The existence of aberrations in image formation by mirrors and lenses was well appreciated, even in the 17th century. Newton, for example, devised and used a method for making paraboloidal mirrors, which were used. in telescopes to avoid the spherical aberration of the axial image of a distant object which is always present when a spherical reflector is used.

The special demands for OTF measuring instruments are discussed. The development of commercially available instruments from direct measuring instruments to highly sophisticated devices is described, as a trend from complicated test-charts and mechanical set-ups to simpler slit-imaging systems and use of minicomputers integrated in the instruments. A survey of 8 commercial instruments showing different steps of this trend is given.

If asked for an opinion concerning image formation with coherent ( or partially coherent) light you are most likely to get one of the following reactions. (a) Avoid it like the plague. (b) Make sure that your system is designed incoherently! (c) Ignore it, it will go away.

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.

This paper describes some of the results of an exercise conducted via the SIRA Group on Image Assessment and involving the intercomparison of several different and independent OTF calculation programs. Ten Laboratories throughout Europe and Japan performed calculations based on the specification of a particular wide-angle lens.

In this paper I am attempting to review the work on o.t.f. that has been carried out by the Optical Design Group at Imperial College, and in the short time that is available I will not be able to discuss many topics in much detail. We are intending to publish several papers on various aspects of o.t.f., and these papers will include more detailed descriptions of particular subjects.

MTF (Modulation Transfer Function) is a very important tool which is used extensively in the design of lenses for Xerox copy machines.

Within the framework of the German Standards Institution, a study group for the subject "Quality Assessment of Optical Systems" was established in 1968 and was originally assigned to the "Lenses" committee. In view of its importance, however, the study group was transformed into an independent committee in 1972. The committee is composed of representatives of the German companies Elektro Spezial, Leitz, Rodenstock, Zeiss, the Swiss Wild company and representatives of Physikalisch-Technische Bundesanstalt, of the Optical Institute of Berlin Technical University and of the Tubingen Optical Research Institute. It is the purpose of the committee to define measurement conditions that allow proper determination of the OTF. The OTF of any optical or electro-optical system is a physical function determined by the type and the design of the system. Consequently, its measurement must be independent of any specific equipment parameters. In addition, great care must be taken to ensure that the specified physical measurement con-ditions are satisfied within the desired measuring accuracy.

Although more research work over the past 35 years or so has gone into the assessment of lenses for aerial reconnaissance and survey than perhaps for any other photo-graphic application, it is only comparatively recently that really objective techniques have begun to be brought into use in the production of air cameras. The reasons for this are probably the complexity of what, on the surface, appear to be rather simple problems, and reluctance on the part of those concerned with the hard facts of camera production to become involved with techniques that may appear more esoteric than practicable. The subject of image formation has been a rich field for high-level academic activity for a long time, and the real need today is to bring the theories and methods evolved into routine use in specifications and manufacturing processes.

A working group of the Japan Optical Engineering Research Association (JOERA) has been organized on April, 1974 and has made a start for making Japanese OTF standard by 1976. This working group will make the draft for OTF standard such as 1) optical systems to be applied, 2) definition of OTF and MTF, 3) standard graphical representation of OTF and MTF, and 4) inspection standard for the accuracy of MTF measuring instruments.

Three trends are at present apparent in image-evaluation methods. The first trend is to leave the OTF to the theoreticians and replace it by the measurement of imaging characteristics which cover the over-all imaging performance of the device under test as completely as possible. In such cases the measuring methods and even the measuring equipment have to be specified.

A practical image quality criterion was developed which is easily calculated and directly measurable and which gives consistent evaluations of system performance. The image quality merit function was evaluated for a wide variety of MTF shapes which include chromatic and nonsymmetric image errors. The results of the experimental program are that the image quality merit function is able to predict image quality within normal reader error and is linearly correlated with the measured data. The tests of the proposed quality criterion for color and black-and-white images have been limited to physically realizable optical systems producing grain-free images and to a range of image quality from excellent to unusable.

A new figure of merit - visual efficiency - is presented, which is derived from objective quality measures (such as MTF) and the working state of the eye. It is shown that, whilst no single figure of merit can apply absolutely to all types of presented object, visual efficiency can be used to derive relative performance for many definable objects.

