Photophys.com: The Science of Photography

Myhrvold and I made claims and provided supportive links, and I suspect that both of us are reasonably happy with what we wrote.  However, I have noticed that debates prompted by the essay and the appended comments are still continuing in the forums.  There is still some confusion and misunderstanding about what was said and not said.  Accordingly, I would like to give a brief summary of our debate and to report a simple experiment.

1.  My essay on equivalent images stands alone.  Assumptions were made and the consequences were discussed.  It was all classic optics presented for the situation where photographers encounter a variety of sensor sizes.  Pixel size (pixel pitch) was not considered other that to assume that pixels were too small to limit resolution.  Myhrvold did not attack the article.  In fact he made kind comments about it.</o:p>

2.  Myhrvold wrote to provide another perspective.  Instead of selecting a circle of confusion (CoC) to control both the depth-of-field (DoF) and the diffraction broadening, he was concerned with a choice of CoC that would permit the maximum resolution that his sensor could provide.  That is to say, he wanted to obtain the maximum resolution in the plane of focus rather than to control the DoF.  His conclusion was that the diffraction broadening of the image could be sufficiently limited by selecting an f-stop about equal to the pixel size in microns.  He also expressed the opinion that pixel sizes much smaller than the diffraction spot diameter would be a waste of sensor capabilities.</o:p>

I was reasonably happy with Myhrvold’s comments; and, considering the practical problems associated with experimental tests of the determinants of resolution, I could/should have let it stand.  After all, I do agree with the arguments and illustrations in the cited links including the cambridgeincolor web site.  Instead, I raised an esoteric point. Basically, for a monochrome sensor if the pixel size is smaller than the diameter of the diffraction spot, the resolution might be better than if the pixel size matches the diffraction spot size.  This point may only matter to astronomers who photograph stars and must select optimum pixel sizes for their sensors.  If the image spot is broadened for any reason to the size of a pixel, then with multiple exposures each image acquired will be probably be slightly different because of small shifts in position and one time the star image will fit in one pixel, the next time the image will overlap parts of two pixels, etc.  Of course, even if the star image fits in one pixel, the image will be square, not circular.  The argument is a little different for color sensors with color filter arrays.</o:p>

I still think that, in principle, oversampling can help.  With my limited knowledge of image processing, I believe that the same resolution enhancement effect can be achieved by combining serial images.  Myhrvold suggested the use of super-resolution methods based on combining serial images, so there may not be much disagreement.  The web link for matching pixel size to the capabilities of optical instruments is given below, and the link to super-resolution was previously given by Myhrvold.</o:p>

 </o:p>So where does this leave real world (terrestrial) photographers?  If ones wishes to adjust DoF for a print, the ideas in my essay can be used as a starting point.  If one wishes to obtain the ultimate resolution from their lens and sensor, then trial and error will probably be required.  As Myhrvold and I have said repeatedly, our analyses assume diffraction limited lenses.  Your lenses and especially your zoom lenses are unlikely to be diffraction limited.  Therefore, diffraction will be only one of the contributors to the broadening function.  The lower the quality of the lens, the more difficult it will be to isolate the contribution of diffraction.  I am reminded of the early box cameras where aberrations were so severe that there was no definite plane of focus, and over a wide range of distances objects were in “pretty good” focus.

 </o:p>Anyway, I have performed a simple experiment to see what difference pixel size makes in the presence of diffraction broadening with typical equipment.  I tested a Canon 10D (pixel size = 7.4 microns) and a Rebel XTi (pixel size = 5.7 microns), each with the same Sigma 105 mm macro lens.  The cameras were mounted in turn on a solid tripod about 10 ft from a resolution chart (see link below) that contained a series of vertical black lines with spacings that decreased continuously from left to right.  The average distance between centers of the lines was measured for each 10% of the range.  When projected on the sensor the line spacings were found to be 13.9, 15.2, 17.3, 20.0, 23.3, and 28.6 microns for the groups of lines starting from the right end.  The experiment consisted of photographing the chart with f-stops ranging from 4 to 32 with mirror lockup selected.

With the 10D, the resolution was found to be virtually identical from f/5.6 to f/11, and stopping down f/16 showed only a small decrease in resolution.  In particular, the resolution of 17.3 and 20.3 micron spacings was lost at f/16 and f/22, respectively.  In no case was there any resolution of 13.9 micron spacings, and contrast was close to zero for 15.2 micron spacings.  Resolution loss means that the contrast in that part of the pattern vanishes.  With the XTi, maximum resolution was obtained from f/5.6 to f/8.0, and there was an almost imperceptible decrease at f/11.  Amazingly, at f/16 there was still resolution, albeit with low contrast, of 13.9 micron separations.  All the way to f/22 the XTi clearly showed more resolution than the 10D, but at f/32 the patterns were fuzzy and essentially identical for both cameras.  Resolution was completely lost for any spacings below 23.5 microns at f/32.

It is interesting to note that at f/16 the XTi could resolve lines at spacings of 17.3 microns while the 10D could not.  Similarly, the XTi could resolve 20.0 micron spacings at f/22 with much better contrast than the 10D.  The diameters of the diffraction spots are 21.5 and 25.9 microns at f/16 and f/22, respectively.  So even with diffraction broadening (spot size) four times larger that the pixel size, we see that smaller pixels still give an advantage.</o:p>

What can we conclude?  Resolution is limited by lens aberrations, digital sampling (digital resolution), and diffraction broadening.  At the larger apertures (small f-stops), aberrations become important, and resolution improves as the lens is stopped down.  This was not mentioned above, but resolution does improve with both cameras in going from f/4 to f/5.6.  At smaller apertures, digital resolution and diffraction both contribute with diffraction dominating at the smallest apertures (large f-stops).  The best resolution for the Sigma macro lens is found at f-stops close to those predicted by Myhrvold, though the resolution is roughly constant over a considerable range of apertures.  When diffraction broadening is evident, oversampling can help; but when the diffraction spot size reaches six or seven times the pixel size, the pixel size no longer influences the resolution. </o:p>

I end with a note of caution.  You camera may have a different anti-aliasing filter or even no filter.  Also, your lenses are sure to have a differ levels of aberration.  However, there is no way to escape the resolution destroying effect of diffraction at large f-numbers.  Users of DSLR’s should think twice before shooting at f/32 and should be aware of perhaps unacceptable resolution loss even at f/16.   </o:p>

Brad D. Wallis, “Some notes on matter of matching CCD camera pixel size to the capabilities of an instrument.” (Especially, Figure 3)</o:p>

http://geogdata.csun.edu/~voltaire/pixel.html

 </o:p>Resolution Chart:

http://math.berkeley.edu/~ilya/software/tmp/KM_A200-resolution-chart-ACRraw-quadratic-58percent-quartic-60percent.jpg

©2007 Charles Sidney Johnson, Jr.

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