Testing Aspheric Surfaces Research Articles

Dual beam generation at a ray caustic by a multiplexing computer-generated hologram

Computer generated holograms (CGHs) are used for testing aspherical surfaces. They are also used for certifying null lens systems that are in turn used to test large aspheric mirrors. We demonstrate that, in order to minimize size, a null-corrector-certifying CGH can be located at a ray caustic. This placement minimizes the required size of the CGH and so makes it possible to certify some null correctors that otherwise, due to current size limitations of high-precision CGHs, could not be certified. Fabrication limits of precision CGHs are in the size range of 200-250 mm and one part in 10;5 in feature placement. Our proof of principle involves a CGH that is about 20mm in diameter with a fabrication tolerance of one part in 10;4.

이진 컴퓨터 형성 홀로그램을 이용한 비구면 형상 측정용 위상편이 회절격자 간섭계

이진 컴퓨터 형성 홀로그램을 이용한 비구면 형상 측정용 위상편이 회절격자 간섭계

Deflectometer with synthetically generated reference circle for aspheric surface testing

Abstract A deflectometer with a synthetically generated reference circle is proposed for aspheric surface testing. Rotation and translation movements are combined to realize laser scanning and make the measurement of the aspheric surface in polar coordinates. It effectively improves the measurement precision for aspheric surfaces with large relative aperture. The measuring equipment is calibrated using a defocused standard spherical surface, and it achieves a precision of λ/5– λ/10 (λ=0.6328 μm ) , which is close to the precision of the interferometric method (λ/20). This testing technique based on laser deflectometry is capable of measuring most kinds of aspheric surfaces, especially those with large asphericity and those of concave shapes. The feasibility of the technique is shown and experimental results are presented.

Sag and phase descriptions for null corrector certifiers

Null correctors are important in the fabrication of aspheric optics. Although null correctors simplify testing of aspheric surfaces, they can increase the risk of fabricating aspheric surfaces. Undetected errors in the null corrector will result in an aspheric surface that does not meet design specifications. To prevent such problems, a null corrector is certified prior to using it to test an aspheric surface during fabrication. Certification verifies that the null corrector has been produced properly. Current methods of certification that include computer-generated holograms and diamond-turned mirrors require a mathematical description of the certifier. We provide sag and phase formulas for describing such certifiers. The formulas can be used to define certifiers for a broad range of aspheric surfaces. For each aspheric test surface, the specific certifier parameters are found through optimization using default merit functions. Via two different aspheric surfaces, we demonstrate the usefulness and simplicity of our truncated-series sag and phase formulas to define certifiers.

Dynamic null lens for aspheric testing using a membrane mirror

Flexible aspheric surface testing is still a major topic in optical industry. Interferometric null testing of aspheric surfaces requires a compensator element that adapts the spherical wave of the interferometer to the individual surface under test. In this paper we present a new approach for testing aspheric surfaces that avoids static, individually manufactured null lenses: an active null lens that is based on a computer controlled membrane mirror. It can be adapted to different aspheric shapes, thus providing much more flexibility in optical shop testing. In this paper we are giving some details on the characteristics of the 25 mm membrane mirror developed at TU Delft and introduce the setup of the active null lens test system. Measurements and the calibration algorithm of the setup are presented.

Absolute interferometric test of aspheres by use of twin computer-generated holograms.

A complete absolute interferometric test of axially symmetric aspheres is presented. The method is based on a specially designed computer-generated hologram (CGH) that reconstructs an aspherical wave as well as a spherical auxiliary wave. Since both phase functions have the same symmetry and their pattern is simultaneously encoded, we call this type of multiplex hologram a Twin-CGH. The spherical wave is used for calibration. The aberrations of the spherical auxiliary wave are measured absolutely with either a spherical mirror or an absolute test for Fresnel zone plates. Thus the two types of aberration inherent in the CGH can be identified and separated from each other. The errors of the spherical wave can be transferred to those of the aspherical wave. Two different methods thatuse Twin-CGHs for absolute testing of aspheric surfaces are described. Test procedures are explained, equations are derived, and experimental results are presented. A mutual comparison of the two results and a comparison with the established N-position rotation test are given.

Null-screen testing of fast convex aspheric surfaces

A method for null-testing fast convex aspheric optical surfaces is presented. The method consists of using a cylindrical screen with a set of lines drawn on it in such a way that its image, which is formed by reflection on a perfect surface, yields a perfect square grid. Departures from this geometry are due to imperfections of the surface, allowing one to know if the surface is close to the design shape. Tests conducted with a full hemisphere and with the parabolic surface of a lens show the feasibility of the method. Numerical simulations show that it is possible to detect surface departures as small as 5 microm.

Interference imaging for aspheric surface testing

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.

Testing aspheric surfaces: simple method with a circular stop

As an extension of the knife-edge test, a noninterferometric method for inspecting circularly symmetric aspheres is proposed in which the test surface is illuminated by a spherical wave. When a small circular stop is placed around the curvature center of the best-fitting sphere, only rays characteristic for the deviation from a perfect sphere remain unobstructed. An image of the tested surface is thereby obtained, showing light and dark regions whose boundaries are correlated to the surface profile, the stop size, and the stop position along the symmetry axis. The experiment has been carried out with a paraboloid.

