Coherent Microscopy and Optical Coherence Tomography for Biomedical Applications - Bioanalysis Advanced Materials Methods and Devices - page 107

It is clear from the above discussions that although 3D microscopy techniques
might seem quite disparate both in configuration and application, they are similar in
many important respects. With the exception of fluorescent confocal microscopy,
elastically scattered light is collected from the object of interest and interferometric
methods are used to record the phase and the amplitude of the scattered field. In an
abstract sense, all optical techniques derive information from the response of the
object to a set of optical stimuli with known spatial and temporal characteristics.
Hence, it is only the scanning methods that provide the illuminating fields and those
used to record the corresponding responses, which differentiate the various
techniques.
In previous papers [ 21 , 25 ] we have applied scalar diffraction theory to many
optical imaging techniques, characterizing them as 3D linear systems. In addition
we have also considered image enhancing methods such as phase contrast etc. as 3D
linear filtering operations [ 11 ]. Although the details of this analysis are beyond the
scope of the present chapter, the main results provide a useful insight into their
capability. In the following sections the basis of linear imaging theory is presented
and the theoretical performance of coherent microscopy and optical tomography is
then compared.

8.2 Linear Imaging Theory

The foundations of 3D linear imaging theory were laid by Wolf [ 26 ] and Dandliker
[ 27 ] who considered the reconstruction of the 3D form of an object from holo-
graphic recordings. The theory rests on the assumption of weak scattering or the
Born approximation [ 28 ]. In effect it is assumed that the scattered field is a small
perturbation to the field that illuminates the object. This is often the case in flow
measurements, for example, where the fluid is usually sparsely seeded with small
tracer particles. Although the Born approximation is not strictly justified in dense
tissue, linear theory still provides a good estimate of imaging performance as
multiple scattering typically raises noise levels in this situation.
According to linear systems theory [ 21 ], the process of imaging can be thought
of as a filtering operation that is characterized in the space domain by the 3D
convolution integral,

ð þ1

r 0 rðÞ

d 3 r 0

O ð r Þ¼ H r ð Þ D

(8.1)

1

is the point spread function (PSF) and d 3 r d r x d' r y d' r z . The function

where H ð r Þ ¼

represents the object and in this chapter is defined as the refractive index
contrast given by,

Dð r Þ

2 1

Dð r Þ¼ 4 p ð n ð r Þ Þ (8.2)