Biomedical Engineering Reference
into the sample is not included. herefore, the magnitude of the mean for the spherical aberration (mode
11) was much lower compared to that of the other samples. Again, we see that the magnitude of the
variations is declining as the index of the modes increases.
he mean and the standard deviation of the Zernike data for all samples are shown in Figure 4.13 . he
large value found for the mean of the spherical aberration (mode 11) agrees with theoretical expectations
from focusing into a sample of mismatched refractive index (Booth and Wilson 2000; Booth et al. 1998; Hell
et al. 1993). A decrease in the standard deviation of measured Zernike modes occurs with rising order. In
addition to this decrease, superimposed steplike changes of the standard deviation can be seen. his inter-
esting efect can be understood by considering the deinition of the Zernike polynomials (see Table 4.1 ). he
single indexing scheme maps to the two independent azimuthal and radial indices of the Zernike modes.
For example, the wavefronts measured close to the center of the mouse oocyte specimen are expected to
contain mainly radial spatial frequencies. Steps are visible between coeicients (6; 7), (10; 11), (15; 16), and
(21; 22). hese are exactly those pairs of indices i for which the radial frequency of the polynomials changes
(see Section 4.3 ) . he rather constant sections between the steplike features of the standard deviations of
the Zernike modal content of the mouse oocyte specimen are due to relatively constant azimuthal spatial
frequencies, which are underrepresented in an object of this symmetry.
4.10 Setup for Large Numerical Aperture, Specimens
Investigated, and Data Acquisition
To measure the aberrations caused by biological specimens under high NA conditions, a few modiications
had to be made to the setup depicted in Figure 4.4 . Because of the short working distance of high NA
lenses, the specimens were mounted between two coverslips and placed between the two opposing objective
lenses. his required a new design of the specimen holder as well as the stage. Apart from that, the data
acquisition procedure was identical to that for lower NA and is described in Section 4.7 . An XYZ piezo
element scanned the sample in three dimensions. An example for the data acquisition process is shown in
Figure 4.14 (Schwertner 2004).
Figure 4.14 ( See color insert. ) (a) Transmitted light image of the specimen number 5 ( C. elegans ). he red box indi-
cates the scanned region of 50 × 50 μm. (b) Video of the disturbance of the wavefront in the pupil plane of the lens as the
focal spot scans across the specimen. Here the complex wavefront consisting of the amplitude A ( r ,θ) and the wrapped
phase function ϕ( r ,θ) is displayed. he color encodes the phase, whereas the brightness corresponds to the amplitude of
the wavefront. he green dot within the red frame in the lower let corner of the video indicates the relative position within
the scanned area. (AVI video ile online at http://www.opticsinfobase.org/oe/viewmedia.cfm?uri=oe-12-26-6540&seq=1 .)