Due to increasing environmental limitations on the use of certain raw materials used to make optical glasses, there is now an economic desire to minimize the number of glasses used in lens design. This paper presents the results of a study to create a suggested universal catalogue that contains the minimum number of glasses needed to satisfy most possible lens designs. A nearly symmetric double Gauss lens is used in the glass selection process. As part of this study, the relationship between the error function and the number of glasses chosen is studied, and in addition, a glass range study is also carried out. Three different lens libraries were studied using the global optimization method and the most frequently chosen glasses were then compiled into the suggested universal glass catalogue. A suggested universal glass catalogue constructed from this study is presented.

A two-mirror asymmetrical system has been designed to reshape a laser beam into an elliptic uniform beam profile for use in a new superbroadband color center laser system. The surface points of the two mirrors are obtained by solving a second order partial differential equation of the Monge-Ampeere type which is based on conversation of energy and the law of reflection. The technique is illustrated by presenting the design of a two-mirror system which converts a circular Gaussian beam into an elliptic beam with a uniform profile. Such a reshaper system is planned for use in the development of superbroadband or control generation spectrum color center lasers, which have a significant potential for optical communications, signal multiplexing, and information coding as well as laser spectroscopy, photochemistry, medicine, color microscopy, and holography.

Liquids have not found widespread application in optical design for a number of reasons, one of which is the fact that index of refraction data for liquids is available for only very few compounds, and the data that do exist are only in the visible spectral region. In this paper we report on the results of our joint project for measuring the refractive index of liquids in the infrared (IR) spectral region. A number of liquids have transmission passbands that extend well into the IR, to wavelengths of 10 micrometers and beyond. Many of these liquids also have abnormal dispersion and are suitable for low-cost apochromatic lens designs in the infrared. Using these materials, design options that significantly reduce the cost and weight of IR imaging systems become available. These measurements have been made at the Vavilov State Optical Institute, Saint Petersburg, Russia, in collaboration with the Lockheed Palo Alto Research Laboratory.

Abnormal dispersion is found in a large number of optical liquids. These liquids are quite useful in the design of apochromatic lens systems because they are inexpensive and are readily available compared to the expensive abnormal dispersion glasses and crystals more commonly used. Further, there is no practical upper limit on the size of a liquid optical element. However, because the use of these materials as optical elements is quite new, the long term stability of their optical properties after exposure to various environmental conditions must be determined. In this paper, we report on a series of tests performed to determine the optical stability of several abnormal dispersion liquids. The liquids were subjected to: (1) high intensity ultraviolet radiation, (2) high temperatures, and (3) long term exposure to air. Measurements of both optical transmission and refractive index were performed before and after each exposure. The tests were performed on four abnormal dispersion liquids that have been found to be quite useful in the design of apochromatic lenses. The results indicate that long term exposure to either intense ultraviolet radiation or air, produced only negligible changes in the index of refraction. Changes in optical transmission were observed, but they were largely confined to the ultraviolet spectral region. Prolonged exposure to temperatures of 60 degree(s)C did not produce any measurable change in the optical properties. The measurements were performed at the Vavilov State Optical Institute, St. Petersburg, Russia, in collaboration with Lockheed Palo Alto Research Laboratory, Palo Alto, California.

Using the caustic merit function for plane waves incident upon a singlet lens, a comparison between the optical performance of the lens using an axial gradient index with spherical surfaces or aspheric surfaces with constant index material has been investigated. Results indicate that the use of an inhomogeneous medium for the lens material is more effective in the controlling aberrations than the use of aspheric surfaces for a similar lens.

The CVROS scanner, a new approach to high speed serial optical scanning employing a scan disc, has been successfully developed for thermal imaging. Its high speed, high scan efficiency, wide field, and mirror optics suggest applicability to broad band visible scanners and projectors as well as laser and UV printers. This paper reviews the CVROS concept and presents the configuration adaptations required for finite conjugate applications. Design and performance characteristics are given for several configurations as well as key alignment and manufacturing requirements.

Optical elements which are made out of macro gradient refractive material are represented by lines, as opposed to points, on the glass map (n_d Vs. v_d diagram). Thus, optical designers need account for gradient dispersion as well as gradient index. A dispersion model for the material must be readily available and optical design programs must be capable of defining and maintaining this relationship before and during optimization, simplifying user input and confining the material to walk a well defined path on the glass map. Thinking in terms of lines on the glass map for arbitrary glass families yields a simple dispersion model based on least squares fitting of Buchdahl coefficients. This paper introduces the concept of glass lines and outlines a technique to construct a dispersion model for any contiguous family of gradient refractive material.

