Showing papers on "Optical transfer function published in 1986"

Characterization of the point spread function and modulation transfer function of scattered radiation using a digital imaging system

Abstract: A digital radiographic system was used to measure the distribution of scattered x radiation from uniform slabs of Lucite at various thicknesses. Using collimation and air gap techniques, [primary + scatter] images and primary images were digitally acquired, and subtracted to obtain scatter images. The scatter distributions measured using small circular apertures were computer fit to an analytical function, representing the circular aperture function convolved with a modified Gaussian point spread function (PSF). On the basis of goodness of fit criterion, the proposed Gaussian function is a very good model for the scatter PSF. The measured scatter PSF's are reported for various Lucite thicknesses. Using the PSF's, the modulation transfer functions are calculated, and this spatial frequency information may have value in analytical scatter removal techniques, grid design, and air gap optimization.

Variation of the count-dependent Metz filter with imaging system modulation transfer function.

Abstract: A systematic investigation was conducted of how a number of parameters which alter the system modulation transfer function (MTF) influence the count-dependent Metz filter. Since restoration filters are most effective at those frequencies where the object power spectrum dominates that of the noise, it was observed that parameters which significantly degrade the MTF at low spatial frequencies strongly influence the formation of the Metz filter. Thus the radionuclide imaged and the depth of the source in a scattering medium had the most influence. This is because they alter the relative amount of scattered radiation being imaged. For low-energy photon emitters, the collimator employed and the distance from the collimator were found to have less of an influence but still to be significant. These cause alterations in the MTF which are more gradual, and hence are most pronounced at mid to high spatial frequencies. As long as adequate spatial sampling is employed, the Metz filter was determined to be independent of the exact size of the sampling bin width, to a first approximation. For planar and single photon emission computed tomographic (SPECT) imaging, it is shown that two-dimensional filtering with the Metz filter optimized for the imaging conditions is able tomore » deconvolve scatter and other causes of spatial resolution loss while diminishing noise, all in a balanced manner.« less

Modulation transfer function of layered inhomogeneous random media using the small-angle approximation.

Abstract: Many random media such as clouds and fog are often inhomogeneously distributed and often have a layered structure. This paper presents the effects of such inhomogeneities on the image transmission in terms of the modulation transfer function (MTF). We derive an expression of the MTF for a layered inhomogeneous medium using the small-angle approximation which is valid for size parameters of >10 and optical distances of <5. We obtain numerical results and compare them with experimental data for different particle sizes and concentrations showing good agreement. We also explain the shower curtain effect using the expression for the MTF.

Method For Measuring Modulation Transfer Function Of Charge-Coupled Devices Using Laser Speckle

Abstract: A new method has been developed to measure the modulation transfer function (MTF) of an array out to the Nyquist frequency without high quality optical or mechanical components, without precision alignment, and with only one moving part. Test results for an infrared staring array of PtSi Schottky barrier construction show that this technique is a viable MTF measurement approach in the 3 to 5 µm spectral region.

Optical Transfer Function for Imaging Systems Which Change the State of Light Polarization

Abstract: The problem of incoherent imaging of extended objects by optical systems which change the state of light polarization is discussed in detail. The optical transfer function of the system has been determined for two cases, i.e. for objects which emit similarly and differently polarized light. For the second case it was necessary to introduce the vectorial optical transfer function (OTF). Numerical calculations of the OTF have been performed for a perfect system with a simple polarizing mask in the exit pupil.

The performance of CCD array detectors for application in high-resolution tomography

Abstract: Charge coupled device arrays (CCDs) with low noise, small pixel size and high charge storage capacity are available at relatively low cost. Because of this, CCDs are finding increasing use in imaging applications. In this paper we will discuss the performance of a TI-4849 CCD array in an x-ray camera to be used for high-resolution synchrotron radiation tomography. The x-ray image is converted to visible light on a phosphor coated optical face plate which is imaged by a thermoelectrically cooled CCD. The measured modulation transfer function (high-contrast MTF) will be presented for this system. We will describe procedures for choosing and preparing the optimal phosphors for x-ray imaging. Advantages and limitations of CCD arrays over other detectors for tomographic applications will also be discussed.

