Search

Gradient-index (GRIN) media can contain stress birefringence resulting from the variation in material composition. Anisotropy in a GRIN rod lens affects ray propagation and can degrade image quality. A technique, believed to be new, for measuring birefringence in GRIN rod lenses has been developed. The change in optical path difference (OPD) for orthogonal polarizations is measured directly. With this method, effects on OPD from standard imaging aberrations are excluded. Birefringence measurements for various GRIN rod samples are presented. The data are compared with results obtained previously by use of a Twyman-Green measurement method. Also, the polarization effects on tilt fringes observed with the direct measurement method and the Twyman-Green method are presented and modeled theoretically. Tilt fringes for large birefringence test cases are also modeled.

Phase-shifting interferometry is the standard method for testing figure error on optical surfaces. Instruments measuring spheres and flats are readily available, but the accurate measurement of aspheres requires null correction. One problem with the general (nonull) testing of aspheres is the loss of common path. Systematic errors are introduced into the measurement by the fringe imaging optics. The sources and types of error are reviewed, as well as their effect on a wave-front measurement. These nonnull errors are predicted generally, with third-order analytic expressions derived for a tilted or a defocused test surface. An interferometer is built to test the expressions. The imaging system is a single lens, nominally image telecentric. Measurements are performed on a test surface defocused from -5 to 5 mm. The resulting measurement bias is shown to be in good agreement with third-order aberration theory predictions.

A gradient-index axicon with its initial focus offset from the back surface was designed with the thin-lens approximation. Two samples were fabricated by means of the time-varying boundary condition diffusion method, which is based on the modified quasi-chemical diffusion model. Intensity profile measurements were taken along the focal region of the axicons. The samples produced extended line foci. From the intensity measurements, the central spot widths and back focal lengths were determined. The peak widths matched theoretical predictions made with the diffraction theory for the samples and showed good agreement with the predicted widths for a pseudo-Bessel beam, showing that the axicon produced a pseudo-diffractionless beam.

Peak-valley accuracy of lambda/20 over a range of 2lambda is not unusual in an interferometric null test. For the larger dynamic ranges of a nonnull test, however, the fringe-imaging optics degrades the accuracy. We classify the errors introduced and analyze them in the context of both general and third-order aberration theory. We can predict the measurement error from known interferometer parameters, and we illustrate this for a single mirror. The errors are tabulated for the specific case of a fourth-order asphere with 100 mum of sag. We show that the third-order approximation is comparable with exact ray-trace results for this case.

Stress birefringence can be found in gradient-index (GRIN) materials because they contain a variation in composition. GRIN glass fabricated by ion exchange may contain stress from two different processes. These include a size difference between the exchange and the diffusing ions and a variation in the thermal-expansion coefficient across the gradient region. The optical properties of the stressed material are polarization dependent, and therefore image quality is directly affected. We examine birefringence in GRIN rod lenses that have lengths more than ten times greater than their diameters. The effects are more easily observed in long rod lenses because of the large optical path lengths.

A new procedure is presented for testing long, radial-gradient-index rod lenses in a phase-stepping Twyman-Green interferometer. In addition, a method for converting the measured optical phase data to the rod's index of refraction profile is reviewed. This procedure was used to measure refractive-index profile dispersions over the wavelength range of 441 to 1064 nm. These measurements provide the first data for refractive-index profiles of rod lenses in the infrared and show the existence of positive dispersion, negative dispersion, and near-infrared dispersion reversal in some samples. The dispersion results suggest the need for modifications to the current glass model.

Night-vision goggle objectives are often composed of six or more conventional lens elements with spherical surfaces and homogeneous refractive indices. Special elements such as aspheres, diffractive optics, and gradient-index materials can be used to reduce the total number of lenses required to meet military design specifications. A study was performed to examine the use of various combinations of these special surfaces to determine the minimum number of elements that can be used to construct the objective system. We present and compare the best resulting designs.

Relay systems in rigid endoscopes can compensate for aberrations in the objective and the eyepiece. Five classes of rigid relay systems are examined: conventional; glass Hopkins; plastic lens, glass-rod Hopkins; modified Hopkins; and gradient index. First-order theory, including achromatization, is developed for these systems. Design results are presented, and aberration, vignetting, and system length trade-offs are analyzed.