In 1968, those of us at NBS concerned with classical optics, felt it important to resume the testing of optical systems and components and decided to develop a method that was in keeping with the advances being made in lens design and manufacture. The technique previously used at NBS1 was limited to about 200 cycles/mm by considerations of partial coherence, and could measure phase shifts only with great difficulty and low precision. The forthcoming high-quality optics indicated by activity in the design community were clearly beyond the capability of this testing system. Further, the increasing use of microscope optics in such devices as microdensitometers, reduction cameras and other specialized equipment showed the need for an accurate testing technique that would include these kinds of optical components. Our intent was to concentrate on the test and evaluation of high-quality optics such as might be used in microdensitometry, microelectric circuit applications, and high resolution aerial cameras, to develop an inexpensive and accurate measurement technique, and to provide a modest NBS measurement service that would be used by commerical firms and other government agencies when it was necessary (for contractual reasons) to have the NBS imprimatur on the results or when it was impractical for the requestor to have his own test equipment.

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.

Many methods for the measuring of optical transfer function (OTF) have bee ki studied in the last two decades 11. The one dimensional OTF is obtained in the large majority of these methods since the spatial frequ-ency is scanned temporaly at a fixed azimuth. One can recognize the two-dimensional transfer function only after knowing the one-dimensional OTF along every discretely sampled azimuth. Only a few instruments have been developed for measuring both of modu-lation and phase transfer function, MTF and PTF, because the former is more important than the latter.

It was first shown by H. H.Hopkins that the optical transfer function can be directly measured by means of a shearing interferometer. With the advent of lasers in the past ten years, and the need for very high-quality optics both in the laboratory and in field environments, the interferometric technique appears to be ideally suited to single-wavelength measurements. Several laboratory-type interferometers have been described in the literature,2-'7 although in most cases these instruments were not suitable for either routine optical testing or for field use. More recently, a cornercube shearing interferometer was constructed for making MTF measurements on board a KC-135 jet aircraft.8 However, all these past instruments were relatively slow. Very rapid real-time OTF measurements are required in field environments. A new rapid-scanning interferometer has been developed, which requires no adjustments in use and is extremely stable, even in environments where large vibrations are encountered.

This paper presents experimental results obtained when the OTF of a lens is determined from edge-scan measurements of the image of a point source and also from the O.P.D. over the pupil. The OPD (sometimes called the pupil function) is measured on-line by a phase-controlled, digital interferometer. Both theoretical and practical differences between the two methods of measurement are discussed.

The system to be described was conceived, designed and assembled to enable Perkin-Elmer to quickly evaluate production optics and systems by the reduction of interferometric data from which Optical Transfer Functions (OTF) may be calculated.

The optical transfer function(OTF), or more frequently the modulation transfer function(MTF) has been used to evaluate the image quality of lens and optical systems as a objective criteria. But practical aspect of lens testing to evaluate a prototype optical system we must measure many MTF curves for several conditions such as image heights, focus positions and F-stops. In previously developed instruments, it is time consuming to make the MTF measurement and it is troublesome to rewrite the original data for desired correct MTF curves after measurement.

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).

Parameters of MTE tests on military vehicle sights have been investigated and suitable procedures for testing with a Sira-Beck 'Erost equipment evolved. A simplified MTF testing technique operating at a single spatial frequency over all azimuths reduces the amount of test data to a convenient level for subsequent assessment purposes. The equipment to carry out this test can measure dioptre settings of fixed focus eyepieces, field curvature and astigmatism. Specifications are discussed in relation to both establishing comprehensive statements to cover a design and reduced specifications for quality control purposes.

Incoherently illuminated sinewave objects are generally employed as tar-gets in transfer function studies. Since it is not easy to obtain good targets of this type, other targets have been proposed which, by the aid of appropriate filtering, can be transformed into effectively sinusoidal gratings. The rectangular-and triangu-larwave objects are mostly used in this connection (Ref.l) . The latter is especially advantageous since the higher harmonics of its Fourier-series representation converge-more rapidly than those in a rectangular wave. A practical method of generating test objects of triangular waveform is based on the utilization of moire fringes produced by two crossed gratings (Ron-chi rulings) -(]Ref.2 and 3). By ro-tating the two gratings in opposite directions the spatial frequency of the moire fringes can be varied continuously and linearly with time,observing simultaneously the condition that the scanning time-frequency remains the same for all spatial frequencies. In order to achieve the desired accuracy in OTF measurements with an equipment using the mentioned test ob-ject it is necessary to satisfy certain conditions. One of these is good quality of the basic gratings, another is correct positioning in the driving mechanism.

