Biomedical Engineering Reference
In-Depth Information
channels. Here, we describe applications for multiple-wavelength phase unwrapping and
also coregistered phase and fluorescence imaging to provide morphological information in
conjunction with molecular specificity. The primary advantage of using a commercial RGB
camera for multimodality imaging is that all information is captured simultaneously through
different color channels and thus is immune to temporal motion artifacts.
14.4.1 RGB Camera Multiplexing for Phase Unwrapping
QPM is useful for investigating mostly transparent samples. By interferometrically
detecting a transmitted wavefront in weakly diffracting samples, such as cells, microfluidic
chambers, and other protein-based microstructures [26 28] , it is possible to quantify the
OPDs across a field of view. However, any structure delaying the light by more than one
wavelength introduces phase ambiguities, which arise as a direct result of mathematically
calculating phase by an arctangent operation. The two-argument variant of arctangent is
limited to an unambiguous range of
; therefore, any relative phase changes across a
field of view exceeding 2
π
require additional processing to remove the incorrect
discontinuities.
There have been many algorithms developed for removing 2
ambiguities from quantitative
phase measurements, including two-dimensional spatial algorithms with robustness against
noisy data [29 32] and also temporal algorithms [33] . However, these algorithms all
involve minimizing the total phase gradient, which enforces the presumption of a smooth
phase that does not vary by more than
π
between two adjacent points. Samples that have
high aspect ratios or sharp edges violate this condition and therefore require alternative
approaches for accurate phase unwrapping.
π
An alternative approach for digital unwrapping relies on measuring the OPDs at a specific
location using more than one wavelength. The OPDs through a sample are related to the
optical phase,
φ
m , measured modulo 2
π
at a given wavelength,
λ
m , as:
yÞ 5 φ m ð x ; y Þλ m
2
OPD m ðx
;
(14.4)
π
Several methods of two-wavelength unwrapping extend the range of measurable OPDs by
first creating a synthetic phase map,
φ
5
(
φ
2 )
1
2
π
[(
φ
2 )
,
0], that is
12
1
1
j )
[34 36] . While the resulting phase map has a larger range of measurement, the phase noise
in φ 12 is also larger than either φ 1 or φ 2 [34] . Gass et al. [34] reported that if the phase
noise of φ m is defined as 2 πε m , the phase noise in φ 12 becomes 2 πε 12 5 2 π ( ε 1 2 ). For
transparent samples, the noise in OPD m is ε m λ m ; therefore, the noise in OPD 12 is amplified
by a factor of B 2
Λ
5
λ
λ
2 /
unambiguous over the range of the “beat” wavelength, defined as
(
12
1
1
2
λ m . Because of this amplification inherent to the mathematical
process, the beat wavelength OPD map is only used as a guide for adding multiples of
Λ 12 /
λ m
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