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Phase Estimation in Optical Interferometry
book

Phase Estimation in Optical Interferometry

by Pramod Rastogi, Erwin Hack
November 2014
Intermediate to advanced content levelIntermediate to advanced
366 pages
11h 5m
English
CRC Press
Content preview from Phase Estimation in Optical Interferometry
202 Gannavarpu Rajshekhar, Sai Siva Gorthi, and Pramod Rastogi
BOX6.2 MAXIMUM LIKELIHOOD ESTIMATION
Consider a quadratic phase signal as follows:
Γ(y) = exp[jϕ(y)] + η(y)
with
φ=α+α+α∀yyyy() [1,128]
01 2
2
The coefficients are given as [α
0
,α
1
,α
2
] = [0.9, 0.2, 0.004], and the noise
standard deviation σ
η
= 0.1. The phase is shown in Figure6.3a.
To estimate the quadratic coefficients, a maximum likelihood estimation
(MLE) technique is applied. Using Equation (6.26), the bivariate objective
function to be maximized is given as
−+
=
Ux xyjxyxy
y
(, )()exp[( )]
12
1
128
12
2
20 40 60 80 100 120
20
40
60
80
y
100
80
60
40
20
0.1
0
x
2
x
1
–0.1
–2
0
2
20 40 60 80 100 120
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Publisher Resources

ISBN: 9781466598317