Modulation Transfer Function (MTF)
Image sensor MTF: pixel aperture, charge spread, and optical blur contributions.
Nyquist frequency
92.6 lp/mm
f_N = 1/(2p)
MTF at Nyquist
37.0 %
product of the three terms
Pixel aperture at Nyquist
65.3 %
active width 5.26 µm; 2/π = 63.7 % at 100 % fill
Charge spread at Nyquist
56.8 %
1/(1 + (2π f ℓ)²)
Optical blur at Nyquist
100.0 %
exp(−2π² σ² f²)
MTF(f) = |sinc(π f a)| · 1/(1 + (2π f ℓ)²) · exp(−2π² σ² f²), with a = p·√FF for a square active area.
ℓ is the 1/e length of an exponential line spread, e−|x|/ℓ/(2ℓ). It is a fitted spread, not the minority-carrier diffusion length: for the Seib diffusion model with depletion depth and wavelength, use the pixel crosstalk calculator.
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
Product of three terms along one axis: a square pixel aperture of side p·√FF (|sinc|, 2/π at Nyquist for 100 % fill), an exponential charge-spread line spread of 1/e length ℓ (Lorentzian MTF) and a Gaussian optical blur. ℓ is a fitted spread, not a diffusion length. Aliasing is left out, and the phase-averaged sampling MTF sinc(πfp) is not included either; wavelength dependence and the 2D pixel shape are left out too.
- Holst G. C., Lomheim T. S. (2011). CMOS/CCD Sensors and Camera Systems, 2nd ed. SPIE Press. Ch. 10 "MTF": the system MTF as a product of the detector aperture, diffusion and optics terms. doi:10.1117/3.2524677.ch10