An algorithm has been developed for phase unwrapping data that has significant noise content or phase variations. Existing unwrapping algorithms typically operate on a point by point basis. A faulty unwrapping decision will produce an error which will propagate through the rest of the array. The simpler algorithms are sensitive to noisy data or large phase variations. A new algorithm unwraps the data by identifying regions where there are no phase unwrap discontinuities. The regions are then unwrapped by conparing the edge of the region with adjacent regions; and shifting the entire region by 2*pi.

Stylus surface profiling instruments have found application in the characterization of microroughness. Recently, Al-Jumaily [1] has compared data obtained using a stylus profilometer and an optical scatterometer to characterize a metal surface. The stylus profilometer data was found to be inconsistent with the optical data. In resolving this discrepancy, the "transfer functions" of the instruments were identified as the source of the disagreement. Upon investigation of the stylus properties using a computational model, the stylus is found to provide a nonlinear, lowpass filter-like measurement of surface structure. The data provided by the stylus instrument cannot be easily post-processed to give an accurate profile of the surface. These results will be discussed.

A useful way to present scatter data is scattered light power density (dPs/dws) normalized by the incident light power and plotted as a function of angle from specular. Nicodemus pointed out that if this quantity is also normalized by the cosine of the angle between the surface normal and the direction of scatter (Os) that the resulting expression was the differential scattered radiance normalized by the incident irradiance[1]. This expression has become known as the bidirectional scattered (reflectance or transmission) distribution function (BSDF, BRDF or BTDF)[2].

Bidirectional transmittance distribution function, BTDF, measurements of low scatter optical materials require low scatter beam dumps to dissipate energy when the measurements are made at angles away from the specular beam. Many laboratories use beam dumps without knowing their scatter characteristics. We have made BRDF measurements at 0.6328 μm of beam dumps consisting of painted glass test tubes and a stack of razor blades. Low reflectivity flat surfaces, including Martin Black, Nextel Suede Coating, black felt and anodized aluminum were also measured. Results show that when compared with the BRDF measured for a flat surface coated with Martin Black, test tubes with low reflectivity black paint offer 1.5 to 2 orders of magnitude improvement. For flat surfaces, the BRDF of black felt is within a factor of 2 or 3 of that from Martin Black. When using the best performing beam dump, measurements verify that scatter from the beam dump can corrupt transmissive sample data at large angles in a manner not predicted by instrument signature measurements.

When measuring scattered light as an indication of component quality, the measurement device's own scatter and beam profile limit the minimum angle from specular at which scattered light from the test sample can be measured. The broader the focused specular beam, the more difficult it is to make measurements at low angles. It is of interest to limit system scatter and the instrument's beam profile (signature) when truing to make low angle scatter measurements.

The roughness and texture of rough fused-silica surfaces can be characterized by an infrared ellipsometer operating at 5-μm wavelength and at multiple angles of incidence. Anisotropy of the rough surface layer is included in the ellipsometric calculation based on the effective medium theory. The standard deviation of the measured points differs from the theoretical predictions by only two time the precision of the instrument (±0.01) deg in polarizer, analyzer, and angle of incidence). The effective thickness deduced by ellipsometry agrees with the average rms roughness measured by a stylus profilometer. The depolarization factor deduced by ellipsometry can distinguish the textures of the rough surfaces, and it agrees with the average height-to-half-width ratio of voids by stylus profilometry.

The method of stationary phase applied to the boundary wave formulation of Kirchhoff's diffraction theory can be used to approximate the diffracted field from a curved edge that is illuminated by a spherical wave. The resulting equations for the asymptotic field are very simple (only basic trigono-metric functions and square roots are involved), but diverge when the observation point approaches the edge, the geometrical shadow boundary or the focus of the incident beam. These singularities can be removed if additional terms are introduced that force the asymptotic field expression to match the known values for the actual field in these regions. The resulting approximate expression for the total field is continuous and finite throughout space even though it is conveniently expressed as the sum of two discontinuous fields, a geometrical optics component and an edge diffraction component. Numerical calculations indicate that this formulation agrees remarkably well with exact "closed" form solutions that require the evaluation of complex Fresnel integral functions. In addition, the method can be directly applied with little modification to problems involving Gaussian beam illumination or multiple edges (e.g. slits and circular apertures).

