Showing papers on "Point spread function published in 2001"
TL;DR: In this article, the authors describe a mission-independent wavelet-based source detection algorithm called WAVDETECT, which does not require a minimum number of background counts per pixel for the accurate computation of source detection thresholds.
Abstract: Wavelets are scaleable, oscillatory functions that deviate from zero only within a limited spatial regime and have average value zero. In addition to their use as source characterizers, wavelet functions are rapidly gaining currency within the source detection field. Wavelet-based source detection involves the correlation of scaled wavelet functions with binned, two-dimensional image data. If the chosen wavelet function exhibits the property of vanishing moments, significantly non-zero correlation coefficients will be observed only where there are high-order variations in the data; e.g., they will be observed in the vicinity of sources.
In this paper, we describe the mission-independent, wavelet-based source detection algorithm WAVDETECT, part of the CIAO software package. Aspects of our algorithm include: (1) the computation of local, exposure-corrected normalized (i.e. flat-fielded) background maps; (2) the correction for exposure variations within the field-of-view; (3) its applicability within the low-counts regime, as it does not require a minimum number of background counts per pixel for the accurate computation of source detection thresholds; (4) the generation of a source list in a manner that does not depend upon a detailed knowledge of the point spread function (PSF) shape; and (5) error analysis. These features make our algorithm considerably more general than previous methods developed for the analysis of X-ray image data, especially in the low count regime. We demonstrate the algorithm's robustness by applying it to various images.
448 citations
TL;DR: This work discusses image formation in phase-shifting digital holography by developing an analytical formulation based on the Fresnel-Kirchhoff diffraction theory that is derived for general configurations in which a spherical reference is employed.
Abstract: We discuss image formation in phase-shifting digital holography by developing an analytical formulation based on the Fresnel-Kirchhoff diffraction theory. Image-plane position and imaging magnification are derived for general configurations in which a spherical reference is employed. The influences of discrete sampling of the resulting interference patterns by a CCD and numerical reconstruction on qualities of point images are investigated. Dependence of the point images on the ratio of the minimum fringe spacing to pixel pitch of the CCD is numerically analyzed. Two-point resolution and magnification are also investigated as a function of pixel numbers by a simulation using a one-dimensional model. In experiments magnified images of biological objects and a resolution target were reconstructed with the same quality as by conventional microscopy.
367 citations
TL;DR: This work estimates PSF parameters for this ill-posed class of inverse problem from raw data, along with the regularization parameters required to stabilize the solution, using the generalized cross-validation method (GCV).
Abstract: In many image restoration/resolution enhancement applications, the blurring process, i.e., point spread function (PSF) of the imaging system, is not known or is known only to within a set of parameters. We estimate these PSF parameters for this ill-posed class of inverse problem from raw data, along with the regularization parameters required to stabilize the solution, using the generalized cross-validation method (GCV). We propose efficient approximation techniques based on the Lanczos algorithm and Gauss quadrature theory, reducing the computational complexity of the GCV. Data-driven PSF and regularization parameter estimation experiments with synthetic and real image sequences are presented to demonstrate the effectiveness and robustness of our method.
256 citations
TL;DR: In this article, the authors performed detailed simulations with the state-of-the-art algorithm developed by Kaiser, Squires and Broadhurst (KSB) to measure gravitational shear and showed that for realistic PSF profiles the KSB algorithm can recover any shear amplitude in the range with a relative, systematic error of.
Abstract: With the recent detection of cosmic shear, the most challenging effect of weak gravitational lensing has been observed. The main difficulties for this detection were the need for a large amount of high quality data and the control of systematics during the gravitational shear measurement process, in particular those coming from the Point Spread Function anisotropy. In this paper we perform detailed simulations with the state-of-the-art algorithm developed by Kaiser, Squires and Broadhurst (KSB) to measure gravitational shear. We show that for realistic PSF profiles the KSB algorithm can recover any shear amplitude in the range with a relative, systematic error of . We give quantitative limits on the PSF correction method as a function of shear strength, object size, signal-to-noise and PSF anisotropy amplitude, and we provide an automatic procedure to get a reliable object catalog for shear measurements out of the raw images.
207 citations
TL;DR: In this article, the Moffat point spread function (PSF) was used to model the effects of seeing on Sersic r 1/n profile parameters, including central intensities, effective radii, index n and mean effective surface brightness.
