Modulation Transfer Function

Reference: Glenn D. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems, second edition (2021).

Use this reference to connect image formation, detector sampling, and measured system contrast.

Define the transfer function

For linear, shift-invariant incoherent intensity imaging,

\[\mathrm{OTF}(\nu_x,\nu_y)= \frac{\mathcal{F}\{\mathrm{PSF}\}(\nu_x,\nu_y)} {\mathcal{F}\{\mathrm{PSF}\}(0,0)}, \qquad \mathrm{MTF}=|\mathrm{OTF}|.\]

Record field, spectral weighting, focus, and object- or image-space units.

Optics, detector, and sampling

A rectangular sensitive pixel width \(a\) contributes

\[\mathrm{MTF}_{\mathrm{pixel}}(\nu)= \left|\frac{\sin(\pi a\nu)}{\pi a\nu}\right|.\]

This differs from the sampling Nyquist frequency \(1/(2p)\), where \(p\) is pitch. Transfer functions multiply when the required linear, shift-invariant assumptions hold. Aliasing needs separate consideration.

A pupil model predicts a PSF and MTF; a slanted edge estimates system SFR; a USAF target measures square-wave contrast. State processing, noise, phase, field, orientation, focus, and repeatability before comparing these methods.