Phase Estimation in Optical Interferometry

Regularized Phase Estimation Methods in Interferometry ◾ 181

step is to explicitly introduce the spectral response of the lateral shearing

operator

∆ϕ[(,)]Fxy

x

in Equations (5.79) and (5.83):

=

−+

−

=

+η −

|(,)|| (,)|

{[1cos()]sin ()}

|2 2cos()|

sin( )

,

|(,)|| (,)|

sin( )

sin( )[1cos()]

.

221/2

0

0

0

0

HuvHuv

uu

u

xu

x

HuvHuv

xu

xu u

FH SI

SI

(5.84)

As we can see, these spectral responses as a whole compensate for the

spectral poles of the bare lateral shearing operator

∆ϕ(,)xy

x

, and con-

sequently the linear system that estimatesϕ

ˆ

(,)xyhas a well-behaved

(stable) behavior. eir FTFs are illustrated in Figure5.19. Note that the

Fried-Hudgin technique falls faster in ...