8. Spatial Frequency Cuttoff

Written by Scott Sparrold

The maximum spatial frequency an optical system can image is dependent on what is limiting its performance:
  1. Detector Limited
  2. Optically Limited
This assumes an imaging system and is not relevant for an afocal or collimated system. See here (TBD) for similiar afocal equations.

Detector Limited
The spatial frequency cutoff is usually limited by the detector array for an optical system. The pixel cell size d and the cutoff spatial frequency is

Spatial frequency units are lp/mm.

The optical system is usually capable of imaging higher spatial frequency images than Λdetector but they will get aliased with the low detector sampling.

Example: A detector pixel has a 5 µm size (pitch). The cutoff spatial frequency is therefore 100 lp/mm.

Optically Limited
If the detector sampling is not the limiting factor the system is "optical limited":

An optical system with a focal ratio, F/#, used at wavelength, λ, has a spatial frequency cutoff of 
Λoptical (units are line pairs per mm or lp/mm). The modulation transfer function (MTF) goes to zero for the cutoff spatial frequency

Diffraction caused by the optical aperture is essentially limiting the maximum cutoff frequency. 

Example: An F/5 optical system operating in the visible (~0.5µm) has an optical cutoff frequency of 400 lp/mm