Image Processing Reference

In-Depth Information

Performance

65

2

1

2

)

(

2

(

2

)

−

σ

S

=−

1

σ

≈

e

.

(6.5)

p

p

In the case of a long exposure, the core diameter is give by Eq. 6.6 and the peak in-

tensity is shown in Eq. 6.7:

1

2

2

λ

D

2

a

=

122

.

1 517

+

.

σ
α

(6.6)

D

λ

and

(

2

)

−σ

e

p

(6.7)

S

=

,

2

D

2

1517

+

.

σ

α

λ

σ
α
is the mean-square angular tilt and
D
is the aperture diameter. Note that in

Eq. 6.7, when the tilt value is set to zero, this returns to the form of the extended

Marechal approximation.

where

6.4 Performance Evaluation

An evaluation of the performance of the image-stabilization system relies on deter-

mining the uncorrelated individual error sources in the wavefront phase. This is

given as a summation of the individual errors:

2

2

σ

=∑

σ

i
.

(6.8)

phase

The sum of these errors can then be transformed into the Strehl ratio using the ex-

tended Marechal approximation.

In determining the phase error, the fitting error, temporal error, isoplanatic er-

ror, and the error due to sensor noise need to be considered in detail. That summa-

tion can be written explicitly as

2

2

2

2

2

σ

=

σ

+

σ

+

σ

+

σ

+

others .

(6.9)

system

fitting

temporal

isoplanatic

senso

rnoise

The fitting error of a tip-tilt mirror will be very poor if there is any corrugation in

the wavefront. As a result, it will only remove the global tilt from the image. The tilt

included and removed variances are given as