Tomographic Phase Microscopy (TPM) - Biomedical Optical Phase Microscopy and Nanoscopy - page 223

But these techniques do not provide quantitative maps of phase change. Digital
holographic microscopy and phase-shifting interferometric microscopy have been
developed to overcome the qualitative limit of the phase contrast microscopy and
differential interference contrast (DIC) microscopy. They can record the complex field
(both amplitude and phase) of the wave generated by a specimen whose phase part
provides a quantitative phase image of specimen-induced phase changes [5 9] . On the

other hand, these phase microscopy techniques can either provide average refractive
index of cells or cell thickness, but not detailed 3D structure. The imaging of a
complex field is often considered to be 3D imaging due to the possibility of
numerically propagating the recorded field to a different depth. However, the measured
complex field image is only a 2D subset of the 3D object such that the information is
significantly deficient. Depth-dependent information can be obtained only when there
are additional constraints on the target object.

From the viewpoint of information capacity, multiple independent 2D images are to be
acquired in order to obtain the 3D map of the object. In 1969, Wolf first proposed a
theoretical framework known as ODT in which 2D complex field images of a specimen
taken at various illumination angles fill the 3D Fourier space of the specimen [1,2] . Since
then, various methods have been proposed to experimentally record multiple independent
2D complex field images, for example, either for various angles of illumination [10 13] or

for different wavelengths of the light sources [14 15] . In the case of wavelength scanning,

the bandwidth is often limited by the wavelength-dependent index change, i.e., dispersion,
by the sample and optics. Therefore, spatial frequency coverage of the wavelength scanning
is typically narrower than that of the angular scanning. In the case of the angular scanning
method, there are two ways to change the relative angle of illumination with respect to the
specimen. One is to rotate the sample with the illumination beam fixed, and the other is to
rotate the illumination beam with the sample fixed. Rotating the sample makes it possible
to cover the entire angular range, and thus ensures the same axial resolution as the
transverse resolution. But it is difficult to fix the axis of rotation, and rotation inevitably
perturbs the sample. In addition, data acquisition speed is limited due to the mechanical
rotation of the sample. Therefore, the use of sample rotation is typically restricted to solid
nonbiological objects such as optical fibers [10,16] . Special sample preparation is required
for imaging biological cells [12,17] .

On the other hand, the rotating-beam approach does not perturb the sample during data
acquisition and is thus suitable for imaging live cells in their native state [11,13] . Data
acquisition can be fast enough to study the dynamics of the live cells. Only small
modifications are necessary for the instrument to fit into a conventional high NA
(numerical aperture) optical microscope. A drawback of this method is caused by the lack
of complete angular coverage due to the finite numerical aperture of an imaging system. In
fact, conventional optical microscopes share the same limitation. Thus, the axial resolution