We describe the concept of controlled or natural motion of an object in a spatially varying field as the basis for high resolution coherent optical sensing and imaging. Examples presented are for microscopy with interfering laser beams and speckle formed by scattering from a random medium. Biomedical and environmental applications are presented and resolution issues discussed.
Progress in developing optical imaging for biomedical applications requires customizable and often complex objects known as "phantoms" for testing, evaluation, and calibration. This work demonstrates that 3D printing is an ideal method for fabricating such objects, allowing intricate inhomogeneities to be placed at exact locations in complex or anatomically realistic geometries, a process that is difficult or impossible using molds. We show printed mouse phantoms we have fabricated for developing deep tissue fluorescence imaging methods, and measurements of both their optical and mechanical properties. Additionally, we present a printed phantom of the human mouth that we use to develop an artery localization method to assist in oral surgery.
We describe intensity correlations as a function of object position as a means to determine the field incident on a randomly scattering medium and to obtain information about objects within a scattering medium. The approach requires robust phase retrieval, presenting the central challenge to key applications. The experimental method is described and example results presented.
Maximum a posteriori (MAP) estimation has been shown to be an effective method for reconstructing images
from optical diffusion tomography data. However, one disadvantage of MAP reconstruction is that it typically
requires the use of iterative methods which are computationally intensive. However, the direct reconstruction
of MAP images is possible when the forward model is linear (or linearized) and the noise and image prior are
assumed Gaussian. These non-iterative MAP reconstruction techniques only require the multiplication of an
inverse matrix by a data vector to compute the reconstruction, but they depend on a combination of lossy source
coding techniques and sparse matrix transforms to make the required matrix-vector product computation both
computationally and memory efficient.
In this paper, we show examples of how non-iterative MAP reconstruction methods can be used to dramatically
reduce computation and storage for MAP reconstruction. Simulations of fluorescence optical diffusion
tomography (FODT) measurements and corresponding reconstructions are used to demonstrate the potential
value of these techniques. Numerical examples show the non-iterative MAP reconstruction can substantially
reduce both storage and computation, as compared to traditional iterative reconstruction methods.
A multigrid inversion approach is proposed to solve Poisson noise model-based inverse problems. The algorithm works by moving up and down in resolution with a set of coarse scale cost functions, which incorporates a coarse scale Poisson mean defined in low resolution data and image spaces. Applications of the approach to Bayesian reconstruction algorithms in transmission and emission tomography are presented. Simulation results indicate that the proposed multigrid approach results in significant improvement in convergence speed compared to the fixed-grid iterative coordinate descent (ICD) method.
Speckle intensity correlations are used to study polarized coherent
light propagating through scattering media. In particular, using measured speckle patterns as a function of frequency, second and third order intensity correlations with frequency are formed and then employed to determine the co-polarized and cross-polarized temporal impulse responses. The polarized impulse response provides information on the scattering medium that could aid in characterization. Determination of the temporal response from intensity only data is especially convenient in the optical domain.
A variety of new imaging modalities, such as optical diffusion tomography, require the inversion of a forward problem that is modeled by the solution to a three-dimensional partial differential equation. For these applications, image reconstruction can be formulated as the solution to a non-quadratic optimization problem.
In this paper, we discuss the use of nonlinear multigrid methods as both tools for optimization and algorithms for the solution of difficult inverse problems. In particular, we review some existing methods for directly formulating optimization algorithm in a multigrid framework, and we introduce a new method for the solution of general inverse problems which we call multigrid inversion. These methods work by dynamically adjusting the cost functionals at different scales so that they are consistent with, and ultimately reduce, the finest scale cost functional. In this way, the multigrid optimization methods can efficiently compute the solution to a desired fine scale optimization problem. Importantly, the multigrid inversion algorithm can greatly reduce computation because both the forward and the inverse problems are more coarsely discretized at lower resolutions. An application of our method to optical diffusion tomography shows the potential for very large computational savings.
A Bayesian optimization scheme is presented for reconstructing fluorescent yield and lifetime, the absorption coefficient, and the scattering coefficient in turbid media, such as biological tissue. The method utilizes measurements at both the excitation and emission wavelengths for reconstructing all unknown parameters. The effectiveness of the reconstruction algorithm is demonstrated by simulation and by application to experimental data from a tissue phantom containing a fluorescent agent.
