Showing papers on "Point spread function published in 1991"

Digital wavefront measuring interferometer for testing optical surfaces and lenses

Abstract: A self-scanned 1024 element photodiode array and minicomputer are used to measure the phase (wavefront) in the interference pattern of an interferometer to lambda/100. The photodiode array samples intensities over a 32 x 32 matrix in the interference pattern as the length of the reference arm is varied piezoelectrically. Using these data the minicomputer synchronously detects the phase at each of the 1024 points by a Fourier series method and displays the wavefront in contour and perspective plot on a storage oscilloscope in less than 1 min (Bruning et al. Paper WE16, OSA Annual Meeting, Oct. 1972). The array of intensities is sampled and averaged many times in a random fashion so that the effects of air turbulence, vibrations, and thermal drifts are minimized. Very significant is the fact that wavefront errors in the interferometer are easily determined and may be automatically subtracted from current or subsequent wavefrots. Various programs supporting the measurement system include software for determining the aperture boundary, sum and difference of wavefronts, removal or insertion of tilt and focus errors, and routines for spatial manipulation of wavefronts. FFT programs transform wavefront data into point spread function and modulus and phase of the optical transfer function of lenses. Display programs plot these functions in contour and perspective. The system has been designed to optimize the collection of data to give higher than usual accuracy in measuring the individual elements and final performance of assembled diffraction limited optical systems, and furthermore, the short loop time of a few minutes makes the system an attractive alternative to constraints imposed by test glasses in the optical shop.