The technique of optical differentiation is applied to confocal microscopy for the purpose of quantitative phase imaging. One-dimensional absorptive filters are placed in the pupil of the microscope objective to produce images related to the local phase slope in the object. With suitable signal processing and integration, a quantitative phase profile is obtained. This method is demonstrated in a reflection-based surface-profiling instrument.

A new method for controlling the shape and increasing the maximum index change in the radial gradient-index profile of sol-gel bodies is demonstrated. This is accomplished by modifying the relative rates of the intricate reactions responsible for forming the gradient. In practice the changes reported here are effected solely by varying the leaching conditions. Through the proper choice of a solution to arrest the leaching action, the index change can be maximized for a given shape to double that of the previous technique. A detailed composition analysis of the data reveals that dopant diffusion and precipitation are the dominant factors influencing the observed results.

The composition of the molten salt bath was shown to exert a strong influence on the gradient-index profile that resulted from the ion exchange of silver for sodium. Two types of additives were used to enhance the ion exchange from a base AgCl melt. Both techniques reduced the profile degradation that normally occurred with long diffusion times, while one technique also increased the refractive index change at 0.6328 microm in a regular fashion from 0.06 to 0.15.

Two different aspherical singlets, four types of axial gradient-index singlet, and one radial gradient-index singlet achieving the same performance are toleranced for thickness, curvatures, base index, and special coefficient (aspheric or gradient) sensitivities. The results show that the singlet with the most relaxed tolerances has a linear axial gradient which extends through the lens, followed in order by a singlet with a parabolic radial gradient, a singlet with an aspheric surface on the front, and a singlet with a parabolic axial gradient crossing the first surface.

Two new techniques for altering the gradient-index profile shape are presented using ion exchange of Li(+) for Na(+) in an aluminosilicate glass. By varying the alkali concentration in the base glass and salt melt, the functional form of the index profile is modified to range in shape from convex to concave. The success of these techniques is attributed to the unusual characteristics of the initial system, which are shown to be caused by a nonlinear dependence of refractive index on dopant concentration.

This study investigates the role of gradient-index materials in the design of Cooke triplets for use as 35-mm format photographic objectives. Cooke triplet designs are presented with different types of gradient-index profiles. Both linear axial and shallow radial gradients are shown to provide effective control of spherical aberration and astigmatism. In particular, a Cooke triplet with a combination of both linear axial and radial gradients attains performance comparable to a six-element double Gauss lens. In virtually all cases, the use of gradient-index components improves the Cooke triplets' performance significantly.

A set of simple analytic expressions has been developed for calculating the third-order aberration coefficients in weak or nearly thin axial and radial gradient-index lenses.

A series of TiO(2) flint glasses has been developed for producing GRIN glass by ion exchange. Both positive and negative axial and radial gradients were fabricated in high index glasses by exchange of Li(+) for Na(+) and Na(+) for Li(+), respectively. Index changes to 0.05 and depths up to 6 mm were achieved and a wide variety of index profiles are shown.

Phase-locked moiré systems have the advantage of rapid data acquisition and accuracy of better than one twentieth of the fringe spacing. In conventional moire systems data acquisition is performed by making a photographic plate and taking measurements from the plate either visually or with a microdensitometer. This is slow, and the accuracy is about one-quarter of the fringe spacing. The phase-locked system is more accurate and permits a more favorable trade-off between accuracy and working depth. The equations governing moire contouring are examined, and the theory of phase-locked moire fringe analysis is presented. The design and operation of the phase-locked moire contouring system are described, and the results of measurements made with the instrument are presented.

The ring-shaped polisher analyzed by Vinokur is modified to be a high-speed polisher for aspherical surfaces. The mathematical modeling of the ring polisher has been reformulated to examine the uniformity of surface polishing over the workpiece. The fabrication of a ring polisher is described, and experimental results of direct polishing of ground aspherical surfaces are discussed.

A schlieren system of the z type has been designed and used to characterize the chromatic variation of index of refraction gradients. Samples of gradient-index glass produced by Bausch & Lomb (Rochester, New York), Schott Optical (Mainz, West Germany), and University of Rochester (Rochester, New York) have been characterized.

