A hologram of a point object on the optical axis is recorded at using a plane…

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

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

Problem

A hologram of a point object on the optical axis is recorded at

\lambda = 633\ \mathrm{nm}

using a plane reference wave

R

incident at

\theta_R = 25^\circ

to the axis. The recording is linear, so the developed amplitude transmittance is

t_A = t_0 + t_1(OR^* + O^*R)

with

t_0, t_1

real constants and

O

the diverging spherical object wave. ((a)) Write the recorded irradiance

|O+R|^2

as its four terms and state which term, on replay with

R

, reproduces

O

itself (up to a real constant). ((b)) The hologram is illuminated for reconstruction by the same beam

R

. Give, to three significant figures, the angle to the axis of (i) the reconstructed object wave, (ii) the undiffracted zero-order light, and (iii) the twin (conjugate-image) term.

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