The chapter's BK7 singlet

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

What an Instrument Can See, Ch Aberrations: the phase written on the pupil

Problem

The chapter's

100\ \mathrm{mm}

BK7 singlet, in its best-form bending with the stop at the lens and the object at infinity, has

W_{040} = 10.6

waves at

587.6\ \mathrm{nm}

when used at f/4. Take the image-space index as

n = 1

and the reference-sphere radius as

R \approx f

. ((a)) Starting from

\boldsymbol{\varepsilon} = -(R/n)\nabla W

with

W = W_{040}\rho^4

, show that the marginal ray misses the paraxial focus by

\mathrm{TSA} = 8(f/\#)\,W_{040}

, with

W_{040}

in length. ((b)) At fixed focal length

W_{040}

grows as the fourth power of the aperture radius in use, and at the best focus pure spherical aberration on a clear pupil leaves an rms of

W_{040}/\sqrt{180}

. Find the fastest f-number at which this lens meets Maréchal's criterion

\sigma_W \le \lambda/14

. ((c)) At f/5, find

\sigma_W

at the best focus in waves, and decide whether the Maréchal approximation can be used to estimate the lens's Strehl ratio there.