Optical system
nm
–
–
Wavefront aberrations (waves @ λ)
λ
λ
λ
Detector / analysis
µm
lp/mm
Detector MTF = |sinc(ν·pixel)| (geometric pixel aperture); the system MTF is the product
of the optical and detector curves — what the sampled image actually contains.
Summary
What this means
MTF vs spatial frequency
Through-focus MTF at 50 lp/mm
Method: OTF(ν) = ∬ P(ξ+s/2)·P*(ξ−s/2) dA / ∬|P|² dA with normalized pupil shift
s = 2ν/νc and complex pupil P = exp[i2πW(ρ,θ)] inside the annulus ε ≤ ρ ≤ 1.
W = W₀₂₀ρ² + W₀₄₀ρ⁴ + W₂₂₂η². Tangential MTF shifts along the astigmatism axis (η), sagittal along ξ.
Defocus equivalence: δz = 8·λ·(f/#)²·W₀₂₀. Detector MTF = |sinc(ν·pixel)|; the system MTF is the product
of optical and detector curves. Polychromatic mode averages the optical MTF over a ±10% wavelength band.
Learn: optical vs system MTF
The optical MTF is the best the lens can do. But the sensor blurs too: each pixel integrates light over its area, which multiplies in a sinc(ν·pixel) factor. The system MTF = optics × pixel is what your file actually contains — always the lower green curve.
Q = λ·f/# / pixel ties the two together. Q ≈ 2 is critically sampled. Below ~1.5 the optics out-resolve the pixels and high frequencies fold back as aliasing; above ~2.5 you're spending megapixels the lens can't fill.
For a real lens, sum your Zernike or Seidel terms into the W coefficients, or use the Zernike tool's PSF and take its transform — both routes give the same MTF.