Tomographic Phase Microscopy (TPM) - Biomedical Optical Phase Microscopy and Nanoscopy - page 224

is poorer than the transverse resolution. In an effort to attenuate the effect of this drawback,
various algorithms have been developed to solve missing angle information with a prior
knowledge of the specimen [18 20] .

Along with the data acquisition in the experiment, the reconstruction algorithm is an
important factor for the spatial resolution and accuracy of the complex refractive index
measurement. The way of interpreting the experimentally measured complex field
images determines the algorithm to be used. If the phase of the transmitted field is
interpreted as a line integral of the refractive index along the propagation direction,
then the filtered back-projection algorithm based on the inverse Radon transform can
be applied [21] . For weakly scattering biological cells, this is often a good
approximation [12,13] for points close to the plane of focus. However, since the effect
of diffraction is ignored, there is loss of resolution for samples which are large
compared to the depth of focus of the imaging system.

ODT is more of general approach in the sense that the effect of diffraction is taken into
consideration. The Born approximation was first adopted by Wolf to make the relation
linear between the complex refractive index of the object and the complex electric field
(E-field). Several experimental studies have implemented diffraction tomography based
on Born approximation in the optical regime [11,16,22] . But it turned out that the
validity of the Born approximation was in question when the phase retardation by the
specimen reached to / 2 [21] even if the attenuation of amplitude was negligible. This

has led to the introduction of Rytov approximation in which the approximation is made
on the complex phase of the scattered wave [2,23] . The Rytov approximation is more
robust to perform imaging of the phase object than the Born approximation.

π

In this chapter, we introduce TPM [13,24,25] as an experimental method for
quantitative 3D mapping of refractive index in live cells in their native state. TPM can
collect angular images ranging from 2 70 to 70 in as little as 1/30 s. The rotating-
beam geometry was adopted to avoid perturbation of specimens during data acquisition,
and filtered back-projection along with an iterative constraint algorithm was used at the
original development for the 3D reconstruction. Later, the first experimental
implementation of ODT was carried out based on the Rytov approximation to image
live biological cells and to provide quantitative 3D refractive index maps. It was
demonstrated that the Rytov approximation is valid for live cell imaging, while
reconstruction based on the Born approximation leads to severe distortions. An iterative
constraint algorithm is applied to minimize the effects of incomplete angular coverage.
The acquired quantitative refractive index maps were used to quantify molecular
concentrations without adding fluorescent agents [26] . They also provide a means of
studying the light scattering of single cells [27] , which helps the development of
in vivo light scattering instruments for disease diagnosis.