The angle-resolved scattering measurement is an important indication of the fabrication errors and manufacturing limitations in the emerging technology of binary optics. A simple instrument is described which is capable of measuring scattered light from 1 degree to 0.01 degrees or closer to the main transmitted beam, and down to levels of one-billionth of the peak intensity. Scatter measurements are reported for a binary optic and are compared to the power spectral density function determined by a WYKO profiler. It is found that the binary fabrication process has increased the near-angle scatter by about a factor of 30X the scatter from the smooth surface. The power spectral density measurement does not compare well with the scattering data.

Light scattered by optical components is becoming an increasingly troublesome problem in many modern optical designs. Serious attention is now being paid to this issue by several government and industry labs who are using, or are planning to use, scatter measurements as acceptance criteria for optical components. One of the difficulties associated with scatter measurements is the large number of variables that can vary the scatter distribution. In addition to sample parameters, such as roughness, bulk defects and contamination, there are sample independent parameters such as polarization, angle of incidence and wavelength. Separating the various effects is not trivial; although, there can be strong economic motivations to do so. The usual approach has been to make scatter measurements under the conditions expected for actual use--that is, to use the polarization, incident angle and wavelength that are intended for eventual use to make the scatter measurements. Polarization and incident angle are relatively east to adjust in most instruments, but generating different wavelength capabilities is more expensive. In addition, the variable of incident angle has already been examined for the case of reflective optics. [1] This paper examines the possibility that scatter measurements made at one wavelength can be used through a process commonly referred to as wavelength scaling to predict scatter at other wavelengths.

The first serious attempts to measure optical scatter and use it to infer surface finish quality came about through the use of total integrated scatter (TIS) measurements. [1,2] In the early 1970's, one of the ASTM study groups ran a series of round robin measurements to determine the validity of comparing (TIS) measurements from one lab to another. Initial results were very discouraging. TIS values varied over orders of magnitude between labs and measurements were difficult to repeat from one round to the next at the same lab. Slowly, experience was gained in reducing operator error, limiting contamination problems and recognizing basic differences between the instruments under use. The importance of surface spatial frequency bandwidths was recognized and comparison results showed some improvement. In the mid-seventies, measurement of scatter, as a function of angle from specular, was used to obtain more information about surface finish. [2,3,4,5,6] The scatter research of the 1970's is now being combined with the computers of the 1980's to produce fast, accurate scatter inspection systems to help meet the increased demands for low scatter optics. [2,7] Although most of these systems produce the bidirectional scatter (reflectance, transmission) distribution function (BSDF, BRDF, BTDF), some are capable of producing surface statistics as well. The BRDF can be used to calculate a surface power spectral density (PSD) function, which in turn provides values of root mean square roughness and a transverse length parameter. The question of how these instruments relate to the surface statistic nproduced by surface profiling instruments is now being studied. [8] More basic, however, is the old question of whether BRDF (or PSD) measurements can be repeated from lab to lab. The authors decided to do a comparison between a Lawrence Livermore National Laboratory instrument, the Angle Resolved Scatterometer (ARS) [2], and a Complete Angle Scatter Instrument (CASI) developed at Toomay, Mathis & Associates. [7]

Several methods besides the conventional grind/lap/polish are available for working metal optics such as laser scanning polygons. Among the more interesting from a cost standpoint is the single point diamond-turned surface; in one operation an optically flat surface can be produced at an exact angle and position. A question remains, however: will the periodic machined grooves on the optical surface diffract sufficient light so as to distort the primary image formed by the optical system, and will the scattered light interfere with the function of the laser scanner to produce accurate, cosmetically acceptable images?

The use of an ellipsometer as an in situ thin film deposition monitor is usually complicated by the calculations required to arrive at an estimate of the index and thickness values. In general, the ellipsometer parameters Φ and Δ are derived from the measured readings. The calculation for index and thickness from the (Φ and Δ values is by successive approximation and can require considerable time. Because of this, real-time control is not possible even for modest evaporation rates. The direct use of the Fourier coefficients of the signal from the ellipsometer analyzer can significantly increase the data acquisition rate. One quick way to analyze the data from the ellipsometer is to compare the numerical Fourier analysis of the ellipsometer signal with the expected values calculated prior to the deposition. Several commercial ellipsometers can provide such a signal for accurate layer thickness measurements, in near real-time, during the thin film coating process, thus, enabling computer control of multiple evaporation sources. Variations of the measured ellipsometer Fourier parameters can provide a great deal of information on the index, thickness, and inhomogeneity of the film during growth. A method for realizing the above is presented, along with examples of films grown using this technique.