Abstract: ABSTRA C T The effects of seeing on Sersic r 1/n profile parameters are extensively studied using a Moffat function. This analytical approximation to the point spread function (PSF) is shown to provide the best fit to the PSF predicted from atmospheric turbulence theory when b , 4:765. The Moffat PSF is additionally shown to contain the Gaussian PSF as a limiting case Ob! 1U. The Moffat function is also shown to be numerically well behaved when modelling narrow PSFs in HST images. Seeing effects are computed for elliptically symmetric surface brightness distributions. The widely used assumption of circular symmetry when studying the effects of seeing on intrinsically elliptical sources is shown to produce significant discrepancies with respect to the true effects of seeing on these sources. A prescription to correct raw (observed) central intensities, effective radii, index n and mean effective surface brightness is given.
201 citations
TL;DR: Transmission functions are derived that are valid in the nonparaxial case for a class of lenses that will image a continuum of points along an optical axis to a single image point in a digital camera.
Abstract: Transmission functions are derived that are valid in the nonparaxial case for a class of lenses that will image a continuum of points along an optical axis to a single image point This lens, which we call a logarithmic asphere, is then used in a digital camera The resolution of the camera is limited by the pixel size of the CCD; ie, it is not diffraction limited Digital processing is used to recover the image, and image-plane processing is used for speed We find a tenfold increase in the depth of field over that for the diffraction-limited case
188 citations
TL;DR: In this paper, a self-referencing scheme was proposed to identify new features associated with vascular dynamics from the analysis of time-series image data, based on the observation that analysis of such data can produce high contrast images that reveal features that are mainly obscured in individual image frames or in time-averaged image data.
Abstract: Methods used in optical tomography have thus far proven to produce images of complex target media (e.g., tissue) having, at best, relatively modest spatial resolution. This presents a challenge in differentiating artifact from true features. Further complicating such efforts is the expectation that the optical properties of tissue for any individual are largely unknown and are likely to be quite variable due to the occurrence of natural vascular rhythms whose amplitudes are sensitive to a host of autonomic stimuli that are easily induced. We recognize, however, that rather than frustrating efforts to validate the accuracy of image features, the time-varying properties of the vasculature can be exploited to aid in such efforts, owing to the known structure-dependent frequency response of the vasculature and to the fact that hemoglobin is a principal contrast feature of the vasculature at near-infrared wavelengths. To accomplish this, it is necessary to generate a time series of image data. In this report we have tested the hypothesis that through analysis of time-series data, independent contrast features can be derived that serve to validate, at least qualitatively, the accuracy of imaging data, in effect establishing a self-referencing scheme. A significant finding is the observation that analysis of such data can produce high-contrast images that reveal features that are mainly obscured in individual image frames or in time-averaged image data. Given the central role of hemoglobin in tissue function, this finding suggests that a wealth of new features associated with vascular dynamics can be identified from the analysis of time-series image data.
157 citations
TL;DR: In this paper, the Moffat point spread function (PSF) was shown to provide the best fit to the PSF predicted from atmospheric turbulence theory when beta=4.765.
Abstract: The effects of seeing on Sersic r^{1/n} profile parameters are extensively studied using a Moffat function. This analytical approximation to the point spread function (PSF) is shown to provide the best fit to the PSF predicted from atmospheric turbulence theory when beta=4.765. The Moffat PSF is additionally shown to contain the Gaussian PSF as a limiting case beta->infinity. The Moffat function is also shown to be numerically well behaved when modelling narrow PSFs in HST images. Seeing effects are computed for elliptically symmetric surface brightness distributions. The widely used assumption of circular symmetry when studying the effects of seeing on intrinsically elliptical sources is shown to produce significant discrepancies with respect to the true effects of seeing on these sources. A prescription to correct raw (observed) central intensities, effective radii, index n and mean effective surface brightness is given.
152 citations
TL;DR: In this article, a robust algorithm for cosmic-ray rejection, based on a variation of Laplacian edge detection, was proposed, which identifies cosmic-rays of arbitrary shapes and sizes by the sharpness of their edges.
Abstract: Conventional algorithms for rejecting cosmic-rays in single CCD exposures rely on the contrast between cosmic-rays and their surroundings, and may produce erroneous results if the Point Spread Function (PSF) is smaller than the largest cosmic-rays. This paper describes a robust algorithm for cosmic-ray rejection, based on a variation of Laplacian edge detection. The algorithm identifies cosmic-rays of arbitrary shapes and sizes by the sharpness of their edges, and reliably discriminates between poorly sampled point sources and cosmic-rays. Examples of its performance are given for spectroscopic and imaging data, including HST WFPC2 images.
