Showing papers on "Optical transfer function published in 1974"

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.

Calculations on the Optical Modulation Transfer Function of the Human Eye for White Light

Abstract: Modulation transfer functions of the dioptrics of the human eye for white (equal energy distribution) light were calculated for different pupil sizes from experimental data on the aberrations. The largest aberration is the chromatic difference of focus. Since this aberration is well known quantitatively and is subject to small individual differences only, the calculated modulation transfer functions can be considered as representative for human eyes in general. The present calculations, the fundus reflection measurements of the line-spread function by Campbell and Gubisch [1], and the measurements of retinal scattering by Ohzu and Enoch [2] confirm each other. Modulation transfer functions were also calculated for just noticeable focusing errors, and may be informative on the tolerance limit to visual image quality. The calculations have been extended to the special conditions of vision at low luminances.

Carrier diffusion degradation of modulation transfer function in charge coupled imagers

Abstract: Expressions for the modulation transfer function due to minority carrier diffusion in charge coupled imagers are calculated, following the approach used by Crowell and Labuda. Both front and rear optical illumination of the charge coupled imager are considered; for the rear illumination case interference effects are included. The modulation transfer function for high energy electron excitation is also considered. In all cases, the expressions for the modulation transfer function have been evaluated using typical charge coupled imager parameters. The quantum efficiency predicted by the minority carrier diffusion model is also briefly discussed.

Optical quality of the living cat eye

Abstract: 1. The optical quality of the living cat eye was measured under conditions similar to those of cat retinal ganglion cell experiments by recording the aerial image of a nearly monochromatic thin line of light.2. Experiments were performed to assess the nature of the fundal reflexion of the cat eye, which was found to behave essentially as a diffuser.3. The optical Modulation Transfer Function (MTF) was calculated from the measured aerial linespread using Fourier mathematics; the MTF of a ;typical' cat eye was averaged from data collected from ten eyes.4. The state of focus of the optical system, the pupil size and the angle of the light incident on the eye were all varied to determine their effect on image quality.5. By using an image rotator, the aerial linespread was measured for several orientations of the line; these measurements yielded an approximation of the two-dimensional pointspread completely characterizing the optical system.6. Evidence is reviewed to show that the optical resolution of the cat, albeit some 3-5 times worse than that of human, appears to be better than the neural resolution of its retina and its visual system as a whole.

Device and process for testing a lens system

Abstract: Device and process for testing the optical transfer function of a lens system which comprise employing as the object or target the laterally moving-fringe pattern produced by convergence of two monochromatic coherent-radiation beams of equal size and intensity and slightly different frequency. A second fringe pattern may be employed as the reference standard. Both the target and reference patterns can be varied simultaneously in spatial frequency or fringe period. The system and process can test both modulation transfer function and phase transfer function accurately at any monochromatic wavelength produced by an available coherent-radiation source to which the test lens system is transparent, e.g., ultraviolet or shorter, visible, and infrared or longer. When polarized monochromatic radiation is used, the invention can also be employed to determine the polarization characteristics of the lens. The system and process can also test chromatic aberration by successive use of different coherent monochromatic radiation wavelengths.

Measurement of averaged squared modulus of atmospheric-lens modulation transfer function

Abstract: The theory of speckle interferometry shows that the averaged squared modulus of the atmospheric-lens modulation transfer function becomes proportional, for high frequencies, to the lens modulation transfer function. The experimental curve obtained by comparison of the power spectrum of a turbulence-degraded image and that of a nondegraded image of the solar granulation is consistent for high frequencies with the theoretical curve. We propose to use it to correct power spectra obtained with a large ground-based telescope, at frequencies up to the diffraction limit.

Analysis of double-exposure speckle photography with two-beam illumination

Abstract: Speckle photography offers a technique for measuring small strains on an object in the presence of large displacements. An analysis is presented of this technique, which accounts for the phenomena observed and predicts its capabilities and limitations. The analysis is sufficiently general to describe either of two related techniques, one that permits measurement of strains in the absence of large displacements and one that permits measurement of large displacements alone.

Calculation of Axial Polychromatic Optical Transfer Function

Abstract: Polychromatic or white-light OTF is put forward as a criterion of image quality for systems under actual working conditions. The formulae necessary to extend from the monochromatic to the polychromatic OTF are developed for the axial case. A computer programme has been developed and calculated results are compared with measurements.

Method of determining the modulation transfer function

Abstract: The invention relates to a method of determining the modulation transfer function of a recording support or of an optical system. In the context of the invention, an optical system includes any components with finite apertures which are required for forming an image of an object. A coherent-optically produced scatterer of known noise distribution or with a known spatial frequency spectrum is used for determining the required modulation transfer function. The modulation transfer function can be determined through the density of transparency distributions present on the recording support.