We proposed an all-optical bistable unit made of a Faraday medium and investigated theoretically its unique characteristics. Optical bistability in our proposed unit was experimantally confirmed. In this paper, using a 830 nm wavelength laser diode and a thin garnet film rotator as a Fabry-Perot resonator, optical bistability is confirmed again. Bistable characteristics, threshold incident power, on-off power ratio, and dynamic characteristics, are examined to attain controllability with the external magnetic field. In our proposed unit's construction, an all-optical sensing device (a magnetic field sensor) is proposed and evaluated for application to the OB operation.

Multi-level approximated Fresnel zone lenses with reduced level numbers in the outer zones are investigated and compared with Fresnel zone lenses of unique level numbers over the whole lens. Calculations of the fabrication error effects on diffraction efficiency for both lens types are performed. Measurements of focussing efficiency show that. especially for Gaussian beam illumination, segmented Fresnel zone lenses can reach nearly as high focussing efficiencies as normal Fresnel zone lenses. Arrays of segmented lenses can be fabricated using only one binary Fresnel zone lens mask with the aid of a modified optical stepper with fixed scaling down factors in the ratio of 1: 1/(root)2 from one to the next step of pattern transfer in the lithographic process. The fabrication of such lenses could be advantageous because the generation of precise e-beam written masks with a large number of binary ring zones is time consuming and expensive.

In this paper we discuss the design of Diffractive Optical Elements that can be used for optical interconnections. Q uite general computer programs have been realized for the design and the validation of such optical elements. As examples, in the paper we discuss the design of a 1 to 3, a 1 to 5 and a 1 to 4 interconnections, workingeither in reflection or in transmission.

Large computer generated diffractive optical elements (DOE's) are useful in many applications. Typical sizes of DOE's range from 6 inches up to two meters in diameter. Current state-of-the-art techniques for fabricating these DOE's involve photolithographic processing where photoresist is used as the light sensitive medium and an etchable metal layer is used to form the pattern of the DOE. Handling and costs associated with photolithographic methods become critical issues when the DOE's become large. It is therefore advantageous to have a technique that would not require the photolithographic step in the process. This paper will discuss the instrument and the technique used at the Optical Sciences Center (OSC) for fabricating large computer generated DOE's. A non-photolithographic technique of thermally selective oxidization is used to transfer the DOE pattern onto a metallic film on the substrate. The subsequent etching part of the process takes advantage of the differential etch rates of a non-oxidized and oxidized metal. Figure results indicate the accuracy of using this approach to fabricate DOE's is better than (lambda) /100 rms.

Based on an exact solution of the pertinent boundary-value problem, a method is presented for finding the electromagnetic fields scattered or guided by dielectric gratings having arbitrary profiles. This method unifies the treatment of both perpendicular (TE) and parallel (TM) polarization by using the Boundary Element Method (BEM). To illustrate the method, the results are presented for a four layer waveguide with trapezoidal grating.

With the present trends toward miniaturization, the demand for complex optical elements with surface features is increasing. If these complex optical elements, such as Fresnel and diffractive optics, are fabricated in glass they should be superior to plastic, both in optical quality and environmental stability. To demonstrate the replication of diffractive and Fresnel optics, Fresnel lenses were prepared by a sol-gel molding technique. The optical quality and performance and dimensional characteristics of the lenses are reported. Optical and physical properties tested included glass homogeneity, UV/VIS/NIR transmission, light scattering and surface profilometry. Optical performance testing indicated that these glass Fresnel lenses are as good as their parent plastic Fresnel lenses from which they are molded.

This paper describes an application of the diamond turning technology for the manufacturing of cylindrical micro lenses. A lens doublet consisting of an aspherical PMMA lens mounted on a sapphire plate was designed. Various surface curvatures are transferable to a crooked stripe of optical material like polymethylmethacrylat. A diamond tool cuts the circular ring at its outer periphery. The approximately 80 cm long, circular lens stripe relaxes after taking off from the chuck to the original straight condition. Microlenses of any length are gotten by separating the long lens stripe to individual lenses. For a quality inspection the surface was examined by a laser interferometer measurement and the collimation performance of the doublet was tested. The measured surface roughness is better than 12 nm RMS. To apply a 10 mm diode bar a lens with 12 X 1,5 mm² entry aperture was used in the collimating tests. Experimental results show collimating rates for high performance diode laser applications of 70% in a divergence angle of about 4 mrad.

