Film Scanner Optics

What is modelled

A Super 35 frame (24.89 x 18.66 mm, 19.05 mm pitch) is lit from behind, imaged by a lens onto an area sensor, and sampled by pixels. The page combines the diffraction limit of the lens, the box aperture of the pixel and a Gaussian film grain response into one contrast-against-frequency curve, shows how detail above the Nyquist frequency folds back, and relates film speed, strobe time, bit depth and data rate. The 3D page supplies the frame format and the transport; it has no imaging model.

Equations

• Magnification m = N_pix p / 24.89 mm; working f-number N_w = N (1 + m).
• Diffraction MTF (2/pi)(acos x - x sqrt(1 - x2)) with cut-off m / (lambda N_w) on the film.
• Pixel MTF sinc(pi f p / m); Nyquist m / (2 p).
• Film MTF exp(-ln2 (f / f50)2).
• Alias frequency |f - round(f / fs) fs|; bits needed D / log10(2).

Checks run in the page

• Pixel aperture contrast by numerical averaging.
• Diffraction MTF by counting the overlap of two circular pupils.
• Alias frequency by a windowed DFT of the sampled pattern.
• Film transport by stepping a clock, strobe time and data rate.
• Minimum linear bit depth for the film density range.

Honest simplifications

An incoherent, monochromatic (550 nm) diffraction-limited lens without aberrations, defocus or vignetting; a Gaussian film response with an assumed MTF50; a monochrome area sensor with a perfect 100 percent fill factor and no colour filter array; no sensor noise, flare or film grain texture; the pattern strips are drawn schematically. A teaching model, not a scanner calibration.

• Press 2K review scan, then 8K archive scan, and see which of lens, pixel or film limits the resolution.
• Raise the f-number to 16: diffraction becomes the limit and more pixels stop helping.
• Lower Dmax or the bit depth and read the note on crushed shadows.