Spatial Resolution Analysis of Computed Tomographic Images

Abstract: Methods are presented for the quantification of spatial resolution in x-ray computed tomographic (CT) images. Model-dependent methods are derived and compared with model independent methods for computation of the Modulation Transfer Function (MTF). These techniques are applied to phantom images of point, line, edge, and ring discontinuities. The model-dependent methods utilize multiparameter fits of a two-dimensional model function to the image data. Model predictions are compared with results obtained in a model-independent way by numerical transformation of the data. Results of resolution measurements of an Imatron C-100 CT scanner at UCSF and a second experimental scanner at the UCSF Physics Research Laboratory are presented.

Sampling and reconstruction of a turbulence-distorted wave front

Abstract: This paper examines the problem of linear least-mean-squares reconstruction of a wave front distorted by turbulence described by the Kolmogorov 5/3 law. The wave-front sensors are assumed to be of the Hartmann imaging type, with circular apertures of arbitrary size and location relative to the beam to be reconstructed and having a four-quadrant photodiode detector in the focal plane. The weighting function for x1 and x2 slopes across the sensor aperture is determined, and the sensor signal-to-noise ratio, modulation transfer function, and cross-correlation matrix are calculated. Some examples involving various sensor configurations and the interpolation functions for their outputs are presented as well as the least-squares estimation of a low-order Zernike coefficient.

Two-pupil synthesis of optical transfer functions: 2: pupil function relationships.

Abstract: Although different methods have been proposed for realizing bipolar point spread functions in hybrid two-channel incoherent spatial filtering systems, each method relies either on interference or noninterference between the two channels to achieve the desired synthesis. It is shown that the pupil functions appropriate for synthesis in these two regimes are related through a linear transformation. Furthermore, the pupil functions appropriate for a noninteractive synthesis can be used to specify pupil functions appropriate for any other synthesis.

Reduction of aliasing in modulation transfer function measurements

Abstract: The images formed by many radiological systems are difficult to sample at spatial intervals small enough to avoid aliasing in the calculation of the system's modulation transfer function. However, if a system's response can be assumed to be symmetrical, this assumption can be used to effectively double the sampling density and to double the frequency limit before aliasing occurs. To accomplish this, a more complex algorithm is required. In this work, the formula for the calculation of the modulation transfer function from a symmetrical, one-dimensional line spread function is derived and a similar result for a symmetrical, two-dimensional point spread function is presented. The effect of noisy data and errors in the estimation of the offset of the center of the line spread function from a sampling point are investigated by simulation studies. For low noise (relative standard deviation of 1%) and an offset error of no more than 2% or 3% of a sampling interval, reasonable precision is obtained. These conditions appear to be achievable, especially when the noise is Poisson distributed.

Measurements of ocean wave spectra and modulation transfer function with the airborne two frequency scatterometer

Abstract: The results of this research show that the directional spectrum and the microwave modulation transfer function of ocean waves can be measured with the airborne two frequency scatterometer-microwave resonance technique. The results here are favorable to the future application of this or similar techniques from airborne or spaceborne platforms. Similar to tower based observations, the aircraft measurements of the modulation transfer function show that it is strongly affected by both wind speed and sea state. Also detected were small differences in the magnitudes of the MTF between downwind and upwind radar look directions, and variations with ocean wavenumber. Unexpected results were obtained that indicate the MTF measured from an aircraft is larger than that measured using single frequency, wave orbital velocity techniques such as tower based radars or “ROWS” measurements from low altitude aircraft. Possible reasons for this are discussed. The ability to measure the ocean directional spectrum with the two frequency scatterometer, with supporting MTF data, is demonstrated.

Electro-optical imaging system and lens therefor

Abstract: An electronic imaging system includes an optical system for imaging radiation from a scene onto the image sensing surface of an imaging device for a selected sample period. The imaging device may take the form of a two dimensional array of photoresponsive areas having a device specific upper spatial frequency limit. In order to eliminate alias signal components in the output video signal caused by spatial frequency components in the scene radiation greater than the Nyquist spatial frequency of the device, the optical system is designed to have a spatial frequency limit no higher than the Nyquist frequency of the imaging device and thus functions as a low pass optical filter. The spatial frequency response of the optical components can be controlled by controlling the rotationally symmetric aberrations, and in the preferred form, higher order terms, third and above, which contribute to the spherical aberration of a lens system are designed to have balancing non-zero values to provide the necessary characteristics of the modulation transfer function of the optical system.