The lanthanide trifluorides show promise as vacuum ultraviolet (VUV) coating materials. The optical properties of single-layer coatings vary with deposition temperature, and with ion-beam energy and current density. The optical constants, stoichiometry, durability, moisture adsorption, and crystallinity are studied for trifluoride films made under a variety of deposition conditions.

This paper discusses multifaceted mirror configurations for transforming an arbitrary laser beam irradiance pattern into a uniform irradiance pattern. Three configurations are presented and compared, one of which allows for the elimination of diffraction effects. Aberration effects associated with the relaying or imaging of the irradiance pattern and a novel technique for correction are also discussed.

In this paper an inherent effect of laser diodes is presented to explain considerable disturbances like mode hoppings in optical communication systems. In general the switching processes of the laser modes are clarified. The effect is connected with an extended mode competition in index guided Fabry-Perot lasers and bases on a gain ripple in longitudinal direction. This leads to a distributed positive optical feedback. One result of the increased mode competition are fast switching transients of the laser modes (mode-hoppings) as can be measured in time-resolved spectra of index guided 1.3μm diodes.

A static laser model is presented based on travelling waves inside an active Fabry-Perot resonator with optical feedback from an external boundary surface(e.g. a fiber coupling arrangement). Using complex optical transfer functions for the electric fields and rate equation for the carrier density, the laser output spectrum can be computed with the insertion of conditions such as optical feedback, gain-compression and spectral hole burning. The model allows better comprehension for internal interdependence.

In recent years, there has been considerable interest in the study of various physical properties of ultrathin films of optoelectronic materials in the presence of size quantization where the restriction of the motion of the carriers in the direction normal to the surfaces of the film (say, the z-direction) leads to the quantization of the wave vector along z-direction. In the presence of a quantizing magnetic field along the above direction, the free motion parallel to the film is also quantized forming Landau levels and exhibits diamagnetism (X d. ) Moreover, the spinning motion of the electrons leads to paramagnetism due to spin-splitting of Landau leves (Xp). In the present communication, an attempt is made for the first time to investigate the dia-and paramagnetic susceptibilities on the electrons ultrathin films of A-4-LBX opto-electronic materials in the presence of magneto-size quantizati:m within the frame work on the generalized k formalism and taking into account the different types of anisotropies of the energy spectrum. It is found taking n-CdGeAs2 as an example, which finds extensive applications in non-linear optoelectronic materilas and light emitting diodes, that tne values of Xd and Xp are much higher than their bulk values in CdGeks2 and incL.ease with increasing carrier degeneracy. Besides, they also exhibit oscillatory dependence with the film thickness and are in excellent qualitative agreement with the experimental observation as reported elsewhere. In addition, the corresponding well-known expressions of the above type of materials having relatively large band gap are also obtained from the expressions derived.

A diamond turned, super polished mirror surface was observed using an Olympus acoustic microscope. Subsurface tool marks, porosity, grain size and coated metal thickness were measured.

Procedures for measuring the linear optical properties of small, transparent crystals are described. Using a spindle stage refractometer, the refractive indices for light from 0.38 to 1.10 μm can be determined. The methods are employed to study new nonlinear crystals to evaluate their potential as second and third harmonic generators of light at 1.064 μm. The measurements can be made on single crystal fragments as small as 50 μm, thus permitting preliminary evaluations to be made prior to extensive crystal growth efforts.

Beryllium mirrors have shown excellent stability over a wide range of thermal conditions. Experiments were conducted using flat mirrors which remained flat from room temperature down to 89 degrees K. LUPI interferometer measurements confirmed calculated data. The surface was monitored during the thermal cycle from room temperature to 89°K. The results have good agreement with calculation. For a spherical mirror, the radius of curvature changes as predicted. For an elliptical mirror, the radius of curvature at the vertex changed but eccentricity remained the same.

In this article, according to diffractive theory, the author discusses the problem of optical theory in differential inspection by optics, that is , the change of the shape of light aperture and the change of the size and selection of the position of the field stop of the optical system in the Infrared Dynamic Automation sorting Instrument for example, and deduces and calculates the exact spatial spread formulas and their approximate formulas for calculating the energy of a photoelectric receiver for light apertures of different shapes, and analyzes the influence of the change of the size and the selection of the position of the field stop on inspection accuracy. The differential inspection method by optics has rarticulr advantages over other methods. This inspection is based on the output intersection signal due to two beams, and thus various interference factors have the same influence on the two beams, therefore inspection errors are greatly reduced. We take an example--Infrared Dynamic Automation Sorting instrument. This instrument also has high brightness and low threshold, adapting itself to production circumstance. Its wavelength is in the infrared field.