An important step in the fabrication of an optical component involves the imparting of a precise contour on the optic, which can be expensive and time consuming. Ion beam figuring is the imparting of a contour on an optical component by removing material through the impingement of a broad beam of accelerated neutral particles, and provides a highly deterministic method for the final precision figuring (or correcting) of optical components with advantages over conventional methods. The high predictability allows the possibility of single step figuring, resulting in significant time and cost savings. And unlike grinding, polishing and lapping, ion figuring is non-contacting and so avoids several problems including: edge roll off effects, tool wear, and loading of the work piece. It has previously been demonstrated that ion figuring is effective for the correcting of large optical components. These implementations typically use the process for final figure correction on meter class optical components. The work discussed here is the development of the Precision Ion Machining System (PIMS) at NASA's Marshall Space Flight Center, designed for the processing of smaller (less than 10 cm diameter) optics. Initial experiments using a Kaufman type ion source to figure 8 cm diameter fused silica and silicon carbide samples were successful. Experiments involved correcting flat samples and imparting spherical and aspherical contours.

An ion beam milling system, used for precision optical fabrication, was modified to easily allow deposition of thin films onto the same optics within a single vacuum operation. A series of coating experiments was performed to assess this approach to integrated ion milling and optical coating. Attempts were made to maximize the deposition rates while maintaining a narrow distribution of coating material to provide the optimum total process time. A series of shaped sputter targets was found to maintain high deposition rates similar to those of a flat target but without having the desired effect of narrowing the material distribution. Apertured shields produced narrow material distributions but at the expense of significantly lowering the deposition rates. Despite these limitations, analysis shows that thin optical films can be produced in a reasonable time by this approach.

In this paper, a new method used to calculate the Zernike coefficients of wave aberration from ray aberration and from finite shearing of wavefront is proposed. The simulated results are compared with the least squares fitting method, and indicate that the Zernike coefficients of wave aberration can be calculated as accurately with the new method as with the least squares fitting method, but with less computation and operation.

A commonly used estimator for the microtopography of a surface is its RMS-roughness. Raw surface profile data may contain trending components. Therefore they should be subjected to a detrending procedure before estimating the RMS-value. This procedure is limited in most cases to the removal of piston, slope and curvature. Consequently, undesired artifacts may arise, which negatively influence the precision of RMS-roughness estimation. In scanning surface metrology, the principal surface computed by using eigenvalues and eigenvectors of the covariance matrix of the surface data under consideration can be used for a robust and precise multivariate estimation of RMS-roughness.

The development of a null test configuration to measure the accuracy of an aspheric surface is presented. The surface form was measured using a refractive compensator lens in conjunction with a 170.52 transmission sphere to provide an interferogram representing the aspheric form deviation from the nominal. The interferometric data is compared to data obtained using a contact stylus profilometer. Keywords: null compensator, interferometric, oblate spheroid, aspheric

The conjugate null test is commonly used to test surface errors of conic mirrors. Unfortunately, its accuracy is limited by rigid body misalignment errors. This paper derives the misalignment aberrations for these errors.

An automated Ronchigram analysis system capable of analyzing cross grating ronchigrams, produced by a single channel Ronchi system, is being developed. Because of the complexity of the Ronchigrams it is necessary to separate the vertical and horizontal components. Two basic approaches of component separation, Fourier decomposition and differentiation, are described and evaluated.

The AXAF observatory is the third of NASA's `Great Observatories' designed to image cosmic x-rays in the energy regime of 0.1 to 10 keV (124 - 1.24 angstroms). The mirror assembly consists of four concentric, confocal, Wolter type I telescopes. Each telescope includes two conical grazing incidence mirrors, a paraboloid followed by a hyperboloid, for a total of eight cylindrical elements. The largest element pair was successfully fabricated and tested in x-rays in 1991, at which point the production program to fabricate the remaining six mirrors was initiated. This process is well underway, with mirrors in various stages of production. This paper describes the fabrication requirements, discusses the status of each mirror, and presents summary information on the convergence of the computer controlled fabrication process and examples of the fabrication results.

