way of understanding how things work. The circles-of-confusion and their consequences are entirely governed by physical optics, they are always present and relevant, and there is no way to circumvent them. All one can do is to strive for the best (personal) way of thinking about and understanding the situation, and he offers another perspective in his second way.
I believe that one of the greatest problems with expositions of lenses, CoC and DOF (including Merklinger's and all others that I have seen) resides in how all the explanations confuse four conceptually different circles: they use the same name, the circle-of-confusion, for all four of these different circles. Using the same name for all, this conflation makes all those explantions confusing to many people, and it leads to seemingly endless misunderstandings and arguments. The four different circles are the following. There are, first and foremost, the "circles-on-the-negative" that lenses produce from objects. These circles exist in different sizes for objects at different distances from the lens. Second, there are the "circles-on-the-print" that are produced when the "circles-on-the-negative" are magnified to make the print. Third, there is the "smallest-observable-circle-on-the-print" that one can actually resolve when one looks at the print. Fourth and finally, there is the size of the "smallest-observable-circle-on-the-negative" which is the DE-magnified size of the "smallest-observable-circle-on-the-print". The first two of these circles are related in size by the print magnification. The third and fourth circles are again related in size by the print magnification. The sizes of the first, second and fourth circles are determined by physical optics. The size of the third circle is jointly determined by the magnification of the negative, by the visual acuity of the viewer and by the viewing distance.
Strictly speaking, it is only the size of the fourth circle that should be called the circle-of-confusion and which should be involved in determining DOF. After all, if you can resolve an object's circle in a print, then you will perceive it as out-of-focus; if you can't resolve its circle, then it will appear in-focus, and it will be within the DOF for that print and under those viewing conditions. This fourth circle is dividing line between "circles-on-the-negative" that you can see in the print and those that you can't and it determines the DOF. It is also the circle that lens manufacturers like Leica and Zeiss, etc employ and for which they specify a value when they determine by calculations where to put the DOF marks on their lenses. Not every manufacturer uses the exact same value for this fourth circle, but every one uses a value which is close to one-thirtieth of a millimeter. Unfortunately, the manufacturers don't often tell us what they've done when they publish DOF tables/graphs in their lens data sheets.
When Merklinger introduces his "disk-of-confusion" he is introducing a fifth circle which I described above. I don't find Merklinger's fifth circle to be useful, but that doesn't make it wrong. It is completely consistent with optical physics, and other readers may find it revelatory.
Merklinger wrote before the advent of digital technology, and he wrote almost entirely about the situation for 35mm full-frame negatives. The principles and results he discusses apply without sigificant changes to full-frame digital sensors. However, many people now use APS-C sized digital sensors which are 2/3 the linear dimensions of full-frame, and considering those requires some adjustments. In particular, Merklinger's results assume three things about a print: 1) the print size will be 8x10inch (20x25cm); 2) the magnification will be about 8x; 3) the viewing distance will be 250mm. But an 8x magnification from an APS-C image will produce only a 5.3x6.67inch print. On this print, the standard, one-thirtieth mm, circle-of-confusion will just be observable, so the DOF will match that from a full-frame sensor's identical circle-of-confusion when both are viewed from 250mm. The APS-C sensor will require a 12x magnification to produce an 8x10 print. In that case, the one-thirtieth mm circle-of-confusion will be 1.5x bigger than expected and will be easily visible. The "smallest-observable-circle-on-the-print" will be smaller, the corresponding "smallest-observable-circle-on-the-negative" will be smaller. Since one will be seeing smaller circles in the print, the DOF of this APS-C print will consequently be less than Merklinger calculates. The lesson from this is that using an APS-C sensor requires one to work with a circle-of-confusion that is 2/3 the size (2/3 * 1/30mm = 1/45mm) that Merklinger has assumed. Merklinger's equations all still apply to the APS-C sensor, but one must change the values of one or more of the values he assumes to get valid results. That is hard to accomplish in detail, because he has suppressed the relevant variables by assuming them to take the standard values appropriate only to full-frome negatives/sensors, just as the DOF marks on lenses are made using those same assumptions. But one has two easy choices available: one can take his result liteally by considering 1) 5.3x6.67inch prints from APS-C sensors; 2) 8x10inch prints but substitute 1/45mm for the circle-of-confusion everywhere in his discussion. Interpreting the DOF marks on lenses for the APS-C world involves detail that Merklinger has suppressed, so it is a complicated subject for another day.
