## Non-contact fluorescence optical tomography with scanning patterned illumination

Optics Express, Vol. 14, Issue 14, pp. 6516-6534 (2006)

http://dx.doi.org/10.1364/OE.14.006516

Acrobat PDF (1818 KB)

### Abstract

This article describes a novel non-contact fluorescence optical tomography scheme which utilizes multiple area illumination patterns, to reduce the ill-posedness of the inverse problem involved in recovering interior fluorescence yield distributions in biological tissue from boundary fluorescence measurements. The image reconstruction is posed as an optimization problem which seeks a tissue optical property distribution minimizing, for all illumination patterns simultaneously, a regularized difference between the observed boundary measurements of light distribution, and the boundary measurements predicted from a physical model. Multiple excitation source illumination patterns are described by line and Gaussian sources scanning the simulated tissue phantom surface and by employing diffractive optics-generated patterns. Multiple measurement data sets generated by scanning excitation sources are processed simultaneously to generate the interior fluorescence distribution in tissue by implementing the fluorescence tomography algorithm in a parallel framework suitable for multiprocessor computers. Image reconstructions for single and multiple fluorescent targets (5*mm* diameter) embedded in a 512*ml* simulated tissue phantom are demonstrated, with depths of the fluorescent targets from the illumination plane between 1*cm* to 2*cm*. We show both qualitative and quantitative improvements of our algorithm over reconstructions from only a single measurement.

© 2006 Optical Society of America

## 1. Introduction

1. M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Reradiation and imaging of diffuse photon density waves using fluorescent inhomogeneities,” J. Luminescence **60**, 281–286 (1994). [CrossRef]

16. B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. Sunshine Osterman, U. L. Osterberg, and K. D. Paulsen, “Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: Pilot results in the breast,” Radiology **218**, 261–266 (2001). [PubMed]

17. E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. **30**, 901–911 (2003). [CrossRef] [PubMed]

21. R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with noncontact measurements,” IEEE Trans. Med. Imaging **23**, 492–500 (2004). [CrossRef] [PubMed]

13. R. Roy, A. B. Thompson, A. Godavarty, and E. M. Sevick-Muraca, “Tomographic fluorescence imaging in tissue phantoms: A novel reconstruction algorithm and imaging geometry,” IEEE Trans. Med. Imaging **24**, 137–154 (2005). [CrossRef] [PubMed]

22. A. B. ThompsonE. M. Sevick-MuracaNIR fluorescence contrast enhanced imaging with ICCD homodyne detection: Measurement precision and accuracy.” J. Biomed. Opt. **8**, 111–120 (2002). [CrossRef]

24. A. Joshi, W. Bangerth, K. Hwang, J. Rasmussen, and E. M. Sevick-Muraca,” “Plane wave fluorescence tomography with adaptive finite elements,” Opt. Lett. **31**, 193–195 (2006). [CrossRef] [PubMed]

## 2. Methods and formulation

### 2.1. The photon transport model

*x*and

*m*denote the excitation and the emission light fields, respectively.

*u*,

*v*are the complex-valued photon fluence fields at excitation and emission wavelengths, respectively;

*D*

_{x,m}are the photon diffusion coefficients;

*µ*

_{ax,mi}is the absorption coefficient due to endogenous chromophores;

*µ*

_{ax,mf}is the absorption coefficient due to exogenous fluorophore;

*ω*is the modulation frequency;

*ϕ*is the quantum efficiency of the fluorophore, and finally, τ is the fluorophore lifetime associated with first order fluorescence decay kinetics. All these coefficients, and in particular the fluences

*u*,

*v*and the absorption/scattering coefficients are spatially variable.

*n*denotes the outward normal to the surface and

*γ*is a constant depending on the optical refractive index mismatch at the boundary. The complex-valued function

*S*=

*S*(

**r**) is the spatially variable excitation boundary source. There is no source term for the emission boundary condition. The goal of fluorescence tomography is to reconstruct the spatial map of coefficients

*µ*

_{axf}(

**r**) and/or τ(

**r**) from measurements of the complex emission fluence

*v*(

**r**) on the boundary. In this work we will focus on the recovery of only

*µ*

_{axf}(

**r**), while all other coefficients are considered known a priori. For notational brevity, and to indicate the special role of this coefficient as the main unknown of the problem, we set

*q*=

*µ*

_{axf}in the following paragraphs.

