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Arjun G. Yodh - One of the best experts on this subject based on the ideXlab platform.
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Reflection and transmission coefficients for diffuse Photon Density waves in a diffuse/non-diffuse interface
Biomedical Optical Spectroscopy and Diagnostics, 2000Co-Authors: Jorge Ripoll, Manuel Nieto-vesperinas, Britton Chance, J P Culver, Vasilis Ntziachristos, Arjun G. YodhAbstract:Diffuse Photon Density Waves (DPDWs) have lately been used to characterize diffusive media to locate and characterize hidden objects, such as tumors, in soft tissue. Measurements are often taken in the exterior non-diffuse medium, and therefore, the DPDW suffers reflection at the interface. To analyze these, the basic expressions for the reflection and transmission coefficients for diffuse/non-diffuse interfaces are put forward. Interesting effects on the reflected DPDW occur for certain values of the diffusive parameters, which significantly distort the incident DPDW. Also, the expression for the transmission coefficient can also be used to determine the value of the extrapolated distance, or, if this parameter is known, the source shape and its position.
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Near-field diffraction tomography with diffuse Photon Density waves.
Physical Review E, 2000Co-Authors: D N Pattanayak, Britton Chance, T Durduran, J P Culver, Arjun G. YodhAbstract:An angular spectrum algorithm is presented for fast, near-field diffraction tomographic imaging with diffuse Photon Density waves in highly scattering media. A general relation in K space is derived that connects the spatial variations of the optical properties of heterogeneities to the spatial spectra of the measured scattered diffuse Photon Density waves. The theory is verified experimentally for situations when boundary effects can be neglected. We further describe how to reconstruct absorption and scattering properties simultaneously, and how to incorporate boundary conditions into this angular spectrum algorithm for a turbid medium of finite size ~e.g., the slab medium!. Limitations and potential improvements of the near-field diffraction tomography are also discussed. fraction tomography @16,17#, it is possible to rapidly recon- struct thin slice and spherical objects whose absorption and/or scattering parameters differ from the background ho- mogeneous scattering medium @20#. Our image reconstruc- tion algorithm, based upon diffraction tomography technique ~called angular spectrum algorithm in this paper!, is rapid, permitting object localization and characterization in ;1000 volume-element samples on sub-second computational time scales. Such an angular spectrum algorithm has recently at- tracted the attention of many researchers in Photon migration field@18,19#. In this paper we provide a more complete dis- cussion of the results reported in those earlier papers, and we provide a detailed analysis of this algorithm incorporating the effects of finite boundaries. We first derive the general integral solution of the total and scattered Photon Density waves in a heterogeneous turbid medium within the first or- der Born approximation ~Secs. II, III, and IV!. These ses- sions are largely reviews, but are included for completeness and clarity. We next derive a relation in K space between the spatial spectrum of the heterogeneity function and the spatial spectrum of the measured scattered diffuse Photon Density wave ~Sec. V A!. Experimental results are presented to verify the feasibility of the angular spectrum algorithm for image reconstruction. We then describe a method to recon- struct the absorption and scattering properties simultaneously with this algorithm. Some limitations and potential improve- ments of the diffraction tomography are discussed in Sec. VI. Finally, we illustrate how to incorporate boundary conditions into the angular spectrum algorithm for a turbid medium of finite size, in particular, the slab medium and the semi- infinite medium~Sec. VII!.
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Near-field diffraction tomography with diffuse Photon Density waves.
Physical review. E Statistical physics plasmas fluids and related interdisciplinary topics, 2000Co-Authors: D N Pattanayak, Britton Chance, T Durduran, J P Culver, Arjun G. YodhAbstract:An angular spectrum algorithm is presented for fast, near-field diffraction tomographic imaging with diffuse Photon Density waves in highly scattering media. A general relation in K space is derived that connects the spatial variations of the optical properties of heterogeneities to the spatial spectra of the measured scattered diffuse Photon Density waves. The theory is verified experimentally for situations when boundary effects can be neglected. We further describe how to reconstruct absorption and scattering properties simultaneously, and how to incorporate boundary conditions into this angular spectrum algorithm for a turbid medium of finite size (e.g., the slab medium). Limitations and potential improvements of the near-field diffraction tomography are also discussed.