Aspheric surface testing with a liquid compensatory interferometer

A simple method of testing deep aspheric surfaces is pre- sented. The apparatus consists of a Twyman-Green interferometer and a liquid compensatory container. Two lenses, one with spherical sur- faces and the other with a spherical surface and an aspheric surface, were tested by using this method. The device is very simple and easy to assemble. © 1998 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(98)01804-2)

Measurement accuracy of interferometers with self-pumped phase-conjugate mirrors

Quantitative measurements of the accuracy of interferometers with self-pumped phase-conjugate mirrors (SPPCM’s) involving the application of different kinds of SPPCM’s as the reference mirror, the cat-conjugator SPPCM, the backscattering SPPCM, and an external resonator SPPCM are shown, for the first time to our knowledge. We prove that the only way to achieve the same measurement accuracy as with classical interferometric systems is by use of the cat-conjugator SPPCM. Because of the external feedback in both of the other types of SPPCM, a phase error is introduced, resulting in a phase error in the interferogram. In addition, experimental data describing the time behavior of SPPCM’s, which is important for some interferometric applications, are given. An interferometer with a SPPCM for testing aspherical surfaces is presented.

William Edwin James: Designer and Maker of Astronomical Optics

AbstractWe give an account of the life and work of William James, including his many contributions to astronomy in Australia mainly through his skill in designing, figuring and testing aspheric surfaces.

The testing of a general rotationally symmetrical aspherical surface by using a null lens in a Zygo interferometer

In this paper formulae are derived for calculating the normal aberration of a general rotationally symmetrical aspherical surface. The arrangement of a null lens in aspherical surface testing using a Zygo interferometer is discussed. An example of null lens design and manufacture is presented. By using Wyko software, the surface error is analysed.

Fiber optic interferometer for testing conic section surfaces

A null test method for testing aspheric optical surfaces based on geometric considerations of conic sections is presented. The basic principles have been investigated experimentally by designing and building a modified Mach-Zehnder interferometer. By using optical fibers the inconvenience of alignment has partly been overcome. Phase shifting has been implemented and the measurements are performed with the help of a microcomputer. The performance of the interferometer has been investigated by testing an elliptical toroid mirror. Further improvement of the test procedure by Zernike polynomial decomposition is discussed and performed. Finally, an even more compact conic section interferometer is proposed.

Testing aspheric surfaces

Testing aspheric surfaces

The Corneal EyeSys System: Accuracy Analysis and Reproducibility of First-Generation Prototype

The EyeSyS Corneal Topography System manufactured by EyeSys Laboratories, Inc., Houston, Tex utilizes a unique data-acquisition design to perform rapid, cost-effective quantitative photokeratoscopy. We evaluated a first-generation prototype system. Repeated testing with this prototype demonstrated an accuracy and reproducibility to within 0.25 D on spherical surfaces. Similar results were obtained in testing aspherical surfaces without refocusing. Data from preliminary clinical studies are displayed for the following corneal conditions: normal, keratoconus, post-keratoplasty, and post-keratoplasty with wound ectasia. Advantages of the EyeSys System include rapid data analysis and display, ease of operation, and compact table-top size.

Profile of WYKO Corporation

WYKO Corporation is a company which produces optical measurement equipment. It specializes in phase-measuring interferometry systems for a wide variety of applications from measuring microsurface roughness to contouring large surfaces. This paper outlines the history of WYKO and then describes some of the research and development projects now in progress. These projects include multiple-wavelength profiling, holographic interferometry, projected-fringe contouring, and aspheric surface testing.

Aspherical mirror testing with an area detector array

A deep aspherical surface testing method using an interferometer and an area array sensor is presented. The method is based on a fringe-scanning phase-detecting method. The method has high accuracy and does not require an aspherical reference surface, a null lens, or a hologram. After calculating the object-wavefront phase, a computer displays the sag difference map between a measured surface and an ideal aspherical surface. Results for testing an f/3 200-mm diam parabolic mirror are presented.

Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors

Various interferometric methods can be used for testing aspheric surfaces with high accuracy. Using a partially compensating lens in a Twyman-Green arrangement together with a computer-generated hologram instead of a null corrector gives great flexibility. For quantitative analysis a high-resolution automatic fringe analysis is necessary. The interferometric arrangement and the setup for the interferogram data acquisition are described along with different algorithms for calculating the wave front data. Tilt and decentering of the aspheric surface and the synthetic hologram as well as the actual aspherical parameters can be derived from the calculated wave front using Zernike polynomials to communicate with a ray tracing program. For small adjustment and shape errors the linearity will hold, leading to fast correction and numerical compensation of their effects on the surface error. The method is verified by several examples. Experimental results agree with the proposed model.

Best-fit Spheres and Conics as an Aid in the Manufacture and Testing of Diamond-turned Aspheric Optics

Abstract The development of high-quality and high-accuracy diamond turning has led to an increase in the use of aspheric surfaces in optical systems, especially those operating in the infrared. In the interests of economy it is important to start from a ‘best-fit’ spherical surface, which can be produced by cheaper conventional methods. The testing of these aspheric surfaces also poses a problem, which can often be partially solved by considering the departure of the aspheric from a best-fit conic rather than the more usual sphere. This paper looks at the computation of these best-fit spheres and conies.