Diffraction Limit

Started Aug 28, 2013 | Discussions thread
Krich13
Regular MemberPosts: 466
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Re: Diffraction Limit
In reply to Erik Magnuson, Aug 28, 2013

Erik Magnuson wrote:

Krich13 wrote:

Obviously, if the diffraction limited spot is smaller than a pixel, diffraction limit of resolution can not be reached. Megapixels still matter.

This is where you go off track: diffraction spots do not line up perfectly with pixel centers. Imagine two images, one with the spots lined up with pixel center and then one with the same spots offset by the pixel radius so each "spot" overlaps two pixels. The second image will have lower edge contrast than the first -- and we measure resolution via contrast retained, e.g. MTF50.

I said the diffraction limit wouldn't be reached if the spot is smaller than a pixel. I did NOT say or imply that it would if the spot size is equal to the pixel size. Indeed the pixel size should be at least half the diffraction spot (two times oversampling, Nyquist theorem)), higher degree of oversampling is even better. Such oversampling would take care of "improper" centering of pixels and light spots.

However, beyond Nyquist actual resolution gain would be small.

Diffraction always limits resolution.

I wouldn't call it "limiting". It always contributes to smearing, yes. The minimum achievable spot size would be a convolution of several factors: pixel size, aberrations and diffraction. However, in presence of stronger smearing factors (e.g. aberrations or pixel  size) the effect of weaker ones is negligible. The true limiting factors of modern FF and even m43 cameras is still the pixel size. As I showed before, at f/4 diffraction spot is just ~2.5 microns. At f/2 it would be ~1.25 microns.

OM-D's "pixel" pitch is 3.7 microns (actually it is a pitch of the photosites, it would be equivalent to pixel pitch for a Foveon sensor). Actual Bayer sensor resolution is ~2 times worse than Foveon, so make effective pitch ~5 microns. In absence of any aberrations THAT would be a limiting factor, not the diffraction spot size (for moderately fast lenses).

Megapixel's don't matter except that they can resolve everything better: detail, diffraction, and other lens aberrations. Megapixels mean you make larger prints or greater crops which magnifies both defects and details.

Megapixels matter as stated above: in absence of aberrations, you can only get close to the diffraction limit if your megapixel count is sufficiently high.

Absence of aberrations (or aberration contribution lower than diffraction smearing) is not something very difficult to achieve. Locally at least, say in the image sensor. I do it every day even with very simple lenses (aspheric singlets) though I work with lasers, and there is no concern of chromatic aberrations.

Obviously, the same diffraction-limited spot would occupy larger portion of the smaller sensor than of a larger sensor.

Which is important if comparing the same size output (print or screen) using the entire sensor area. And why f/64 or f/128 is not usually much of an issue for 8x10 film cameras.

Yes, indeed that is the case. From the perspective of an optical engineer, designing a diffraction-limited lens of f/16 speed is orders of magnitude easier than an f/4 lens, let alone f/1.4-f/2 ones.

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Another way to look at resolution is angular resolution (this is tha one relevant for photography. Minimum resolvable angle depends only on the wavelength and the lens diameter (or absolute aperture).

The minimum angle resolvable (in radians, multply by 57 for degrees)

is 1.22/1.02/0.98 D/lambda (Rayleigh/Abbe/Sparrow) where D is the diameter of the lens/aperture.

This agrees with what I say above: diffraction always limits resolution. Stop thinking about pixels: diffraction, DOF and lens aberrations limit the resolution before point sampling occurs.

No it doesn't. Whatever the diameter and quality of the lend is, if you do not have enough pixels to properly sample diffration limit is of secondary importance. And with modern sensors and moderately fast lenses you still don't.

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