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Diffraction tomography for biochemical imaging with diffuse-Photon Density waves
Optics Letters, 1997Co-Authors: T Durduran, Britton Chance, Arjun G. Yodh, D N PattanayakAbstract:The spatial structure of optically heterogeneous turbid media is probed with diffusive light. Projection images are obtained experimentally by deconvolution of the scattered diffuse-Photon Density waves on a planar boundary by use of a fast Fourier transform. The method is very fast, permitting object localization and characterization in ∼1000 volume-element samples on subsecond computational time scales. The optical properties of slice-shape inhomogeneities are accurately determined.
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fluorescent diffuse Photon Density waves in homogeneous and heterogeneous turbid media analytic solutions and applications
Applied Optics, 1996Co-Authors: M A Oleary, David A. Boas, Britton Chance, Arjun G. YodhAbstract:We present analytic solutions for fluorescent diffuse Photon Density waves originating from fluorophores distributed in thick turbid media. Solutions are derived for a homogeneous turbid medium containing a uniform distribution of fluorophores and for a system that is homogeneous except for the presence of a single spherical inhomogeneity Generally the inhomogeneity has fluorophore concentration, and lifetime and optical properties that differ from those of the background. The analytic solutions are verified by numerical calculations and are used to determine the fluorophore lifetime and concentration changes required for the accurate detection of inhomogeneities in biologically relevant systems. The relative sensitivities of absorption and fluorescence methods are compared.
Enrico Gratton - One of the best experts on this subject based on the ideXlab platform.
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Fluorescence Photon-Density waves in optically diffusive media
Optics Communications, 2000Co-Authors: Sergio Fantini, Enrico GrattonAbstract:Abstract Intensity-modulated light launches traveling Photon-Density waves into optically diffusive media. In the presence of a fluorophore, excitation Photon-Density waves generate fluorescence Photon-Density waves that can be quantitatively described using diffusion theory. We examine a number of limiting cases of the fluorescence Photon-Density wave to clarify its physical meaning and its implications in quantitative fluorescence spectroscopy of diffusive media. Our discussion may guide the development of experimental protocols for quantitative fluorescence spectroscopy in optically diffusive media.
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Exploring tissue dynamics by Photon-Density-wave fluctuation correlation spectroscopy
Saratov Fall Meeting '98: Light Scattering Technologies for Mechanics Biomedicine and Material Science, 1999Co-Authors: Vlad Toronov, Sergio Fantini, Mattia A. Filiaci, Maria Angela Franceschini, Enrico GrattonAbstract:We propose Photon-Density-wave fluctuation correlation spectroscopy as a method to study the dynamics of tissue optical properties. Phantom measurements have shown that our frequency-domain instrument is appropriate to explore intensity, modulation and phase fluctuations in the frequency band from 0 to 125 Hz. Preliminary in vivo studies have revealed a rich optical dynamics in human tissues.
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Photon-Density WAVE CORRELATION SPECTROSCOPY DETECTS LARGE-SCALE FLUCTUATIONS IN TURBID MEDIA
Physical Review E, 1998Co-Authors: Vlad Toronov, Sergio Fantini, Mattia E. Filiaci, Enrico GrattonAbstract:PHYSICAL REVIEW E VOLUME 58, NUMBER 2 AUGUST 1998 Photon-Density wave correlation spectroscopy detects large-scale fluctuations in turbid media V. Toronov, * M. Filiaci, S. Fantini, and E. Gratton Laboratory for Fluorescence Dynamics, Department of Physics, University of Illinois at Urbana–Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080 ~Received 10 December 1997! We study the fluctuations in the Photon-Density wave parameters @average intensity ~dc!, modulation ampli- tude, and phase# caused by macroscopic fluctuations in the optical properties of turbid media. We present both a theoretical analysis based on diffusion theory and its experimental verification on a strongly scattering suspension containing absorbing particles ~1–1.6 mm effective diameter! in turbulent motion. The Photon- Density waves are induced by the laser diode output ~750 nm!, which is intensity-modulated at 110 MHz. The dc, amplitude, and phase are acquired with an acquisition time per data point of 8 ms, which corresponds to a frequency bandwidth of 62.5 Hz. We have found that in the presence of the absorbing particles, the dc and phase average values and power spectra are in good agreement with our theoretical predictions. We have verified that our instrument can extend the measured frequency band up to the kHz region, which is appropriate for the study of fluctuations of optical parameters in biological tissues. @S1063-651X~98!01708-5# PACS number~s!: 87.64.Ni, 42.25.Gy, 41.20.Jb, 42.62.Be I. INTRODUCTION In recent years the correlation spectroscopy technique was used to study optically thick media that exhibit a high degree of multiple scattering @1–4#. This technique, called diffusing wave spectroscopy ~DWS!, relates scattered light fluctua- tions to the motion of scattering particles. DWS was pro- posed as a tool for the study of microscopical particle motion ~over