Phase Estimation in Optical Interferometry

Local Polynomial Phase Modeling and Estimation ◾ 197

elucidate the working of this operation, consider two adjacent segments

i and i + 1, wherein the polynomial coecients have been estimated as

…

αα[

ˆ

,,

ˆ

]

0iiM

and

…

αα

++

[

ˆ

,,

ˆ

]

(1)0 (1)

ii

M

, respectively, using one of the tech-

niques mentioned in the next sections. e corresponding phases in the

two segments are given, respectively, as

∑

φ=α∀∈

=

ˆ

()

ˆ

[1

,]

0

yy

yL

iim

m

M

m

s

(6.19)

∑

φ=α∀∈

++

=

ˆ

()

ˆ

[1

,]

1(1)

0

yy

yL

iim

m

M

m

s

(6.20)

Note that the phases in both segments are computed on the same interval 1

≤ y ≤ L

s

. For a continuous phase, the values ofφ

ˆ

()

y

i

at y = L

s

+ 1 and

φ

+

ˆ

()

1

y

i

at y = 1 should be identical. Hence, we compute the oset as

γ=φ+−φ

++

ˆ

(1)

ˆ

(1)

11

L

iisi

(6.21)

Using the oset γ

i+1

, the phase in the segmen ...