Determination of the transfer function of an optical instrument

Abstract: For measuring the optical transfer function of an optical instrument having an input pupil, a device comprises a source of spatially coherent light for illuminating the pupil of the instrument. Two separate zones are isolated in the input pupil of the instrument by a system comprising a grating, a lens for forming an image and a spatial filter which eliminates the zero diffraction order. The two zones have a spacing which is in direct relation to the spatial frequency. The position and mutual spacing of the fringes are determined. A computer derives the transfer function from the measurements made for a plurality of pairs of zones.

Combined optimization of image-gathering optics and image-processing algorithm for edge detection

Abstract: This paper investigates the relationships between the image-gathering and image-processing systems for minimum mean-squared error estimation of scene characteristics. A stochastic optimization problem is formulated in which the objective is to determine a spatial characteristic of the scene rather than a feature of the already blurred, sampled, and noisy image data. The Wiener filter for the sampled image case is obtained as a special case, where the desired characteristics is scene restoration. Optimal edge detection is investigated. It is shown that the optimal edge detector compensates for the blurring introduced by the image-gathering optics, and, notably, that it is not circularly symmetric. The lack of circular symmetry is largely due to the geometric effects of the sampling lattice used in image acquisition.

Space telescope performance prediction using the optical surface analysis code (OSAC)

Abstract: The optical surface analysis code (OSAC) is used to predict the optical performance of the Hubble Space Telescope We describe the analysis in detail and compare some of the results with those of a standard optical transfer function analysis Also, we discuss the mathematical foundation of the OSAC code and describe in detail the error data that were used as input OSAC is shown to be a valuable tool for separating and analyzing the effects of misalignments, figure errors, and mid and high frequency statistical mirror surface errors on optical performance

A high-resolution digital dosimetric system for spatial characterization of radiation fields using a thermoluminescent CaF2:Dy crystal.

Abstract: A high-resolution digital dosimetric system has been developed for the spatial characterization of radiation fields. The system comprises the following: 0.5-mm-thick, 25-mm-diam CaF2:Dy thermoluminescent crystal; intensified charge coupled device video camera; video cassette recorder; and a computerized image processing subsystem. The optically flat single crystal is used as a radiation imaging device and the subsequent thermally stimulated phosphorescence is viewed by the intensified camera for further processing and analysis. Parameters governing the performance characteristics of the system were measured. A spatial resolution limit of 31 +/- 2 microns (1 sigma) corresponding to 16 +/- 1 line pairs/mm measured at the 4% level of the modulation transfer function has been achieved. The full width at half maximum of the line spread function measured independently by the slit method or derived from the edge response function was found to be 69 +/- 4 microns (1 sigma). The high resolving power, speed of readout, good precision, wide dynamic range, and the large image storage capacity make the system suitable for the digital mapping of the relative distribution of absorbed doses for various small radiation fields and the edges of larger fields.

Spatial frequency filtering in an optical imaging system with an extended incoherent light source.

Abstract: A single-lens imaging system is described that provides spatial frequency filtering to an extended incoherent light source. Two ways to calculate the modified image are considered: First, the image is derived from the filtered diffraction pattern by Fourier synthesis. Second, the convolution of the object function with a Fourier transform of the filter function has to be evaluated with regard to a phase function that corresponds to the light source position.

Characterization Of A Liquid Crystal Television Display As A Spatial Light Modulator For Optical Processing

Abstract: The recent availability of inexpensive, video-addressable liquid crystal displays has generated interest in the use of such devices for optical processing applications. This paper will present some pertinent performance characteristics for a device of this type, the Radio Shack (Tandy Corp.) Pocketvision. Specific characteristics to be considered are screen transmission, linearity, modulation depth, modulation transfer function (MTF), temporal response and optical flatness. Examples of device performance as a coherent and incoherent processing element will be briefly considered.

A logit model for the modulation transfer function of screen-film systems.

Abstract: An empirically derived logit function is proposed to describe the modulation transfer function of x‐ray screen–film systems. Simple and exact weighted linear regressionanalyses are performed to characterize the function and to describe the data within experimental accuracy. Calculations comparing the proposed function and the complementary error function (probit) representations of the modulation transfer function are given and discussed.

Holographic incoherent optical transfer function synthesis: analysis and optimization

Abstract: Holographic incoherent optical transfer function (OTF) synthesis offers many of the advantages of coherent holographic spatial filtering, yet it can use spatially incoherent (but quasi-monochromatic) light. Thus CRT images, as well as light from diffuse objects, can be processed with no need for spatial light modulators. We show that paraxial analysis of holographic incoherent OTF synthesis is often inadequate. Carelessly designed systems may exhibit intolerable levels of aberrations and distortions. Specifically, incoherent holographic OTF synthesis systems may exhibit partial loss of space variance as well as aberrations that affect the resolution of the output pattern. One must apply nonparaxial analysis to the design of holographic incoherent OTF synthesis systems in order to exploit their full potential. Typical results and some optimization approaches are presented.

