Showing papers on "Optical transfer function published in 1985"

Accommodation-dependent model of the human eye with aspherics

Abstract: We consider a schematic human eye with four centered aspheric surfaces. We show that by introducing recent experimental average measurements of cornea and lens into the Gullstrand-Le Grand model, the average spherical aberration of the actual eye is predicted without any shape fitting. The chromatic dispersions are adjusted to fit the experimentally observed chromatic aberration of the eye. The polychromatic point-spread function and modulation transfer function are calculated for several pupil diameters and show good agreement with previous experimental results. Finally, from this schematic eye an accommodation-dependent model is proposed that reproduces the increment of refractive power of the eye during accommodation. The variation of asphericity with accommodation is also introduced in the model and the resulting optical performance studied.

Three-dimensional imaging by a microscope

Abstract: In transmission microscopy, many objects are three dimensional, that is, they are thicker than the depth of focus of the imaging system. The three-dimensional (3-D) image-intensity distribution consists of a series of two-dimensional images (optical slices) with different parts of the object in focus. First, we deal with the fundamental limitations of 3-D imaging with classical optical systems. Second, a transfer theory of 3-D image formation is derived that relates the 3-D object (complex index of refraction) to the 3-D image intensity distribution in first-order Born approximation. This theory applies to weak objects that do not scatter much light. Since, in a microscope, the illumination is neither coherent nor completely incoherent, a theory for partially coherent light is needed, but in this case the object phase distribution and the absorptive parts of the object play different roles. Finally, some experimental results are presented.

A photon dose distribution model employing convolution calculations.

Abstract: A three-dimensional photon beam calculation is described which models the primary, first-scatter, and multiple-scatter dose components from first principles Three key features of the model are (1) a multiple-scatter calculation based on diffusion theory, (2) the demonstration of the modulation transfer function of the radiation dose transport process, and (3) the use of the finite fast Fourier transform to perform the required convolutions The results of calculations for cobalt-60 in a homogeneous phantom are used to verify the accuracy of the model

Scanning holography and two-dimensional image processing by acousto-optic two-pupil synthesis

Abstract: An implementation of an acousto-optic heterodyning image processor was reported earlier [ Opt Lett4, 317 ( 1979)] However, details of that report are limited only to the confirmation of the basic principle of operation In this paper, we present and emphasize the mathematical structure of the processor We also compare this processor with other kinds of scanning and nonscanning processors The analysis is then extended to the defocused case, where the optical transfer function is derived A potential application of this in scanning holography is discussed

Reconstructing 3-D light-microscopic images by digital image processing

Abstract: A reconstruction procedure based on linear system theory has been developed for 3-D light-microscopic images. Inverse filtering with the 3-D optical transfer function was used for image reconstruction. The procedure allows a significant improvement in spatial resolution in the image planes perpendicular to the optical axis.

A simplified approach for modulation transfer function determinations in computed tomography.

Abstract: In order to determine the modulation transfer functions (MTF's) for x-ray computed tomography (CT) scanners, a measurement must be performed to obtain either the point spread function (PSF) or the line spread function (LSF). Thereafter, the usual procedure is to interpolate between the measured points and to determine the Fourier transforms numerically in order to obtain the MTF. Since this must usually be done many times to evaluate various reconstruction kernels and scan modalities, the process is tedious. Fortunately, it can be greatly simplified by utilizing a mathematical function to describe the PSF or LSF. Measured data for five CT scanners indicates that the PSF can usually be described by a Gaussian function. Hence, the MTF can be written in a generalized form eliminating the necessity of performing Fourier transformations each time. The MTF is determined directly from a single performance characteristic related to the full width at half maximum. The accuracy of the approach is compared with detailed MTF calculations for five CT scanners and it is shown to agree favorably with this data.

Investigation of basic imaging properties in digital radiography. 6. MTFs of II-TV digital imaging systems

Abstract: We devised a new, simple technique for measuring the modulation transfer function (MTF) of a digital imaging system by using an image of an angulated slit. With this technique, the "presampling" analog MTF, which includes the geometric unsharpness, the detector unsharpness, and the unsharpness of the sampling aperture, can be measured even beyond the Nyquist frequency. A single-frame image of a slightly angulated slit was employed in order to obtain Fourier transforms of line spread functions at different alignments. The presampling MTF was determined by averaging the two Fourier transforms which we obtained from two extreme alignments (center and shifted) of the slit relative to the sampling coordinate. The presampling MTFs of our digital subtraction angiographic system were determined in two orthogonal directions for three different image-intensifier modes.

