Biomedical Engineering Reference
In-Depth Information
1.25
StdDev
Mean
1
0.75
0.5
0.25
0
0.25
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
Zernike mode index
i
Figure 4.16
Mean and standard deviations of the Zernike mode amplitudes, in the Zernike mode units, for the
C. elegans
, specimen 5. Modes 2 through 22 are shown.
Figure 4.16. he Zernike mode standard deviation declines with rising order. his general behavior
was found for all the specimens. he aberration efect that is contributed from the individual coei-
cients is proportional to the square of the Zernike mode amplitude, as can be inferred from Equation
4.12. hus, the efect of the higher-order modes could be considered to decline even faster than the
amplitudes shown in Figure 4.16. he magnitude of the Zernike mode amplitudes of all specimens
was within the range of up to 1.5 for modes 5 through 11. Maximum magnitudes smaller than 1
Zernike unit were observed for modes from 12 through 22, and for modes above 22, all magnitudes
were smaller than 0.5.
4.12 Simulation of the Zernike Modal Correction
First we assume that the Zernike mode composition was extracted from each wavefront using the pro-
cedure detailed in
Section 4.3
. hen it is a simple matter to mathematically subtract this combination of
the Zernike modes from the original wavefront up to a certain Zernike mode order
O
:
O
∑
1
ψ
corr
( ,
r O
θ
,
)
=
ψ θ
( , )
r
−
M Z r
i
( , )
θ
(4.10)
i
i
=
his simulates the process of the Zernike modal wavefront correction.
Figure 4.17
shows examples of measured wavefronts (top) and their simulated correction (bottom)
up to the Zernike mode order
O
= 22. Image (1) shows an interferogram from rat brain tissue, 30 μm,
covering half of the pupil. Two efects are visible: a rather strong spherical aberration component
(note the colored rings at the edge of the top half of the pupil) is introduced and a modulation of the
phase function with high spatial frequencies is visible. he Zernike mode-based approach can cor-
rect for the lower-order terms but cannot correct the high spatial frequency components; a partial
correction is achieved and can be considered optimal for the modes included in the correction. his
method worked well for 30-μm-thick brain slices. However, for thicker brain specimens of about 90 μm