--- Mike
Merklinger first describes how lenses work, how circles-of-confusion arise and how those circles affect DOF. Then he presents a second way of thinking about the situation and these same factors. In his first chapters, he regards a lens as making a negative, and he shows how to compute the characteristics of that image. In the second way in later chapters, he imagines the lens as PROJECTING a negative into object space and analyses the projected image. That projected negative is taken to have the same circles-of-confusion that are associated with the lens settings in the first way. That is the focal length, f-stop and focused distance are the same. So the projection of that negative will magnify the circles-of-confusion into the projected scene, and these magnified circles-of-confusions become Merklinger's disks-of-confusion, and he proceeds to calculate and interpret them. When he describes this second way, it is not correct to interpret that he "completely leaves the theories and ideas about any circle of confusion." Metaphorically speaking, he is considering the "other side of the coin." He imagines running the light backwards, and he hopes that doing so will be a useful alternative way of understanding how things work. The circles-of-confusion and their consequences are entirely governed by physical optics, they are always present and relevant, and there is no way to circumvent them. All one can do is to strive for the best (personal) way of thinking about and understanding the situation, and he offers another perspective in his second way.
I believe that one of the greatest problems with expositions of lenses, CoC and DOF (including Merklinger's and all others that I have seen) resides in how all the explanations confuse four conceptually different circles: they use the same name, the circle-of-confusion, for all four of these different circles. Using the same name for all, this conflation makes all those explantions confusing to many people, and it leads to seemingly endless misunderstandings and arguments. The four different circles are the following. There are, first and foremost, the "circles-on-the-negative" that lenses produce from objects. These circles exist in different sizes for objects at different distances from the lens. Second, there are the "circles-on-the-print" that are produced when the "circles-on-the-negative" are magnified to make the print. Third, there is the "smallest-observable-circle-on-the-print" that one can actually resolve when one looks at the print. Fourth and finally, there is the size of the "smallest-observable-circle-on-the-negative" which is the DE-magnified size of the "smallest-observable-circle-on-the-print". The first two of these circles are related in size by the print magnification. The third and fourth circles are again related in size by the print magnification. The sizes of the first, second and fourth circles are determined by physical optics. The size of the third circle is jointly determined by the magnification of the negative, by the visual acuity of the viewer and by the viewing distance.
Strictly speaking, it is only the size of the fourth circle that should be called the circle-of-confusion and which should be involved in determining DOF. After all, if you can resolve an object's circle in a print, then you will perceive it as out-of-focus; if you can't resolve its circle, then it will appear in-focus, and it will be within the DOF for that print and under those viewing conditions. This fourth circle is dividing line between "circles-on-the-negative" that you can see in the print and those that you can't and it determines the DOF. It is also the circle that lens manufacturers like Leica and Zeiss, etc employ and for which they specify a value when they determine by calculations where to put the DOF marks on their lenses. Not every manufacturer uses the exact same value for this fourth circle, but every one uses a value which is close to one-thirtieth of a millimeter. Unfortunately, the manufacturers don't often tell us what they've done when they publish DOF tables/graphs in their lens data sheets.
When Merklinger introduces his "disk-of-confusion" he is introducing a fifth circle which I described above. I don't find Merklinger's fifth circle to be useful, but that doesn't make it wrong. It is completely consistent with optical physics, and other readers may find it revelatory.
Merklinger wrote before the advent of digital technology, and he wrote almost entirely about the situation for 35mm full-frame negatives. The principles and results he discusses apply without sigificant changes to full-frame digital sensors. However, many people now use APS-C sized digital sensors which are 2/3 the linear dimensions of full-frame, and considering those requires some adjustments. In particular, Merklinger's results assume three things about a print: 1) the print size will be 8x10inch (20x25cm); 2) the magnification will be about 8x; 3) the viewing distance will be 250mm. But an 8x magnification from an APS-C image will produce only a 5.3x6.67inch print. On this print, the standard, one-thirtieth mm, circle-of-confusion will just be observable, so the DOF will match that from a full-frame sensor's identical circle-of-confusion when both are viewed from 250mm. The APS-C sensor will require a 12x magnification to produce an 8x10 print. In that case, the one-thirtieth mm circle-of-confusion will be 1.5x bigger than expected and will be easily visible. The "smallest-observable-circle-on-the-print" will be smaller, the corresponding "smallest-observable-circle-on-the-negative" will be smaller. Since one will be seeing smaller circles in the print, the DOF of this APS-C print will consequently be less than Merklinger calculates. The lesson from this is that using an APS-C sensor requires one to work with a circle-of-confusion that is 2/3 the size (2/3 * 1/30mm = 1/45mm) that Merklinger has assumed. Merklinger's equations all still apply to the APS-C sensor, but one must change the values of one or more of the values he assumes to get valid results. That is hard to accomplish in detail, because he has suppressed the relevant variables by assuming them to take the standard values appropriate only to full-frome negatives/sensors, just as the DOF marks on lenses are made using those same assumptions. But one has two easy choices available: one can take his result liteally by considering 1) 5.3x6.67inch prints from APS-C sensors; 2) 8x10inch prints but substitute 1/45mm for the circle-of-confusion everywhere in his discussion. Interpreting the DOF marks on lenses for the APS-C world involves detail that Merklinger has suppressed, so it is a complicated subject for another day.
--- Mike
bmattock
Veteran
Likewise, I am not interested in doing the math.
