Properties of photon density waves in multiple-scattering media

Article · February 1993with26 Reads
DOI: 10.1364/AO.32.000607 · Source: PubMed
Amplitude-modulated light launched into multiple-scattering media, e.g., tissue, results in the propagation of density waves of diffuse photons. Photon density wave characteristics in turn depend on modulation frequency (omega) and media optical properties. The damped spherical wave solutions to the homogeneous form of the diffusion equation suggest two distinct regimes of behavior: (1) a high-frequency dispersion regime where density wave phase velocity V(p) has a radicalomega dependence and (2) a low-frequency domain where V(p), is frequency independent. Optical properties are determined for various tissue phantoms by fitting the recorded phase (?) and modulation (m) response to simple relations for theappropriate regime. Our results indicate that reliable estimates of tissue like optical properties can be obtained, particularly when multiple modulation frequencies are employed.
    • Light propagation in turbid media is governed by the radiation transport theory. In the context of the steady-state diffuse approximation, the light penetration depth of conventional uniform or planar illumination depends on tissue optical absorption and scattering properties, which is calculated from the following equation (Tromberg et al., 1993):
    [Show abstract] [Hide abstract] ABSTRACT: Structured-illumination reflectance imaging (SIRI) provides a new means for enhanced detection of defects in horticultural products. Implementing the technique relies on retrieving amplitude images by illuminating the object with sinusoidal patterns of single spatial frequencies, which, however, are limited in interrogating the tissues at different depths. This study presented a first exploration of using composite sinusoidal patterns that integrated two and three spatial frequencies of interest, in SIRI for enhanced detection of defects in food (e.g., bruises in apples). Three methods based on Fourier transform were proposed to retrieve amplitude images at different frequencies by using either phase shifting with or without spiral phase transform (SPT) or frequency-domain filtering. The phase-shifting method involves solving a linear system that is composed of multiple phase-shifted pattern images in the Fourier space, and SPT that acts as a two-dimensional quadrature transform operator is used to reduce the images needed for amplitude retrieval; while the filtering-based method directly extracts different frequency components from only one pattern image that are then subjected to SPT processing. The three methods were tested for dual-frequency and triple-frequency patterns through numerical simulations and experiments on the detection of fresh bruises in apples by SIRI. The phase-shifting methods showed good performance in terms of small demodulation errors and strong image contrast for bruise detection; the filtering-based method, although viable in numerical simulation, needed improvement due to the worst practical performance. In addition, more frequency components introduced in the pattern would deteriorate the performance of these methods, and grid composite patterns were superior over the fringe ones due to reduced interactions between different frequency components.
    Full-text · Article · Dec 2016
    • In a typical DRS measurement scheme, light is injected into the sample at a certain location and the diffusely reflected light is collected by a detector placed at a distance from the light injection location. One of the DRS variants employs an intensity modulated light source to investigate the light amplitude demodulation and phase delay introduced by the turbid sample which can be in turn utilized to quantify the sample's absorption (μ a ) and reduced scattering (μ s ') properties[5,6]. Such techniques are usually categorized as the frequency-domain (FD) DRS method and has been successfully used in conjunction with the standard diffusion equation (SDE)[7]to characterize the optical properties of deep tissues, such as breast and brain, with source-detector separations (SDSs) longer than 10 mm[8][9][10].
    [Show abstract] [Hide abstract] ABSTRACT: Diffuse reflectance spectroscopy (DRS) based on the frequencydomain (FD) technique has been employed to investigate the optical properties of deep tissues such as breast and brain using source to detector separation up to 40 mm. Due to the modeling and system limitations, efficient and precise determination of turbid sample optical properties from the FD diffuse reflectance acquired at a source-detector separation (SDS) of around 1 mm has not been demonstrated. In this study, we revealed that at SDS of 1 mm, acquiring FD diffuse reflectance at multiple frequencies is necessary for alleviating the influence of inevitable measurement uncertainty on the optical property recovery accuracy. Furthermore, we developed artificial neural networks (ANNs) trained by Monte Carlo simulation generated databases that were capable of efficiently determining FD reflectance at multiple frequencies. The ANNs could work in conjunction with a least-square optimization algorithm to rapidly (within 1 second), accurately (within 10%) quantify the sample optical properties from FD reflectance measured at SDS of 1 mm. In addition, we demonstrated that incorporating the steady-state apparatus into the FD DRS system with 1 mm SDS would enable obtaining broadband absorption and reduced scattering spectra of turbid samples in the wavelength range from 650 to 1000 nm.
