AA filter question - Joe?

Started Feb 9, 2012 | Discussions thread
DSPographer Senior Member • Posts: 2,464
Re: The two sides of "insane resolution"

Richard Frederick wrote:

Thanks, Joe:

The last thing I would want to do is call you from a sick bed to do lens testing.

Hopefully no more testing, but if you (and others) feel up to it, more questions.

I still have a hard time letting go of normal lens "lines per millimeter" of about 50, as reported in magazine tests in the film era. The highest I remember was 80 for something like a Leica 50mm F2.0 Summicron. Do any of you recall these numbers? I would hope that I am not getting so dotty I misremembered all of that. It seems so clear. Anyway,

Those values may be for the MTF point where contrast drops to 50%. Without sharpening the 50% MTF point is a good indicator of how sharp a lens appears to be. But, contrast below 50% can still cause aliasing artifacts. Another consideration is that for low noise images we can use sharpening to raise the contrast of fine details to make them more visible. In the extreme case we could make contrast that starts at only at about 9% usable after sharpening a very low noise image. The 9% point is the Rayleigh criteria for the resolution of a "perfect" lens (a lens that has such low aberrations that diffraction is what limits its resolution). This is the value I used in my calculations.

50 lines/mm equals 100 line pairs per mm. (24 X 100) X (36 X 100) = 8.64 megapixels.

You are using the wrong term. 50 lines/mm means 50 line pairs per millimeter = 100 line widths per millimeter.

80 lines/mm equals 160 line pairs per mm. (24 X 160) X (36 X 160) =(3840) X (5760) = 22.12 megapixels.

This would be right for a monochrome sensor. But, for a color Bayer array sensor we use the spacing of the green pixels for the unambiguous luminance sampling. We then need to consider that the lines could be at a 45 degree angle: then the green pixels are 1.414 times as far apart as the base pixel spacing. The result is you need to double your pixel counts for a color sensor.

These calculations square with the seeming consensus that about 12 -17 megapixels (or less) will be the equivalent of film in this narrow sense.

As to how many linear megapixels are required to create "line pairs per millimeter", I figure the following: black line (spot) = first pixel; while line (spot) = second pixel, and so forth. For a b&w sensor, I get the same number of pixels per mm as I do for the same number of line pairs per mm. Am I wrong?

On 10 Feb, in this thread, DSPographer posted the following:

"The point is that if the smallest point the lens can produce spreads over 4 pixels anyway then you don't need to spread it further with an AA filter."

Presuming the four pixels are in two dimensions, two pixels would represent a linear problem. The lower 100 lp/mm would require 200 pixels/mm while the higher 160 lp/mm would require 360 pixels/mm. This works out to 34.56 megapixels and about 112 megapixels, respectively.

By my reasoning, the Nikon D800 sensor should avoid moiré patterns with a lower resolution lens (100 lp/mm) but we will have to wait for a 112 megapixel sensor for the 160 lp/mm lens for the same result.

But that doesn't consider very sharp lenses at the resolution limit of 9% MTF contrast.

OK, so straighten me out (please). As before, I am presenting my concepts not to argue but to let you know my reasoning process and better able you to get my mind right (if you so choose).

My interest in this lies in the fact that I have a Ricoh GXR equipped with an "M mount" module that allows the fitting of older rangefinder lens designs. Those lenses are designed to mount much closer to the sensor (film) plain than later designs that usually must clear a mirror box. A Jupiter lens (apparently Eastern European design) in a Leica screw mount just about touches the sensor. These lenses can project light at extreme angles to the sensor creating some challenges to digital camera designers. Reportedly, AA filters create problems in this environment and the GXR M module and the Leica M9 are both produced without an AA filter.

Thanks to all for contributing to a vary informative and civil thread.

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Dick Frederick

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