Modulation transfer function and image transmission through randomly distributed spherical particles

Abstract: Image transmission through a random medium is important in many areas. Transmitted images are often affected by the presence of particulate matter and turbulence between the object and the detector. This paper presents the results for controlled experiments for the modulation transfer function (MTF) through a random distribution of polystyrene microspheres suspended in water. Experimental results show that the MTF has two distinct regions separated by a cutoff frequency. When the spatial frequency is higher than the cutoff frequency, the MTF becomes almost constant. On the other hand, when the spatial frequency is less than the cutoff frequency, the MTF increases exponentially with decreasing spatial frequency, and the slope depends on the optical distance of the medium. The cutoff frequency increases as the particle size increases. The results are obtained for particle sizes of 0.109, 0.46, 1.101, 2.02, 5.7, and 11.9 μm, densities much less than 1%, and optical distances between 0 and 15. The experimental results are compared with the results of the small-angle approximation for the equation of transfer.

Transfer functions and spatial filtering in grating interferometers.

Abstract: Diffraction grating interferometers, under extended source monochromatic illumination and with appropriate spatial filtering, are seen to be essentially imaging systems, linear in amplitude. By broadening the spectrum of the illumination, the system becomes linear in irradiance.

Line of sight of an aberrated optical system

Abstract: The line of sight of an aberrated optical system is defined in terms of the centroid of its point-spread function (PSF). It is also expressed in terms of its optical transfer function as well as its pupil function. Whereas the PSF’s obtained according to wave-diffraction optics and ray geometrical optics are quite different from each other, they have the same centroid. Although different amplitude distributions across an aberration-free pupil give the same centroid location, in the case of an aberrated pupil not only the phase but also the amplitude distribution affects the centroid location. If the amplitude across a pupil is uniform, then the centroid may be obtained from the aberration only along the perimeter of the pupil, without regard for the aberration across its interior irrespective of its shape. Next, an optical system with aberrated but uniformly illuminated annular pupil is considered. The aberration function is expanded in terms of Zernike annular polynomials. It is shown that only those aberrations that vary with angle as cos θ or sin θ contribute to the line of sight. A simple expression is obtained for the line of sight in terms of the Zernike aberration coefficients. Similar results are obtained for annular pupils with radially symmetric illumination. Finally, as numerical examples, some specific results are discussed for annular pupils aberrated by classical primary and secondary coma. As an example of a radially symmetric illumination, we obtain numerical results for Gaussian illumination of aberrated annular pupils. It is emphasized that the centroid and the peak of the PSF’s aberrated by coma are not coincident. Moreover, as the amount of the aberration increases, the separation of the centroid and peak locations also increases.

An MTF method immune to aliasing.

Abstract: The variance derived from the images of cyclic bar patterns can be used to determine the modulation transfer function(MTF) of an imaging system. Unlike most MTF methods, it is applicable even when the imaging system undersamples the test object and generates aliasing errors. The validity of the variance method in the presence of aliasing is established theoretically and by computer simulation.

Theoretical Bases And Measurement Of The Mtf For Integrated Image Sensors

Abstract: By analogy with optics, the spatial resolution of image sensors is generally characterized by the Modulation Transfer Function (MTF). This notion assumes the system being a linear filter, which is not the case in integrated image sensors, since they have a discrete photoelement structure. These sensors must in fact be considered as integral samplers. Their response to any irradiance distribution can thus be computed, knowing the pitch of photoelements and using a characteristic function. This function is more or less similar to the MTF. Once exact theoretical foundations have been defined, a computer simulation enables the various MTF measuring methods to be compared this makes it possible to rule out er-rors inherent to experiments. The most accurate and reliable method appears to be the knife edge method, applied with a relative displacement of the sensor and of the image. This avoids the occurence of aliasing phenomenon. Experimentation of this method for measurement of the CCD sensors characteristic function, which we call MTF as agreed, is described. This method also makes it possible to evaluate the transfer inefficiency of shift registers.

Method of two-dimensional bipolar incoherent image processing by acousto-optic two-pupil synthesis.

Abstract: An incoherent optical technique for two-dimensional bipolar processing by acousto-optic two-pupil synthesis is proposed. Experimental results are presented.

Wavefront sensing deconvolution and adaptive optics

Abstract: For large telescopes, the fundamental limit set by the diffraction to the angular resolution can be reached if the aberrations are perfectly corrected. Two solutions are practicable: image restoration by numerical processing or real time correction by adaptive optics. These two processes require the determination of the wavefront or of the optical transfer function. New large detectors arrays can be used in wavefront sensing which then allow the measurement of the wavefront at a large number of point. The general lay-out of such an instrument is given and its accuracy evaluated. The wavefront sensing contribution to numerical image processing is studied mainly for the case of degradation by atmospheric turbulence. The improvement of numerical processing by a partial active correction is discussed.