136 citations
TL;DR: Wavelet-based processing tools turn out to be very effective in application to three-dimensional confocal images, and a quantitative assessment of the gain in quality achieved by wavelet-aided restorations over classical deconvolution schemes is provided.
136 citations
TL;DR: This paper shows that calibration of the emitter strength and detector efficiency/gain can be done successfully in a linear reconstruction model with simulated continuous-wave data and is general for frequency and time domain data.
Abstract: In order for diffuse optical tomography to realize its potential of obtaining quantitative images of spatially varying optical properties within random media, several potential experimental systematic errors must be overcome One of these errors is the calibration of the emitter strength and detector efficiency/gain While in principle these parameters can be determined accurately prior to an imaging experiment, slight fluctuations will cause significant image artifacts For this reason, it is necessary to consider including their calibration as part of the inverse problem for image reconstruction In this paper, we show that this can be done successfully in a linear reconstruction model with simulated continuous-wave data The technique is general for frequency and time domain data
TL;DR: A significant but limited class of blurs that can be expressed as convolutions of two-dimensional symmetric Levy "stable" probability density functions is considered, which includes and generalizes Gaussian and Lorentzian distributions.
Abstract: Blind deconvolution seeks to deblur an image without knowing the cause of the blur. Iterative methods are commonly applied to that problem, but the iterative process is slow, uncertain, and often ill-behaved. This paper considers a significant but limited class of blurs that can be expressed as convolutions of two-dimensional symmetric Levy "stable" probability density functions. This class includes and generalizes Gaussian and Lorentzian distributions. For such blurs, methods are developed that can detect the point spread function from one-dimensional Fourier analysis of the blurred image. A separate image deblurring technique uses this detected point spread function to deblur the image. Each of these two steps uses direct noniterative methods and requires interactive tuning of parameters. As a result, blind deblurring of 512 × 512 images can be accomplished in minutes of CPU time on current desktop workstations. Numerous blind experiments on synthetic data show that for a given blurred image, several di...
TL;DR: The theory shows that methods used in the past to compensate for the effects of background nonuniformities in far-field problems are also effective in reducing near-field artifacts.
Abstract: Coded apertures for imaging problems are typically based on arrays having perfect cross-correlation properties. These arrays, however, guarantee a perfect point-spread function in far-field applications only. When these arrays are used in the near-field, artifacts arise. We present a mathematical derivation capable of predicting the shape of such artifacts. The theory shows that methods used in the past to compensate for the effects of background nonuniformities in far-field problems are also effective in reducing near-field artifacts. The case study of a nuclear medicine problem is presented to show good agreement of simulation and experimental results with mathematical predictions.
TL;DR: The theoretical basis for resolution enhancement in standing-wave total internal reflection microscopy (SW-TIRM) is examined in this article, which relies on the formation of an excitation field containing super-diffraction-limited spatial-frequency components.
Abstract: The theoretical basis for resolution enhancement in standing-wave total internal reflection microscopy (SW-TIRM) is examined. This technique relies on the formation of an excitation field containing super-diffraction-limited spatial-frequency components. Although the fluorescence generated at the object planes contains high-frequency information of the object distribution, this information is lost at the image plane, where the detection optics acts as a low-pass filter. From the perspective of point-spread-function (PSF) engineering, one can show that if this excitation field is translatable experimentally, the high-frequency information can be extracted from a set of images where the excitation fields have different displacement vectors. We have developed algorithms to combine this image set to generate a composite image with an effective PSF that is equal to the product of the excitation field and the Fraunhofer PSF. This approach can easily be extended to incorporate nonlinear excitation modalities into SW-TIRM for further resolution improvement. We theoretically examine high-resolution imaging based on the addition of two-photon, pump–probe, and stimulated-emission depletion methods to SW-TIRM and show that resolution better than 1/20 of the emission wavelength may be achievable.
TL;DR: A mathematical model for a three-dimensional omnidirectional integral recording camera system that uses either circular- or hexagonal-based spherical surface microlens arrays is derived and the influence of depth on the point-spread dimensions for each type of microlense and imaging condition is discussed.