The secondary mirrors required for 8-meter class telescopes have increased apertures and must fit with faster primary mirrors. As dome seeing has been improved, the wavefront accuracy requirements have become significantly tighter than for previous instruments. These requirements as a set yield a different list of criteria for the determination of the final test configuration. In addition,k the desire to reduce the weight of the secondary, to either increase the first mechanical resonance mode of the spider or to decrease the inertia for chopping, has led to the use of structured mirror substrates. The importance of mechanical analysis of the support of both the secondary and the test optics becomes crucial. As part of an existing contract, a trade study was undertaken to evaluate various methods for testing convex hyperboloids of 1.4-meter aperture. Included in this discussion is a unique, compressed Hindle test. This test uses two auxiliary lenses to allow the use of a sub-sized Hindle sphere for full aperture testing. This test was demonstrated on the WIYN telescope secondary mirror fabrication. The final result of a trade study will vary from institution to institution due to differences in existing test equipment, funding methods, and overall goals. However, the starting point will be similar.

This paper evaluates the experimental performance of satellite profile measurements using digital correlation techniques in optical spread spectrum systems. The digital correlation achieved a 3 cm spatial resolution. To the authors best knowledge this is the best resolution reported to date with a non-coherent system. The advantages of the approach are also discussed with reference to synchronization performance.

Infrared Focal Plane Array (FPA) sensors are commonly tested using various means of scene generation. At the Arnold Engineering Development Center a Direct Write Scene Generator (DWSG) is being developed. The DWSG projects the scene onto the focal plane array by scanning a rake of beams across the sensor. The rake consists of up to 256 synchronous beams generated by passing a single laser beam through an acousto-optic deflector (AOD). A complex radio frequency signal input into the AOD diffracts the laser beam into multiple beams. Each pixel of the focal plane is illuminated by one of the beams in the rake. The Direct Write Scene Generator is being designed to test a focal plane area as large as a 512 X 512 pixel array. Scan optics focus an expanded laser beam to a spot smaller than the focal plane pixel pitch over the entire test area. Several optical configurations and multiple AODs are needed to achieve the test requirements at various wavelengths. Some important considerations in the optical design are spot size, crosstalk, and background radiation.

A fundamental study on evaluating an epoxy-based coating was conducted. The study aimed to determined the performance of the coating on a low carbon steel as a result of chemical contaminations. Coated samples were tested in a local tap water by using the method of real time— holographic interferometry. A mathematical model was used along the obtained experimental data. The model described processes of detecting the early corrosion of the the steel under the coatings by holographic interferometry. Consequently, the holographic interferonxetry technique was found very useful in detecting the early corrrosion processes of the coated steel Also, a relationship between the displacement of the coating ,dueto metal corrosion under the coating, and corrosion current density of the coated steel was established for the epoxy-based coating with and without an addition of sodium chloride to the coating.

This paper deals with the enhancement of a laser speckle photography technique by means of a modification of the film development procedure. Using a holographic film, an amplitude characteristic of the film can be changed to a phase characteristic. This conversion is achieved during the film development procedure by a controlled bleaching of the exposed film. The experimental arrangement and the method to get a phase specklegram are described in detail. First experimental results are presented, the phase specklegram characteristics and the fields of application are discussed. Keywords: laser speckle photography, amplitude specklegram, phase specklegram

The operation and behavior or arrays of active transducers comprising complex compliant structures depends on their true structural dynamics. Such structures are characteristic of sonar system assemblies, control elements for active optical systems, and other continuously deformable structures. Their dynamics are directly related to the mechanical and physical interfaces between transducers and their supporting and radiating structures. Such complex assemblies require sophisticated bonding and processing of compliant materials which determine their operational parameters. Understanding the effects of structural anomalies and defects is of critical importance to insuring correct array operation, and a non-destructive method for the visualization of structural characteristics would be of great value in both development and testing of such systems. Knowledge of the mechanisms for acoustic energy transfer through these structures into adjoining media can be inferred from such visualizations. Holographic interferometry has presented itself as a viable and useful method for the realization of this type of information.

Characterizing two-dimensional image sensors is not accurate enough when using one- dimensional methods. The response of a photoelement may be fully characterized by the function of two space variables (Photoelement Response Function). A simple and rigorous method was developed to measure this function, using a new two-dimensional pattern and a differential operator. The first results are indeed not complete, but there is no doubt about the interest of this method. Two patents have already been taken out.