Image transfer through a scattering medium

Abstract: 1 Introduction.- 1.1 A Brief History.- 1.2 Structure of the Book.- 1.3 Notes on Terminology.- 2 Radiation Field and Scattering Medium Characteristics.- 2.1 Radiation Field.- 2.2 Optical Parameters of a Volume Element.- 2.3 Radiation Transfer Equation.- 2.4 Similarity Principle and Modeling.- 2.5 Corollaries of the Optical Reciprocity Theorem.- 3 Light Scattering in Semi-Infinite Media and Plane Layers Illuminated by Infinitely Extended Plane Sources.- 3.1 Basic Equations.- 3.2 Asymptotic Regime in Deep Layers.- 3.2.1 Asymptotic Attenuation Coefficient and Angular Radiance Distribution.- 3.2.2 The Light Field in Absolute Units.- 3.3 Reflection from a Semi-Infinite Medium.- 3.3.1 Nonabsorbing Media.- 3.3.2 Weakly Absorbing Media.- 3.3.3 Absorbing Media with Strongly Anisotropic Scattering.- 3.4 Reflection and Transmission by Layers of Finite Thickness.- 3.5 Reflection and Transmission by Optically Thick Scattering Layers.- 3.5.1 Nonabsorbing Media.- 3.5.2 Weakly Absorbing Media.- 3.5.3 Absorbing Media with Strongly Anisotropic Scattering.- 3.6 Approximate Indicatrix Model Solutions.- 3.6.1 Forward Peak Truncation. Similar Media.- 3.6.2 Transport Approximation.- 3.6.3 Quasi-Single Scattering Approximation.- 3.6.4 Small-Angle Solution Iteration.- 3.6.5 Sobolev Approximation. Conservative Scattering.- 3.7 Two-Stream Approximation.- 3.7.1 Irradiance Coefficients. Boundary Conditions.- 3.7.2 Four-Parameter Variant of the Two-Stream Approximation.- 3.7.3 Two-Parameter Variant of the Two-Stream Approximation.- 4 Radiation Transfer in Scattering Media Illuminated by Localized Sources.- 4.1 Transfer Equation for a Narrow Beam. Spatial Radiance and Irradiance Distribution Moments.- 4.2 Local and Asymptotic Properties of Transfer Equation Solutions.- 4.3 The Diffusion Equation.- 4.3.1 Derivation of the Diffusion Equation.- 4.3.2 Solution of the Diffusion Equation for an Isotropic Point Source.- 4.3.3 Radial Irradiance Distribution from a Monodirectional Point Source.- 4.4 Small-Angle Approximation.- 4.4.1 Various Approaches.- 4.4.2 Transfer Equation in the Small-Angle Approximation.- 4.4.3 Solution of the Small-Angle Transfer Equation.- 4.4.4 Irradiance and Radiance of a Medium Illuminated by an Infinitely Extended Source.- 4.4.5 The Spread Function and its Moments.- 4.4.6 Light Flux.- 4.4.7 Radiation Fields in Scattering Media with Fluctuating Optical Parameters.- 4.4.8 The Merits and Weaknesses of the Small-Angle Approximation.- 4.5 Small-Angle Diffusion Approximation.- 4.5.1 Transfer Equation in the Small-Angle Diffusion Approximation.- 4.5.2 Light Fields Generated by an Infinitely Wide Source.- 4.5.3 Characteristics of Light Fields Produced by Narrow Beams.- 4.5.4 Oblique Medium Illumination.- 4.5.5 Light Fields in Media with Depth-Dependent Optical Characteristics.- 4.5.6 The Scope of the Small-Angle and Small-Angle Diffusion Approximations.- 4.5.7 Modified Small-Angle Diffusion Approximation.- 4.6 Notes on Multiple Backscattering.- 4.7 Generalized Multiple Scattering Theory Parameters and Applicability of Approximate Solutions.- 4.8 Nonstationary Radiation Field from Localized Pulsed Sources.- 4.8.1 The Nonstationary Transfer Equation.- 4.8.2 Pulse Propagation in Optically Thick Media.- 4.8.3 Pulse Reflection from a Semi-Infinite Scattering Medium.- 4.8.4 Forward Pulse Spread in a Strongly Anisotropic Scattering Medium.- 4.8.5 Mean Time and Variance of Photon Paths.- 5 Elements of Vision Theory.- 5.1 Image Quality Characteristics.- 5.1.1 Contrast and Signal-to-Noise Ratio.- 5.1.2 Threshold Contrast.- 5.1.3 General Image Quality Criterion.- 5.1.4 Threshold Signal-to-Noise Ratio.- 5.1.5 Signal-to-Noise Ratio in a Medium with Fluctuating Optical Parameters.- 5.2 Image Transfer Characteristics.- 5.2.1 Point Spread Function. Optical Transfer Function.- 5.2.2 Aspect Invariance of a System.- 5.2.3 Image Recording Techniques.- 5.2.4 Aspect Invariance Applicability.- 5.2.5 PSF and OTF Measurements.- 5.3 Active Vision Systems.- 5.3.1 Basic Relations.- 5.3.2 Classification of Vision System.- 5.3.3 Comparison of Vision Systems.- 5.3.4 Systems with Scattered Light Suppression.- 5.4 Visual Perception. Real Object Detection and Discrimination Range.- 5.4.1 The Johnson Criteria.