Optical diffusion tomography is a new imaging modality that offers significant potential in medical applications. The resulting nonlinear image reconstruction problem is further complicated by the fact that for practical imaging variable source excitation and detector coupling needs to be accounted for in order to obtain quantitative images. We formulated the joint problem of coupling coefficient estimation and three-dimensional image reconstruction in a Bayesian framework, and the resulting estimates are computed in an iterative coordinate-descent optimization scheme. Simulations show that this approach is an accurate and efficient method for simultaneous reconstruction of absorption and diffusion coefficients, as well as the coupling coefficients.
We demonstrate accurate and efficient three-dimensional optical diffusion imaging using simulated noisy data from a set of measurements at a single modulation frequency. A Bayesian framework provides for prior model conditioning, and a dual-step cost function optimization allows sequential estimation of the data noise variance and the image.
We demonstrate a convenient technique for determining the temporal response and scattering parameters of a diffusive medium using laser speckle pattern frequency correlations. Experimental results using an external-cavity tunable laser diode are presented. This approach can be extended to provide data for image reconstruction based on a diffusion model.
Optical diffusion imaging is a new imaging modality that promises great potential in applications such as medical imaging, environmental sensing and nondestructive testing. It presents a difficult nonlinear image reconstruction problem however. An inversion algorithm is formulated in Bayesian framework, and an efficient optimization technique that uses iterative coordinate descent is presented. A general multigrid optimization technique for nonlinear image reconstruction problems is developed and applied to the optical diffusion imaging problem. Numerical results show that this approach improves the quality of reconstructions and dramatically decreases computation times.
Frequency-domain diffusion imaging is a new imaging modality which uses the magnitude and phase of modulated light propagation through a highly scattering medium to reconstruct an image of the scattering and/or the absorption coefficient in the medium. In this paper, the inversion algorithm is formulated in a Bayesian framework and an efficient optimization technique is presented for calculating the maximum a posteriori image. Numerical result show that the Bayesian framework with the new optimization scheme out-performs conventional approaches in both speed and reconstruction quality.
A weighted distorted Born iterative method is presented for reconstruction optical diffusion images from scattering data. A generalization of the distorted Born iterative method that uses a preconditioned cost function and an elliptical constraint allows a weighting matrix to be applied to the gradient term in the iterative algorithm according to the reconstruction history. The proposed algorithm shows stable and fast convergence for reconstruction of high contrast inhomogeneities.
The concept of optimized waveguide mode control elements allows for the design of improved components such as mode converters and waveguide transitions. This concept can also be applied to the realization of a new type of waveguide phase shifter through the modification of a waveguide geometry. Some examples for the optical control of a waveguide dimension in several different types of waveguide are provided. These designs require accurate numerical electromagnetic solvers and the use of nonlinear optimization tools, resulting in an iterative process where constraints such as bandwidth and manufacturability can be imposed.
We introduce a low cost apparatus utilizing a PIN photodiode receiver and a LED transmitter for frequency domain optical diffusion imaging. We present sample data to demonstrate the system performance and discuss the performance of LED sources and solid state detectors.
A micro-Raman apparatus was used to detect an object embedded within a scattering medium. The Raman vibrational frequency of diamond in an intralipid scattering medium was detected at different radial distances from the diamond. Scanned images of a single diamond, two diamonds, and a diamond through an aperture are presented. This experiment shows that Raman spectroscopy can be a useful tool in locating and characterizing heterogeneities contained within a scattering medium.
The finite element method is used to model the near field of optical components with dimensions on the order of a wavelength. Because open region problems are considered, a conformable local radiation boundary condition is used to truncate the domain and preserve the sparsity of the resulting matrix equation. Diffractive surface examples are presented.
Design issues related to implementation of the scattering optimization method for aperiodic gratings are discussed. Critical design parameters are highlighted and it is shown how their selection affects the final grating structure. The aperiodic grating design technique is then implemented to develop a grating for TE11 to TE11 mode conversion in a circular waveguide at 20 GHz. The length of the grating is 19cm and it has a conversion efficiency of 98.34%.