On-screen pre-deblurring of digital images using the wavefront aberration function of the human eye to improve computer access for the visually impaired

Traditional Optics has provided ways to compensate some common visual limitations (up to second order visual impairments) through spectacles or contact lenses. Recent developments in wavefront science make it possible to obtain an accurate model of the Point Spread Function (PSF) of the human eye. Through what is known as the Wavefront Aberration Function of the human eye, exact knowledge of the optical aberration of the human eye is possible, allowing a mathematical model of the PSF to be obtained. This model could be used to pre-compensate (inverse-filter) the images displayed on computer screens in order to counter the distortion in the user\u27s eye. This project takes advantage of the fact that the wavefront aberration function, commonly expressed as a Zernike polynomial, can be generated from the ophthalmic prescription used to fit spectacles to a person. This allows the pre-compensation, or onscreen deblurring, to be done for various visual impairments, up to second order (commonly known as myopia, hyperopia, or astigmatism). The technique proposed towards that goal and results obtained using a lens, for which the PSF is known, that is introduced into the visual path of subjects without visual impairment will be presented. In addition to substituting the effect of spectacles or contact lenses in correcting the loworder visual limitations of the viewer, the significance of this approach is that it has the potential to address higher-order abnormalities in the eye, currently not correctable by simple means

The application of Bayesian statistics and maximum entropy to Ion beam analysis techniques

Bibliography: pages 128-129.The elimination of some blurring property, such as the detector response function, from spectra has received a considerable amount of attention. The problem is usually complicated by the presence of noise in the data, and in general, there exists an infinite set of possible solutions which are consistent with the data within the bounds imposed by the noise. Such a problem is known, generally, as an ill-defined inverse problem. Many techniques have been developed in an attempt to solve inverse problems, for example the problem of deconvolution, but these techniques employ ad hoc modifications to solve different problems. Bayesian Statistics has been proved to be the only consistent method for solving inverse problems of the type where the information is expressed in terms of probability distributions. This dissertation presents results of applying the Bayesian formalism, together with the concepts of maximum information entropy and multiresolution pixons, to various inverse problems in ion beam analysis; The results of this method of deconvoluting Rutherford Backscattering Spectrometry (RBS) and Proton Induced X-ray Emission (PIXE) spectra are compared to the results from other deconvolution techniques, namely Fourier Transforms, Jansson's method and maximum entropy (MaxEnt) without pixons. All the deconvolution techniques show an improvement in the resolution of the RBS spectra but only the MaxEnt techniques show a significant improvement in the resolution of the PIXE spectra. The MaxEnt methods also produce physically acceptable results. The MaxEnt formalism was applied to the extraction of depth profiles from RBS and PIXE spectra and yielded good results. The technique was also used to deconvolute the beam profile from one-dimensional nuclear microprobe scans

Optimal application of Morrison's iterative noise removal for deconvolution. Appendices

Morrison's iterative method of noise removal, or Morrison's smoothing, is applied in a simulation to noise-added data sets of various noise levels to determine its optimum use. Morrison's smoothing is applied for noise removal alone, and for noise removal prior to deconvolution. For the latter, an accurate method is analyzed to provide confidence in the optimization. The method consists of convolving the data with an inverse filter calculated by taking the inverse discrete Fourier transform of the reciprocal of the transform of the response of the system. Various length filters are calculated for the narrow and wide Gaussian response functions used. Deconvolution of non-noisy data is performed, and the error in each deconvolution calculated. Plots are produced of error versus filter length; and from these plots the most accurate length filters determined. The statistical methodologies employed in the optimizations of Morrison's method are similar. A typical peak-type input is selected and convolved with the two response functions to produce the data sets to be analyzed. Both constant and ordinate-dependent Gaussian distributed noise is added to the data, where the noise levels of the data are characterized by their signal-to-noise ratios. The error measures employed in the optimizations are the L1 and L2 norms. Results of the optimizations for both Gaussians, both noise types, and both norms include figures of optimum iteration number and error improvement versus signal-to-noise ratio, and tables of results. The statistical variation of all quantities considered is also given

