An incoherently illuminated imaging system has a clear circular pupil with on the…

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

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

Problem

An incoherently illuminated imaging system has a clear circular pupil with NA=1.25\mathrm{NA} = 1.25 on the object side, used at λ=633 nm\lambda = 633\ \mathrm{nm}. ((a)) Compute the incoherent cutoff frequency νc\nu_c at the object, in cycles per millimetre. ((b)) Using the closed-form MTF of a clear circular pupil, 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) with ν^=ν/νc\hat\nu = \nu/\nu_c, compute the MTF at ν=νc/2\nu = \nu_c/2.

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