Biomedical Engineering Reference
In-Depth Information
far from the back focal plane, the prism only makes the rays parallel. But those beams are
spatially displaced and hence are not recombined. Therefore, the Smith-shearing DIC
scheme requires special design for the microscope objective lenses so that the Wollaston
prism can be incorporated within.
Nomarski
[4,5]
took another approach and proposed in 1952 the use of a special
polarization prism. This Nomarski prism (see insert in
Figure 2.1
) introduced spatial
displacement and angular deviation of orthogonally polarized beams simultaneously. The
prism can therefore be placed outside of the objective lens. By using crystal wedges with
appropriately oriented axes, the Nomarski prism recombines the two beams that were
separated by the condenser Wollaston as though a regular Wollaston prism were located at
the back aperture plane in the objective lens. This feature enables the use of the Nomarski
DIC scheme with regular high NA microscope objectives.
A DIC image can be modeled as the superposition of one image over an identical copy that
is displaced by a small amount
d
and phase shifted by bias
Γ
. For simplicity, consider a
phase nonbirefringent specimen, which is described by Cartesian coordinates
X
O
Y
in the
object plane. The specimen is illuminated by monochromatic light with wavelength
λ
. The
intensity distribution
I
(
x
,
y
) in the images depends on specimen orientation and varies
proportionally with the cosine of the angle made by the gradients azimuth
θ
and the relative
direction of wavefront shear
σ
[6]
:
π
λ
ðΓ
1
d
Þ
5
I
~
sin
2
I
ð
x
;
y
γð
x
;
y
Þ
cos
ðθð
x
;
y
Þ
2
σÞÞ
1
I
c
ð
x
;
y
Þ
(2.2)
where
I
~
is the initial beam intensity,
γ
(
x
,
y
) and
θ
(
x
,
y
) are the gradient magnitude and
azimuth, and
I
c
(
x
,
y
) corresponds to a constant offset of the intensity signal.
It follows from
formula (2.2)
that if the shear direction is parallel to the optical path
gradient (
θ
2
σ
5
180
) the image contrast is maximal. Where the shear
direction is perpendicular to the gradients (
θ
2
σ
5
0
or
θ
2
σ
5
270
) the contrast equals
zero. Thus, the regular DIC technique shows the two-dimensional distribution of optical
path gradients encountered along the shear direction. It is therefore prudent to examine
unknown objects at several azimuth orientations
[5,7]
.
θ
2
σ
5
90
or
The DIC microscopy demonstrates remarkable optical sectioning capability, like confocal
microscopy. The depth in specimen space that appears to be in focus within the image,
without readjustment of the microscope focus, is the depth of field. In a regular bright-field
microscope, the total depth of field
d
tot
is given by the sum of the diffraction-limited wave
and geometrical optical depths of field as
[8,9]
:
d
tot
5
λ
n
NA
2
1
n
M
3
NA
e
(2.3)
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