Abstract: A mathematical model for a three-dimensional omnidirectional integral recording camera system that uses either circular- or hexagonal-based spherical surface microlens arrays is derived. The geometry of the image formation and recording process is fully described. Matlab is then used to establish the number of recorded micro-intensity distributions representing a single object point and their dependence on spatial position. The point-spread function for the entire optical process for both close and remote imaging is obtained, and the influence of depth on the point-spread dimensions for each type of microlens and imaging condition is discussed. Comparisons of the two arrangements are made, based on the illustrative numerical results presented.
TL;DR: A novel whole-field three-dimensional fluorescence lifetime imaging microscope that incoporates multispectral imaging to provide five-dimensional (5-D) fluorescence microscopy is reported.
Abstract: We report a novel whole-field three-dimensional fluorescence lifetime imaging microscope that incoporates multispectral imaging to provide five-dimensional (5-D) fluorescence microscopy. This instrument, which can acquire a 5-D data set in less than a minute, is based on potentially compact and inexpensive diode-pumped solid-state laser technology. We demonstrate that spectral discrimination as well as optical sectioning minimize artifacts in lifetime determination and illustrate how spectral discrimination improves the lifetime contrast of biological tissue.
TL;DR: In this paper, a reduction pipeline for CCD images was built to search for variable sources in highly crowded fields like the M31 bulge and to handle extensive databases due to large time series.
Abstract: We present a reduction pipeline for CCD (charge-coupled device) images which was built to search for variable sources in highly crowded fields like the M31 bulge and to handle extensive databases due to large time series. We describe all steps of the standard reduction in detail with emphasis on the realisation of per pixel error propagation: Bias correction, treatment of bad pixels, flatfielding, and filtering of cosmic rays. The problems of conservation of PSF (point spread function) and error propagation in our image alignment procedure as well as the detection algorithm for variable sources are discussed: We build difference images via image convolution with a technique called OIS (Alard & Lupton, 1998), proceed with an automatic detection of variable sources in noise dominated images and finally apply a PSF-fitting, relative photometry to the sources found. For the WeCAPP project (Riffeser et al., 2001) we achieve 3 sigma detections for variable sources with an apparent brightness of e.g. m = 24.9 mag at their minimum and a variation of dm = 2.4 mag (or m = 21.9 mag brightness minimum and a variation of dm = 0.6 mag) on a background signal of 18.1 mag/arcsec^2 based on a 500 s exposure with 1.5 arcsec seeing at a 1.2 m telescope. The complete per pixel error propagation allows us to give accurate errors for each measurement.
Patent•
27 Sep 2001TL;DR: In this article, a point spread function generating unit generates varying point spread functions corresponding to various distances based upon two-dimensional distance distribution information indicating the 2D distance distribution of the subject detected by a distance detection unit and an image blur signal indicating an image blurred occurring during the exposure period which is detected by the blur detection unit.
Abstract: An image-capturing unit generates an image signal corresponding to an image of a subject formed by a photographing optical system. A point spread function generating unit generates varying point spread functions corresponding to various distances based upon two-dimensional distance distribution information indicating the two-dimensional distance distribution of the subject detected by a distance detection unit and an image blur signal indicating an image blur occurring during the exposure period which is detected by a blur detection unit. An image repair unit divides the image signal into partial images based upon the distance distribution information, executes image processing to repair the blur in the individual partial images by using the point spread functions corresponding to the various distances and creates a whole image by synthesizing the partial images in which the blur has been repaired.
TL;DR: A method for increasing lateral as well as axial resolution in fluorescence microscopy is presented and theoretical calculations show an almost isotropic point-spread function with a FWHM near 100 nm.
Abstract: A method for increasing lateral as well as axial resolution in fluorescence microscopy is presented. A passband with a high cutoff frequency throughout reciprocal space can be achieved by illumination of the object with spatially harmonic excitation patterns generated by the interference of two collimated laser beams. Theoretical calculations show an almost isotropic point-spread function with a FWHM near 100 nm.
04 Nov 2001
TL;DR: In this paper, an exact expression for the pinhole response function on the imaging plane that includes the effect of aperture penetration is derived by calculating the flux for photons passing through the aperture and those passing through attenuating material.
Abstract: Pinhole collimators are widely used to image small organs and animals. The pinhole response function (PRF) of knife-edge pinhole collimators has been estimated previously using geometric constructions without considering penetration and using "roll-off" models that employ an exponential model for the flux. An exact expression for the PRF on the imaging plane that includes the effect of aperture penetration is derived in this paper by calculating the flux for photons passing through the aperture and those passing through the attenuating material. The PRF is then used to estimate the angular-dependent root-mean-square resolution in the directions parallel and perpendicular to the tilt of the point source. The formulas are then compared with experimental data.