Extraction of empirical water droplet impingement characteristics from records of wind tunnel dye-tracer experiments has been an extremely time consuming process in the past. Described are a method for extracting impingement data by measuring optical reflectance and a computer controlled laser reflectometer which was designed and built for making these measurements. The instrument increases the efficiency of the data extraction process by at least an order of magnitude. The accuracy of the reflectometer is discussed and some results obtained with the reflectometer are presented. The results are used to verify three-dimensional particle trajectory computer codes, which may then be used for design analysis and certification of aircraft anti-icing/de-icing systems.

A new optical design has been incorporated into an instrument for use in digital imaging and quantitative analysis of fundus images. By using an optical design program, in combination with custom electronics, we have developed a new instrument for fundus imaging.

A discussion of field-of-view (F.O.V.) and expected wavefront errors for the standard solid and open cube-corner retroreflector (C.C.R.) is compared with a catseye retroreflector (C.E.R.). The asymmetry of the C.C.R. F.O.V. will be compared to the completely symmetrical F.O.V. for a C.E.R. Ray trace spot diagrams for a catseye design will be presented that show the interaction on requirements for (clear aperture)-(wavefront quality)-(field of view). A discussion of retroreflector design considerations will show that a catseye retroreflector design performs well at large field-of-view angles where a basic C.C.R. has no performance. The thermal considerations, when using a C.C.R. in an outdoor environment, would add to the design complexity for mounting the elements of a hollow or open C.C.R. The catseye retroreflector, while having tight manufacturing tolerances, would be relatively free of mounting design complexity. The simpler mounting design requirements are obtained from a less critical alignment requirement for the assembled C.E.R. The polarization effects that a C.C.R. would introduce into a return beam would be totally eliminated by a C.E.R.

In recent years, the need for wide-angle, unobscured, all-reflecting optical designs has increased significantly. This paper takes a look at several of these types of designs, and compares their performance and limitations. Each example have constant f-numbers and entrance pupil diameter, but the wide-angle strip fields-of-view are varied. This work provides the optical designer with a measure of the optical design complexity required for his specifications.

The change in image caused by turning reflecting prism in a large angle has been discussed in this paper. Moving image characteristic of the reflecting prism is expressed by characteristic direction and image deflection extreme value plane, it provides the theory basis for designing, scanning and tracing instruments.

It is shown that the optimum size of a polygonal mirror scanner for a given scan angle, entrance pupil diameter and beam folding angle of an afocal optical system is determined by the position of the axis of rotation with respect to the centre of the exit pupil. Equations for the minimal size polygon and its location are derived in the present work. This optimum size is shown to yield a facet length identical to that of a planar oscillating scanner mirror placed at the same exit pupil and for the same given parameters.

Several beam-combining schemes for on-axis and off-axis optical system layout are presented. The on-axis approaches include two crossed plates with dichroic coatings placed at 90 deg, with respect to each other, and a pentaprism arrangement. The off-axis layout of the cathode ray tubes (CRTs) requires that the images be combined at the display screen. These image-combining approaches are compared for the standard television rates of 525 lines and the high-resolution television at 1200/2000 lines under development in Japan. The optimal color-combining scheme and the optical system that is designed with it depend on the specific performance requirements of the projection optical system. For the high-resolution requirements, an on-axis optical layout is necessary. For the high-performance, high-color fidelity, and high-resolution projection systems, which are expected to fit into a small volume of space such as a space station display or a cockpit panoramic display, a folded configuration with either crossed plates or penta-prism plates will result in an optimum color display. A slightly longer optical system will be needed if the color performance associated with the plate pentaprism layout is desirable.

Dynamic on-line color separation measurement of printed graphic images is a process which is difficult to accomplish in real time. Variations in the paper and ink quality can significantly add to the difficulty in measuring the area coverage of each of the primary colors. For some applications, this type of measurement must often be performed while the graphic image is moving, thus requiring the sensor to both measure and process the image data in real time. An optical technique for primary color separation in graphic color ink images will be described. A suitable system model has been developed which includes the contributions from the optical source, paper, inks and system optics. Detection algorithms and computer software have also been developed to simulate the color separation process. In addition, a laboratory detection system has been assembled and used to test the validity of the system model. The system model, algorithms, and the experimental detection system will be discussed, and the results of this color separation capability will be presented for both the simulation mode and the actual laboratory measurement mode.