Modulation Transfer Function For The Display Engineer

Abstract: The International Commission on Optics (ICO) defines the modulation transfer function (MTF) as the modulus of the Fourier transform of the line spread function. The purpose of this paper is to introduce, from an engineering standpoint, the MTF and its properties to the display engineer.

A Technique For The Objective Measurement Of MRTD

Abstract: The minimum resolvable temperature difference of a thermal imager is generally accepted as being the performance parameter most closely related to the imager's performance in the field. It is, however, universally conceded that an objective test technique is urgently required to replace the current subjective method of measurement, thus removing the dependence on trained operators. Simplistically this can, at first sight, be easily achieved via the measurement of the system modulation transfer function, noise power spectrum and signal transfer function. However, the practice of measuring these system parameters is not so straight forward. This paper deals with a practical implementation of such an objective method of testing, based upon a method proposed by the Royal Aircraft Establishment, Farnborough, subsequently developed at GEC Avionics, Basildon. It deals with the mathematical subtleties of applying the required discrete Fourier transforms in software and of integrating waveforms to achieve acceptable signal to noise ratios. The paper also gives examples of the objective results achieved, and a comparison with the corresponding subjective results.

The Design Of Linear And Quasi-Linear CCD Detectors And Detector Arrays To Meet System Performance Requirements

Abstract: The use of Linear and Quasi-Linear Time Delay and Integra-tion) CCD imagers has expanded greatly over the last decade. Applications have ranged from airborne reconnaissance, to facsimile, to automated mail-sack sorting. Early device performance was primarily set by what it was possible to fabricate, and systems were limited by the devices available. Subsequent detectors have been progressively more influenced by system-dominated performance requirements, which have determined many imager chip functional parameters, such as; pixel size, pixel number, number of TDI integrations, pixel/phase structure, saturation charge, readout rate, spectral window, and tailored optical admittance. This paper discusses some ways in which required system performance and device design rules interact to establish specifications for detector/array designs. Since unique system-specific device configurations are not cost-effective, general classes of systems may be established which bound the needs for a finite number of device designs. Examples are presented to illustrate performance/design relationships.

Propagator for the modulation transfer function of a wide-angle scatterer

Abstract: A propagator that expresses the change in modulation transfer function with the optical path is defined for a wide angle scatterer medium. The expression compares favorably with moire deflectometer measurements on colloidal suspensions of various concentrations.

The Influence of Spatial Coherence on the Monochromatic Optical Transfer Function

Abstract: It is widespread practice to measure the optical transfer function (OTF) by scanning the images of ‘simple’ objects. However, the illumination used in such systems is (generally) partially coherent, and not incoherent as is required by theory. The influence of spatial coherence is explicitly examined in order to obtain a general equation for the observed OTF for the case of one-dimensional test objects. The equation is applied to the case of a ‘perfect’ rotationally symmetric lens, using a slit object, and, on comparing the results with the true (incoherent) OTF of such a lens, significant differences have been found.

An Improved Approach To Characterizing And Presenting Streak Camera Performance

Abstract: The performance of a streak camera recording system is strongly linked to the technique used to amplify, detect and quantify the streaked image. At the Lawrence Livermore National Laboratory (LLNL) streak camera images have been recorded both on film and by fiber-optically coupling to charge-coupled devices (CCD's). During the development of a new process for recording these images (lens coupling the image onto a cooled CCD) the definitions of important performance characteristics such as resolution and dynamic range were re-examined. As a result of this development, these performance characteristics are now presented to the streak camera user in a more useful format than in the past. This paper describes how these techniques are used within the Laser Fusion Program at LLNL. The system resolution is presented as a modulation transfer function, including the seldom reported effects that flare and light scattering have at low spatial frequencies. Data are presented such that a user can adjust image intensifier gain and pixel averaging to optimize the useful dynamic range in any particular application.

Organic photochromics for spatial light modulation

Abstract: The photochromic properties of a class of fatigue-free thermally stable fulgide derivatives are outlined, and their applicability as optically addressed spatial-light modulators is discussed with reference to the requirements for coherent linear optical processing.