A two-element axial gradient-index binocular objective has been designed and fabricated by the ion exchange technique. A prototype system has been assembled and tested.

The theory of multiple-wavelength ac interferometry has been developed. A system has been constructed and used to measure simultaneously the index of refraction profile and the chromatic variation of the index of refraction gradient. Samples of gradient-index glass manufactured by Bausch & Lomb (Rochester, N.Y.), University of Rochester (Rochester, N.Y.), and Schott Optical (Mainz, West Germany) have been characterized.

Compact Luneburg-type lenses of rectangular outline as viewed from above have been made by thermal evaporation of As2S3 glass onto single-mode LiNbO(3):Ti waveguides through suitably shaped masks and subsequent exposure of the glass to ultraviolet light. The best lenses had speeds of f/5.5 at an aperture of 10 mm and focal spots at reduced aperture about 1.2 times the diffraction-limited size. These lenses have a field of view of at least 25 degrees inside the waveguide.

Lenses with radial gradients can exhibit zero Petzval curvature of field. This class of lens is examined in terms of its other third-order aberrations.

The solution of the Euler-Lagrange equations for a power series expansion of the ray path yields a ray trace algorithm for an anamorphic gradient-index medium.

A study of gradient-index eyepieces was conducted. The general performance of homogeneous eyepieces having two and three elements was examined. Axial gradients were introduced into the eyepieces in an attempt to increase the half-fields of view to 25 degrees and extend the eye reliefs to 12 mm. The homogeneous eyepieces examined were of the Huygenian, Ramsden, and Kellner configurations. These eyepieces were scaled to the specifications of f/13, 21.4-mm focal length, and magnifying power of 10X. These classic systems were optimized to produce two- and three-element homogeneous eyepieces to determine how homogeneous systems could perform with the extended eye relief and larger field of view. Axial gradient eyepieces having two and three elements were designed to the same specifications. The balance of third-order aberrations, color, and distortion was maintained or improved compared to the homogeneous systems.. The additional degrees of freedom associated with the gradient made it possible to extend the eye relief and increase the field of view of these eyepieces.

The refractive index as a function of spatial coordinate in three Czochralski grown germanium-silicon alloy GRIN crystals has been measured using ac interferometric techniques. The interferometer is capable of high phase resolution and is computer controlled for real-time data processing. The measured refractive-index profiles were compared to theoretical profiles which were calculated from a model based on the segregation effect of silicon in germanium.

A new instrument for measuring the evolution of index profiles during diffusion in hot (500 degrees C) glass is presented. This instrument, called the oven interferometer, has a spatial resolution of 10 microm at 0.6471 microm and a phase resolution of lambda/50. The development of index profiles with both time-dependent and constant boundary conditions is shown.

The possibilities of transmitting spatial information through a long gradient-index rod are presented. Spatial resolution vs rod diameter are optimized for both visible and IR transmitting systems.

A 20-cm clear aperture modified Twyman-Green interferometer is described. The system measures phase with an AC technique called phase-lock interferometry while scanning the aperture with a dual galvanometer scanning system. Position information and phase are stored in a minicomputer with disk storage. This information is manipulated with associated software, and the wavefront deformation due to a test component is graphically displayed in perspective and contour on a CRT terminal.

Three- and four-element eyepiece designs are presented each with a different type of radial gradient-index distribution. Both quadratic and modified quadratic index profiles are shown to provide effective control of the field aberrations. In particular, the three-element design with a quadratic index profile demonstrates that the inhomogeneous power contribution can make significant contributions to the overall system performance, especially the astigmatism correction. Using gradient-index components has allowed for increased eye relief and field of view making these designs comparable with five- and six-element ones.

A two-element gradient-index photographic objective was designed. It operates at f/2 and has a focal length of 50 mm. The half-field of view is 21.8 degrees . The design is compared to the six-element new double Gauss photographic objective and performs well in comparison.

The phase structure of the optical field diffracted from a straightedge has been measured using an ac interferometer. The measured phase distribution is in good agreement with the predictions of scalar diffraction theory.

The subject of gradient-index optics dates from the 1850s. However, only in the last 10 years has it been possible to design lenses, manufacture materials, measure the properties, and fabricate finished lens elements. The current status of gradient-index optics is reviewed.