Methods for testing amorphous life, erasing rate and amorphizing sensitivity in situ are presented. SbxTe1-x films are characterized using these methods and it is shown that the fastest erasing rate and the longest amorphous life can be achieved at almost the same compositional value of x = 0.4. Sb-Te disk properties are studied with a one-beam head whose focused beam diameter is 1.4 μm. The carrier-to-noise ratio for 1.0 μm diameter amorphous marks recorded at a mark pitch of 2.5 pm is 47 dB. An investigation of erasing performance with the circularly focused beam revealed that the crystallization rate is fastest at a temperature comparatively lower than the melting temperature.

The focusing grating coupler (FGC) can be constructed using holographic techniques. Due to the wavelength scaling between the construction of the FGC and its final end-use operation, aberrations exist ill the final spot. A design method is demonstrated, using a commercially available ray trace code, that models the FGC as a holographic optical element (HOE). The method also includes techniques to eliminate the aberrations due to the wavelength scaling.

The theory of Gaussian beam propagation assumes a perfect, infinitely wide beam profile. In real life, when such beams pass through limiting apertures such as lenses, the profile is truncated. Even tiny amounts of truncation can have profound effects on subsequent beam parameters: clipping as little as one percent of the beam power, for example, can result in a ten percent divergence increase. Dark rings are created, and defocussing can create patterns with dark centers. For small truncation ratios (aperture/beam radius), the aperture is almost uniform and the focussed output approaches the traditional Airy disc pattern. In this paper, we will present a summary of the various truncation effects, with special attention to the most common case of a round aperture centered on a circularly symmetric beam. A computer program, based on one written at NASA, was used to generate plots of divergence versus truncation ratio for this case. Also discussed briefly are some of the possible deviations from circular symmetry: square beams and apertures, knife-edge obstructions, decentered apertures, and aberrations. Finally, the results reported by others have been summarized, with an extensive bibliography.

This paper examines the polarization aberrations in optical systems of isotropic radially symmetric weak polarizers in the paraxial approximation. Optical systems which fit this description are composed of uncoated and coated lenses and mirrors. Polarization aberrations are variations in phase, amplitude, and polarization state of the electromagnetic field across the exit pupil. Some are dependent on the incident polarization state and some are not. Expressions through fourth order for phase, amplitude, linear polarization, and linear retardance aberrations are derived in terms of the chief and marginal ray angles of incidence and Taylor series expansion coefficients of the Fresnel equations for reflection and transmission at interfaces.

An alternative to Damped Least Squares (DLS) optimization of lens systems is described that involves Generalized Simulated Annealing (GSA) techniques in conjunction with DLS. The resultant method can often overcome local minima and boundary value problems associated with optimizations conducted with DLS methods exclusively. The process is particularly useful during the intermediate design stages. As a result fewer demands are made on the designer to intervene in the optimization of a system to a given stage and better quality designs can be produced by less skilled designers. Searches for improvements to existing designs can be automated.

The method of Generalized Simulated Annealing is explained and its merits as applied to lens design are discussed. A lens design program using this method is described, its use on a monochromatic doublet and other lens systems is detailed, and improvements to the method are suggested.

A 1:1 Offner mirror system is modified to work as a grating spectrometer for the infrared by placing a grating on the secondary convex mirror of the system. Slight adjustment of the configuration combined with tilt of the secondary provide the necessary degrees of freedom to correct for astigmatism of the system. Additional control may be obtained by using a holographic optical element (HOE), constructed to add necessary compensating aberrations. Details of the best configuration and the limitations of performance are presented.

The rotatable shearing plate interferometer provides a fast and simple manual method of measuring defocus, astigmatism and coma in a collimated laser beam. The shearing plate is mounted at a 45 degree angle relative to the incident beam. The plate in its housing is rotated about the axis of the incident beam. This allows the beam to be sheared in the horizontal, the vertical, or any other direction. Astigmatism and defocus can be calculated from fringe tilt measurements taken at any three angles, for example, 0, 45 and 90 degrees. Coma can be calculated from fringe curvatures measured at 0 and 90 degrees.