a fraction of the optical wavelength! in multiply scat- tering media such as colloids and microemulsions. Biological tissues typically display strong light scattering, and therefore can be important subjects for DWS applica- tions. However, in addition to the small-scale fluctuations due to the motion of the microscopical scatterers, biological activity in tissues may produce large-scale spatial and tem- poral fluctuations of tissue optical properties in the near- infrared band. It was demonstrated that such fluctuations in the brain may result, for example, from hemodynamics @5,6# and neuronal activity @7#. In particular, it was found that visual stimulation induces local changes in the optical prop- erties of the human brain visual area @7#. It was also noted that near-infrared tissue spectroscopy has an advantage over other techniques for studying neuronal processes in that it potentially combines good temporal resolution ~10–50 ms! with a spatial resolution of the order of 5 mm @5,7#. There- fore, the analysis of large-scale fluctuations in near-infrared Photon migration may provide a useful tool for the study of functional processes. In this paper we present a theoretical and experimental study of a system exhibiting large-scale (;mm) optical pa- rameter fluctuations. The idea is to induce Photon-Density waves in a turbid medium using an intensity-modulated light source. The phase velocity and the attenuation of these pho- ton Density waves depend on optical properties of the me- dium and on the modulation frequency @8–11#. The localized areas having optical properties differing from those of the II. EXPERIMENTAL SETUP AND METHOD The central part of our experimental setup ~Fig. 1! con- sists of a container ~a 1-L beaker! filled with an aqueous * FAX: ~217! 244-7187. 1063-651X/98/58~2!/2288~10!/$15.00 background medium affect the Photon-Density waves by ab- sorption and refraction processes. Similarly to the DWS method, we relate the fluctuations in the Photon-Density wave parameters to the optical fluctuations in turbid media. The differences from DWS are that ~i! in our case the mea- surable parameters are the average intensity ~dc!, the modu- lation amplitude ~ac!, and the phase (F) of the Photon den- sity wave ~having a frequency of ;100 MHz!, while in DWS the only measurable value is the light intensity, and ~ii! in our case the process under study is the large-scale (; mm! local optical property change, while in DWS it is the microscopic particle displacement (; nm!. The purpose of our investigation is to show the potential of this approach for in v i v o studies of biological systems, and to determine the instrumental capabilities. The experi- mental part of our work is based on frequency-domain mea- surements of the diffuse Photon-Density wave propagating in a Liposyn suspension with fluctuating optical properties. The spatial and temporal fluctuations of the scattering and ab- sorption coefficients are caused by the motion of absorbing particles having a size of 1.0–1.6 mm. The frequency- domain parameters analyzed in this study are the dc and phase of the Photon-Density wave. Similarly to the standard DWS approach, we use the diffusion approximation of light transport in a turbid medium @8–11# to express the statistical characteristics of frequency domain parameters ~average val- ues and autocorrelation functions! in terms of those of the particle motion. The paper is organized as follows. In Sec. II we describe our experimental apparatus and methods. In Sec. III we de- rive the expressions for the mean values and autocorrelation functions of the frequency-domain parameters based on a simplified statistical model for the motion of the absorbing particles. In Sec. IV we compare the experimental measure- ments with the theoretical predictions. The discussion of the results is presented in Sec. V. PRE 58 © 1998 The American Physical Society
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Photon Density waves scattered from cylindrical inhomogeneities theory and experiments
Applied Optics, 1998Co-Authors: Scott A Walker, David A. Boas, Enrico GrattonAbstract:We present an analytical solution for the scattering of diffuse Photon Density waves from an infinite circular, cylindrical inhomogeneity embedded in a homogeneous highly scattering turbid medium. The analytical solution, based on the diffusion approximation of the Boltzmann transport equation, represents the contribution of the cylindrical inhomogeneity as a series of modified Bessel functions integrated from zero to infinity and weighted by different angular dependencies. This series is truncated at the desired precision, similar to the Mie theory. We introduce new boundary conditions that account for specular reflections at the interface between the background medium and the cylindrical inhomogeneity. These new boundary conditions allow the separate recovery of the index of refraction of an object from its absorption and reduced scattering coefficients. The analytical solution is compared with data obtained experimentally to evaluate the predictive capability of the model. Optical properties of known cylindrical objects are recovered accurately. However, as the radius of the cylinder decreases, the required measurement signal-to-noise ratiorapidly increases. Because of the new boundary conditions, an upperlimit can be placed on the recovered size of cylindrical objects with radii below 0.3 cm if they have a substantially different index of refraction from that of the background medium.
