Tomographic Phase Microscopy (TPM) - Biomedical Optical Phase Microscopy and Nanoscopy - page 249

of the nucleus observed in Figure 12.17B and C , which is due to the azimuthal averaging of
the spectrum, equivalent to the averaging of the various cross-sectional diameters.
As shown in this example, the implication of finding the object function, which is the map
of 3D refractive index and absorption coefficient, is beyond the identification of a structure.
It enables us to estimate the light scattering by individual compartment constituting the
object. This will in return lead to developing the method to find the structure of interest
with minimal amount of data acquisition, which is the key concept of light scattering
spectroscopy.
12.6 Conclusion
Throughout this chapter, the TPM was introduced that can experimentally record angle-
dependent complex field images of a sample. Detailed data processing methods were
explained for the application of ODT for the 3D reconstruction from the acquired 2D
images. It was found that the first-order Rytov approximation enabled accurate imaging of
biological cells, whereas the first-order Born approximation caused distortion in the
reconstructed images. The iterative constraint algorithm helped to reduce the effect of
missing angles. But the employed prior knowledge, non-negative constraint, is a rather
weak constraint. With a better constraint such as the support constraint using cell boundary,
the accuracy of reconstruction can be further improved, especially in the axial direction.
Theoretically, the spatial resolution of the ODT can be better than twice the diffraction
limit due to the Ewald sphere mapping [11] , which was experimentally demonstrated for
nonbiological objects [35] . But in imaging biological cells, weak contrast due to small
index differences poses practical limits to the resolution beyond diffraction limit.
For biological and biomedical applications, quantitative index maps can provide molecular
concentrations without the need of fluorescent agents [23] . Furthermore, since the refractive
index is an intrinsic quantity, the dynamics of molecules can be studied without such
artifacts as photobleaching. Refractive index maps can also help understand the way
individual organelles in single live cells contribute to light scattering, and thus help in the
design of in vivo light scattering instruments for disease diagnosis [24] .
In addition to the mapping of the structure, refractive index data can be used to characterize
sample-induced aberrations in microscopy. Characterization and correction of such
aberrations may be particularly important for modern super-resolution techniques such as
STED [36] and structured illumination [37] . The TPM system can also be used to measure
the transmission matrix of a turbid medium such as biological tissue, which
deterministically characterizes the input output response of the medium. Using the matrix,
it was recently shown that the image can be delivered through turbid medium, and the
turbid medium can be used to break the diffraction limit posed by the conventional
lens [38] .