Modulation Transfer Function (MTF) and Resolution

Resolution is often reduced to the finest line pair a system can separate, but a frequency alone is incomplete because contrast may already be very low there. MTF expresses contrast transfer: M = (Imax−Imin)/(Imax+Imin), and MTF(ν)=Mimage(ν)/Mobject(ν). Spatial frequency ν is commonly in lp/mm; higher frequency means finer detail. An MTF curve should also state field height, sagittal/tangential direction, aperture, wavelength, and conjugate distance.

For a linear, shift-invariant approximation to incoherent imaging, the optical transfer function of point-spread function h(x,y) is OTF(fx,fy)=∬h(x,y)e^(−i2π(fx x+fy y))dxdy; MTF(fx,fy)=|OTF(fx,fy)|/|OTF(0,0)|. Real lens performance varies with field, orientation, and operating conditions, so multiple field points are measured or modeled. Coherent imaging has a different transfer description; the incoherent formula should not be applied without its assumptions.

Common approaches include sinusoidal or bar targets, the slanted-edge method, and interferometric/wavefront measurements. A reported result may be optical lens MTF alone or system MTF including sensor pixel aperture, optical low-pass filter, ISP sharpening, and demosaicing. A test report should state target, wavelength, magnification/working distance, aperture, processing chain, and sampling conditions.

For sensor pixel pitch p, Nyquist frequency is 1/(2p) cycles/mm, or 1/(2p) lp/mm when p is in millimeters. A 2 μm pixel pitch (0.002 mm) therefore has a Nyquist frequency of about 250 lp/mm. Higher MTF at the task frequency generally preserves more contrast at that detail scale, but MTF is not a standalone sharpness score; noise, sampling, chromatic aberration, distortion, and processing also matter. Set thresholds around task frequency and required edge-location accuracy.