- 5.4.2 Object Detection Range.- 5.4.3 Object Discrimination Range.- 5.5 Television and Location Target Detection Systems.- 5.5.1 Location in a Given Direction (Laser Echo-Ranging).- 5.5.2 Image Forming Location.- 5.6 Basic Characteristics of the Eye and Other Photodetectors.- 5.6.1 The Human Eye as a Radiation Receiver.- 5.6.2 Photographic and Photoelectric Recording.- 5.6.3 Notes on Infrared Imaging.- 6 Optical Transfer Function of a Scattering Medium.- 6.1 OTF of a Homogeneous Layer.- 6.1.1 OTF within the Small-Angle Approximation.- 6.1.2 The Small-Angle Diffusion Approximation.- 6.1.3 The Diffusion Approximation.- 6.1.4 MTF Dependence on Optical Medium Parameters.- 6.1.5 Scattering Layer MTF under Pulsed Source Illumination.- 6.2 OTF of an Inhomogeneous Layer.- 6.2.1 The Small-Angle Approximation.- 6.2.2 OTF of an Inhomogeneous Strongly Scattering Layer.- 6.2.3 MTF Dependence on the Scattering Layer Position along the Observation Path.- 6.2.4 Stochastic Medium MTF.- 6.3 Scattering Layer OTF along an Oblique Path. Phase Transfer Function.- 6.4 Nonlinear Distortions in Thick Scattering Layers.- 6.5 Object Image Contrast.- 6.5.1 Small Object Contrast.- 6.5.2 Contrast in the Johnson Striped Test Object.- 6.5.3 Finite Object Contrast as a Function of the Scattering Layer Position along the Observation Path.- 6.6 The Function ? in Object Detection and Discrimination.- 7 Image Transfer in Coherent Light.- 7.1 Coherent-Holography Imaging Through a Scattering Medium.- 7.1.1 Time-Averaged Holography.- 7.1.2 Limited Time Coherence (LTC) Method.- 7.1.3 Reference-Free Image Plane Holography (RFIPH).- 7.2 Comparison of Holographic and Incoherent Vision Systems.- 7.2.1 Mutual Coherence Function as Related to Radiance.- 7.2.2 Quality Characteristics of Rough Object Images in Reference Wave Holography.- 7.2.3 Contrast and Signal-to-Noise Ratio in Time-Averaged Holography and the Limited Time Coherence Technique.- 7.2.4 Contrast and Signal-to-Noise Ratio as Functions of the Averaging Time and Optical Parameters of a Scattering Medium.- 8 Viewing in Atmosphere.- 8.1 Optical Parameters of the Atmosphere.- 8.1.1 Cloudless Atmosphere.- 8.1.2 Cloud and Fog.- 8.2 Light Source Visibility.- 8.3 Object Visibility in Sunlight.- 8.3.1 Meteorological Visibility Range.- 8.3.2 Visibility Range in Clouds.- 8.4 Vision Characteristics in Cloud and Fog.- 8.4.1 OTF and Single-to-Noise Ratio.- 8.4.2 Cloud Microstructure Effect on the OTF and SNR.- 8.4.3 Estimation of Cloud OTF from Microstructure Data.- 8.5 Viewing Through Stochastic Clouds.- 8.5.1 Viewing System OTF and Signal Power Fluctuations.- 8.5.2 Irradiance and Radiation Flux Fluctuation Variances.- 8.5.3 Signal-to-Noise Ratio.- 9 Underwater Vision and Location in Sea Water.- 9.1 Optical Properties of Sea Water.- 9.1.1 Experimental Data.- 9.1.2 Simple Model of Optical Sea Water Characteristics.- 9.2 Object Visibility in Sea Water.- 9.2.1 Light Source Visibility.- 9.2.2 Range of Visibility of a Sunlit Object at Ocean Depth.- 9.2.3 Sekky's Disc Depth of Visibility.- 9.3 Underwater Television.- 9.3.1 Underwater TV Systems.- 9.3.2 MTF and Valid Signal and Noise Energy in Underwater Vision Systems.- 9.3.3 Limiting Ranges of Underwater Vision.- 9.4 Image Transfer Through a Rough Sea Surface.- 9.4.1 Rough Sea Surface Model.- 9.4.2 Image Transfer Characteristics.- 9.5 The Range of Optical Pulsed Location in Sea Water.- 10 Image Quality Problems in Photographic Layers and Luminescent Screens.- 10.1 Optical Parameters of a Photographic Layer.- 10.1.1 Undeveloped Layer.- 10.1.2 Exposed Developed Layer.- 10.2 Modulation Transfer Function of Photographic Materials.- 10.2.1 Optical and Photographic Modulation Transfer Functions.- 10.2.2 Empirical and Approximate MTF Formulas.- 10.2.3 MTF Dependence on the Optical and Emulsion Parameters of Photographic Materials.- 10.3 Optical Parameters of a Luminescent Screen.- 10.4 Modulation Transfer Function of Luminescent Screens.- 10.4.1 Nonscattering Luminescent Screens.- 10.4.2 Screens Weakly Absorbing Exciting Radiation.- 10.4.3 Screens Strongly Absorbing Exciting Radiation.- 10.4.4 Modulation Transfer Function of Cathode-Ray Screens.- 10.4.5 Influence of Technological Screen Parameters on MTF.- List of Symbols and Abbreviations.- References.