Sinusoidal determination of limiting optical resolution

Abstract: An optical system limiting resolution determination arrangement employing sinusoidal intensity modulated bar pattern input stimuli including two sequences for determining the modulation transfer function (MTF) component of limiting resolution; one of these and the disclosed aerial image modulation (AIM) curve determination are based on sinusoidal intensity modulated bar patterns, while the other MTF determination uses a Heaviside edge function stimulus and a sinusoidally determined AIM curve. The disclosed limiting resolution is especially useful in the consideration of aerial image devices such as cameras.

High-Resolution Luminescent Screens for Image Intensifier Tubes

Abstract: Publisher Summary This chapter discusses the high-resolution luminescent screens for image-intensifier tubes In image intensifier tubes, the picture quality can be characterized by the modulation transfer function (MTF), the output contrast versus spatial frequency for 100% input contrast This function depends on several parameters such as the photoelectron energies, tube voltages, distance between electrodes, channel diameters (for MCP intensifiers), screen granularity, and fiber optic pitch The chapter discusses the improvement of the modulation transfer function of the screen when it is settled on a fiber-optic output window Luminescent screens are often settled on fiber optics to reduce the light spread from the emitting phosphor particles and to minimize the veiling glare of the tube Twisted fiber optics allows the image to be inverted with low-light losses To increase the contrast, Piedmont and Pollehn proposed the intagliation of the phosphor particles in holes scooped out at the input of each elementary fiber

Three-Dimensional Object Representation In Imaging Systems

Abstract: In image-forming optical systems the image of a three-dimensional object consists of a superposition of focused and defocused object layers. For a quantitative evaluation of the object it is necessary to decompose the superposi-tion image into different images corresponding to single object layers. For this purpose the object radiation is measured with different optical transfer func-tions of the imaging system, for example, by simply changing the focus plane. Each image contains focused and defocused parts of the object and can be described as a linear equation of the object layers, assuming linear space-invariant imaging properties. From these images the real object distribution can be calculated by the evaluation of the resulting linear system of equations in the Fourier domain. Due to noise in the detected images it is only possible to get an estimate of the true object distribution. In our case this estimate is based on an integral minimal mean square error in the reconstructed object. The algorithm is presented and demonstrated by simulation experiments and reconstructions of real human cell images in optical microscopy.

Optical performance of synthetic aperture telescope configurations

Abstract: The diffraction-limited performances of synthetic aperture configuration arrays of four telescopes, used for coherent imaging or beam transmission, are calculated and compared The optical performance of phased telescope arrays was found to be more sensitive to rms piston errors than to rms tilt errors Image degradation due to pupil mapping errors imposes tight tolerances upon the structural integrity of the telescope One part in 10,000 pupil mapping error limits the field-of-view to approximately 30 arcsec Field curvature of the independent telescopes provides a fundamental limit to the field-of-view for phased arrays made up of two-mirror telescopes These field-of-view limitations may profoundly affect target acquisition, tracking, or imaging applications

Pattern Recognition Using Incoherent OTF Synthesis and Edge Enhancement

Abstract: This paper describes a system for pattern recognition using an incoherent-optical correlator. The system uses optical transfer function synthesis to perform correlations with an edge-enhanced image of the object or pattern being sought. The resulting correlations are free of bias and show good discrimination between objects. In addition, the difficult or time-consuming computations are performed before the operation of the system; this reduces the amount of postprocessing by computer and should allow real-time operation at video rates.

Pattern recognition using incoherent OTF synthesis and edge enhancement.

Abstract: This paper describes a system for pattern recognition using an incoherent-optical correlator. The system uses optical transfer function synthesis to perform correlations with an edge-enhanced image of the object or pattern being sought. The resulting correlations are free of bias and show good discrimination between objects. In addition, the difficult or time-consuming computations are performed before the operation of the system; this reduces the amount of postprocessing by computer and should allow real-time operation at video rates.

Effects of finite spectral bandwidth and focusing error on the transfer function in stellar speckle interferometry

Abstract: The normal model of light propagation through a turbulent atmosphere is used to investigate the telescope–atmosphere transfer function in stellar speckle interferometry. The effect of the finite bandwidth of a spectral filter on the transfer function is considered. The permissible focusing errors for successful processing in stellar speckle interferometry are obtained based on the normal model. Some observational results are presented and compared with theory. The normal model leads to an analytically simple solution and properly describes light scattering from turbulent atmosphere. The results for the normal model are compared with those for the log-normal model.

