Coherent Microscopy and Optical Coherence Tomography for Biomedical Applications - Bioanalysis Advanced Materials Methods and Devices - page 112

Fig. 8.5 Coherent
microscopy configuration

Focal
Plane

K r

Object

where G NA ð represents the wave vectors collected by the system. For the case of a

coherent microscope operating at wavelength, l , the plane wave components
collected by the circular aperture can be represented in k -space by wave vectors,
k r that fall on a spherical shell with a radius equal to the wave number k 0 ¼

k Þ

1

= l .

G NA ð

Accordingly k Þ is given by,

q

1

o
k o

j
4 pk o d

k

G NA ð

k Þ¼ ð

jj

k k 0 Þ N A

step (8.7)

where N A is the NA of the objective, o is a unit vector in the direction of the viewing
axis, and ( x ) and step( x ) represent the Dirac delta function and Heaviside step

function, respectively.
It is clear that ( 8.3 ) and ( 8.6 ) have identical form; however, it is important to
emphasize that the TF,

d

H

ð k Þ in ( 8.3 ), is applied to the spectrum of the object

function , Dð

, whereas G NA ð modifies the spectrum of the scattered field, E s k Þ k Þ ð k Þ .

H DHM ð

In order to calculate the TF for DHM, , it is necessary to consider the

illumination. From the discussions in Section 2 it is apparent that if the object
is illuminated by a plane wave described by the vector k i ,

k Þ

G NA ð

H DHM ð

k Þ , and k Þ

are related such that,

H DHM ð

Þ¼ G NA k

k ð þ k i Þ

q

1

o

j
4 pk o d

ð k þ k i Þ

N A ¼ ð j k þ k i j k 0 Þ step (8.8)

k o