## 2.2. The inverse problem for multiple illumination patterns

23. A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element modeling of optical fluorescenceenhanced tomography,” Opt. Express **12**, 5402–5417 (2004). [CrossRef] [PubMed]

*W*different area excitation light patterns

*S*

^{i}(

**r**),

*i*=1,2, …,

*W*, to excite the embedded fluorophore in the phantom. For each of these experiments, we can predict fluences

*u*

^{i},

*v*

^{i}satisfying (1)–(3) with

*S*

^{i}(

**r**) as source terms if we assume knowledge of the yield map

*q*. In addition, we take fluorescence measurements on the measurement boundary G for each of these experiments that we will denote by

*z*

^{i}. The fluorescence image reconstruction problem is then posed as a constrained optimization problem wherein an

*L*

_{2}norm based error functional of the distance between fluorescence measurements

**z**={

*z*

^{i},

*i*=1,2, …,

*W*} and the diffusion model predictions

**v**={

*v*

^{i},

*i*=1,2, …,

*W*} is minimized by variation of the parameter

*q*; the diffusion model for each fluence prediction

*v*is a constraint to this optimization problem. In a function space setting, the mathematical formulation of this minimization problem reads as follows:

^{i}*J*(

*q*,

*v*) incorporates a least squares error term over the measurement part Γ of the boundary ∂Ω and a Tikhonov regularization term:

*β*is the Tikhonov regularization parameter. The Tikhonov regularization term

*βr*(

*q*) is added to the minimization functional to control undesirable components in the map

*q*(

**r**) that result from a lack of resolvability. The constraint

*A*

^{i}(

*q*; [

*u*

^{i},

*v*

^{i}])([ζ

^{i},ξ

^{i}])=0 is the weak or variational form of the coupled photon diffusion Eq.s (1)–(3) with partial current boundary conditions for the

*i*

^{th}excitation source, and with test functions [ζ,ξ] ∊

*H*

^{1}(Ω):

25. J. Nocedal and S. J. Wright. *Numerical Optimization*. (New York: Springer, 1999). [CrossRef]

*i*

^{th}source, respectively, and we have introduced the abbreviation

*x*={

**u**,

**v**,

*λ*

^{ex},

*λ*

^{em},

*q*} for simplicity;

**u**={

*u*

^{i},

*i*=1,2, …,

*W*} and

**v**={

*v*

^{i},

*i*=1,2, …,

*W*} are excitation and emission fluences for the

*W*excitation sources;

*λ*

^{ex}={

*i*=1,2, …,

*W*} and

*λ*

^{em}={

*i*=1,2, …,

*W*} denote the Lagrange multipliers corresponding to the excitation and emission equation constraints for the

*W*excitation sources.

*u*and

*v*on the parameter

*q*by solving diffusion equations for a given parameter map and substiuting the solution in place of

*v*in the error functional. Rather this dependence is implicitly enforced by treating

*u*,

*v*,

*q*as independent variables and including diffusion equations as a constraint on the the error functional.

## 2.3. Solving the inverse problem

*L*(

*x*), and therefore a solution of the constrained minimization problem (4), is found using the Gauss-Newton method wherein the update direction

*δx*

_{k}={

*δ*

**u**

_{k},

*δv*

_{k},

*δ*

_{qk}} is determined by solving the linear system

*L*

_{xx}(

*x*

_{k}) is the Gauss-Newton approximation to the Hessian matrix of second derivatives of

*L*at point

*x*

_{k}, and

*y*denotes possible test functions. These equations represent one condition for each variable in

*δx*

_{k}, i.e. they form a coupled system of equations for the 4

*W*+1 variables involved: all

*W*excitation and emission fluences, excitation and emission Lagrange multipliers, and the yield map

*q*. Once the search direction is computed from Eq. (8), the actual update is determined by calculating a safeguarded step length

*α*

_{k}:

*α*

_{k}can be computed from one of several methods, such as the Goldstein-Armijo backtracking line search [26

26. R. Roy and E. M. Sevick-Muraca, “Truncated Newton’s optimization schemes for absorption and fluorescence optical tomography: Part(1) theory and formulation,” Opt. Express **4**, 353–371 (1999). [CrossRef] [PubMed]

