Freeman C. Lin

Image estimation from scattered field data

The purpose of this paper is to reappraise the linearizing methods frequently used to solve inverse scattering problems. We describe inversion algorithms based on the Born and the Rytov approximations and the nature of the distortions obtained in the reconstructions when using them. We present extensions of these methods, namely, the distorted‐wave Born and the distorted‐wave Rytov approximations, which incorporate prior knowledge about part of the scattering structure. A method for inverting scattered field data using these distorted‐wave approximations is described, which retains the computational simplicity of the Born and the Rytov techniques. Some examples of their use with simulated and real data are given. A further extension of our distorted‐wave formalism, which leads to improvements of the reconstructed image, is suggested. This entails a spectral estimation procedure also based on the incorporation of prior knowledge about the scatterer. This spectral estimation procedure can be useful for interpolation of scattered field data as well as resolution enhancement.

A homomorphic filtering method for imaging strongly scattering penetrable objects

This paper describes a new method for determining the structure of strongly scattering penetrable objects having permittivity fluctuations with scales comparable to the illuminating wavelength. We are concerned with the case when small wavelength or weakly scattering approximations, such as the Born or distorted wave Born approximations, or slowly varying approximations such as the Rytov approximation, are not valid. The problem is formulated as one of recovering, in principle, a quantitative image of the objects permittivity distribution function from a set of perturbed images. Each perturbed image is obtained by backpropagating the scattered field measured around the object for different illumination directions. These backpropagated images are filtered in the differential cepstral domain to recover the object permittivity distribution, and we show reconstructions from both simulated and real microwave scattered data. >

Inversion of 10-GHz scattered field data using distorted-wave Born approximations

Abstract not available.

The dual twin image effect from a waveguide hologram

A new phenomenon called the dual twin image effect is reported. The mechanisms of the dual twin image effect and the twin image effect are discussed. A sandwich-like waveguide hologram unit, which can be used for fingerprint recognition, is described and verified experimentally.

Inverse scattering methods applied to nonlinear optical component design

A random medium model is applied to study propagation and multiple scattering of laser beams in nonlinear media containing microparticles. Refractive indices of these nonlinear media are considered to be isotropic and intensity-dependent. After applying a probabilistic model, we obtain an autocorrelation function with exponential-decay shape for the random medium assuming a two-phase mixture. Using the parabolic approximation, we have calculated the mean value of the intensity-dependent part of refractive index from the mutual coherence function. The Feynman diagrammatic technique, bilocal, and distorted-wave Born approximations are then invoked to formulate a Fourier relationship between the autocorrelation function and the forward scattered field of the incident light beam. Finally, our Fourier-based inversion algorithm is employed to extract information about the medium from the measured scattered field data.

Cepstral filtering for recovery of object from scattered field data

In this paper, we calculate information about the structure of strongly scattering objects with permittivity fluctuations having scales comparable with the illuminating wavelength. This is the situation for which small wavelength approximations or weakly scattering approximations are not valid. We formulate the problem as one of recovering an object function from a set of noisy versions of itself, which is a problem that frequently arises in imaging. We employ homomorphic filtering and differential cepstral filtering and show that information about the scattering object can be obtained.

Image Estimation from Scattered Field Data (at 10 GHz) Using the Distorted Wave Born Approximation and Other Prior Knowledge

A practical inversion algorithm based on the Fourier relation between scattered field data and the scatterer is presented; this procedure attempts to go beyond the limitations of conventional diffraction tomographic techniques which are largely limited to scatterers that satisfy the first Born or the Rytov approximation. A distorted wave approximation is used and reconstructions based on this have been compared with (first) Born inverted images and those based on the Rytov approximation. The new procedure is evaluated using microwave scattered field data taken from sand filled cylinders with diameters of 15.24cm and 30.48cm using 10GHz radiation. The approach adopted, being Fourier based, lends itself to further improvement through the application of well known signal processing (spectral estimation) techniques. The latter can improve the resolution of the reconstructed data by interpolating and extrapolating the available Fourier data, which lie on semicicular arcs in the Fourier domain, through the minimization of a cost function which incorporates prior knowledge about the scatterer, such as its support.

Ray-Tracing Approach to Computer-Generated Holography for Precision 3D Beam Patterns

Computer-generated holography [1, 2, 3] is a well known way to produce holograms. It is widely used in integrated optics [4], for holographic components [5, 6], in medical detection [7], for image-enhancement in electronic microscopes [8], and for three-dimensional displays [9, 10]. Most of the computer-generated holograms (CGHs) described in existing papers are Fourier holograms which are generated using the FFT (Fast Fourier Transform) [11, 12]. In this paper, a method which is based on ray tracing is described and demonstrated. This method can encode and reconstruct not only two-dimensional but also three-dimensional objects.

Quantitative image recovery and restoration from scattered field data at 10GHz

Numerical methods developed to invert scattered field data are applied in this paper to data collected from a styrofoam target. The imaging methods used are based on the distorted wave extension to the well-known first-order Born approximation for linearized inverse scattering. These methods allow a wider class of more strongly scattering objects to be imaged. Also, the distorted-wave approximation is described and the procedure enabling it to be used for high resolution imaging of weakly scattering features is presented.

Inversion of 10 GHz scattered field data from strong scatterers

In the inverse scattering problem, a quantitative image of an object can be determined from measurements of its scattered field. To solve this problem linearizing approximations such as the first-order Born and the Rytov approximations are frequently adopted because of the resulting ease with which a numerical procedure for inversion can be established. The authors have developed inversion algorithms using distorted-wave Born and Rytov approximations in order to extend the range of validity, while retaining the numerical advantages associated with the linearized methods. They have also used homomorphic filtering to separate the secondary source distribution into the scattering distribution and the total field components in the scatterers for different viewing directions.<<ETX>>