During the past decade substantial advances in processing speed, memory size and software have occurred in computer technology. Similar advances have resulted in highly sophisticated communication systems. These developments have enabled digital electronic methods to become a practical photographic image processing technique. For example, a recently developed change detection system (Ref. 1) is capable of processing 400,000 image points per second. This and other digital image processing systems generally result from special purpose applications of algorithms developed on large scale, general purpose digital computers.

The accuracy -and often the feasibility - of MTF evaluations of light sensitive recording materials is a question of signal-to-noise ratio of the measuring procedure.

The choice of suitable criteria for production testing of binoculars and similar afocal systems is discussed and the conclusion is arrived at that the measurement of MTF at a single spatial frequency in all azimuths, on-axis and for one field point, in conjunction with measurements of "scatter index" (glare) and axial transmission factor forms the basis of an adequate production test. An instrument is described embodying this test philosophy. The instrument is designed so that it can be used by relatively unskilled workshop personnel and acceptance or rejection of a system under test is indicated by means of lights. The results of preliminary field trials of the instrument are described.

An earlier paper (Ref. 1) described the setting of focus in aerial cameras by locating the plane giving maximum modulation at the spatial frequency corresponding to the low contrast resolving power. A modified apparatus has been applied to determine the area weighted average modulation over the whole field (AWAM) as a function of focus, and hence to locate the best compromise focus having regard to field curvature, etc., and to the asymmetry almost invariably present in production lenses. For four types of lens, the best AWAM focus was not significantly changed by the presence of typical amounts of asymmetry. The agreement between the foci determined by the single frequency measurements and those determined by photographic picture quality was within acceptable limits.

Monitoring of high-volume lens manufacture for Polaroid Land photog-raphy requires an acceptance criterion which is relevant to picture quality and suitable for automatic testing. In a hardware test based upon the Modu-lation Transfer Function, the problem is to choose what not to measure, while obtaining enough information about a lens to assign it a useful figure of merit. The predominant defects of manufacture are field tilt, resulting from tilting or decentering of the components, and field curvature, from small errors in spacing, thickness, radius, or index. Field tilt and curvature are not "local" defects of the image surface, insofar as they may be removed by a local refocus. We therefore need a test procedure which can (perhaps simultaneously) examine image quality over an extended field, but which is principally called upon to evaluate focus differences. At multiple field locations a single-frequency modulation measurement adequately defines the MTF for the low spatial frequencies of interest, and can be interpreted easily in terms of the root-mean-square blur of the Point Spread Function. We will discuss the logic of 100% lens acceptance testing and two types of instrumentation we have used.

The automated testing of mirrors in a manner related to system function has become increasingly important to Xerox because flatness checking is presently carried out at a high sampling rate using the time-consuming tools of optical flats or Fizeau interferometers. Consequentially. reduction in the amount of time and labor involved in these measurements is needed. A secondary benefit might be reaped if the subjectivity and, hence, the skill required to interpret these interference patterns could be removed.

Over the past few years, MTF measurements have been made on several hundred photographic lenses. Certain routines have emerged which reduce the number of measure-ments required to assess the general behaviour of a lens. Sets of through focus MTF response curves on axis, at half field, three-quarter field, and full field reveal the character-istics of the radial and tangential focal surfaces from which a focus setting may be chosen to give the best overall response for the specific requirements of the lens. A standard format of MTF curves through field at this focus setting is then obtained. For a quick assessment of a lens or for a comparison of several lenses in a production run, an ab-breviated test routine with the object and image slits at 45° orien-tation has proven useful. Examples of the application of these routines are given.

Optical testing in production is becoming increasingly complex as component specific-ations become tighter. It is no longer satisfactory to evaluate lenses by the visual appearance of the image they produce and objective test methods are becoming more commonly used in the optical workshop. The most important objective test parameters to be considered are optical transfer function, transmission, distortion and veiling glare. Most of the comments which follow relate specifically to m t f but also in a general sense to all optical measurements.

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.