Characterizing digital image acquisition devices

Abstract: Despite the popularity of digital imaging devices (e.g., CCD array cameras) the problem of accurately characterizing the spatial frequency response of such systems has been largely neglected in the literature. This paper describes a simple method for accurately estimating the optical transfer function of digital image acquisition devices. The method is based on the traditional knife-edge technique but explicitly deals with fundamental sampled system considerations: insufficient and anisotropic sampling. Results for both simulated and real imaging systems demonstrate the accuracy of the method.

The point‐spread function of a confocal microscope: its measurement and use in deconvolution of 3‐D data

Abstract: SUMMARY We have measured the point-spread function (PSF) for an MRC-500 confocal scanning laser microscope using subresolution fluorescent beads. PSFs were measured for two lenses of high numerical aperture—the Zeiss plan-neofluar 63 × water immersion and Leitz plan-apo 63 × oil immersion—at three different sizes of the confocal detector aperture. The measured PSFs are fairly symmetrical, both radially and axially. In particular there is considerably less axial asymmetry than has been demonstrated in measurements of conventional (non-confocal) PSFs. Measurements of the peak width at half-maximum peak height for the minimum detector aperture gave approximately 0·23 and 0·8 μm for the radial and axial resolution respectively (4·6 and 15·9 in dimensionless optical units). This increased to 0·38 and 1·5 μm (7·5 and 29·8 in dimensionless units) for the largest detector aperture examined. The resulting optical transfer functions (OTFs) were used in an iterative, constrained deconvolution procedure to process three-dimensional confocal data sets from a biological specimen—pea root cells labelled in situ with a fluorescent probe to ribosomal genes. The deconvolution significantly improved the clarity and contrast of the data. Furthermore, the loss in resolution produced by increasing the size of the detector aperture could be restored by the deconvolution procedure. Therefore for many biological specimens which are only weakly fluorescent it may be preferable to open the detector aperture to increase the strength of the detected signal, and thus the signal-to-noise ratio, and then to restore the resolution by deconvolution.

Confocal scanning optical microscope using single-mode fiber for signal detection

Abstract: A single-mode fiber is employed as a detector in a confocal scanning optical microscope (CSOM) instead of a pinhole and its optical property is studied. The optical system is always coherent, which is fundamentally different from the CSOM with a finite-sized pinhole. The coherent transfer function and the axial response are calculated. Experimentally, the coherent image is taken and the axial response is also measured.

Synthetic aperture ultrasonic imaging system using a minimum or reduced redundancy phased array

Abstract: A synthetic aperture ultrasonic imaging system for imaging a target with a resolution limited by a designated aperture. A phased array of nonuniformly spaced ultrasound transducers having an average inter-transducer spacing which is greater than a λ/2 Nyquist spacing for the transducers is used for imaging in a manner so as to either obtain a desired point spread function which is unattainable by a single image taken by the nonuniformly spaced transducers or to provide coarray equivalence to a phased array of transducers which are uniformly spaced at the λ/2 Nyquist spacing for the designated aperture. Coarray equivalence makes possible the technique of applying amplitude weightings to each of the nonuniformly spaced ultrasound transducers during transmit and receive modes and by forming a number of component images which when added together form a sum image substantially equivalent to a single image formed by a scan beam of the uniformly spaced transducers with the designated aperture. The complex values of the resulting component images are then added on a point by point basis, preserving phase, such that a point spread function of the sum image is substantially equivalent to the desired point spread function of the single image formed by the uniformly spaced transducers with the designated ape STATEMENT OF GOVERNMENT INTEREST This invention was made with government support under contract N00014-89-J-1538 awarded by the Department of the Navy. The government has certain rights in the invention.

X‐ray focusing using square channel‐capillary arrays

Abstract: A class of imaging, condensing, and collimating devices for x rays is investigated which is based on the use of an array of small channels of square cross section. The focusing and collimating effect arises from external reflection of near‐grazing‐incidence rays at the interior channel surfaces. Rays are redirected by being singly reflected from two orthogonal channel surfaces and are imaged from a source point to a square region with a side length MT+1 times that of the channel side length, where MT is the transverse magnification. The image and source locations are related by a thin‐lens formula. The point spread function and the efficiency of these focusing devices are calculated. Two energy regimes with different channel reflectivity characteristics are examined in detail: the hard x‐ray regime (E>8 keV) and the soft x‐ray regime (E<200 eV). For these cases the efficiency of focusing x rays depends only on the channel aspect ratio and reflectivity parameters. A discussion is made of channel plates of ...

Modeling phase-shifting masks

Abstract: An algebraic image perturbation model is introduced which used the point spread function of the lens and the mutual coherence of the illumination to give insight into the interactions of auxiliary patterns with features for the phase shifting mask technology. The model is based on adding electric field contributions and the cross term is shown to characterize the dominant interaction as a function of the number of auxiliary features, the relative coherence of the illumination, and the spreading of the image of the auxiliary pattern toward the feature. Data on the point/line spread functions and the mutual coherence are given and used to verify the accuracy of quantitative predictions of the change in peak intensity for lines and contacts when nonprinting phase shifting auxiliary patterns are added.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Limited degree-of-freedom adaptive optics and image reconstruction.

