A slanted-edge test of a camera whose lens is set to f/5.6

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Optics & Photonics · Fourier optics and image formation

What an Instrument Can See, Ch The transfer function of an imaging system

Problem

A slanted-edge test of a camera whose lens is set to f/5.6, in green light of wavelength λ=550 nm\lambda = 550\ \mathrm{nm}, gives, after the row averaging described in this chapter, an edge profile sampled every 2 μm2\ \mu\mathrm{m} across the edge at the sensor. From x=−8 μmx=-8\ \mu\mathrm{m} to x=+8 μmx=+8\ \mu\mathrm{m} the samples are 0.0010.001, 0.0080.008, 0.0550.055, 0.2120.212, 0.5000.500, 0.7880.788, 0.9450.945, 0.9920.992 and 0.9990.999. ((a)) Take the difference of each pair of neighbouring samples, assigned to the midpoint between them, to get the line-spread function LjL_j at xj=±1x_j=\pm1, ±3\pm3, ±5\pm5 and ±7 μm\pm7\ \mu\mathrm{m}. ((b)) Compute the measured MTF at ν=50\nu = 50 cycles per millimetre as ∑jLjcos⁡(2πνxj)/∑jLj\sum_j L_j\cos(2\pi\nu x_j)\big/\sum_j L_j, and say why no sine terms are needed. ((c)) Compute the diffraction-limited MTF of a clear f/5.6 pupil at the same frequency from H(ν^)=2π(arccos⁡ν^−ν^1−ν^2)\mathcal{H}(\hat\nu)=\frac{2}{\pi}\left(\arccos\hat\nu-\hat\nu\sqrt{1-\hat\nu^2}\right), taking NA=1/(2×5.6)\mathrm{NA}=1/(2\times5.6), and give the ratio of the measured value to it. Name what, besides the lens's own pupil, the measured value includes.

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