The S-190A Multispectral Photographic Facil-ity, has produced a large volume of imagery from Skylabs 2,3, and 4. The imagery has been analyzed in detail to a) assist users of the film in evaluating the potential and limitations of the photographic data; and b) to assess the performance of the camera. This program has also provided an opportunity to assess the effectiveness and precision of certain image evaluation techniques. Resolution has been evaluated as a function of spectral band, EREP pass, target orientation, field of view, exposure, contrast, et al. Methods being employed in the analysis are Visual Edge Matching (VEM), and Edge Slope Analysis ("MTF"), for the resolution evaluation. The quality of registered imagery is being analyzed by utilizing the Itek Registration Printer and a computer assisted stereo comparator, image matching technique.

This paper is concerned with the measurement of the Optical Transfer Function (OTF) of earth orbiting imaging sensors, from typical operational imagery. Historically, the OTF of aerial systems has been obtained from special targets, such as artificial edges (Ref. 1) or lines (Ref. 2), or their naturally occurring counterparts in the form of coastlines, field boundaries, etc. The OTF, T(f), can then be obtained directly from the Fourier spectrum, I(f), of the image by the imaging equation,

Prior to the launch of the Earth Re-sources Technology Satellite (ERTS-1) and Skylab vehicles the performance characteristics of the different sensors (Table I) were ambiguously defined in relation to proposed cartographic and earth resources applications (Ref. 1,2,3,4). As a result, opinions con-cerning anticipated image quality differed, and factors contributing to the various interpretations of potential image quality included: 1) differences in the photographic and electro-optical engineering definitions of resolving power; 2) a general lack of experience with ultra small-scale imagery; and 3) problems encountered in attempting to relate design criteria and performance estimates to image quality (Ref. 5,6,7). In the latter instance, limited communications between system design engineers and earth scientists/cartographers further confused the issues. As a consequence of these and other factors, an independent effort was made to predict and measure ERTS and Skylab system performance using MTF analysis techniques, and to translate the results of these analyses into the photographic resolution values with which the cartographic community are most familiar (Ref. 8,9,10). Since the approach used to evaluate sensor performance has involved comparisons of predicted and measured MTF values, it has also been possible to assess the reliability of the techniques employed.

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.

Image Intensifiers are used to detect, recognize, and identify objects of, or in, radiation of low intensity. The type of radiation for which image intensification can be used, ranges from x-rays into the near infrared region. In this review, x-ray intensifiers will not be considered. A review of the various types of image inten-sifiers has been given recently (Ref 1).

To measure the modulation transfer function of image intensifier tubes or optical systems with built-in image intensifier tubes, the basic parts of our measuring system Odeta can be used, completed with a specially developed set of accessories.

The subject of image assessment and specification is of canonical importance to those involved in the research, development, and utilization of imaging systems. The quantitative assessment of something as subjective as the value of an image is essential in quantifying and communicating the needs and results of an imaging system or its components. In spite of the urgent need and the vigorous effort of the technologist responding to this need, no universally accepted standards for the measurement of image quality are available. The utilization of Fourier methods in image assessment and specification problems is currently in vogue because of their dexterity in fulfilling at least two necessary conditions as a measure of image quality. First, the Fourier methods provide a quantitative measure of image quality which reasonably correlates with the subjective effectiveness of an imaging system, and second, the analysis and performance prediction of a cascaded imaging system from a knowledge of the performance of its individual components are facilitated.

A short review is given concerning some general aspects of thermal imaging quality criteria. Some of the most important figures of merits (e.g.MTF, Minimum Resolvable Temperature - MRT, Signal Noise Power Densi-ty-SNPD) are discussed with the aid of a test system and illustrated by measurements with a mechanical scanner (AGA 680) and a pyroelectric vidicon (Heimann).

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.

The measurement of the Modulation transfer Function (MTF), is becoming a standard procedure for specifying the quality of lenses and complete optical systems. Since MTF measurement does not rely on photographic emulsions, visual observation or subjective judgement, the numerical values obtained enable the optical manufacturer and the purchaser to specify the system performances in purely objective terms.

An instrument is described which can be used for measuring directly the MTF of infrared optical systems operating in the wavelength range 2 to l4 /μm. The instrument uses a moire fringe technique for generating the test target, but a novel arrangement permits measurements at single spatial frequencies as well as over a continuous range of frequencies. The instrument is designed to give automatic normalization and has facilities enabling the line spread function to be measured directly. Some results of measurements on typical lenses are given and comparisons are made between some of these results and the MTF calculated from line spread function measurements and/or from the design data of the lens.