Abstract: A methodology and concomitant system for the reconstruction of an object from measurements of the transmitted intensity of scattered radiation effected by irradiating the object with a source of radiation. The measurements of the transmitted intensity are both spatially sampled and limited. The transmitted intensity is related to either the absorption coefficient or diffusion coefficient, or both, of the object by an integral operator. The image is directly reconstructed by executing a prescribed mathematical algorithm, as determined with reference to the integral operator, on the transmitted intensity of the scattered radiation. In a preferred embodiment, the data is measured using a paraxial arrangement composed on a single source and a small number of on-axis and off-axis detectors with the arrangement being moved over the measurement surface to measure the set of sampled and limited data.

Abstract: A methodology and concomitant system for the reconstruction of an object from measurements of the transmitted intensity of scattered radiation effected by irradiating the object with a source of radiation. The measurements of the transmitted intensity are both spatially sampled and limited. The transmitted intensity is related to either the absorption coefficient or diffusion coefficient, or both, of the object by an integral operator. The image is directly reconstructed by executing a prescribed mathematical algorithm, as determined with reference to the integral operator, on the transmitted intensity of the scattered radiation. In a preferred embodiment, the data is measured using a paraxial arrangement composed on a single source and a small number of on-axis and off-axis detectors with the arrangement being moved over the measurement surface to measure the set of sampled and limited data.

Abstract: A method for the reconstruction of a tomographic image of an object from measurements of scattering data resulting from probing waves. The scattering data is related to a forward scattering operator by an integral operator. The tomographic image is reconstructed by executing a prescribed mathematical algorithm, as determined with reference to the integral operator, on the scattering data.

Abstract: A methodology and concomitant system for the nonlinear reconstruction of an object from measurements of the transmitted intensity of scattered radiation effected by irradiating the object with a source of radiation. The transmitted intensity is related to either the absorption coefficient or diffusion coefficient, or both, of the object by an integral operator. The image is directly reconstructed by executing a prescribed mathematical algorithm, as determined with reference to the integral operator, on the transmitted intensity of the scattered radiation. The mathematical algorithm includes computing a functional series expansion for the coefficient(s) in powers of the transmitted intensity.

Abstract: A method for the direct reconstruction of an object from measurements, called scattering data, of scattered waves due to probing waves as emitted by a source. The scattering data is related to a scattering kernel by an integral operator. The image is directly reconstructed by executing a prescribed mathematical algorithm, as determined with reference to the integral operator, on the scattering data.

Abstract: A methodology and concomitant system for three-dimensional near-field microscopy achieves subwavelength resolution of an object without retrieval of the optical phase. The features of this approach are three-fold: (i) the near-field phase problem is circumvented by employing measurements of the power extinguished from probe fields; (ii) the fields on which the power measurements are performed may be monitored far from the object and thus subwavelength resolution is obtained from far zone measurements; and (iii) by developing an analytic approach to the inverse problem in the form of an explicit inversion formula, an image reconstruction algorithm is produced which is strikingly robust in the presence of noise.

Abstract: A methodology and concomitant system for three-dimensional near-field microscopy achieves subwavelength resolution of an object via total internal reflection. The features of this approach include: (i) the evanescent waves used for illumination encode on the scattered field the subwavelength structure of the scattering object—it is thus possible to obtain subwavelength resolved images of the sample as is done in other near-field techniques such as near-field scanning optical microscopy without the technical difficulties encountered with probe-sample interactions; and (ii) the results of the reconstruction are unambiguous in the sense that the relation between the scattered field and the three-dimensional structure of the sample, as described by the spatial dependence of the susceptibility, is made manifest.

Abstract: A method for the reconstruction of a tomographic image of an object from measurements of scattering data resulting from probing waves. The scattering data is related to a forward scattering operator by an integral operator. The tomographic image is reconstructed by executing a prescribed mathematical algorithm, as determined with reference to the integral operator, on the scattering data.

Abstract: A method for the direct, mathematical reconstruction of the image of an object from measurements of the transmitted intensity of the scattered radiation effected by irradiating the object. The transmitted coefficient is related to the image by an integral operator. The image is directly, mathematical reconstructed by executing a prescribed mathematical algorithm, as determined with reference to the integral operator, on the transmitted coefficient, the algorithm further relating the absorption coefficient, the diffusion coefficient, or both to the transmitted coefficient by a different integral operator.

Abstract: A method for the direct reconstruction of an object from measurements of the transmitted intensity of diffusively scattered radiation effected by irradiating the object with a source of continuous wave radiation. The transmitted intensity is related to the diffusion coefficient by an integral operator. The image is directly reconstructed by executing a prescribed mathematical algorithm, as determined with reference to an integral operator, on the transmitted intensity of the diffusively scattered radiation.

Abstract: A method for the direct reconstruction of an object from measurements of the transmitted intensity of diffusively scattered radiation effected by irradiating the object with a source of continuous wave radiation. The transmitted intensity is related to the absorption coefficient by an integral operator. The image is directly reconstructed by executing a prescribed mathematical algorithm, as determined with reference to an integral operator, on the transmitted intensity of the diffusively scattered radiation.

Abstract: A method for the direct reconstruction of an object from measurements of the quantum efficiency determined from both a diffusing wave and a reradiated diffusing wave effected by irradiating the object with a source of radiation. The quantum efficiency is related to the number density of the fluorescent source distribution defining the image to be reconstructed by an integral operator. The image of the object is directly reconstructed by executing a prescribed mathematical algorithm, as determined with reference to the integral operator, on the quantum efficiency.

Abstract: A method for the direct reconstruction of the absorption and diffusion images from measurements of the transmitted intensity of the scattered radiation effected by irradiating the object with a time-domain source. The transmitted intensity is related to the absorption and the diffusion coefficients by an integral operator. The images are directly reconstructed by executing a prescribed mathematical algorithm, as determined with reference to the integral operator, on the transmitted intensity.

Abstract: A method for the direct reconstruction of an object from measurements of the transmitted intensity of diffusively scattered radiation effected by irradiating the object with a source of continuous wave radiation. The transmitted intensity is related to the absorption and the diffusion coefficients by an integral operator. The images are directly reconstructed by executing a prescribed mathematical algorithm, as determined with reference to the integral operator, on the transmitted intensity of the diffusively scattered radiation.

Abstract: A method for the direct reconstruction of an object from measurements of the transmitted intensity of the scattered radiation effected by irradiating the object. The transmitted intensity is related to the image by an integral operator. The image is directly reconstructed by executing a prescribed mathematical algorithm, as determined with reference to the integral operator, on the transmitted intensity.