Coherent Microscopy and Optical Coherence Tomography for Biomedical Applications - Bioanalysis Advanced Materials Methods and Devices - page 108

where, n is the refractive index. The PSF can be thought of as the image of an

idealized point scattering particle and its size effectively defines the resolution of the
system.
In many ways it is more intuitive to characterize the response of optical systems
in the spatial frequency domain ( k -space or inverse-space) and then go on to
calculate the corresponding PSF if required. In this case the transfer function
(TF) describes how the individual spatial frequency components that make up the
object function are modified by the imaging process. In the frequency domain the
3D convolution of ( 8.1 ) can be written, more simply, as the product,

ð r Þ

ÞDð

O

Þ¼ H ð k ð k k Þ (8.3)

H

where tilde represents Fourier transformation such that, ð k Þ , the system TF, is

defined as,

ð þ1

H

d 3 r

ð k Þ¼ H ð r Þ

exp 2 pjk

ð r Þ

(8.4)

1

In the spatial frequency domain it is noted that each point represents a 3D periodic
structure or Bragg grating within the object [ 29 ]. The 3D structure of a Bragg grating
makes it reflect selectively according to both the wavelength, l , and the angle of
incidence. If the incident and reflected waves are represented by the wave vectors k i
and k r kjj¼

kjj¼ k 0 ¼ 1

= l then the vector representing k g is given by,

k g ¼ k r k i (8.5)

The reflection process is illustrated in Fig. 8.1a , while the relationship described
by ( 8.5 ) is represented schematically by the wave vector diagram in Fig. 8.1b .
Under the assumption of weak scattering it can be shown that the amplitude of the
reflected wave is directly proportional to the amplitude of the refractive index
contrast variation [ 26 ]. Consequently it is possible to measure the amplitude of a
particular spatial frequency component by measuring the response of the object to
appropriately chosen illumination and observation directions. In practice, however,
source availability and restrictions in the possible illumination and observation
directions limit the spatial frequency content that can be measured. In the following
sections, the main methods used in 3D imaging systems are described and compared
in terms of PSF and transfer characteristics and their potential as measurement tools
for the study of micro- and nano-flow studies are then discussed.

8.3 Digital Holographic Microscopy

Digital Holographic Microscopy (DHM) is the name given to techniques that
reconstruct the phase and amplitude of the scattered field from a single, coherent
measurement of the light incident on an imaging array. A fundamental requirement