**u**,v,

*λ*

^{ex}, and

*λ*

^{em}are discretized and solved for on meshes with continuous finite elements, while the unknown parameter map

*q*is discretized on a separate mesh with discontinuous finite elements. Whenever Gauss-Newton iterations on these meshes have reduced the error function by a factor of 10

^{-3}or the Gauss-Newton step length returned by the line search algorithm has fallen below 0.15, the meshes are refined using

*a posteriori*refinement criteria. The advantage of function space Lagrangian framework lies in its ability to provide a mathematically cohesive view of the multiple experiment tomography problem. As the inverse iterations are derived in a discretization independent manner, it makes it easier to implement optimal finite elementmeshes corresponding to different excitation sources.

*δx*

_{k}. It has the following form:

*δp*

_{k}=[

*δ*

**u**

_{k},

*δ*

**v**

_{k}]

^{T},

*δd*

_{k}=[

^{T}. Since each of these 4

*W*+1 variables is discretized with several ten or hundred thousand unknowns on our finite element meshes, the matrix on the left hand side can easily have a dimension of several million to over 10 million. At first glance, it therefore seems infeasible or at least very expensive to solve such a system. In the past, this has led researchers to the following approach: use one experiment alone to solve for the fluorescence map, then use the result as the starting value for inverting the next data set and so on; one or several loops over all data sets may be performed. While this approach often works for problems that are only moderately ill-posed, it is inappropriate for problems with the severe ill-posedness of the one at hand. The reason is that if we scan the source over the surface, we will only be able to identify the yield map in the vicinity of the illuminated area. Far away from it, we have virtually no information on the map. We will therefore reconstruct invalid information away from the source, erasing all prior information we have already obtained there.

*at the same time*, in a joint inversion scheme. Fortunately, we can make use of the structure of the problem: because experiments are independent of each other, the joint Gauss-Newton matrix is virtually empty, and in particular has no couplings between the entries corresponding to primal and dual variables of different illumination experiments. The only thing that keeps the matrix fully coupled is the presence of the yield map

*q*on which all experiments depend.

*M*, the second derivative of the measurement error function with respect to state variables

*u*

^{i},

*v*

^{i}for all the excitation sources, is a block diagonal matrix {

*M*

_{1},

*M*

_{2},…,

*M*

_{W}}. Likewise

*P*=blockdiag{

*P*

_{1},

*P*

_{2},…,

*P*

_{W}} is the representation of the discrete forward diffusion model for all the excitation sources. Finally, the matrix

*C*=blockdiag{

*C*

_{1},

*C*

_{2},…,

*C*

_{W}} is obtained by differentiating the semi-linear form

*A*

^{i}in Eq. (6) with respect to the parameter

*q*. For reasons explained below, we choose different meshes for individual measurements. Consequently the individual blocks

*M*

_{i},

*P*

_{i},

*C*

_{i}all differ from each other. Finally, the right hand side

*F*denotes the discretized form of -

*L*

_{x}(

*x*

_{k})(

*y*). The detailed formulation of the individual blocks

*M*

_{i},

*P*

_{i},

*C*

_{i}and the right hand side

*F*is provided in Ref. [23

23. A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element modeling of optical fluorescenceenhanced tomography,” Opt. Express **12**, 5402–5417 (2004). [CrossRef] [PubMed]

*R*block that reflects the independence of experiments:

*δq*

_{k}, and then for updates of state and adjoint variables for all the experiments individually and independently, a task that is obviously simpler than solving for the one big and coupled matrix in (10). Note in particular that the Schur complement matrix

*λq*

_{k}is done iteratively; in each iteration, one multiplication between

*S*and a vector is required. Given the structure of the matrix, this can be implemented on separate computers or separate processors on a multiprocessor system, each of which is responsible for one or several of the experiments (and corresponding matrices

*C*

_{i},

*P*

_{i},

*M*

_{i}). Since multiplication of a vector with the matrices

*M*

_{i}

*C*

_{i}is completely independent, a workstation cluster with

*W*nodes is able to perform the image reconstruction task within approximately the same time as a single machine requires for inverting a single excitation source. For the examples shown in Section 3, reconstructions took between 10 and 20 minutes on a cluster of Opteron machines, independently of the number of experiments

*W*.

