cc vs. lp/mm as it relates to hyperfocal distance

[bglick]

The basic tried and tested HYPERFOCAL formula needs to have a desired min. circle of confusion (cc) value entered to calc. the hyperfocal distance. However, most all the photographic world since the early 1900's discuss resolution in lp/mm. So if you know the min lp/mm you want to enter into the DOF equation, how do you convert from lp/mm to cc? Using QT's excellent post on this site, I took the diffraction limited values of both and backtracked the mathematical relationship between lp/mm and airy disc diam (cc), as I assume diffraction limited values produce only one resolution. And Diffraction seems to be a "common demonimantor" that pulls the two "units of measure" together, whereas we know the values must be equal.

fstop resolution limit.

N - R (lp/mm) - d (mm)

11 - 136 .014

16 - 93 - .021

22 - 68 - .029

32 - 46 - .042

45 - 33 - .059

64 - 23 - .085



Assuming these are equal values, the formula, 1/lp/mm * 2 would covnert lpmm to cc values. So if one wanted a min. of 23 lp/mm to record on film (leaving out 1/R and other issues for now) would the proper cc value entered into the hyperfocal formula be equal to

1 / 23 * 2 = .085

TYIA

[paulr]

"However, most all the photographic world since the early 1900's discuss resolution in lp/mm."

Since the 1970s or so, all the lens and film manufacturers started using the much more involved MTF measurements, since it's been shown that lp/mm measurements rarely correlate with how sharp a picture looks.

If you want to know how circle of confusion size correlates with MTF, I can only imagine that there's no simple answer.

[Witold Grabiec]

My own word of caution on cc vs. HD:

Work with any numbers you like, but keep in mind that all these calculations are purely theorethical and WILL not yeild the results you expect. .

What is resolved by one eye, it will NOT be by another. Your final desired effect will thus be on the money for some viewers and way off for others. Add to that how the viewing distance will affect the perceived "sharpness" of an image and you've got a formula for disaster. In other words: stick to published (read average) tables on Hyperfocal Distance / Depth of Field and more viewers will see what you see than with any other approach.

[robc]

you have forgotten to include the consideration of enlargement unless it is included in your desired lp/mm on film.

the often quoted figure of 0.1 mm coc for large format is a joke if you are aiming for a 20x16 print from a 4x5 negative, so yes you do need something better but what.

My personal rule of thumb (not as scientific as some but usually good enough) is that diffraction limited means the point at which diffraction due to the aperture edge becomes more significant than other lens aberations. This usually occurs where the physical aperture diameter is around 5 to 7mm. Working back from your lens focal length you can calculate the aperture at which the diameter will be 5 to 7 mm. This aperture gives the maximum lp/mm. Whether that gives the optimum depth of field is determined by the subject, bearing in mind that optimum dof is not necessarily the same as maximum lp/mm. Dof requirements usually overide lp/mm in importance for most landscape subjects since the aperture giving max lp/mm often provides too little dof.

[bglick]

> since it's been shown that lp/mm measurements rarely correlate with how sharp a picture looks.

Well, today, it is still the best and easiest method of objective comparison. Of course, it does not account for the many variables that can effect the results of a test.

> but keep in mind that all these calculations are purely theorethical and WILL not yeild the results you expect.

For diffraction limited lp/mm values (which is not the basis of my question), if you check chris Perez lens test of Modern glass, it turns out, these lenses, such as M7 in normal fl range, are mostly aperture diffraction limited! This demonstrates how much of other abberations have been removed from lenses through the years. Older lenses are limited by other forms of optical diffraction, as you will see by his test results. A Schneider optical engineer explained there is 5 forms optical diffraction for photographic lenses. Its my guess, these forms of optical diffraction have been tamed through the years and of course aperture diffraction will never be controlled, as it is true limitation.

As for the modern lenses, the diffraction limited values he acheived on film, even after running them through 1/R, produce values which are almost dead-on to where one would expect.... mostly in the center readings. This is strong evidence that 1500/f is an excellent representation of lp/mm which can be acheived on film, i.e. the tests match the theory quite well.

