A grating with lines per millimetre is placed in the front focal plane of a lens with…

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

A grating with

\nu_0 = 120

lines per millimetre is placed in the front focal plane of a lens with focal length

f = 250\ \mathrm{mm}

and clear aperture diameter

D = 50\ \mathrm{mm}

, illuminated over a patch

2\ \mathrm{mm}

across, centred on the axis, by a plane wave of wavelength

\lambda = 632.8\ \mathrm{nm}

. ((a)) Find the spacing between adjacent diffraction orders in the back focal plane. ((b)) State the highest order number

n

that is transmitted by the lens aperture, given that the aperture passes spatial frequencies up to

\nu_{\max} = D/2\lambda f