Abstract: The use of limited degree-of-freedom adaptive optics in conjunction with statistical averaging and a linear image reconstruction algorithm is addressed. Image reconstruction is traded for full predetection compensation. It is shown through analytic calculations that the average optical transfer function (OTF) is significant for high spatial frequencies in the case of imaging through atmospheric turbulence with an adaptive optics system composed of a Hartmann-type wave-front sensor and a deformable mirror possessing far fewer actuators than one per atmospheric coherence diameter (r(0)). Statistical averaging is used to overcome the effects of measurement noise and randomness in individual realizations of the OTF. The imaging concept and signal-to-noise considerations are presented.

Helical-scan computed tomography using cone-beam projections

Abstract: A fast data-acquisition method for 3-D X-ray computed tomography is proposed The method continuously rotates a cone-beam X-ray source and a 2-D detector constructed by stacking 1-D circular detector arrays for the fan-beam computed tomography Simultaneously, a patient is translated in the field of view of the X-ray source This method is called helical-san, because it provides cone-beam projections measured by moving an X-ray source on a helix surrounding the patient An approximate convolution backprojection image reconstruction algorithm for the helical-scan is developed by extending LA Feldkamp's (1984) cone-beam reconstruction algorithm, for the circular-scan How one should choose geometrical parameters of the data-acquisition system is discussed Furthermore, the performance of the proposed method is analyzed by evaluating the point spread function of the reconstruction algorithm >

Imaging through scattering media using spatial incoherence techniques

Abstract: Imaging of objects embedded in scattering media can be accomplished by sources with reduced spatial coherence instead of pulsed light or short temporal coherence light.

Comparison of two three-dimensional x-ray cone-beam-reconstruction algorithms with circular source trajectories

Abstract: We compare two algorithms of three-dimensional (3D) cone-beam tomography: a 3D backprojection algorithm and a Radon algorithm, with a circular source trajectory. We recall the principle of these algorithms and show that when the source trajectory is circular, an exact reconstruction cannot be performed. We evaluate structures that cannot be detected and show that, for each algorithm, assumptions must be made about the object to estimate the missing information. Using simulated data, we measured the modulation transfer function of the two algorithms, evaluated the density resolution, and measured the artifacts due to missing information. We show that the 3D backprojection algorithm has good geometrical resolution along the axis of rotation and that, from the standpoint of density resolution, its useful limit is ±3°. We also show that it is sensitive to the lack of information in the horizontal planes. The useful aperture of the Radon algorithm is ±12°; for apertures lower than this limit, the algorithm is much less sensitive to the lack of information in the horizontal planes than the 3D backprojection algorithm. We present two examples of reconstructions that illustrate the limitations of these algorithms when applied to realistic samples and discuss the limits of using each algorithm when the source trajectory is circular.

Simple empirical model of the oceanic point spread function

Abstract: The point spread function (PSF) is an important property for predicting beam propagation and imaging system performance. Measurements of the PSF in three different locations (Pacific Ocean, Tongue of the Ocean, and Sargasso Sea) are presented. These measurements are used to validate extensive laboratory measurements [S. Q. Duntley, "Underwater Lighting by Submerged Lasers and Incandescent Sources," SIO Ref. 71-1, Scripps Institution of Oceanography, U. California, San Diego (1971)]. In all three locations a simple exponential expression describes the angular variation of the PSF in the 4-100-mrad range. The exponent in this relationship has a simple location specific dependence on attenuation length and the ratio of the absorption to beam attenuation coefficient. These relationships can be used to predict the PSF for an arbitrary path length.

Point spread function in ocean water: comparison between theory and experiment

Abstract: A new instrument to measure the point spread function (PSF) in the ocean has provided the opportunity for direct comparison between theoretical predictions and experimental measurement. Theoretical predictions are derived from small angle scattering theory using a simple algebraic fit to the single scattering phase function. The resulting predictions for the PSF are found to match the experimental measurements over a wide range of angles and optical depths.