Now, if f/750 is also an accurate represntation of resolvable diam airy disc, then the two must correlate. The missing link in my mind is, how does airy disc diam, and the ability for the human eye resolve them relate to lp/mm?

My simple approach of correlating the two is taking lp/mm, then shorten the lines so they become squares, a square leg is equal to the diam of a circle that fits within it, so the two are close enough for these discussions.......now you have a checkerboard pattern.... at some point, as the squares become smaller you will see solid grey vs. a checkerboard (assuming B&W squares). However, when I ran some numbers on this theory, the newly created squares did not coincide with airy disc diams, when comparing the relationship of d and lp/mm in the diffraction tables. I expressed that relationship above, cc = 1 / lp/mm * 2.

> What is resolved by one eye, it will NOT be by another.

For matters of this discussion, I am avoiding all the other issues involved in resolution at the final print size and the differences in human vision amongst people..... This strictly relates to a method that is satisfactory that can allow us to enter a cc that correlates to a lp/mm value we are trying to acheive.

I want to reiterate.... I am NOT trying to ascertain or understand diffraction limited values here. That's old news and quite proven. The only reason I mentioned diffraction, is because it is the only place in photographic documentation I can find the two "units of measure" as they relate to a common demonitaor. I am suggesting they represent the same value, hence how I can backtrack their relationship between them, i.e. I know what lp/mm I want, but Hyperfocal Calc is asking for cc. Where is the transition of this formula when the world switched from airy disc diam. to lp/mm / MTF ? Seems to be a missing link, as i have not found this documented in any books or literature.

[robc]

If you have not read this then you may find the answer to your question in the notes.zip here www.bobwheeler.com/photo/Documents/documents.html

[bglick]

I read Bob Wheelers cc definition on page 19, and he has the same conclusion that I drew when I first attacked this issue. Bobs position is, to convert lp/mm to cc, you simply take the reciprocal of the lp/mm, so 68 lp/mm, 1/68 = .014mm per airy disc (cc) pair.

I even went a step further and assumed since this is the diam (height) of a line PAIR, or an airy disc PAIR...... then a single airy disc diam (which is a single cc) would have a diam of 1/2 this, or .007. And since airy disc are measured per disc, not per pair, this appealed to my common sesne. However, this widened the gap even more, (from 2x descrepancy) before this....to now now a factor of 4, .03mm vs. .007mm. Just too much to easily dismiss....

Also, if we never knew of cc, and simply worked with lp/mm, and reduced them as I suggested above, reciprocal, then chop the pair in half, this would create cc in the hyperfocal calc of 1/2 what most people normally use who covnert from lp/mm, such as Wheeler..... this extra halving of cc doubles the hyperfocal distance. If it was not for f/750, I then I find this the most sensible approach, regardless how much painful it is.

Bob Wheeler certainly put a lot of time and energy into his work, I am suprised he did not address this issue. In his focus book, Merklinger actually went into the field and tested hyperfocal and DOF limits using these conventional formulas and he could not make any of the real world DOF values (using test targets at different distances) appear on film....not even close, hence why he developed his own methodology of what resolves on film. I am not sure his new system is quite as elegant as hyperfocal / DOF formulas, but I suspect this same cc / lp/mm could have been the reason for his failed test.

It's my suspicion, based on the way photograhy has progressed through the years, the airy disc diam itself may be accurate, but the ability to objectively test airy discs with human vision, vs. line pairs, might be the shortcoming of the airy disc method. So possibly, the usefulness of using d (cc) as I suggested in my original post, is not an accurate representation of the newer lp/mm units of measure, as the lp/mm method has real world tests which validate their existence. I never saw an airy disc diam test as it relates to resolvable detail. It is also possible as QT explains, the airy disc is not a clear cut black disc vs. white disc, such as line pairs which have black lines and white lines, the densities vary throughout the disc, and this also may alter how humans resolve them, making their diameters not a fair comparison to the diameters of a solid color line.

My concern is, f/750 has been around since optics began....(even though its for diffraction, there still should be some correlation between it, and lp/mm for a given f stop) I hate to just dismiss f/750 on the grounds it doesn't correlate with a newer unit of measure. Hopefully Struan or QT can provide an explanation....