We present a theoretical method which makes it possible to analyze 3-D integrated optical waveguides with arbitrary refractive index profiles. With this method it is easy to obtain effective indexes, propagation constants and coupling/switching properties of planar and channel optical waveguides. This theoretical approach involves modelling the original optical waveguide by means of an Equivalent Optical Waveguide whose effective index is evaluated by applying a technique that we call the Asymptotic Effective Index Method. The theoretical results show good convergence and accuracy for effectives indexes, propagation constants and coupling/switching characteristics.

Prior publications dealing with techniques for estimating axial contact stresses in lenses mechanically clamped axially near their rims have assumed the lenses to be single elements. In this paper, we expand the theory to include multiple-element lenses such as cemented doublets and optomechanical designs with spacers or equivalent cell features between separated lenses. Examples are given to illustrate the use of these new analytical techniques.

The basis of confocal microprobes, in general, is that light or other radiation is focused to a point where it is scattered by some material under study and then collected by a lens and detector system which is also focused on that point. The amount of radiation collected at the detector is then indicative of the scattering properties of the material at the common focus. This paper describes a family of related microprobes using optical fibers for delivering light to and from the focus. A novel arrangement is described wherein the focal points of the source and detector are not confocal but adjacent. This quasi-confocal arrangement has some very useful properties for detecting surfaces and investigating surface topography.

Electromagnetic forces can be used to deform the free surface of a reflective liquid. Such forces can be obtained through flowing of electrical current in the liquid itself or using its ferro-magnetic properties. For the first approach a ground-based experiment to characterize an adaptive mirror is briefly reported. For the second approach a technique to deploy in nearly- zero gravity environment a large concave mirror is shown. For this space-based application an example of case study is briefly given.

Design of mechanical features such as spacers, retainers and/or cell shoulders used to locate and constrain lens components within a mount entails application of geometric relationships that depend upon the types of glass-to-metal interfaces to be provided. This paper describes the pertinent geometry of the most common surface-contact interface types (`sharp corner', spherical, tangential and toroidal) and gives equations for locating key features of the mechanical parts relative to the associated lens vertices. Examples illustrate the use of these equations to dimension mechanical features in typical lens/mount configurations.

With large-ground based telescopes it is not possible to achieve the theoretical diffraction-limited spatial resolution. The reason is the turbulent earth atmosphere which disturbs the light wavefronts coming from the observed astronomical objects. Due to this influence, short exposures consist of bright and dark interference patterns, and they are therefore called speckle interferograms. With correlation techniques the diffraction-limited information about the observed object can be deconvolved from a set of such speckle interferograms. The investigation of the detector accuracy, which is required for a successful working of the correlation methods, manifests this simple fact: one bit of dynamic range is enough to feasibly detect astronomical speckle interferograms for the high-resolution methods. The method of correlating interferometric data having only a dynamic range of one bit is seen to be useful for astronomical high-resolution imaging at optical wavelengths. The new detector principle was first investigated in detail in computer simulations. It is now motivated additionally by laboratory simulations which should give a more realistic view of true astronomical observations, because in them nearly all technical problems should be considered sufficiently.

The characteristics of a new twin-track absolute position optical encoder are presented. One tract containing a pseudorandom code and the second a periodic pattern are synchronously engraved on a glass slab. The optical reading head design composed of a LED, a gradient index lens and a linear CCD array, with simple intensity-based signal processing to read the code pattern is described in detail. This design is combined with a standard Moire method to enhance resolution. Performance enhancement of the optical reading head is studied in terms of track illumination versus code density, detector geometry versus the lens point-spread function (Airy disk); and reduction of extrinsic spatial noise by the application of thick films. Each parameter was considered in terms of the optimal field of view and depth of field of the system.

The ultimate goal of optical instrumentation is to achieve the desired image quality in a given application. This requires a homogenous blend of optical and mechanical design, fabrication, system integration and testing tasks. The space optical systems generally require near theoretical performances in hostile environments within size, weight and cost constraints. Hence a careful tolerance analysis plays a crucial role in these systems. For space optics, the importance of image quality, cost and related tolerance analysis cannot be over-emphasized. In this paper, we have tried to address the challenge of achieving an optimum image quality through a cost effective tolerance analysis. Two different space optical systems are considered: the UV imager for the International Solar Terrestrial Physics (ISTP) Mission and an afocal telescope for the Advanced Polarized IR Imaging Sensor (APIRIS). These systems are described along with their required performances and designs, with an explanation of the tolerance study conducted. The effect of tolerances on the image quality and cost are investigated.

