Biomedical Engineering Reference
In-Depth Information
(A)
(B)
1
1
0.8
0.8
Γ = λ /20
Γ = λ /4
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
0.1 0.2 0.3
Optical path difference γ d (wavelength)
0.4
0
0.1 0.2 0.3
Optical path difference γ d (wavelength)
0.4
Figure 2.4
Contrast as a function of the sample optical path difference at biases 1/20th the wavelength (A)
and quarter wavelength (B). The green color illustrates a case without depolarization (infinity
extinction) and the red one corresponds to extinction 100. (For interpretation of the references to
color in this figure legend, the reader is referred to the web version of this topic.)
The maximal and minimal intensities can be determined using Eq. (2.2) . For the specimen
under consideration, the contrast of the DIC image is the following:
sin
ðð
2
π=λÞΓÞ
sin
ðð
2
π=λÞγ
d
Þ
C 5
(2.14)
1 2 cos
ðð
2
π=λÞΓÞ
cos
ðð
2
π=λÞγ
d
Þ 1 ð
2
=ξÞ
Derivative @C / of this equation is the next:
ð
@
C
5 sin
2
π
λ γ
1 1 ð
2
=ξÞÞ
cos
ðð
2
π=λÞΓÞ 2 cos
ðð
2
π=λÞγ
d
Þ
d
(2.15)
1 2 cos
ðð
2
π=λÞΓÞ
cos
ðð
2
π=λÞγ
d
Þ 1 ð
2
=ξÞ
d . Thus, the best optical contrast is achieved when bias
equals optical path difference in the sample. This result agrees with data obtained by
Salmon and Tran [31] . They found that for the edges of organelles and cells, the optical
path difference corresponds to about λ /10th the wavelength or greater but for microtubules
and tiny organelles in cell, optical path difference is very small, less than 1/100th the
wavelength of green light. Salmon and Tran recommend using about 1/15th 2 1/20th the
wavelength bias for observation of microtubules in order to have sufficient light at the
camera. A similar result was found by Schnapp [32] .
Γ γ
The derivative is zero at
Contrast curves computed with formula (2.14) at different biases and extinctions are given
in Figure 2.4 . According to Figure 2.4 , the contrast of microtubules and tiny organelles with
a phase difference
λ
/100 equals 0.38 at bias
λ
/20 and infinity extinction, 0.27 at bias
λ
/20
and extinction 100, and 0.06 at bias
/4 and both extinctions. The contrast at the small bias
is greater than 6 times the contrast at the large bias. However, it is very important to have a
λ
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