Wide aperture, high-dynamic range, solid-state scanning diode arrays up to 1 inch with 1024 diodes have been available for chemical and astronomical spectroscopy instrumentations. However, the expanding scientific applications, as in the detection of nuclear particles, has created demands for longer diode arrays with a wide aperture; i.e., 25 microns by 2500 microns for each pixel. Driven by these demands, an array with 2048 contiguously aligned diodes was designed and developed. Because of the stringent requirements for dynamic range and milliseconds readout time, the array was partitioned into segments with multiple video lines accessing the diodes. Using this structure, the array die length was just over 2 inches with four segments with four sets of video lines. Associated with each segment is an independent shift register which controls the diode readout. This layout structure provides a variety of readout configurations, among them the sequential readout mode. An additional aspect of the array is its mechanical structure in the package design. It was designed to mate with an especially designed fibre-optic face plate which was mounted to the die. This paper discusses the new scientific device's design, its structure, its implementation, and its measurements.

The design of a wide field imaging camera suitable for use with a glancing incidence X-ray telescope is complicated by the sharply concave nature of the optimum focal surface of such a telescope. We are currently designing such a camera made up of a mosaic of Charge Coupled Devices (CCD's) intended for flight aboard the Advanced X-ray Astrophysics Facility (AXAF). We discuss the design rationale and tradeoffs and present our layout for the imaging CCD array. We also discuss the related issue of optimizing performance of transmission objective gratings and present the array of CCD orientations suitable for this problem.

The VIDEK MEGAPLUS camera is described. The MEGAPLUS is a high resolution charge coupled device (CCD) camera designed for scientific and industrial imaging applications. The camera features a solid-state full-frame imager containing 1320 H x 1035 V light-sensitive pixels. The camera's design and features are discussed.

The figuring of large optical components using mechanical techniques is a time and money consuming operation. Neutral Ion Beam Figuring (IBF) is shown to be a practical and flexible alternative to mechanical figuring. Ion Beam Figuring is performed by directing a broad beam high current ion source (Kaufman type) onto an optic in a carefully controlled manner, removing substrate material by ion beam sputtering, and resulting in a specified surface figure. The IBF technique is shown to have some interesting performance advantages over other methods, including very high removal rates, minimal surface damage, and no edge effects. Practical issues involving IBF are discussed and experimental results using the UNM prototype IBF machine to figure a 30cm fused silica optic are presented. Scaling problems are identified and discussed.

The basic electroforming process exactly reproduces finely finished surface details from a master mold or mandrel. The process promises high potential for fabricating imaging quality optical components. This requires, however, the electrodeposition to be nearly stress free to attain accuracy within fractions of a wavelength (1.06 um) of light. Prior to this work, this level of accuracy had never been accomplished. This paper presents the advances made to the method and the process of electroforming in creating the routine production of imaging quality nickel metal mirrors. Work to date includes the electroforming of self-aligning two mirrored telescopes; the development of a large electroforming workstation to produce several mirrors simultaneously, and the development of a process for electroforming secondary mandrels. A generic process overview is presented along with opto-mechanical testing and results. Also included is a description of the general computer controlled closed loop process (Martin Marietta U.S. Patent #4,647,365 & #4,648,944). The work described was performed at Martin Marietta Corporation (Orlando) with the majority conducted under contract DAAHO1-85-C-1072 for the U.S. Army Missile Command, Redstone Arsenal, August 1985 through August 1987

The effective zonal correction using a ring tool off centered will be presented. The diameter of the ring polisher and shift of the tool center defines the zone under correction. The removal rate is consistent. An example of a 13 inch diameter F/0.77 beryllium mirror figuring procedure is described.

