A Nd:YAG laser beam of wavelength and diameter is focused by an objective of focal…

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 Nd:YAG laser beam of wavelength

1064\ \mathrm{nm}

and diameter

3.0\ \mathrm{mm}

is focused by an objective of focal length

15\ \mathrm{mm}

to be spatially filtered through a pinhole. The encircled-energy fraction of an Airy pattern at

v = k\,\mathrm{NA}\,r

takes the standard values

83.8\%

91.0\%

93.8\%

and

95.2\%

at the successive dark rings

v = 3.83

7.02

10.17

and

13.32

. ((a)) Find the diameter of the Airy focal spot. ((b)) Choose the pinhole diameter as three times the Airy spot diameter, and state its value. ((c)) Estimate, by interpolating the table above, the percentage of the beam power transmitted through this pinhole, and the percentage lost. ((d)) Find the highest spatial frequency of beam structure that this pinhole passes.

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