Phase Estimation in Optical Interferometry

318 ◾ Erwin Hack

described in Chapter 1 of this book. Let the fringe signal including a car-

rier frequency be written as

=γ =+ φ+⋅

Γ

() () () ()cos( () ),SISS

B

xxxx xfx

(9.57)

where f is a frequency vector adding a linear carrier to the phase ϕ, and x

is short for (x,y).

e Fourier transform of this fringe pattern is

=+ +









Γ

φ+⋅

Γ

−φ +⋅

F[ ()]F[()] F[ () ]F ()

1

2

(())

1

2

((

))

SS Se Se

B

ii

xx

xx

xf

xx

fx

(9.58)

e rst term, which describes the background signal, is found

in the center of the Fourier plane around low frequencies. Figure9.5

shows a test fringe pattern with a carrier in the y-direction of around

96 fringes across the image. e Fourier tran ...