Nano-Holographic Interferometry for In-Vivo Observations - Biomedical Optical Phase Microscopy and Nanoscopy - page 362

Figure 17.12
(A) Gray-level image recorded for a prismatic nanocrystal without central symmetry;
(B) FT pattern of the image.
along the vertical axis f y of the FT space (see Figure 17.12B ). This is done because the
pattern shown in Figure 17.12A actually is the FT of the nanocrystal.
The results of thickness measurements carried out for four different nanocrystals are listed
in Table 17.2 . The table also shows the average of the thicknesses obtained by the two
procedures outlined in Section 17.7 (see Ref. [23] for more details).
Table 17.3 shows the experimentally measured aspect ratios of nanocrystal dimensions
compared with the corresponding theoretical values [23] —the average error on aspect ratios
is 4.59% while the corresponding standard deviation is 6 6.57%.
Table 17.4 , on the basis of aspect ratios, shows the theoretical dimensions of the sides of
nanocrystals and compares them with the measured values. Thicknesses reported in
Table 17.3 are the average values shown in Table 17.2 . The average absolute error on
dimensions is 3.06 nm, the mean error is 2 1.39 nm, and the standard deviation of absolute
errors is 6 3.69 nm. A conservative assumption to estimate the accuracy of measurements is
to adopt the smallest dimensions of the crystals as given quantities from which the other
dimensions are then estimated. The smallest dimensions are the ones that will have the
larger absolute errors.
Another example of the determination of the thickness of a nanocrystal through the change
of optical path is the determination of the step present in the cross-square crystal. The
theoretical structure 5 3 4 3 4 corresponding to this crystal (side length L 5 86 nm) has one
step in the depth dimension.