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Study of large scale fluctuations in turbid media by Photon-Density-wave fluctuation correlation spectroscopy
Advances in Optical Imaging and Photon Migration, 1998Co-Authors: Vlad Toronov, Sergio Fantini, Mattia A. Filiaci, Enrico GrattonAbstract:We propose Photon-Density-wave fluctuation correlation spectroscopy as a method to study the macroscopic dynamics of tissue optical properties. Phantom measurements have shown that our frequency-domain instrument is appropriate to explore intensity, modulation and phase fluctuations in the frequency band from 0 to 125 Hz. Preliminary in vivo studies have revealed a reach optical dynamics in human tissues.
Oliver Reich - One of the best experts on this subject based on the ideXlab platform.
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Photonic sensing in highly concentrated biotechnical processes by Photon Density Wave spectroscopy
2017 25th Optical Fiber Sensors Conference (OFS), 2017Co-Authors: Roland Hass, Michael Sandmann, Oliver ReichAbstract:Photon Density Wave (PDW) spectroscopy is introduced as a new approach for Photonic sensing in highly concentrated biotechnical processes. It independently quantifies the absorption and reduced scattering coefficient calibration-free and as a function of time, thus describing the optical properties in the vis/NIR range of the biomaterial during their processing. As examples of industrial relevance, enzymatic milk coagulation, beer mashing, and algae cultivation in photo bioreactors are discussed.
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Fiber-optical Photon Density Wave spectroscopy applied to highly concentrated biotechnical processes
Imaging and Applied Optics 2016, 2016Co-Authors: Roland Hass, Oliver ReichAbstract:Photon Density Wave (PDW) spectroscopy is a novel approach for monitoring biotechnical processes, by independently quantifying the absorption and reduced scattering coefficient of the biomaterial. Enzymatic milk coagulation, beer mashing and blood deoxygenation are discussed.
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Particle sizing in highly turbid dispersions by Photon Density Wave spectroscopy: Bidisperse systems
Journal of Quantitative Spectroscopy and Radiative Transfer, 2015Co-Authors: Lena Bressel, J. Wolter, Oliver ReichAbstract:Abstract Photon Density Wave (PDW) spectroscopy is applied for characterizing the scattering properties, i.e. the reduced scattering coefficient μ s ′ , of highly concentrated mono- and bidisperse polymer latices. The theory for dependent scattering is reviewed and analytical expressions for the structure factors for hard sphere interaction in mono- (HSPYA) and bidisperse (BHSPYA) systems are given. From the scattering properties particle sizes of mono- and bidisperse polystyrene latices are determined as well as the relative amount of small and large particles for the bidisperse case.
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Fiber-optical particle sizing by Photon Density wave spectroscopy
23rd International Conference on Optical Fibre Sensors, 2014Co-Authors: Lena Bressel, Roland Hass, Marvin Münzberg, Oliver ReichAbstract:Photon Density Wave (PDW) spectroscopy is introduced as a fiber-optical technique for the in-line and dilution-free determination of the droplet or particle size in highly turbid emulsions and suspensions, respectively. Here, focus is laid on the monitoring of the Phase Inversion Temperature (PIT) emulsification process. The different stages like the inversion from an oil-in-water to a water-in-oil macroemulsion and finally to an oil-in-water nanoemulsion are observed and the droplet size is determined with high temporal resolution. This process shows the capability of PDW spectroscopy to determine particle or droplet sizes over a wide range from the nanometer to micrometer scale.