[Paul Fitzgerald]

Hi Bill,

The old Kodak formula for hyperfocal distance for critical enlargement was based on f/1720, 2 min.of arc, 2 inches at 100 yards. YMMV. I don't know if this can be converted to lpmm><cc. but it works on the speadsheet.

Just a thought.

[Struan Gray]

Diffraction and defocus will both blur the on-film image, but in different ways, and finding an exact equivalence between them is a matter of taste. If you have found a figure that works for you and your photography I would just use it and not worry too much.

People who need to extract information from images that lies at the resolution limit have developed techniques for doing so without being fooled by artefacts or their own expectations, but we're talking about aerial recon, astronomy, microscopy and scientific imaging, not conventional pictorial photography. The analysis requires an understanding of image convolution, and to actually work in a reasonable time you need to get to grips with Fourier transforms. Not rocket science, but not high school math either.

It is easiest to understand the blur of a point object like a star or a distant light at night. Diffraction through a circular aperture turns the focussed image from an ideal point into an Airy function: a bright central spot surrounded by increasingly dim rings. The same thing happens to an extended image, and you have to think in terms of spreading the light from all the parts of the image so that any point on the film receives light from its own central spot plus the edges of the spots created by neighbouring parts and the rings of even more distant neighbours. Mathematically this is a convolution of the image with an Airy function.

Defocus of an abberration-free lens changes the point-like image of a star into a circular disc. Again, you can extend the idea to a complex image by adding and overlapping the spread-out discs from all the light in the ideal image. However, now you have to remember that light from objects at different distances will be spread by different amounts. Also, any real lens will have aberrations, and so the disc will be more like a ring or a bright spot, and what is more, that pattern will change with focussing distance too. Every part of the image has its own little pattern to be convolved with, and you end up in that Slough of Despond called Bokeh. To make things simple, and because you end up with a result that is simple, analytical and universal, you tend to backtrack to the assumption of simple little discs and derive DOF limits from there.

So there are two problems if you try to relate a COC and a diffraction-limited Airy disc numerically. First, the COC is itself a simplification that gets increasingly coarse as you introduce aberrations by going off axis, opening the aperture or focussing closer than the lens' optimised repro ratio. Second, the COC and an Airy disk are different shapes, so they have different effects on the look of the image.

On that second point, it is worth noting that the 'width' of the Airy disc is usually given as the diameter of the first dark ring. This overestimates the visual effect of blurring through diffraction, which is one reason why most people find they can get away with more diffraction than the formula would suggest.

MTFs come into the picture when you want to do a full analysis. The MTF is half of the Fourier transform of the lens's response to a point source - it summarises the Airy function and the little discs and aberration patterns in so-called Fourier space. If you have MTFs for various positions in the image plane it is easy enough to construct the missing half and produce what is called the Optical Transfer Function, or OTF. This is worth doing because on a computer any convolution of the image can be done much, much faster (and understood much, much more easily) as a multiplication in Fourier space. Better, you can do the de-convolution with a simple division, rather than trying to figure out which bit of light got spread out into which little disc. Thus modelling lenses and processing images they have taken becomes a practical proposition. That said, even with a higher degree in a numerical science there is not enough information in published MTFs to do anything useful like determine the on-film resolution. If you really want to know, a practical test is the key.

[bglick]

Struan, you continue to amaze me.... I follow most of your description and had a strong suspicion there was not an easy conversion between cc and lp/mm. I truly do not want to turn this into a 6 month scientific experiment, as I have seen this happen on many web sites.

So in short, if this was YOU, and you wanted to prepare a table of hyperfocal distances based on:

1) you desire nothing less than 5 lp/mm resolved on film

2) Using ultra sharp modern lenses, shot at the most favorable f stop, f11

3) high resolving film such as Velvia,

4) you have good focus mechanism,

5) focus relatively close, say 10 - 25 ft.

6) Lenses are slightly wide to normal fl.

7) Good film flatness

Based on this criteria, what CoC value would you enter into the Hyperfocal equation? And if its not to complicated, how did you arive at such? Thanks again....