A sinusoidal amplitude transparency of pitch

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

\Lambda = 8\ \mu\mathrm{m}

, with transmittance

t(x) = \tfrac12[1 + 0.6\cos(2\pi x/\Lambda)]

, sits against the front focal plane of a lens of focal length

f = 200\ \mathrm{mm}

. It is illuminated at

\lambda = 633\ \mathrm{nm}

. ((a)) Find the position

x_1

of the

+1

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

+1

order to that of the zeroth order.