Fresnel transforms and Bragg cell processors

Abstract: In the analysis of coherently illuminated optical systems we distinguish between space planes and spatial frequency or Fourier planes. Between these two planes exists a continuum of Fresnel transform planes; the Fresnel domain therefore shares, more or less equally according to its position, the properties of the space and frequency domains. Since Fresnel transforms are space-variant operations, generalized results are difficult to obtain. When implemented by Bragg cell processors, however, Fresnel transforms have some interesting and useful spatial/temporal properties. We examine the application of Fresnel transforms to analog signal scrambling techniques. We derive the optimum geometry for obtaining the maximum time spreading for a given signal bandwidth. We derive the system response to impulse, short pulse, and cw signals. We show how a permutation of time samples can be achieved and illustrate some of the key features through simulations.

Lithographic apparatus performance measurement

Abstract: In a lithographic apparatus, radiation from a source (2) passes through a mask (4), and an image is formed by a lens (6) on a semiconductor wafer (28). Radiation detectors in the wafer surface generate signals which are fed by conductors (13) to a computer (3). The computer regulates a Z-drive (7) and an X-Y drive (5) which adjust the wafer, lens and mask so that the computer receives a related sequence of signals. The radiation can be UV, optical E-beam, ion-beam or X-ray, and the computer measures performance characteristics of the apparatus, such as intensity, modulation transfer function (MTF), focus and alignment.

Measured performance characteristics of a solid-state linear detector array.

Abstract: Experimental studies of a solid-state linear detector array developed for a prototype scanning slit digital chest radiographic unit have been completed. The detector consists of a strip of scintillating material, optically coupled to a linear silicon photodiode array. Measured performance characteristics of the detector, such as sensitivity, modulation transfer function, and detective quantum efficiency, are presented for several different scintillators. Results indicate that direct x-ray absorption events in the silicon photodiode can degrade detective quantum efficiency. Results also indicate that the inexpensive preamplifier circuits used in the digital chest prototype contribute negligible noise at diagnostic x-ray photon fluence rates.

Eye examining apparatus

Abstract: An eye examining apparatus is disclosed which is capable of the accurate detection of any abnormality in the optical system of a patient's eye which might exist at any position of the eye, and also which is capable of providing easy measurement of the degree of refration of the patient's eye. The apparatus comprises a target projecting system for projecting onto a retina a target image to be measured; focalizing means for detecting the focus of the target to be measured and for focalizing it on the retina; and an optical transfer function measuring system for detecting the con­ trast of the target image to be measured, which is focalized on the retina, and thereby measuring the optical transfer function of the patient's eye. The apparatus may further comprise means for compar­ ing the measured optical transfer function with that of a normal eye, and the target projecting system may include a means for rotating the target image to be measured around an optical axis.

Polychromatic MTF-based Criteria for Evaluating Photographic Image Quality

Abstract: The validity of a series of criteria for evaluating image quality based on the modulus of the polychromatic optical transfer function (polychromatic MTF, or PMTF) of the image-forming instrument is studied. The criteria are based on the area determined by the coordinate axes and the curve of the one-dimensional PMTF (calculated for objects varying only in one direction: bar test, sinusoidal test, slit). Quality criteria based on the two-dimensional character of the actual PMTF function (the Fourier transform of the point-spread function) are also proposed; these are especially suitable for image evaluation in off-axis zones of the instrument. A series of guidelines is set out for commercial optical systems (existing camera lenses), operating with reversal colour film processed in such a way that S n S = 1.

The effect on optical performance of grain boundaries in germanium

Abstract: Differences between the modulation transfer function obtained via inverse transformation of the line spread function, and autocorrelation of the pupil function obtained by interferometry can be significant. The origin of the differences and magnitude of discrepancies are discussed together with results from recent work using computer modelling. The method described offers a useful means of explaining the differences and assessing the effect of grain boundaries on lens performance.

Volume defined by the two-dimensional modulation transfer function surface: approximation obtained from its sagittal and tangential sections. Application to image quality criteria

Abstract: In order to assess the quality of images obtained by an optical system the most successful criteria (either on axis or in field zone) have been those based in computations involving the volume bounded by the two-dimensional modulation transfer function (MTF) surface in a three-dimensional space. In practice, however, it is more usual to measure two one-dimensional MTF functions (sagittal and tangential sections) operating with simple standard methods (slit image, bar test, etc.). The authors develop an approximation that permits the calculation of the aforementioned volume from the knowledge of its two main cited sections, testing its accuracy and limitations.