Passive ranging and rapid autofocusing

Abstract: Apparatus and methods based on signal processing techniques are disclosed for determining the distance of an object from a camera, rapid autofocusing of a camera, and obtaining focused pictures from blurred pictures produced by a camera. The apparatus of the present invention includes a camera characterized by a set of four camera parameters: position of the image detector or film inside the camera, focal length of the optical system in the camera, the size of the aperture of the camera, and the characteristics of the light filter in the camera. In the method of the present invention, at least two images of the object are recorded with different values for the set of camera parameters. The two images are converted to a standard format to obtain two normalized images. The values of the camera parameters and the normalized images are substituted into an equation obtained by equating two expressions for the focused image of the object. The two expressions for the focused image are based on a new deconvolution formula which requires computing only the derivatives of the normalized images and a set of weight parameters dependent on the camera parameters and the point spread function of the camera. In particular, the deconvolution formula does not involve any Fourier transforms and therefore the present invention has significant advantages over prior art. The equation which results from equating two expressions for the focused image of the object is solved to obtain a set of solutions for the distance of the object. A third image of the object is then recorded with new values for the set of camera parameters. The solution for distance which is consistent with the third image and the new values for the camera parameters is determined to obtain the distance of the object. Based on the distance of the object, a set of values is determined for the camera parameters for focusing the object. The camera parameters are then set equal to these values to accomplish autofocusing. After determining the distance of the object, the focused image of the object is obtained using the deconvolution formula. A generalized version of the method of determining the distance of an object can be used to determine one or more unknown camera parameters. This generalized version is also applicable to any linear shift-invariant system for system parameter estimation and signal restoration.

On modeling the focus blur in image restoration

Abstract: The point spread function (PSF) of a defocused lens, in the continuous spatial coordinates, can be modeled using the principles of either geometrical optics or physical optics. The authors compare the PSFs and the corresponding optical transfer functions obtained on the basis of these two models under different amounts of blurs and different imaging sensor resolutions, in the discrete spatial domain. Different approximations for the discretization of the PSF are considered. The effect of using geometrical versus physical optics-based models on the quality of restored images is investigated experimentally in the case of images recorded by a charge-coupled device (CCD) camera. >

Three-dimensional coherent transfer functions in fiber-optical confocal scanning microscopes

Abstract: After analyzing the three-dimensional image formation in fiber-optical confocal scanning microscopes, a three-dimensional effective point-spread function is introduced. For both reflection-mode and transmission-mode microscopes of small circular aperture, analytical expressions for the three-dimensional coherent transfer functions are derived. The relation between the three-dimensional and the two-dimensional (for thin objects) coherent transfer functions in these microscopic systems is further investigated. Three-dimensional numerical plots of the coherent transfer functions reveal their dependence on the fiber spot size.

Imaging a randomly moving object from quantum-limited data: applications to image recovery from second- and third-order autocorrelations

Abstract: New methods are described for forming intensity estimates of randomly moving objects from quantum-limited data. These methods assume a preprocessed data set consisting of photon differences. Image estimates are formed with the use of the method of maximum likelihood. Algorithms for recovering an image from a measurement of its autocorrelation or triple correlation are derived by considering the limit as the photoconversion rate tends toward infinity.

Experimental validation of a Monte Carlo procedure for the evaluation of the effect of a turbid medium on the point spread function of an optical system

Abstract: The presence of particulate matter interposed between the object and the receiver affects the quality of the image produced by an optical system. This paper presents the results of measurements pertaining to the effect of a turbid medium on the point spread function of an optical system. The results refer to transmitted received power measurements obtained in controlled laboratory experiments. A random distribution of polystyrene microspheres suspended in water constituted the investigated turbid medium. Measurements were carried out for particulate with diameters of 0·33 μm, 0·995 μm, 15·7 μm at a wavelength of 0·6328 μm and for different values of sphere concentration in water. The measured data are favourably compared with results obtained by means of a Monte Carlo based numerical method. This numerical procedure allows us to obtain the point spread function and the modulation transfer function (MTF) of an optical system when a turbid medium is present. Examples of calculated MTFs that refer t...

Image processing for a scanning acoustic microscope that measures amplitude and phase

Abstract: Several image-processing techniques for a low-frequency (3 to 10 MHz) scanning acoustic microscope (SAM) that measures amplitude and phase are described. This microscope is capable of measuring both the amplitude and phase of the reflected and transmitted signals, in contrast with most earlier implementations that only measure the amplitude. By measuring phase, the authors can carry out quantitative nondestructive evaluation (NDE) and image processing that cannot be done with amplitude or phase alone. The effective 2-D point spread function of the microscope is modified by spatial filtering of the digitized complex images. In various images, the transverse resolution is improved by about 20%, aberration of images of subsurface features is corrected, and surface features are numerically defocused. The last process is used to remove the obscuring effect of surface roughness from images of subsurface features. >

