A sinusoidal amplitude grating with transmittance

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

t(x) = \tfrac12\big[1+m\cos(2\pi\nu_0 x)\big]

m=0.60

and

\nu_0 = 80

lines per millimetre, is illuminated by a unit-amplitude plane wave and placed in the front focal plane of a lens with

f=125\ \mathrm{mm}

, wavelength

\lambda = 650\ \mathrm{nm}

. ((a)) Find the position of the

n=+1

diffraction order in the back focal plane. ((b)) Find the ratio of the amplitude of the

n=+1

order to that of the

n=0

order.