A hologram of an on-axis point object at distance is recorded at with 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 an on-axis point object at distance

z_o

is recorded at

\lambda = 633\ \mathrm{nm}

with a plane reference wave

R

incident at

\theta_R = 22^\circ

to the axis, using linear recording so that

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

. ((a)) Derive which term of the replayed field, when the hologram is illuminated instead by the phase-conjugate reference beam

R^*

(a plane wave tilted at

-\theta_R

), forms a real image at the same distance

z_o

from the plate as the original object, propagating undeviated along the axis. State the ratio of this image distance to

z_o

. ((b)) Find, to three significant figures, the deviation angle (magnitude) of the remaining diffracted term from the axis.