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industrial applications of Photon Density wave spectroscopy for in line particle sizing invited
Applied Optics, 2013Co-Authors: Roland Hass, Lena Bressel, Marvin Münzberg, Oliver ReichAbstract:Optical spectroscopy in highly turbid liquid material is often restricted by simultaneous occurrence of absorption and scattering of light. Photon Density Wave (PDW) spectroscopy is one of the very few, yet widely unknown, technologies for the independent quantification of these two optical processes. Here, a concise overview about modern PDW spectroscopy is given, including all necessary equations concerning the optical description of the investigated material, dependent light scattering, particle sizing, and PDW spectroscopy itself. Additionally, it is shown how the ambiguity in particle sizing, arising from Mie theory, can be correctly solved. Due to its high temporal resolution, its applicability to highest particle concentrations, and its purely fiber-optical probe, PDW spectroscopy possesses all fundamental characteristics for optical in-line process analysis. Several application examples from the chemical industry are presented.
Britton Chance - One of the best experts on this subject based on the ideXlab platform.
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Reflection and transmission coefficients for diffuse Photon Density waves in a diffuse/non-diffuse interface
Biomedical Optical Spectroscopy and Diagnostics, 2000Co-Authors: Jorge Ripoll, Manuel Nieto-vesperinas, Britton Chance, J P Culver, Vasilis Ntziachristos, Arjun G. YodhAbstract:Diffuse Photon Density Waves (DPDWs) have lately been used to characterize diffusive media to locate and characterize hidden objects, such as tumors, in soft tissue. Measurements are often taken in the exterior non-diffuse medium, and therefore, the DPDW suffers reflection at the interface. To analyze these, the basic expressions for the reflection and transmission coefficients for diffuse/non-diffuse interfaces are put forward. Interesting effects on the reflected DPDW occur for certain values of the diffusive parameters, which significantly distort the incident DPDW. Also, the expression for the transmission coefficient can also be used to determine the value of the extrapolated distance, or, if this parameter is known, the source shape and its position.
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Near-field diffraction tomography with diffuse Photon Density waves.
Physical Review E, 2000Co-Authors: D N Pattanayak, Britton Chance, T Durduran, J P Culver, Arjun G. YodhAbstract:An angular spectrum algorithm is presented for fast, near-field diffraction tomographic imaging with diffuse Photon Density waves in highly scattering media. A general relation in K space is derived that connects the spatial variations of the optical properties of heterogeneities to the spatial spectra of the measured scattered diffuse Photon Density waves. The theory is verified experimentally for situations when boundary effects can be neglected. We further describe how to reconstruct absorption and scattering properties simultaneously, and how to incorporate boundary conditions into this angular spectrum algorithm for a turbid medium of finite size ~e.g., the slab medium!. Limitations and potential improvements of the near-field diffraction tomography are also discussed. fraction tomography @16,17#, it is possible to rapidly recon- struct thin slice and spherical objects whose absorption and/or scattering parameters differ from the background ho- mogeneous scattering medium @20#. Our image reconstruc- tion algorithm, based upon diffraction tomography technique ~called angular spectrum algorithm in this paper!, is rapid, permitting object localization and characterization in ;1000 volume-element samples on sub-second computational time scales. Such an angular spectrum algorithm has recently at- tracted the attention of many researchers in Photon migration field@18,19#. In this paper we provide a more complete dis- cussion of the results reported in those earlier papers, and we provide a detailed analysis of this algorithm incorporating the effects of finite boundaries. We first derive the general integral solution of the total and scattered Photon Density waves in a heterogeneous turbid medium within the first or- der Born approximation ~Secs. II, III, and IV!. These ses- sions are largely reviews, but are included for completeness and clarity. We next derive a relation in K space between the spatial spectrum of the heterogeneity function and the spatial spectrum of the measured scattered diffuse Photon Density wave ~Sec. V A!. Experimental results are presented to verify the feasibility of the angular spectrum algorithm for image reconstruction. We then describe a method to recon- struct the absorption and scattering properties simultaneously with this algorithm. Some limitations and potential improve- ments of the diffraction tomography are discussed in Sec. VI. Finally, we illustrate how to incorporate boundary conditions into the angular spectrum algorithm for a turbid medium of finite size, in particular, the slab medium and the semi- infinite medium~Sec. VII!.