*q*. The results shown below are created using a program implementing this algorithm developed by Bangerth [27] with the help of the open source deal.II finite elements library [28

28. W. Bangerth, R. Hartmann, and G. Kanschat, deal.II *Differential Equations Analysis Library, Technical Reference*, 2006. http://www.dealii.org/.

23. A. Joshi, W. Bangerth, and E. M. Sevick-Muraca, “Adaptive finite element modeling of optical fluorescenceenhanced tomography,” Opt. Express **12**, 5402–5417 (2004). [CrossRef] [PubMed]

## 2.4. Choice of meshes

*M*

_{i}are equal, and similarly for the matrices and

*P*

_{i}. (The blocks

*C*

_{i}are still different since their elements are computed using the forward solutions

*u*

^{i},

*v*

^{i}.)

## 3. Image reconstruction simulations

*ml*cubical tissue phantom with optical properties of 1% Liposyn by running a highly accurate finite element forward simulator with a yield map that is assumed to be known. For the simulated background absorption coefficient, we chose

*µ*

_{axi}=0.023

*cm*

^{-1}and

*µ*

_{ami}=0.0289

*cm*

^{-1}[30]. The absorption coefficient due to fluorophore at the excitation wavelength was set to

*µ*

_{axf}=0.23

*cm*

^{-1}in the target. The associated emission wavelength absorption coefficient was

*µ*

_{amf}=0.023

*cm*

^{-1}in the target. The lifetime of the fluorophore was taken to be τ=0.56

*ns*and the quantum efficiency was

*ϕ*=0.016 to match the corresponding properties of Indocyanine Green (ICG) dye used in experiments. The excitation wavelength for ICG is 785

*nm*and the emission data is collected at 830

*nm*. The reduced scattering coefficient was taken as

*cm*

^{-1}in both the target and the background, and for this study was taken to be the same at excitation and emission wavelengths.

*cm*]

^{3}. The top surface at

*z*=8

*cm*was used as the illumination and detection plane. We assumed a detector with an infinite number of pixels, by providing synthetic measurements at all the quadrature points when numerically evaluating integrals over the measurement surface. Excitation light modulated at 100

*MHz*was delivered to the illumination plane via one of the following schemes: (i) four line sources, (ii) four Gaussian sources, or (iii) a combination of diffractive optics patterns. Figure 3 shows these patterns. With these assumed patterns used as sources

*S*

^{i}(

**r**), we computed fluorescence amplitude and phase across the domain containing fluorescent targets of 5

*mm*diameter spheres filled with 1

*µM*Indocyanine Green solution in 1% Liposyn. The phantom background was assumed to be devoid of fluorophore. As mentioned above, we use different meshes to compute fluences for different illumination patterns; Fig. 4 demonstrates how meshes are generated through adaptive mesh refinement for a single one of each of the three kinds of sources. It is clear that for resolving complex source patterns generated by diffractive optics, adaptive mesh refinement is a necessity since the incident excitation source is poorly resolved during the first couple of refinement stages, and at least 4 adaptive refinements are required. Resorting to

*a priori*global mesh refinement would incur an exorbitant computational burden in the simulation of scanning and patterned area incident illumination.

## 3.1. Single target reconstruction

*cm*from the center of the illumination plane. We then run our image reconstruction algorithm using synthetic data generated for this situation.

## 3.2. Multiple target reconstructions

*cm*deep fluorescent targets, performed with synthetic data generated from (a) a single Gaussian excitation source with half a width of 4

*cm*centered on the illumination plane [23

**12**, 5402–5417 (2004). [CrossRef] [PubMed]

*cm*focused on different parts of the surface, and (d) the four diffractive optics patterns.

*cm*, 1.5

*cm*, and 2.0

*cm*. Figure 7 shows the reconstructed images for the threemultiple source patterns. The reconstructed parameter contour level cutoff needed to be reduced to 80% of the maximum level for resolving the three targets. Since excitation light penetration descreases exponentially with depth, the deeper targets do not fluoresce as much as the shallower targets resulting in a nonuniformity in the reconstructed fluorescence absorption in the three targets. The scanning Gaussian source doesn’t resolve the 1.5

*cm*and 2

*cm*deep targets clearly, while the scanning line source illumination results in the detection of only the 1

*cm*and 1.5

*cm*deep targets. Diffractive optical pattern based illumination provides the best image reconstructions as all the targets can be identified and there is no overlap.