However, I am interested in taking creative control of my photography in areas I care about.
Lots of people do this, although they do not usually describe it this way.
We talk about composition. We talk about framing.
We talk about exposure and focus.
Then we go further and talk about various films, processing, focal lengths and lens formulae and even about aperture leaf shape and the 'bokeh' they produce. All part of the creative control many of us seek.
Not everyone is interested in all these things. And that's perfectly OK of course.
But the point here, I think is that in the realm of producing the photograph we want, under our control to the extent that we can manage it, we can take more control than might otherwise have been considered acceptable.
I have long argued that 'correct' exposure is the exposure one intends, not simply a formulae or a zone or a chart in a book somewhere. If I intend to expose a photograph a certain way, it's correct if that's what I wanted to do. There is no universal 'correct exposure', although of course the usual exposure is generally preferable for most people, which is why it is the usual one.
This author appears to be taking the same approach to focus and depth-of-field. Rather than taking a standard formulae for DOF and the like, he has created his own way of setting focus to suit his own sensibilities, and suggested that it might be a way others would want to consider as well.
Although I am not likely to sit down and do the math regarding circles of confusion and all of that, I am appreciative of what he is trying to accomplish.
pyeh
Member of good standing
Mike mrmeadows, thank you for your clear exposition on Merklinger. Most useful.
And bmattock, thank you for graciously tidying up some of the narky posts above.
And bmattock, thank you for graciously tidying up some of the narky posts above.
David Hughes
David Hughes
Hi,
If it's anything to anyone, my thinking goes like this; I am never going to print/enlarge above 8" x 12" and so this works for me.
Others never go above 4" x 6" and these are the people who are happiest without any maths or worries.
And somewhere in between are the rest of us.
There's also a few doing posters and slides and I'm happy to let them worry themselves to bits. BTW, they can avoid a lot of worries by using a tripod &c and the DoF scale on the lens but going one aperture beyond what it tells them.
Regards, David
If it's anything to anyone, my thinking goes like this; I am never going to print/enlarge above 8" x 12" and so this works for me.
Others never go above 4" x 6" and these are the people who are happiest without any maths or worries.
And somewhere in between are the rest of us.
There's also a few doing posters and slides and I'm happy to let them worry themselves to bits. BTW, they can avoid a lot of worries by using a tripod &c and the DoF scale on the lens but going one aperture beyond what it tells them.
Regards, David
Richard G
Veteran
Thank you.
Roger Hicks
Veteran
Start with an average visual acuity of about 1 second of arc. This is roughly equivalent to a black human hair on a white tile at 10 feet/3 metres. It's still only an average, of course, and may well rely on visual correction (glasses) to accomplish.
As soon as you think of it this way, the utter nonsense of ignoring viewing distances is revealed. Stipulating a fixed viewing distance does not answer this objection: it merely simplifies it to near-uselessness.
Next consider a contact print of a negative of that hair, where the hair is life-sized in the negative.
Next consider an optical print or projected image on which the hair is (a) life-sized, printed 1:1 (b) 1/10 life size, enlarged 10x (c) 10x life size, reduced to 1/10. Reflect upon the difference that the quality of both the taking lens and the enlarging/projecting lens may make. Substitute "scanner quality" for the latter if you wish.
This is before we start to consider the subject matter or aesthetic preferences.
Perhaps more people will now be able to understand what I said about looking for more precision than exists in the system.
I was writing in Shutterbug at the same time as Merklinger, and I never had much time for his arguments then, because I had already thought a great deal about the nature of depth of field after reading the second-of-arc argument in Miniature and Precision Cameras, Lipinski, 1955.
Cheers,
R.
As soon as you think of it this way, the utter nonsense of ignoring viewing distances is revealed. Stipulating a fixed viewing distance does not answer this objection: it merely simplifies it to near-uselessness.
Next consider a contact print of a negative of that hair, where the hair is life-sized in the negative.
Next consider an optical print or projected image on which the hair is (a) life-sized, printed 1:1 (b) 1/10 life size, enlarged 10x (c) 10x life size, reduced to 1/10. Reflect upon the difference that the quality of both the taking lens and the enlarging/projecting lens may make. Substitute "scanner quality" for the latter if you wish.
This is before we start to consider the subject matter or aesthetic preferences.
Perhaps more people will now be able to understand what I said about looking for more precision than exists in the system.
I was writing in Shutterbug at the same time as Merklinger, and I never had much time for his arguments then, because I had already thought a great deal about the nature of depth of field after reading the second-of-arc argument in Miniature and Precision Cameras, Lipinski, 1955.
Cheers,
R.
tvdpid
Member
Thanks mrmeadows & bmattock.
Every theory has its value.
My brother who has little experience in photography recently asked me if there is an easy way to get an idea of the DOF. He doesn't have any lens with a DOF-scale and he "is not much into apps" etc. Merklingers formulas were very useful to explain how things work ...
Kind regards,
Tom