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution

The final report for work on the determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution is presented. Papers and theses prepared during the research report period are included. Among all the research results reported, note should be made of the specific investigation of the determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution. A methodology was developed to determine design and operation parameters for error minimization when deconvolution is included in data analysis. An error surface is plotted versus the signal-to-noise ratio (SNR) and all parameters of interest. Instrumental characteristics will determine a curve in this space. The SNR and parameter values which give the projection from the curve to the surface, corresponding to the smallest value for the error, are the optimum values. These values are constrained by the curve and so will not necessarily correspond to an absolute minimum in the error surface

Mathematical enhancement of data from scientific measuring instruments

The accuracy of any physical measurement is limited by the instruments performing it. The proposed activities of this grant are related to the study of and application of mathematical techniques of deconvolution. Two techniques are being investigated: an iterative method and a function continuation Fourier method. This final status report describes the work performed during the period July 1 to December 31, 1982

Two Dimensional Power Spectral Estimation Using Constrained Iterative Spectral Deconvolution

Two-dimensional power spectral estimation is an important tool for seismic data analysis and other applications. Some datasets, however, have a limited number of points in one or both dimensions. In seismic applications, there are typically fewer points in the spatial domain as compared to the temporal domain. Conventional spectral estimation techniques suffer from poor resolution on short datasets due to inherent smoothing or bias. Ramaswamy and loup developed a one-dimensional method for the estimation of power spectra for short datasets. Constrained Iterative Spectral Deconvolution (CISD) greatly improves the power spectral resolution using a straight-forward algorithm. In a comparison to other techniques, CISD is shown to perform very well on a standard 1-D dataset. Two modifications to the CISD method are introduced that enhance its performance. A simple modification to the algorithm, the inclusion of a relaxation parameter, speeds convergence by a factor of two. Another modification use an equivalent window to calculate multiple iterations between constraint applications. This enhancement did not improve convergence. A method was developed that compensates the CISD technique for missing samples in the dataset. This promises to be of great practical value to real datasets. This method is demonstrated on both model and real datasets. Finally, the CISD method is extended to the two-dimensional case, incorporating both modifications. This algorithm performs very well on a synthetic dataset and on real data from a downhole sonic tool. FORTRAN subroutines are given that implement the modified Constrained Iterative Spectral Estimation technique in both one and two dimensions

An in-process, non-contact surface finish sensor for high quality components generated using diamond turning

The object of this Ph.D. project was to design and construct an in-process, non contact surface finish sensor for high quality components generated using diamond turning. For this application the instrument must have the following properties: i rapid acquisition of data. ii capability of measuring translating and or rotating surfaces. iii ruggedness for in-process use. iv insensitivity to moderate vibrations. v remoteness from the surfaces to be measured. The remoteness requirement virtually excludes the otherwise ubiquitous stylus instrument, while the rapid gathering of data from rotating surfaces excludes other profiling techniques. The above mentioned properties strongly suggest an optical method. An optical diffraction technique has been chosen, since it produces an optical Fourier Transform of the surface. This transform is produced at the speed of light, since the optical system has the property of parallel data processing, unlike a typical electronic computer. With the aid of a microprocessor various surface finish parameters can be extracted from the optical transform. These parameters are respectively the rms surface roughness, slope and wavelength. The actual sensor consists of a measuring head and a minicomputer. It fulfils the above mentioned requirements. Its only limitations are: i limited to surface finishes up to 100nm ii presence of cutting fluids has to be avoided, although certain modern lubricating fluids can be tolerated. The algorithms devised to extract the surface finish parameters from the optical transforms have initially been tested on optical spectra produced by Thwaite. Comparison of the optical roughness values and the values quoted by Thwaite show close agreement. Thwaite's values are obtained by a stylus instrument. Rqopt (um) Rqstylus (um) 0.16 0.156 0.38 0.37 0.44 0.40 In addition a computer program has been devised which simulates the optical sensor head. The input data can be obtained by a profiling instrument, or generated by a computer program. This last option enables the creation of surface profiles with "controllable" machining errors. This program can be utilised to create an atlas, which maps optical diffraction patterns versus machine-tool errors

Estimação dos Sinais Elétricos das Descargas Parciais através da Deconvolução dos Sinais Acústicos gerados por estes.

Este presente trabalho descreve uma utilização de deconvolução para estimação dos sinais elétricos das descargas parciais através da deconvolução dos sinais acústicos captados. Os resultados de simulações mostram que o sinal elétrico estimado é praticamente idêntico ao sinal elétrico original medido. Portanto, os resultados mostram que com a metodologia proposta foi possível estimar o sinal elétrico com exatidão de até 99%