What’s Your Q? A Wavelength-Based Treatment

Seventeen years ago — how time flies — I published a blog post on optimal sensor resolution for diffraction limited lenses. Recently, some people have objected to the formulation that I chose because it talks in terms of sampling frequency, which confuses them. In order to deal with that objection, here’s a version that doesn’t use frequency. The relationship between diffraction, pixel pitch, resolution, and aliasing can be described entirely in terms of spatial wavelengths. Diffraction and the shortest transmitted wavelength Consider a diffraction-limited lens with f-number N, operating at optical wavelength lambda. For incoherent imaging through a circular aperture, the shortest spatial wavelength that the lens can transmit with nonzero contrast is: L_min = lambda * N Here, L is a spatial wavelength measured in the image plane, not the optical wavelength of the light. For green light at 550 nm and f/8: L_min = 0.55 * 8 = 4.4 micrometers The lens cannot reproduce a sinusoidal image…