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Oximetry based on diffuse Photon Density wave differentials
Medical Physics, 2000Co-Authors: Vasilis Ntziachristos, Matthias Kohl, Britton ChanceAbstract:The quantification of tissue optical properties for calculating blood saturation and hemoglobin concentration using measurements of diffuse Photon Density waves at some distance away from an intensity-modulated light source, generally requires the determination of the amplitude and phase of this light source. This determination may become a severe impediment for measurements performed in the clinical environment. In this work we extend a self-calibrating methodology developed for constant wave and modulation depth-phase measurements, to include amplitude and phase measurements of diffuse Photon Density waves. The method uses amplitude and phase changes of intensity modulated light, under the assumption of known index of refraction and invariant reduced scattering coefficient μ s ′ , to quantify the absorption coefficient μ a without requiring initial amplitude and phase knowledge. Quantification of the μ a at selected time points during a measurement can then be employed to calibrate numerical solutions of the diffusion equation and compute the μ a for the remaining time points of the experiment. It is shown that the method is quite insensitive to the knowledge of the exact μ s ′ value so that an assumption on the average μ s ′ value for the tissue measured may be employed. The sensitivity of calculating blood saturation and hemoglobin concentration, as a function of the deviation of the μ s ′ used in the calculation versus the real μ s ′ value is investigated using simulated data. It is also demonstrated that the saturation calculation is especially insensitive to the μ s ′ guess. The performance of the method to quantify blood oxygen saturation and the concentrations of oxy- and deoxy-hemoglobin is examined with experimental measurements at two wavelengths on specially constructed blood model phantoms. To validate the method the measurements are monitored by a time-resolved spectrometer. The method is shown to be accurate to within ±5% in calculating blood saturation and to within ±10% in calculating hemoglobin concentration compared to the results obtained with the time-resolved spectrometer and the expected theoretical values.
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Near-field diffraction tomography with diffuse Photon Density waves.
Physical review. E Statistical physics plasmas fluids and related interdisciplinary topics, 2000Co-Authors: D N Pattanayak, Britton Chance, T Durduran, J P Culver, Arjun G. YodhAbstract:An angular spectrum algorithm is presented for fast, near-field diffraction tomographic imaging with diffuse Photon Density waves in highly scattering media. A general relation in K space is derived that connects the spatial variations of the optical properties of heterogeneities to the spatial spectra of the measured scattered diffuse Photon Density waves. The theory is verified experimentally for situations when boundary effects can be neglected. We further describe how to reconstruct absorption and scattering properties simultaneously, and how to incorporate boundary conditions into this angular spectrum algorithm for a turbid medium of finite size (e.g., the slab medium). Limitations and potential improvements of the near-field diffraction tomography are also discussed.
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Diffraction tomography for biochemical imaging with diffuse-Photon Density waves
Optics Letters, 1997Co-Authors: T Durduran, Britton Chance, Arjun G. Yodh, D N PattanayakAbstract:The spatial structure of optically heterogeneous turbid media is probed with diffusive light. Projection images are obtained experimentally by deconvolution of the scattered diffuse-Photon Density waves on a planar boundary by use of a fast Fourier transform. The method is very fast, permitting object localization and characterization in ∼1000 volume-element samples on subsecond computational time scales. The optical properties of slice-shape inhomogeneities are accurately determined.
David A. Boas - One of the best experts on this subject based on the ideXlab platform.