TL;DR: The laboratory facilities to measure the point spread function (PSF) and MTF of water body by the image transmission method and the restoration methods of under- water blurred images are described.
Abstract: Because light is scattered and absorbed by seawater, the images obtained underwater are always blurry after transmitted through a certain distance. The point spread function (PSF) and modulation transfer function (MTF) are important properties of seawater to predict underwater light propagation and underwater image quality. We describe the laboratory facilities to measure the PSF and MTF of water body by the image transmission method and the restoration methods of under- water blurred images. The measured results are given and compared with the theories. The blurred images of a bar target transmitted through different water paths are restored with the measured MTF using a Wiener filter. © 2001 Society of Photo-Optical Instrumentation Engineers.
TL;DR: Quantitative sharpness analysis of ''ideal sample'' micrographs shows that APEX processing can actually produce sharper imagery than is achievable with optimal microscope settings, and is shown to be useful in enhancing and detecting fine detail not otherwise discernible.
Abstract: Loss of resolution due to image blurring is a major concern in electron microscopy. The point spread function describing that blur is generally unknown. We discuss the use of a recently developed fast Fourier transform (FFT)-based direct (noniterative) blind deconvolution procedure, the APEX method, that can process 5123512 images in sec- onds of CPU time on current desktop platforms. The method is predi- cated on a restricted but significant class of shift-invariant blurs, consist- ing of finite convolution products of heavy-tailed Levy probability density functions. Such blurs considerably generalize Gaussian and Lorentzian point spread functions. The method is applied to a variety of original scanning electron microscopy (SEM) micrographs and is shown to be useful in enhancing and detecting fine detail not otherwise discernible. Quantitative sharpness analysis of ''ideal sample'' micrographs shows that APEX processing can actually produce sharper imagery than is achievable with optimal microscope settings. © 2002 Society of Photo-Optical
TL;DR: This work simulates multistatic radar returns using Fast Illinois Solver Code (FISC) and shows that a good sampling pattern can be used to form a recognizable target image using direct Fourier reconstruction.
Abstract: We investigate passive radar imaging of aircraft using reflected TV signals. Such passive multistatic ``radar'' has been developed to detect and track aircraft with good accuracy. The additional capability of image formation would help to identify targets. The Fourier space sampling provided by passive radar is nonuniform. For a given aircraft flight path, different receiver locations give rise to different sampling patterns. We simulate multistatic radar returns using Fast Illinois Solver Code (FISC) and show that a good sampling pattern can be used to form a recognizable target image using direct Fourier reconstruction. However, a bad sampling pattern can make it impossible to form a useful image. In the Gaithersburg, MD area, we can select a good receiver location using 21 or fewer channels, which provides good enough Fourier-space coverage to form a useful aircraft image.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
TL;DR: Using the concept of the coarray, an expression is derived for the point spread function for wide-band pulse-echo imaging arrays that provides a better understanding of the interplay between bandwidth, element locations, weighting of the elements, pulse shape within the bandwidth, and imaging performance.
TL;DR: It is found that the retinal image or, alternatively, the ocular aberrations, are nearly independent of the state of polarization of the incident light (in the first pass), which means that a significant improvement in the Ocular optics by using a specific type of polarized light could not be achieved.
Abstract: We have previously studied how polarization affects the double-pass estimates of the retinal image quality by using an imaging polarimeter [Opt. Lett.24, 64 (1999)]. A series of 16 images for independent combinations of polarization states in the polarimeter were recorded to obtain the spatially resolved Mueller matrices of the eye. From these matrices, double-pass images of a point source for light with different combinations of incoming (first-pass) and outcoming (second-pass) polarization states were reconstructed and their corresponding modulation transfer functions were calculated. We found that the retinal image or, alternatively, the ocular aberrations, are nearly independent of the state of polarization of the incident light (in the first pass). This means that a significant improvement in the ocular optics by using a specific type of polarized light could not be achieved. However, quite different estimates of the retinal image quality are obtained for combinations of polarization states in both the first and the second passes in the double-pass apparatus.
TL;DR: In this paper, a low-resolution wavelet projection of the echo sequence log spectrum is used as an estimate of the log spectrum of the point spread function, followed by soft thresholding and an inverse wavelet transform.
