I am I correct to assume that the maximum resolution( I really should be calling it contrast) that a lens and sensor can resolve is at the point a lens projects an Airy Disk size at which the sensor’s pixels pitch can accurately measure the size, brightness and location of that disk in an image?
Hi,
That's hard to answer for several reasons, one of which is that the diffraction pattern is not of limited/fixed size. We usually refer to its diameter as the diameter of the first zero (ring) of the Airy disk pattern, which represents something like 83.8% of the total intensity of the pattern, and is not uniform across its diameter (so alignment with the sensel grid also plays a role).
What we do know is at which spatial frequency the diffraction pattern of a perfect circular aperture will reduce image contrast (MTF) to zero amplitude, for 555nm wavelength:
cy/mm = 1 / (wavelength x aperture) , e.g. 1 / (0.000555 x 8) = 225.2 cy/mm
and it takes (more than) one full cycle to allow reconstruction of the original waveform (225.2 / 2 =112.6 mm, or 1/0.00888mm, or 8.88 micron feature size).
We also know that the sensor array has a limiting resolution of maximum:
Nyquist frequency in cycles/mm = 0.5 / senselpitch, e.g. 0.5 / 0.00488 = 102.5 cy/mm
We can therefore calculate the Aperture at which resolution will be totally eliminated by diffraction, and will prevent all aliasing, by reducing contrast to 0% at the Nyquist frequency:
Aperture = (2 x senselpitch) / wavelength, e.g. (2 x 0.00488) / 0.000555 = f/17.6
However, that is only taking diffraction (of a single wavelength) into account. Diffraction, will in practice be combined with the MTFs of residual lens aberrations, a less than perfectly round aperture, defocus (anything not in the thin perfect focus plane), a filterstack with or without AA-filters and a sensor coverglass, and a Bayer CFA pattern that needs to be demosaiced. The diffraction pattern size also changes with focus distance, so the above formula is based on infinity focusing.
So resolution will be totally limited at wider apertures than that for diffraction alone. It is also not simple to calculate, because there are positive and negative wave contributions that will cause interference patterns that may or may not align locally with the sensel grid.
The only thing we do know for certain, is that the absolute diffraction limit to resolution will not be exceeded (if even reached). Instead, the overall image will already deteriorate before that limit is reached by stopping down. It is only high contrast detail that will even theoretically reach that limit, lower contrast features will have lost significant modulation long before that. That's why limiting resolution is often set at lower spatial frequencies, e.g. MTF10 or Nyquist whichever is reached first. It also explains why even lower spatial frequencies, MTF50 are often used to give an overall impression of average performance for comparisons between different systems.
Cheers,
Bart
P.S. Using smaller sampling pitches than can be resolved from a diffraction limited image, still brings a benefit, because the diffraction pattern is not uniform. So smaller sensels allow to more accurately sample the diffraction patterns that are larger than single pixel, and thus allow more accurate deconvolution restoration of the original signal.