Waveform recognition with application to bar codes

Abstract: The authors propose that the location and area under a peak can be the features of choice for a waveform recognition system. If the waveform is a result of the convolution of a Gaussian shape point spread function with a bi-level image, the image can be reconstructed by considering the areas under the waveform peaks. This is demonstrated by using a bar code as the bi-level image and the convolution is performed by scanning the bar code with a commercial bar code laser beam scanner. This waveform recognition system shows improved performance over current bar code readers that use hardware edge detectors to reconstruct the bi-level image. >

Modeling of shot noise in x-ray photoresist exposure

Abstract: New photoresist technologies yielding higher resist sensitivities together with the greater photon energies inherent in x‐ray lithography put lithography systems closer and closer to the shot noise limit. Thus there is a need to address the effects of shot noise on resist exposure. We will present the description of a stochastic model, and its implementation in a simulator, which emulates the exposure process by effecting what amounts to a photon‐by‐photon treatment of the problem, thereby taking into account the effects of shot noise. The model starts with an aerial image, computed using a deterministic model based on Fresnel diffraction, interprets it as the probability density function (pdf) for the distribution of the photons. The stochasticity of the process is taken into account by randomly generating a finite number of events (photons) whose distribution follows the pdf. The penetration depths are stochastically predicted according to the appropriate distribution. At the point predicted, the incident energy is redistributed according to a point spread function or a full Monte Carlo method. The superposition of all of the photons provides us with the latent image. The dissolution process is then modeled using a stochastic cell dissolution model. We will present results of practical importance for chemically amplified resist systems and correlate the results with observations made in the laboratory.

Restorations of real defocused images using blur models based on geometrical and diffraction optics

Abstract: Out-of-focus blur models that have traditionally been used in image restoration are based on geometrical optics. Continuous-focus blurs based on the principles of diffraction optics are reviewed, and their discrete representation is discussed. Restorations are carried out by using both types of blur models for defocused images blurred in a CCD (charge-coupled-device) camera with pixel resolution equal to 6.8 mu . The differences between the restorations performed by using both types of PSF (point-spread-function) models are not significant. The accuracy of the representation of the PSF generated by using diffraction optics and the resulting restoration quality are linked to the pixel resolution. >

A simple, photometrically accurate algorithm for deconvolution of optical images

Abstract: a noise model, has been tested on simulated HST data. This straightforward algorithm displays many desirable features for astronomical image reconstruction, as shown by rigorous numerical tests: (1) The photometric scale of the data is preserved accurately. (2) Information on the local noise level due to Poisson statistics in the input data is preserved. (3) It can accommodate a spatially variable point-spread function. Some of these properties are not shared by any widely used deconvolution algorithm. Some considerations of computing speed, and application to ground-based images, are briefly discussed.

Imaging performance analysis of adaptive optical telescopes using laser guide stars

Abstract: The use of laser guide stars in conjunction with adaptive optical telescopes offers the possibility of nearly diffraction-limited imaging performance from large, ground-based telescopes. We investigate the expected imaging performance of an adaptive telescope, using laser guide stars created in the mesospheric sodium (Na) layer. A 2–3-m class telescope is analyzed for the case of a single, on-axis guide star at an altitude of 92 km (the nominal height of the mesospheric Na layer). We analyze an annular telescope pupil with ∼15 wave-front sensor subapertures and mirror actuators spanning the pupil diameter. The imaging performance is quantified in terms of the pupil-averaged rms wave-front error, the optical transfer function, the point spread function, the Strehl ratio, and finally the angular resolution. The performance analysis takes into account the degradation caused by the limitation of the wave-front sensor as well as the deformable mirror. These limitations include the finite spacing and size of the wave-front sensor subapertures and the spacing and influence function of the mirror actuators. The effects of anisoplanatism and shot noise are also included in the analysis. The results of the investigation indicate that a 3-m adaptive telescope using a single Na guide star is capable of achieving a Strehl ratio of 0.57 and an angular resolution nearly matching that of diffraction-limited performance (0.05 arcsec). This performance is achieved assuming that r0 = 20 cm and a 5-W laser is used to create the guide star. The effect of variations in seeing conditions and guide star brightness is also investigated.

Dynamic modulation transfer function of a display system.

Abstract: A theoretical model for characterizing the dynamic response of a nonscanning electrooptic display system is developed. The model interrelates the spatial frequency degradations of an image display with both phosphor characteristics and relative velocity of the displayed object. Thereafter, the analysis is extended to compare the performances of types P-20, P-42, and P-1052 phosphor based displays.