*q*, for the three different illumination situations. Since the recovered parameter should be the same in all three situations, it is not surprising that the parameter meshes are similar although the illumination scenarios are very different. Note that the parameter mesh is refined only near the reconstructed fluorescent targets and remains coarse elsewhere, including close to the illumination and measurement surface, yielding an optimal distribution of unknowns for the reconstruction of the targets. Fluorescence optical tomography is an illposed inverse problem. In the numerical studies reported in the paper, the ill-posedness is further exacerbated by availability of only the reflectance plane measurements. An adaptive refinement based technique successfully recovers the location of embedded fluorescence targets but fluorescence absorption magnitudes are not uniquely quantified resulting in a variation in the reconstructed fluorescence absorption maps depending on the simulation configuration. Hence, for the ease of visualization of results different contour level cutoffs were used for the single target and three target image reconstructions.

*mm*width. Figure 8(a) depicts the source positions. Figure 8(b) depicts the adaptively refined forward simulation mesh for the first source. The image reconstructions corresponding to the three fluorescent targets placed at the same and varying depths are reported in Fig. 8(c) and Fig. 8(d) respectively. The contour level cutoffs employed are identical to the patterned illumination based image reconstructions. The image reconstruction corresponding to the fluorescent targets at the same depth depicts significant image artifacts in the center of the imaged field of view, while the image reconstruction from the measurements generated for the three fluorescent targets at varying depths completely fails to accurately reconstruct the location and sizes of all the three fluorescent targets. The reason for the failure of point sources in locating three fluorescent targets is primarily because of insufficient excitation light penetration and consequently weaker fluorescence emission. This suggests the inadequacy of point illumination schemes for reconstructing fluorescence distributions in large tissue volumes with multiple targets, especially when only a limited number of sources can be employed to limit data acquisition time.

## 4. Quantitative assessment

35. B. W. Pogue, T. O. McBride, U. L. Osterberg, and K. T. Paulsen, “Comparison of imaging geometries for diffuse optical tomography,” Opt. Express **4**, 270–286 (1999). [CrossRef] [PubMed]

*W*lines and we quantitate the advantages in image reconstruction with the increments in the number of line sources employed (

*W*). The line sources are positioned symmetrically with respect to the center of the measurement surface (see Fig. 3). In the image reconstruction procedure detailed in the preceding sections, a linear problem defined by Eq. (11) is solved within each non-linear iteration to determine the update to the unknown parameter map

*q*. We note that the once the solution has converged to within noise level, the right hand side of Eq. (11) only consists of contributions due to measurement noise, and further updates

*δq*

_{k}will only produce changes within the range of uncertainty. The matrix

*S*defined in Eq. (14) determines this parameter update

*δ*

_{q}. Since it is symmetric and positive definite we can find a complete set of (normalized) eigenvectors

*v*

_{ℓ}and singular values σ

_{ℓ}such that

*S*=Σ

_{ℓ}

_{σℓ}

*v*

_{ℓ}

_{ℓ}are arranged in decreasing order. We can then determine the update to be

*t*

_{ℓ}=

*F*

_{2}-

*F*

_{1}-

*M*

_{i}

*F*

_{3})]. Since we want small random updates

*δ*

_{qk}, it is important that the singular values σ

_{ℓ}be as large as possible.

*S*correspond to image modes

*v*

_{ℓ}that describe features in the solution close to the measurement surface, about which measurements provide enough information. On the other hand, small singular values correspond to high-frequency oscillations and deep objects that are badly constrained by the available measurements. Hence the decay profile of the singular value spectrum of the Gauss-Newton matrix

31. D. L. Everitt, S. Wei, and X. D. Zhu, “Analysis and optimization of diffuse photon optical tomography of turbid media,” Phys. Rev. E **62**, 2924–2936 (2000). [CrossRef]

33. H. Xu, H. Dehghani, B. W. Pogue, R. Springet, K. D. Paulson, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt. **8**, 102–110 (2003). [CrossRef] [PubMed]

34. E. E. Graves, J. P. Culver, J. Ripoll, and R. Weissleder, “Singular-value analysis and optimization of experimental parameters in fluorescence molecular tomography,” J. Opt. Soc. Am. A **21**, 231–241 (2004). [CrossRef]

*S*for a varying number

*W*of scanning line sources were computed for the case of a uniform fluorophore distribution (

*q*=0.01

*cm*

^{-1}). To remove the effect of adaptive mesh refinement on the singular value spectrum, only one iteration on uniform globally refined state and parameter meshes was computed. All the state/forward meshes consisted of 2.5

*mm*cubical voxels, while the parameter mesh consisted of 1

*cm*cubical voxels.