We propose the use of a liquid-crystal switch consisting of a liquid-crystal cell and a polarizing beam-splitter in a single-lens-reflex camera to replace a mechanical hinged-mirror. Since there is no vibration and noise, the proposed switch is very suitable for a fundus camera.

The LP mode in e-core fiber has been analyzed theoretically. It is found that the solution of the modal fields of e-core fiber is a combination of Mathieu and modified Mathieu functions. The modal eigenvalue equations are derived. The mode nondegeneracy and cutoff frequency are discussed. In addition to deriving a general expression for propagation constant, we have also obtained the propagation characteristics curves of several lower-order modes for different core ellipticities.

A high precision mechanical profilometer (MPROS) has been designed and utilized for metrology on the Advances X-Ray Astrophysics Facility (AXAF) optic program. The instrument serves both as a measure of axial figure during the grinding phase of mirror fabrication and as the AXAF program crosscheck for axial sag error. MPROS has demonstrated an accuracy of 0.25 micrometers P-P over nominally 1 meter of travel. The design is relatively simple, employing Hewlett Packard distance measuring interferometers, an air bearing slide, and coated Zerodur reference surface. This paper will present the AXAF axial metrology requirements, MPROS design, and reference surface calibration. System performance and results will be presented and discussed.

The structural influence coefficients for an imaging optical system map the decenter and tilt motions of the system elements to changes in the direction and orientation of the line-of-sight and image. A methodology is presented to calculate the structural influence coefficients for the lenses of long-focus (near-infinity) imaging optical systems. Single-lens systems are considered first, with the method then extended to handle multiple elements. Use of an arbitrary structural reference frame is discussed, along with an algorithmic, recursive approach to numerical calculation of the structural influence coefficients. A complete derivation is presented at each step, and an overview of the geometric optical principles involved is provided for reference. The method described allows ready calculation of influence coefficients without tedious ray-trace perturbations or dedicated optical analysis software. This paper is a companion to a previous paper by the authors, in which the structural influence coefficients for plane-mirror systems are derived. The influence coefficient method of both papers is unique in its use of line-of-sight reference frames as an optical kinematic tool to track pointing direction and image orientation.

Very stringent dimensional stability requirements for metering rods of the NASA/Jet Propulsion Laboratory Cassini spacecraft NAC (Narrow Angle Camera) were the driving forces to select and conduct dimensional stability tests of several dimensionally stable materials. Carbon/carbon composite samples, among the other selected materials, were tested at the University of Arizona Dimensional Stability Laboratory. Fabry-Perot laser- interferometric techniques were used to measure dimensional changes to accuracies in the 0.01 ppm range. Coefficient of thermal expansion (CTE), thermal hysteresis and temporal stability test results at 27.5 degree(s)C and 38 degree(s)C are reported here. The test results indicate that this carbon/carbon composite material, made from 2D fabric and pitch base fiber, appears to be the best among all tested nonmagnetic materials. A CTE of -1.5 ppm/$DEGC over the temperature range of -48 degree(s)C to +52 degree(s)C is reported here along with a temporal stability <EQ 1 ppm/year. However, demonstration of a relatively high thermal hysteresis within the temperature range of -48 degree(s)C to +52 degree(s)C was unexpected and a cause for further evaluation. A possible procedure to resolve this issue and an alternate carbon/carbon material design are also suggested here.

It is well known and described in any geometrical optics textbook that the axial as well as the magnification chromatic aberration may be corrected in a system formed by a pair of thin lenses separated by a certain distance, using only one type of glass. However, it is not so well known that these aberrations may be also corrected in a single thick lens.

When testing an aspheric wavefront with any digital interferogram evaluation method, like phase shifting interferometry, Fourier interferometry, or with a spatial carrier analysis, there is a limit to the maximum degree of asphericity if a null compensator is not used. An analysis of this limitation using different interferogram interpretation methods are described.

It is well known that in Talbot imaging the so called autoimages are reproduced with unit magnification with a constant axial separation known as Raleigh's distance. When the incident wavefront is not flat but spherical, the autoimages are reproduced with magnification. The purpose of this paper is to show that in this second case the images are also curved, with a radius of curvature that depends on the curvature of the incident wavefront.