Biomedical Engineering Reference
In-Depth Information
To retrieve the phase information, several single-frame techniques have been proposed for
the evaluation of the phase
[8]
. These include Fourier transform
[9]
, Hilbert transform
[10]
,
spatial phase shifting
[11]
, windowed Fourier transform
[12]
, and wavelet transform
[13]
.
The phase reconstructions are more or less identical except for spatial phase shifting,
indicating that the reconstruction of the profiles does not suffer from large errors. Temporal
phase shifting
[14]
is a multiframe method for reconstructing the phase information. This
method can obtain accurate results; however, it typically requires five frames.
As an example of the full steps required for retrieving the OPD, the use of the Fourier
transform method is described next. First, a Fourier transform is performed on the spectral data
giving the depth space. A Gaussian bandpass filter is then applied on the positive term of the
complex depth function to remove noise and unwanted reflections. Then, an inverse Fourier
transform is applied returning to wavenumber space and giving the complex expression:
p
R
R
R
S
(13.8)
IðkÞ
5
2
SðkÞ
exp
½jð
2
kΔd
1
θÞ
The phase term can be retrieved as:
ϕðkÞ
5
2
kΔd
1
θ
(13.9)
where
Im
ð
I
Þ
Reð
I
Þ
ϕðkÞ
5
arctan
(13.10)
To determine the OPD, the phase function needs to be unwrapped. First, a least-squares
algorithm is used to determine the slope of the phase as a function of the wavelength. Then,
the slope of the phase function is used as the reference to remove 2
ambiguity, and one
phase component for wavenumber
k
i
is chosen to give the absolute OPD as:
π
floor
ϕ
0
2
Δd
5
ϕð
k
i
Þ
2
k
i
1
k
i
(13.11)
π
ϕ
0
is the phase that was retrieved from the slope of the phase function. An
illustration of the process is shown in
Figure 13.5
.
where
13.4 Phase OCM Applications
In this section, we review several biomedical applications of phase-sensitive OCM. These
applications take advantage of dynamic measuring capabilities and high sensitivity for small
changes in living cells that can be obtained by phase OCM. The high stability of these
systems allows observing biological processes over an extended period of time. In addition,
the imaging technique can be combined with labeling techniques such as using gold
particles, to achieve even greater specificity of the cellular processes.
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