1035:. In this case, the physical process can be considered as an array of band-filters with constant relative bandwidth to the center frequency, using short windows at high frequencies and long windows at low frequencies. Unlike the STFT, the WT method is not constrained by constraint bandwidth and may adapt the window size to a desired frequency. For this method the tradeoff is this between time and frequency resolutions.
25:
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interference terms. Separation between the two overlapping signal terms is challenging as this information is contained within the interference terms. For time-frequency analysis, the WD effectively suppresses the interference terms and as a result compromises joint time-frequency resolution with the level of suppression of the interference terms.
136:. The general principles behind SOCT arise from the large optical bandwidths involved in OCT, where information on the spectral content of backscattered light can be obtained by detection and processing of the interferometric OCT signal. SOCT signal can be used to quantify depth-resolved spectra to retrieve the concentration of tissue
610:
is the
Fourier transform. However, due to the wavelength dependence with depth for both scattering and absorption in tissue, direct Fourier transform cannot be applied to obtain localized spectroscopic information from the OCT signal. For this reason, a time-frequency analysis method must be applied.
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can be used to extract structural knowledge of samples from time-localized information contained within the cross-terms. The Wigner distribution applies a
Fourier transform to the autocorrelation of the OCT interferogram. The drawback of this method lies in its quadratic nature, contained in its
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Similarly another common approach is simply though calibration measurements, if the absorption coefficient of a scattering sample can be obtained through a separate calibration measurement, then isolating the scattering coefficient is pretty straight forward. One problem with this method is it
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2041:, where the scattering dependence on wavelength with a power law. In this approach the absorption spectrum is regarded as the total absorption contribution overall known chromophores, with a least-squares fitting to the measured attenuation values.
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First the number of acquisitions – averaging and multiple integrations are critical for valid measurements due to the presence of speckle noise. But this value reduces with the square root of the number of independent scans in the
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The backscattering coefficient may be experimentally determined as long as a full understanding of zeta. Commonly zeta is measured by separate calibration with a sample having a known backscattering coefficient defined by
315:
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is a spatially confined windowing function that extracts spatially-localized frequency information by suppressing information from outside of the window, commonly a
Gaussian distribution, centered around
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Due to losses in spectral resolution sample inhomogeneity can be a factor, and there are sensitivity issues with system NA and spectrometer roll off that also affect both accuracy and resolution.
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Finally for certain applications, the real and imaginary part of the complex refractive index may be used to isolate the individual contributions from both absorption and scattering. using
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assumes that tissue scattering is equal across various tissue regions, but if different structures have different absorption parameters it would just throw off the measurements.
862:(WT) approach may also be considered. Using both a series of function localized in both real and Fourier space from the complex window function w, by translations and dilations
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showed it was possible to separate the necessary contributions from the real part of the refractive index from a nonlinear dispersion phase term in the OCT signal.
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The following discussion of techniques for quantitatively obtaining localized optical properties using SOCT is a summary of the concepts discussed in
Bosscharrt
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2246:. This is because the imaginary part of the refractive index can be tied to the absorption spectra using Kramer-Kronig relations. Robles
128:) is an optical imaging and sensing technique, which provides localized spectroscopic information of a sample based on the principles of
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allows for extraction of information of both time and frequency components of a signal. In most SOCT applications a continuous
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855:. As a result, there exists an inherent trade-off between spatial and frequency resolution using the STFT method.
