Biomedical Engineering Reference
In-Depth Information
18
m
1
16
14
12
10
8
6
4
2
0
m
2
0
2
4
6
8
10
12
14
16
Figure 7.14
Linear regression phase unwrapping: m
1
(m
2
).
By simply trying different values of
m
2
, we can pick the value at which this equation yields
the result which is closest to a non-negative integer number, thus determining the most
likely number of integer wavelengths.
The linear function
m
1
(
m
2
) is plotted in
Figure 7.14
. The ratio of wavelengths can usually
be determined very accurately, so the uncertainty of the slope of this line is low. Moreover,
it is uniform throughout the image, as both the phases are contained only in the
y
-intercept
term.
Figure 7.15
shows the square of the difference between
m
1
and the nearest integer. In this
case,
m, which increases the range
approximately 16 times. Indeed, the function in
Figure 7.2
has a local minimum every 16
points. Within the range of 0
λ
5
635 and
λ
5
675 nm, so
Λ
5
10.7
μ
1
2
12
16 (the height of the object is less than the synthetic
wavelength), the value of
m
2
is easy to select, directly obtaining the lower noise phase
unwrapped map. Moreover, as some of these local minima are smaller than others, we can
further extend the imaging range by simply selecting the smallest of the local minima,
extending the unambiguous phase measurements well beyond the synthetic wavelength.
In practice, if the phase measurements are noisy, this method may fail and pick the wrong
local minimum, so the total height (maximum value of
m
2
) has to be limited to some
reasonable number. For example, if the approximate size of the imaged object is known,
either through some other technique or simply by looking at a wrapped single wavelength
phase map and estimating the approximate number of phase jump, then there is no need to
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