Measurements Of Optical And Noise Properties Of Screen-Film Systems In Radiography

Abstract: The optical and noise properties of radiographic screen-film systems have often been evaluated by concepts and techniques related to Fourier analysis. Figure 1 illustrates the physical characteristics of these properties. The point spread function (PSF), which is the two dimensional representation of the optical property of the screen-film system, has not been applied experimentally for evaluation. The screen-film system is generally considered to be isoplanatic and isotropic; therefore, the line spread function (LSF) in an arbitrary direction can be used. This function is much simpler to measure than the PSF. In the spatial frequency domain, the optical property is evaluated by the modulation transfer function (MTF), which is the absolute value of the Fourier transform of the LSF. Other optical characteristics such as the edge response are usually related to the LSF or the MTF.© (1974) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Balance Between Resolution And Signal-To-Noise Ratio In Scanner Design For Earth Resources Systems

Abstract: An outline is presented of a method in which a sensor under design can be evaluated by comparison with an existing sensor of similar spectral response, providing certain performance characteristics are known. An approach for calculating errors in radiance measurements is discussed, giving attention to calibration, error caused by resolution factors, noise effects on accuracy, and combined radiance level accuracies for several scanner designs. The derivation of error caused by the modulation transfer function is also considered.

On the electron optics of magnetically focused image tubes: I. Chromatic aberration in uniform fields

Abstract: Methods are devised for obtaining the point spread function, line spread function and modulation transfer function for magnetically focused image tubes. These are applied to a variety of synthetic electron distribution functions which imitate the behaviour of real photocathodes. These distributions lead to analytical solutions for the intensity in the gaussian image plane, but for other planes numerical methods must be adopted. The maximum possible resolution and depth of focus can then be derived. Other limitations on the resolution are discussed.

Imaging of Extended Objects Through a Turbulent Atmosphere

Abstract: The extended Huygens-Fresnel principle is used to derive an explicit expression for the image plane illuminance distribution of an extended object with an arbitrary luminance emittance distribution. The combined simultaneous effects of attenuation, background luminance, and atmospheric turbulence are given. A quantitative comparison of these effects is made, and their contribution to the over-all loss in resolution is given. In particular, we derive a quantitative expression for the point spread function of the combined atmospheric-optical system. Explicit expressions are derived for both the atmospheric-optical system modulation transfer function (MTF) and image plane modulation. Numerical results for the image plane modulation are presented for imaging both up and down along an atmospheric path under various viewing conditions.

Television based fourier holographic system.

Abstract: A system for recording Fourier transform holograms on a television camera for use with an existing real-time reconstruction device is described. Measurements of the system’s visibility, associated efficiency measurements, and a general procedure for determining the system’s optimum operating point are presented. Initial off-line reconstructions and a comparison of various optical synthesis systems for television based Fourier transform holograms are included.

Use Of The OTF In The Cost/Performance Evaluation Of Space Telescopes

Abstract: The optical transfer function (OTF) can be used to give the first order performance characteristics of space telescope systems as a function of cost. Using the effective transfer functions of the optical system, instruments, sensors and communication system, a total system transfer function can be defined. Utilizing the properties of the transfer function, specific quality criteria are applied that are measures of certain astro-nomical objectives; such as imaging, photometry, spectroscopy, etc. The specific criteria are then related to a dominant independent variable which is a measure of the scientific objectives such as spatial resolution, at a given contrast level, for imaging and the amount of energy passing through a slit for spectroscopy. These measures can be related to a set of basic astronomical observations that are to be made by that particular telescope. Since nearly every sub-system has a cost-accuracy relationship, we can evaluate changes in subsystems to their corresponding impact on astronomical observations through changes in the transfer function of the system and the quality criteria.© (1974) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

On The Significance Of The Phase Transfer Function

Abstract: In the application of transfer function theory to the process of image formation, one must necessarily be concerned with complex functions. Even in the case of noncoherent image formation (the formation of the image of a noncoherent object), where the object, the image, and the spread function are all purely real, the Fourier transforms of these functions are generally complex. Only in the rather exceptional case where both the object and the spread function are real and even does the situation reduce to one involving only real functions.© (1974) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A Method of Improving the Optical Transfer Function of an Astigmatic Circular Aperture

Abstract: Expressions have been derived for the transfer function of a circular aperture suffering from astigmatism and operating in non-uniform illumination. The intensity distribution considered is given as t(x, y) = 1 - A(x 2 +y 2). The modifications in the optical transfer function by changing A, the apodization parameter, has been shown graphically.

