A silicon sample carries surface texture whose finest Fourier component has period

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 lens as a Fourier transformer

Problem

A silicon sample carries surface texture whose finest Fourier component has period Λ=250 nm\Lambda = 250\ \mathrm{nm}. It is illuminated at λ=532 nm\lambda = 532\ \mathrm{nm} (a frequency-doubled Nd:YAG laser), and a photodetector is held z=2.0 μmz = 2.0\ \mu\mathrm{m} above the sample. ((a)) Confirm that this component's spatial frequency ν=1/Λ\nu = 1/\Lambda lies above the evanescent cutoff 1/λ1/\lambda. ((b)) Find the distance over which this component's amplitude falls to 1/e1/e of its value at the surface. ((c)) Estimate the fraction of that component's surface amplitude that survives at the detector, and state whether the detector can register this feature of the surface.

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