Contouring with computer numerically controlled (CNC) machines can be accomplished with several different tool geometries and coordinated machine axes. To minimize the number of coordinated axes for nonsymmetric work to three, it is common practice to use a spherically shaped tool such as a ball-end mill. However, to minimize grooving due to the feed and ball radius, it is desirable to use a long ball radius, but there is clearly a practical limit to ball diameter with the spherical tool. We have found that the use of commercially available toroidal wheels permits long effective cutting radii, which in turn improve finish and minimize grooving for a set feed. In addition, toroidal wheels are easier than spherical wheels to center accurately. Cutting parameters are also easier to control because the feed rate past the tool does not change as the slope of the work changes. The drawback to the toroidal wheel is the more complex calculation of the tool path. Of course, once the algorithm is worked out, the tool path is as easily calculated as for a spherical tool. We have performed two experiments with the Large Optical Generator (LOG) that were ideally suited to three-axis contouring--surfaces that have no axis of rotational symmetry. By oscillating the cutting head horizontally or vertically (in addition to the motions required to generate the power of the surface) , and carefully coordinating those motions with table rotation, the mostly astigmatic departure for these surfaces is produced. The first experiment was a pair of reflector molds that together correct the spherical aberration of the Arecibo radio telescope. The larger of these was 5 m in diameter and had a 12 cm departure from the best-fit sphere. The second experiment was the generation of a purely astigmatic surface to demonstrate the feasibility of producing axially symmetric asphe.rics while mounted and rotated about any off-axis point. Measurements of the latter (the first experiment had relatively loose tolerances) indicate an accuracy only 3 or 4 times that achieved by conventional two-axis contouring (10 AM as opposed to 3 pm rms) The successful completion of these projects demonstrates the successful application of three-axis contouring with the LOG. Toroidal cutters have also solved many of the drawbacks of spherical wheels. Work remains to be done in improving machine response and decreasing the contribution of backlash errors.

The Foucault test is a sensitive method of testing a curved mirror surface during the fabrication process. A skilled optician can readily interpret the results of the test and correct the surface accordingly. However, comparisons between different surfaces are more difficult. Fabricating several mirrors to the same focal length can be facilitated by a further quantification of the Foucault test. If h(r) is used to denote the deviation of the mirror surface from a parabola of focal length Fo, then the focal length F at a given radius r from the center of the mirror is given in terms of the derivative h'(r) by- F(r) = Fo 2Fo2 h'(r)/r The Foucault test measures F(r) - Fo and thus can be used to determine h'(r). By fitting a polynomial to hi(r) and integrating term by term, the deviation h(r) from the ideal surface can be determined. Using this knowledge of the surface figure, we have worked four 8-in diameter f/1.8 parabolas so as to bring them to a common focal length. One mirror was chosen as a reference and the focal lengths of the others were worked in the direction of its focal length. Often, the corrections suggested by the requirement that the focal length be changed were different from the corrections that would have been made to obtain the nearest parabola. The focal lengths of the final surfaces were the same to within ± 0.0005 inch (approximately one part in 30,000).

This paper discusses the application of interferometric subaperture testing techniques to a two-dimensional optical surface profiling instrument. The optical profiler, a phase-modulated interference microscope, enables the acquisition of a high density of data over a restricted range. The extent of a profile measurement range is determined by the microscope objective used in the interferometer. However, by overlapping a series of collinear interferograms it becomes possible to increase the limited field of view of this instrument. An outline summarizing the instrument and the algorithms used to concatenate interferograms is presented, as well as experimental data obtained from the instrument. Various methods for characterizing the errors that are introduced by the concatenation of a series of interferograms are discussed. Results of a Monte Carlo simulation study on computer-generated data sets is analyzed to further illuminate error sources and limitations of this technique.

A laser measurement system for precise and fast positioning of an object has been developed. When the speed is low, the movement of the object is measured by comparing the phase change of a light reflected by the object with the phase modulated by an electro-optic crystal (an active device by which the optical phase can be controlled by applying a voltage thereto). When the speed is high the movement is measured using a fringe counting technique. The system achieved an accuracy of 4nm, and a maximum allowable measurement speed of 1100mm/s.

A grazing incidence interferometer was developed at LMSC to sample the surface figure of large adaptive mirrors along narrow swaths utilizing small optical components mounted along the perimeter of the mirror. Preliminary tests have been conducted to determine the statistical limitation to the figure sensing resolution due to vibration of optical components and electronic noise. The results of these tests are discussed and plans for additional tests described.

This article presents two techniques to test the quality of corner reflectors. The first technique uses an autocollimation setup while the second one is based on interferometry. Several corner reflectors were tested with both methods and the results indicate that the characteristics of a corner reflector as provided by the manufacturer are generally not sufficient to select the most appropriate corner reflector for a given experiment.