Testing Image Quality In Electro-Optical Devices

Abstract: Electro-optical devices present a much more complex testing problem than pure optical systems. An optical system is normally fixed and passive making it independent of light level used in testing. An electro-optical device, however, may have gain, wavelength conversion, and electronic or mechanical dynamics associated with their mode of operation. In addition, these systems may use direct imaging, array scanning or line scanning techniques in their image display system. Image testing, therefore, may have to be performed at low light levels in high gain systems to prevent damage to the photocathode. The device may have to be gated in synchronism with the display. For systems with automatic brightness control, the operating point of the imaging test must be carefully defined in order to get accurate and repeatable data. All of these factors must be considered to get valid data on the image quality of electro-optical devices. This paper will cover the generic system types and typical testing configurations for performing these measurements.

Transverse Ray Aberration Measurement At 10.6 Microns

Abstract: In the visible part of the spectrum, Computer Aided Design is firmly established in the groove When an optical system is designed, there is a strong probability that its computed OTF will to some extent resemble its OTF as measured on one of the many proprietary test benches now available The same is not yet entirely true of Far Infra Red optical systems; in the UK for instance, OTF measurement is performed by a variety of methods such as Edge Scanning, Scanning by Moire Gratings, Line Spread Function Scanning and so on Typical disadvantages of such techniques are, in the case of Edge Scanning; the need for a very uniform and highly linear responsivity across a relatively large area detector, which will almost certainly be very noisy In the case of a Moire Scanner, a disadvantage is the need to incorporate relay lenses into the system in order to extend the frequency range to be tested While the OTF of these lenses may be applied as a correction to the final result, they may not be perfectly aligned in the test setup and this means that the test lens is being interrogated by an already perturbed wavefront A disadvantage associated with LSF scanning is that unless very narrow source and scanner slits are used the corrections to be applied are very large indeed and do not inspire the customer with confidence, particularly in the region of the higher spatial frequencies This is, of course, where most of the really interesting information is contained If, on the other hand, the slits are made so narrow that slit-width corrections become negligible the detector signal levels disappear into the noise© (1974) COPYRIGHT SPIE--The International Society for Optical Engineering Downloading of the abstract is permitted for personal use only

MTF Lens Tester For Production Control And Laboratory Measurements

Abstract: Being manufacturers of a great number of different types of photographic lenses, ZEISS was among the first to use the modulation transfer function for the determination of image quality. The first instrument developed for the purpose, was for prototype testing (see eynacher, Ref. 1).© (1974) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The Calculation of the Optical Transfer Function for Systems with Central Obscurations

Abstract: Systems of a catadioptric form generally have central obscurations that give rise to annular-type entrance pupils. These are found in most cases to be well approximated to the region contained within two ellipses which are generally of different eccentricities. The O.T.F. (optical transfer function) for an annular aperture at a given image point may be expressed as the combination of four integrals, one for each of the possible overlap areas which together describe the form of the overlap region between the two ellipses. Each integral is of a similar nature to the one giving the O.T.F. associated with an elliptical aperture. A computer programme has been written to calculate the O.T.F. using Hopkin's algorithm (1957). Because only one analytical example (aberration-free case) could be obtained for a comparison with this programme, O.T.F. measurements were carried out experimentally on a simple doublet having a central obscuration in order that a more substantial check could be made. The maximum error enco...

The Application of Linear Systems Analysis to Image Processing. Some Notes.

Abstract: The Fourier transform is a convenient tool for analyzing the performance of an image-forming system, but must be treated with caution. One of its major uses is turning convolutions into products. It is also used to transform a problem that is more naturally thought of in terms of frequency than time or space. We define the point-spread function and modulation transfer function in a two-dimensional linear system as analogues of the one-dimensional impulse response and its Fourier transform, the frequency response,respectively. For many imaging devices, the point-spread function is rotationally symmeteric. Useful transforms are developed for the special cases of a "pill box,", a gaussian blob, and an inverse scatter function. Fourier methods are appropriate in the analysis of a defocused imaging system. We define a focus function as a weighted sum of high frequency terms in the spectrum of the system. This function will be a maximum when the image is in focus, and we can hill-climb on it to determine the best focus. We compare this function against two others, the sum of squares of intensities, and the sum of squares of first differences, and show it to be superior. Another use of the Fourier transform is in optimal filtering, that is, of filtering to separate additive noise from a desired signal. We discuss the theory for the two-dimensional case, which is actually easier than for a single dimension since causality is not an issue. We show how to construct a linear, shift-invariant filter for imaging systems given only the input power spectrum and cross-power spectrum of input versus desired output. Finally, we present two ways to calculate the line-spread function given the point-spread function.

Modulation Transfer Function By Measurement Of The Pupil Function

Abstract: The accuracy and reproducibility of measurement of the optical transfer function are dependent upon the differing sources of noise in various measurement approaches. These noise sources include: fluctuations in the light source, noise and drift in the detector, atmospheric turbulence and stratification, mechanical vibrations, and distortions in the structure of the bench. In addition, uniformity of illumination of the aperture of the system and uniformity of collection of the detector may affect the results.