Abstract: Methods and associated apparatuses for imaging a target. An echo sequence image of the target is acquired (10) and a log spectrum of at least a portion of the echo sequence image is computed. A point spread function is estimated (14) by one of two methods. According to the first method, a low-resolution wavelet projection of the echo sequence log spectrum (22) is used as an estimate of the log spectrum of the point-spread function. According to the second method, an outlier-resistant wavelet transform of the echo sequence log spectrum is effected (44), followed by soft-thresholding (46) and an inverse wavelet transform (48). Under both methods, a frequency domain phase of the point spread function also is estimated. The relevant portion of the echo sequence image is deconvolved using the estimated point spread function.
TL;DR: The quality of an image can be significantly improved by digital deconvolution with the (two-dimensional) point spread function (PSF) of the imaging system as long as magnified images are obtained and digitized and Wiener filtering is used.
Patent•
04 May 2001TL;DR: In this article, a point spread function (PSF) is expressed in terms of the Green's function for the transport equation, which provides weighting functions for use in a generalized series expansion method.
Abstract: Photon migration methods are employed to image absorbing objects embedded in a turbid medium such as tissue. For improved resolution, early arriving photons are detected to provide data with image reconstruction based on optical computed tomography (CT). The CT method is generalized to take into account the distributions of photon paths. A point spread function (PSF) is expressed in terms of the Green's function for the transport equation. This PSF provides weighting functions for use in a generalized series expansion method. Measurements of turbid medium with scattering and absorption properties included coaxial transmission scans collected in two projections. Blurring associated with multiple scattering was removed and high-resolution images can be obtained.
07 Oct 2001
TL;DR: A new method for making spatial matched filter focusing of RF ultrasound data is proposed based on the spatial impulse response description of the imaging and was applied to in-vivo clinical images of the liver and right kidney from a 28 years old male.
Abstract: Traditionally focusing is done by taking out one sample in the received signal from each transducer element and then sum these signals. This method does not take into account the temporal or spatial spread of the received signal from a point scatterer and does not make an optimal focus of the data. A new method for making spatial matched filter focusing of RF ultrasound data is proposed based on the spatial impulse response description of the imaging. The response from a scatterer at any given point in space relative to the transducer can be calculated, and this gives the spatial matched filter for beamforming the received RF signals from the individual transducer elements. The matched filter is applied on RF signals from individual transducer elements, thus properly taking into account the spatial spread of the received signal. The method can be applied to any transducer and can also be used for synthetic aperture imaging for single element transducers. It is evaluated using the Field II program. Data from a single 3 MHz transducer focused at a distance of 80 mm is processed. Far from the transducer focal region, the processing greatly improves the image resolution: the lateral slice of the autocovariance function of the image shows a -6 dB width reduction by a factor of 3.3 at 20 mm and by a factor of 1.8 at 30 mm. Other simulations use a 64 elements, 3 MHz, linear array. Different receiving conditions are compared and this shows that the effect of the filter is progressively lower, but the approach always yields point spread functions better or equal to a traditional dynamically focused image. Finally, the process was applied to in-vivo clinical images of the liver and right kidney from a 28 years old male. The data was obtained with a single element transducer focused at 100 mm. The improvement in resolution was in this case less evident and further optimization is needed.
TL;DR: How under-resolved images of bar codes may be read by suitable processing is described, which allows the rows within the resultant image to be averaged to reduce noise.
Abstract: This article describes how under-resolved images of bar codes may be read by suitable processing. A two-dimensional im- age of a bar code with insufficient resolution to be able to resolve the individual bars is processed to give a high-resolution image. For this to work, the bar code (or camera) must be slightly rotated to give a fraction of a pixel offset between rows. Since the bars are straight, the offset relative to the first complete row of the bar code increases linearly with vertical position in the image. This offset be- tween rows results in a shift in phase that is proportional to both offset and frequency. A phase image is formed by Fourier trans- forming each row in the image, and retaining the phases. By sub- tracting the first row from subsequent rows of the phase image, a surface is fitted to give the offset between rows. A high-resolution image is then formed by interleaving the pixel values from rows where the offset is nearest to the new pixel spacing. This image appears blurred because of the area sampling caused by the sen- sor, combined with the low pass response of the camera electronics. By modeling the image capture system, the point spread function may be estimated and then removed by using inverse filtering in the frequency domain. The offset between the rows is then removed by using a linear phase filter. This allows the rows within the resultant image to be averaged to reduce noise. © 2001 SPIE and IS&T.