    Full-text · Article · Apr 2016
    • In practice, especially in diffuse optical imaging, the modulation frequency is scanned to obtain corresponding values of modulation index and phase. Then, a non-linear fit of the theoretical prediction with the data provides the estimates for the scattering and absorption properties of the medium [14] . The effect of scattering media on modulation index and phase can also be exploited to attain discrimination of ballistic photons that retain the modulation index and phase.
    [Show abstract] [Hide abstract] ABSTRACT: The efficiency of using intensity modulated light for estimation of scattering properties of a turbid medium and for ballistic photon discrimination is theoretically quantified in this article. Using the diffusion model for modulated photon transport and considering a noisy quadrature demodulation scheme, the minimum-variance bounds on estimation of parameters of interest are analytically derived and analyzed. The existence of a variance-minimizing optimal modulation frequency is shown and its evolution with the properties of the intervening medium is derived and studied. Furthermore, a metric is defined to quantify the efficiency of ballistic photon filtering which may be sought when imaging through turbid media. The analytical derivation of this metric shows that the minimum modulation frequency required to attain significant ballistic discrimination depends only on the reduced scattering coefficient of the medium in a linear fashion for a highly scattering medium.
    Article · Feb 2016
    • Single-modulation-frequency and multiple-modulation-frequency FDPM systems have both been successfully applied to study turbid samples [8, 10]. It has been reported that at higher modulation frequencies, the phase shift introduced by the variation of optical properties is larger [11, 12]. Such phenomenon is beneficial for discerning the minute change of tissue properties and thus is helpful for prognosis and biological status monitoring.
    [Show abstract] [Hide abstract] ABSTRACT: Except the fundamental modulation frequency, by higher-order-harmonic modulations of mode-locked laser pulses and a simple frequency demodulation circuit, a novel approach to GHz frequency-domain-photon-migration (FDPM) system was reported. With this novel approach, a wide-band modulation frequency comb is available without any external modulation devices and the only electronics to extract the optical attenuation and phase properties at a selected modulation frequency in FDPM systems are good mixers and lock-in devices. This approach greatly expands the frequency range that could be achieved by conventional FDPM systems and suggests that our system could extract much more information from biological tissues than the conventional FDPM systems. Moreover, this demonstration will be beneficial for discerning the minute change of tissue properties.
    Full-text · Article · Feb 2014
    • On the other hand, the lack of a practical demand for radiance applications has produced only few theoretical studies [38, 40, 41] that would enrich experiments and stimulate further developments as was done for fluence based techniques. Indeed, the simplicity of basic fluence measurements, the equivalency between the detector and the light source (for example, the isotropic spherical diffuser can act in both capacities) and a relative straightforwardness of results interpretation have triggered a spectacular growth in applications of fluence-based techniques [12, 20, 22,42434445464748495051525354555657. Hence, the lack of the perturbation formalism that can be easily applied to analysis of radiance data for localized inclusions in turbid media seriously impedes further progress of the radiance-based methods.
    [Show abstract] [Hide abstract] ABSTRACT: We analyze a role of a localized inclusion as a probe for spatial distributions of migrating photons in turbid media. We present new experimental data and two-dimensional analysis of radiance detection of a localized absorptive inclusion formed by gold nanoparticles in Intralipid-1% when the target is translated along the line connecting the light source and detector. Data are analyzed using the novel analytical expression for the relative angular photon distribution function for radiance developed by extending the perturbation approach for fluence. Obtained photon maps allow predicting conditions for detectability of inclusions for which proximity to the detector is essential.
    Full-text · Article · Dec 2013
    • While fluence and radiance both measure cw light intensity, angular-resolved measurements of radiance provide added value increasing the information content available to recover the optical properties of tissue. Intensity modulated techniques rely on exploring the diffusive wave in tissue that is produced by modulating the light source with a frequency in a range of 100 MHz −1 GHz [2,42434445464748. In response to an external intensity modulated stimulus, the medium attenuates the signal and introduces a phase shift relative to the input signal.
    [Show abstract] [Hide abstract] ABSTRACT: We present a new method for extracting the effective attenuation coefficient and the diffusion coefficient from relative spectrally resolved cw radiance measurements using the diffusion approximation. The method is validated on both simulated and experimental radiance data sets using Intralipid-1% as a test platform. The effective attenuation coefficient is determined from a simple algebraic expression constructed from a ratio of two radiance measurements at two different source-detector separations and the same 90° angle. The diffusion coefficient is determined from another ratio constructed from two radiance measurements at two angles (0° and 180°) and the same source-detector separation. The conditions of the validity of the method as well as possible practical applications are discussed.
    Full-text · Article · Oct 2012
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