*W*. The larger the number of measurements the larger the number of singular values σℓ of S with significant magnitude, where the latter is determined by the fact that only singular values greater than the regularization parameter

*β*(typically

*β*=10

^{-10}) impact image formation. Figure 10 shows this result in a different manner by plotting the number of singular values beyond the typical regularization parameter. From both these plots we conclude that by adding additional measurements, we can increase the number of resolvable modes by a factor of 4–5. If these modes were isotropically distributed in the domain, this result would imply that 16 measurements will yield a resolution that is a factor of

*v*

_{ℓ}is reduced by a factor of √10.

## 5. Conclusion and future implications

*cm*

^{2}) tissue surfaces may need to be sampled, and no

*a priori*information about the fluorescent target locations is available. Different illumination patterns perform differently in the challenging image reconstruction problems involving multiple fluorescent targets placed at varying depths. Hence, excitation source patterns need to be optimized for covering large tissue surfaces and simultaneously handling fluorescent target distributions varying both in lateral and vertical directions. Since the numerical computations corresponding to multiple sources are distributed to separate compute nodes of a cluster, the proposed tomography scheme enables us to optimize excitation sources as the number of patterns which can be employed is only limited by the amount of computational resources available. The optimal source patterns for fluorescence optically tomography can be determined by an exhaustive search procedure over the illumination surface pixels by maximizing a suitable measure of the conditioning of the Gauss-Newton hessian matrix S with respect to the variation of illumination patterns. Finally, numerical studies such as those presented in this contribution are significantly faster than the comparable tests using actual measurements in the laboratory, and may therefore accelerate the development and deployment of optimal measurement schemes for fluorescence optical tomography in clinic.

## Acknowledgments

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28. | W. Bangerth, R. Hartmann, and G. Kanschat, deal.II |

29. | W. Bangerth, A. Joshi, and E. M. Sevick-Muraca, “Adaptive finite element methods for increased resolution in fluorescence optical tomography,” Progr. Biomed. Optics Imag. |

30. | “Development of a new optical imaging modality for detection of fluorescence enhanced disease,” PhD dissertation, Texas A & M University, 2003. |

31. | D. L. Everitt, S. Wei, and X. D. Zhu, “Analysis and optimization of diffuse photon optical tomography of turbid media,” Phys. Rev. E |

32. | J. P. Culver, V. Ntziachristos, M. J. Holboke, and A. G. Yodh, “Optimization of optode arrangements for diffuse optical tomography: A singular-value analysis,” Opt. Lett. |

33. | H. Xu, H. Dehghani, B. W. Pogue, R. Springet, K. D. Paulson, and J. F. Dunn, “Near-infrared imaging in the small animal brain: optimization of fiber positions,” J. Biomed. Opt. |

34. | E. E. Graves, J. P. Culver, J. Ripoll, and R. Weissleder, “Singular-value analysis and optimization of experimental parameters in fluorescence molecular tomography,” J. Opt. Soc. Am. A |

35. | B. W. Pogue, T. O. McBride, U. L. Osterberg, and K. T. Paulsen, “Comparison of imaging geometries for diffuse optical tomography,” Opt. Express |

**OCIS Codes**

(170.3010) Medical optics and biotechnology : Image reconstruction techniques

(170.3880) Medical optics and biotechnology : Medical and biological imaging

(170.5280) Medical optics and biotechnology : Photon migration

**ToC Category:**

Medical Optics and Biotechnology

**History**

Original Manuscript: April 25, 2006

Revised Manuscript: June 29, 2006

Manuscript Accepted: July 3, 2006

Published: July 10, 2006

**Virtual Issues**

Vol. 1, Iss. 8 *Virtual Journal for Biomedical Optics*

**Citation**

Amit Joshi, Wolfgang Bangerth, and Eva M. Sevick-Muraca, "Non-contact fluorescence optical tomography with scanning patterned illumination," Opt. Express **14**, 6516-6534 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-14-6516

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