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is the OCT signal attenuation coefficient and the factor 2 accounts for the double pass attenuation from depth
1860:{\displaystyle \mu _{b,NA}=\mu _{s}\cdot 2\pi \textstyle \int _{\pi -NA}^{\pi }p(\theta )\sin \theta d\theta }
986:{\displaystyle {\text{WT}}(k,d)=\int _{-\infty }^{\infty }(d')w{\bigg (}{\frac {d-d'}{\kappa }}{\bigg )}d(d')}
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may be applied, where under the right conditions have a reduced resolution penalty. For SOCT purposes the
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From the experimentally determined value of the OCT attenuation coefficient can be further expressed as:
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782:{\displaystyle {\text{STFT}}(k,d;w)=\int _{-\infty }^{\infty }i_{d}(d')w(d-d';\Delta d)e^{-ikd'}d(d')}
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The overall accuracy of SOCT to isolate the localized optical spectra is limited by several factors:
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Several approaches have been used to effectively isolate the individual contributions of absorption (
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The time-frequency analysis methods described above, result in a wavelength resolved power spectrum
2332:"Temporal coherence and time-frequency distributions in spectroscopic optical coherence tomography"
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2137:{\displaystyle \mu _{OCT}=a\cdot \lambda ^{-b}\textstyle \sum _{i}\displaystyle (c_{i}\mu _{a,i})}
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1202:{\displaystyle {\text{WD}}(k,d)=\int _{-\infty }^{\infty }i_{d}(d+d')i_{d}*(d-d')e^{-ikd'}d(d')}
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The first term on the right represents the scattering component with a scaling factor
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1754:. The backscattering coefficient is both sample and source dependent and defined as:
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are the fields returning from sample and reference arm, respectively, with
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the source power spectrum incident on the sample and T the axial PSF. The
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at d = 0. These system-dependent parameters are defined such that with
310:{\displaystyle i_{d}=|E_{s}|^{2}+|E_{r}|^{2}+2\{E_{s}E_{r}\cos(k2d)\}}
2287:. Drexler, Wolfgang, Fujimoto, James G. (Second ed.). Cham.
2285:
Optical coherence tomography : technology and applications
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is sample dependent and is discussed in further detail below.
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is the scaling factor, which dilates or compress the wavelet
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descriptions of the collected OCT signal, can be related by
1381:{\displaystyle S(d)=\xi \cdot \mu _{b,NA}e^{-2\mu _{OCT}d}}
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is the assigned depth location in the tissue. Both the
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577:{\displaystyle i_{d}(2d)=|{\mathcal {F}}\{i_{d}(k)\}|}
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1664:{\displaystyle \mu _{OCT}=\mu _{t}=\mu _{s}+\mu _{a}}
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58:"Spectroscopic optical coherence tomography"
2336:Journal of the Optical Society of America A
2001:) from the overall OCT signal attenuation (
122:Spectroscopic optical coherence tomography
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2330:Graf, Robert N.; Wax, Adam (2007-07-11).
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109:Learn how and when to remove this message
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1673:with the total attenuation coefficient
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171:The general form of the detected OCT
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47:adding citations to reliable sources
167:Localized spectroscopic information
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615:Time-frequency analysis methods
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2244:Kramers-Kronig (KK) relations
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408:{\textstyle k=2\pi /\lambda }
2407:Optical coherence tomography
624:short-time Fourier transform
130:optical coherence tomography
1498:determine the amplitude of
603:{\textstyle {\mathcal {F}}}
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16:Optical imaging technique
1587:{\textstyle \mu _{b,NA}}
1491:{\textstyle \mu _{b,NA}}
132:(OCT) and low coherence
2356:10.1364/josaa.24.002186
2027:{\textstyle \mu _{OCT}}
1415:{\textstyle \mu _{OCT}}
1240:as a function of depth
626:(STFT) method is used,
620:Time-frequency analysis
148:), characterize tissue
2315:: CS1 maint: others (
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1260:. Assuming the first
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2294:978-3-319-06419-2
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1455:{\textstyle \xi }
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2342:(8): 2186–95.
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488:spatial domain
479:{\textstyle d}
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134:interferometry
117:
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173:interferogram
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60: –
59:
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54:Find sources:
48:
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32:This article
30:
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138:chromophores
125:
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99:October 2020
96:
86:
79:
72:
65:
53:
41:Please help
36:verification
33:
832:with width
464:path length
439:. Further,
2396:Categories
2271:References
2263:averaging.
1930:Mie theory
1295:Beer's law
437:wavelength
377:wavenumber
142:hemoglobin
69:newspapers
2364:1084-7529
2311:cite book
2303:912287126
2115:μ
2091:∑
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2073:⋅
2052:μ
2010:μ
1983:μ
1956:μ
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1836:θ
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146:bilirubin
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2254:Accuracy
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