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Direct object localization and characterization from diffuse Photon-Density wave data
Optical Tomography and Spectroscopy of Tissue III, 1999Co-Authors: Misha E. Kilmer, David A. Boas, Eric L. Miller, Dana H. Brooks, Charles A. Dimarzio, Richard J. GaudetteAbstract:In this paper we consider new methods for localizing and characterizing the structure of an anomalous areas embedded in an overall region of interest given sparse observations of diffuse Photon Density wavefields. Unlike traditional techniques which use the scattered field measurements first to form an image of the full region and then post-process the resulting reconstruction to localize areas of interest, our approach finds anomalies directly from the data. To accomplish this, we model the unknowns as a superposition of a slowly varying perturbation on a background of unknown structure. We assume that the perturbation is delineated from the background by a smooth perimeter which is modeled as a spline curve of unknown knot sequence. A greedy-type approach is employed to deform the curve in a manner which optimizes a cost function enforcing both consistency with the data along with a regularization term designed to reflect prior information we have concerning the likely structure of anomalies. As the algorithm progresses, we adaptively determine the optimal weighting coefficients describing both the texture of the anomaly as well as that of the background. Examples of this approach are provided for a diffuse Photon Density wave problem arising in a bio-imaging application.
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Photon Density waves scattered from cylindrical inhomogeneities theory and experiments
Applied Optics, 1998Co-Authors: Scott A Walker, David A. Boas, Enrico GrattonAbstract:We present an analytical solution for the scattering of diffuse Photon Density waves from an infinite circular, cylindrical inhomogeneity embedded in a homogeneous highly scattering turbid medium. The analytical solution, based on the diffusion approximation of the Boltzmann transport equation, represents the contribution of the cylindrical inhomogeneity as a series of modified Bessel functions integrated from zero to infinity and weighted by different angular dependencies. This series is truncated at the desired precision, similar to the Mie theory. We introduce new boundary conditions that account for specular reflections at the interface between the background medium and the cylindrical inhomogeneity. These new boundary conditions allow the separate recovery of the index of refraction of an object from its absorption and reduced scattering coefficients. The analytical solution is compared with data obtained experimentally to evaluate the predictive capability of the model. Optical properties of known cylindrical objects are recovered accurately. However, as the radius of the cylinder decreases, the required measurement signal-to-noise ratiorapidly increases. Because of the new boundary conditions, an upperlimit can be placed on the recovered size of cylindrical objects with radii below 0.3 cm if they have a substantially different index of refraction from that of the background medium.
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fluorescent diffuse Photon Density waves in homogeneous and heterogeneous turbid media analytic solutions and applications
Applied Optics, 1996Co-Authors: M A Oleary, David A. Boas, Britton Chance, Arjun G. YodhAbstract:We present analytic solutions for fluorescent diffuse Photon Density waves originating from fluorophores distributed in thick turbid media. Solutions are derived for a homogeneous turbid medium containing a uniform distribution of fluorophores and for a system that is homogeneous except for the presence of a single spherical inhomogeneity Generally the inhomogeneity has fluorophore concentration, and lifetime and optical properties that differ from those of the background. The analytic solutions are verified by numerical calculations and are used to determine the fluorophore lifetime and concentration changes required for the accurate detection of inhomogeneities in biologically relevant systems. The relative sensitivities of absorption and fluorescence methods are compared.
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scattering of diffuse Photon Density waves by spherical inhomogeneities within turbid media analytic solution and applications
Proceedings of the National Academy of Sciences of the United States of America, 1994Co-Authors: David A. Boas, Britton Chance, M A Oleary, Arjun G. YodhAbstract:Abstract We present an analytic solution for the scattering of diffuse Photon Density waves by spherical inhomogeneities within turbid media. The analytic result is compared to experimental measurements. Close agreement between theory and experiment permits the use of the theory to determine the properties of unknown sphere-like objects embedded in turbid media. The analytic solution is extended to encompass several problems of practical interest in imaging, including the influence of multiple sources, multiple objects, and boundaries on the characterization of spherical inhomogeneities. We also extend the solution to encompass time-domain measurements.
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Reradiation and imaging of diffuse Photon Density waves using fluorescent inhomogeneities
Journal of Luminescence, 1994Co-Authors: M. A. O'leary, David A. Boas, Britton Chance, Arjun G. YodhAbstract:Abstract Experiments demonstrate the reradiation of diffuse Photon Density waves in turbid media by an obstacle filled with fluorescent dye. The reradiated energy was also in the form of a diffuse Density wave that was readily detected at the red-shifted energy. In this process the inhomogeneity was converted into a source of diffuse Photon Density waves, and localization of the object can be accomplished by analysis of the reradiated wavefronts. We will discuss these measurements and demonstrate some simple practical devices which are capable of localizing the center of such a fluorescent inhomogeneity.