A diorama of depth is to be recorded as a hologram

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

What an Instrument Can See, Ch Keeping the phase: holography, wavefront modulation and adaptive optics

Problem

A diorama of depth

d = 220\ \mathrm{mm}

is to be recorded as a hologram, lit and viewed near normal incidence, using a laser whose spectral line is Lorentzian with full width at half maximum

\Delta\nu = 50\ \mathrm{MHz}

. ((a)) State which term(s) of the recorded irradiance

|O+R|^2

carry the depth information of the scene, as opposed to the background terms

|O|^2

and

|R|^2

. ((b)) Find the minimum coherence length

\ell_c

the source must supply for every part of the diorama to record with visibility no worse than

e^{-1}

, and the corresponding maximum permitted Lorentzian linewidth. State whether the given laser satisfies this requirement.

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