In evaluating the performance of a mirror by interferometric methods, a standard procedure used by the optical engineer is to obtain the optical path difference (OPD) map from the fringes of the interferogram and to express the differences in terms of a least squares fit of the classical Zernike polynomials. Since the Zernike polynomials represent the aberrations inherent in the optics, the engineer can determine whether or not the optics will meet performance requirements and if not, what measures need to be taken to reduce the aberrations. This paper examines the least squares fitting process from a statistical point of view and points out the necessary steps and precautions which must be taken to ensure that the analysis rests on a firm foundation so that the conclusions drawn by the optical engineer are warranted. The fitting process is examined from the standpoint of statistical linear regression theory and the following concepts and ideas are introduced: 1) How to determine whether the fit is a good fit and what to do about outliers. 2) Whether the underlying assumptions of normality and constant variance have been met, and, if not, what should be done. 3) How to compute confidence intervals 4) What do the correlation and covariance matrices tell us. 5) How to look at the information contained in the residuals and how to detect influential observations. Regression analysis has proved to be a powerful tool in other fields and there is every reason to believe it can make a significant contribution to optical engineering.

This report describes recent research in application of interferometry to measurement of the aberrations of full spheres using an extension of subaperture testing theory. Theoretical and numerical studies have substantiated the method. Experimental validation has been done by comparison with mechanical roundness traces. Direct comparison is impossible because both methods suffer from misalignment errors. In this paper, a data reduction technique is developed for the mechanical roundness traces and comparison is made of the reduced data from both methods.

It has been proposed that extra-solar planetary systems may be observed if perturbations in star position due to the orbit of Jupiter-type planets could be detected. To see this motion, high accuracy measurements of .01 milliarc second are required over a relatively large field of view. Techniques using a moving Ronchi grating have been proposed for this application and have been successful in ground-based lower resolution tests. The method may have application to other precision angular measurement problems. This paper explores the theoretical description of the method, considers certain of the error sources, and presents a preliminary calculation of the performance which may be achieved.

Numerical analysis and simulation of a technique for automatic alignment of a three-mirror off-axis telescope were carried out using a method of reverse optimization and end-to-end measurements. The techniques uses Hartmann measurements made at multiple field points and multiple focus planes. The reverse optimization method uses the Hartmann data as target values in a standard lens design program and damped least squares optimization to determine the state of misalignment of the system. Once the state of misalignment is determined a single step correction of all misalignments is possible in principle. Our results show that multiple measuring planes make possible a larger capture range, faster convergence, and larger measurement tolerances than does a single measurement plane.

In this paper a design study is described for telescopes to be used in precision astrometry. Specifically, the application is the search for planets outside the solar system. The requirements are stringent because of the need to be spectrally independent, have low distortion, and be free of coma and other asymmetric aberration. The image requirements for astrometry are defined along with two mirror telescope designs for the application. Effects of misalignment and long term stability are considered.

At present, whether the economic benefit of a designed optical system is high is an important mark to judge the optical design level. The "Information -- Price Ratio", the ratio of the spatial information quantity F transferred by an optical system to its manufacturing cost or product price C is proposed , which can be considered as the standard for evaluating the economic benefit of an optical system design in this paper. The calculation formulae of the information quantity are also proposed in this paper. So Four ways to increase the economic benefit are also discussed from the viewpoint of the optical design, and the guided idea and calculation formulae to make the optical tolerance erance are emphatically indicated in this paper. Finally, this paper gives two examples of analysing the economic benefit of the optical system design.

The subject of this paper are new computer procedures that considerably reduce the computing time of polychromatic MTF calculations for electron-optical system of image-converter. The main idea of the method evolves from the procedure which counts the number of electrons separately in strip-shaped regions on the screen. The selection of the electron trajectories is carried out by choosing values for the initial photoelectron parameters so that values of the weight functions for each electron are equal. The polychromatic MTF is calculated as a weighted average of the monochromatic MTFs. Application of our computer programs is limited to systems of cylindrical symmetry but they can be used with arbitrary initial conditions for photo-electrons and spectral characteristics of a given radiation source. The aim of this work is to present special procedures contained in the programs: - automatic, variable step choice of energy and angular coordinates for the photoelectron-emission simulation; - interpolation of the two-dimensional distributions of the endpoints of the electron trajectories on the screen. The last procedure is based on the previously calculated trajectories and takes into account possible asy-mmetric properties of the point spread function. It obtains a large number of endpoints for further analysis from a relatively small number of computed electron rays. Therefore the proposed procedures used for systems with geometrical aberrations result in reduction of the computing time by more than order of magnitude.

An accurate formula for calculating color wave aberration is provided, and the difference between the aberration computed by Conrady's wrong formula and the real aberration is pointed out. At the same time, a new optical design method is put forward.