Testing Aspheric Surfaces Research Articles

Testing aspherics using two-wavelength holography: use of digital electronic techniques

Two-wavelength holography has been shown to be quite useful for testing aspheric surfaces since it can produce interferograms with a wide range of sensitivities. However, TWH has the drawback that the accuracy attainable from measurements on photographs of the fringes is limited. It is shown how this limitation can be overcome by using digital electronic techniques to evaluate the phase distribution in the interference pattern.

Testing concave aspheric surfaces: use of two crossed Babinet compensators

Testing concave aspheric surfaces: use of two crossed Babinet compensators

Interferometric testing of optical aspherical surfaces

This note discusses interferometers using digital information processing, from the viewpoint that these interferometers are a hybrid combination of optical and digital processing techniques. It will be shown that the computerised interferometers are more suitable for testing than computer-generated synthetic hologram interferometers.

Technique for testing aspherical surfaces

The above technique was used for measuring and appropriately processing the results obtained for spherical (concave and convex), parabolic, elliptical, and hyperbolic surfaces (in the case of a spherical surface the measured distance d is the radius r).

Modified Zone-plate Interferometer for Testing Aspheric Surfaces

A new type of common path interferometer using a modified zone-plate developed for testing aspheric surfaces is described. The modified zone-plate is made by combining two kinds of zone-plates; the semicricular part of the plate produces the spherical wave, and the remainder the desired aspheric wave. These are synthesized by digital computation. A method of computation for synthesizing the modified zone-plate and some experimental results of the test of parabolic mirrors are given.

Dual Computer-generated Holograms for Testing Aspherical Surfaces

The use of a dual computer-generated hologram for performing interferometric testing of aspherical surfaces is described. The dual hologram consists of apertures whose positions are modulated along two different directions. The dual hologram allows the simultaneous generation of two different wavefronts whose sum and difference can be obtained with appropriate spatial filtering. This has been proved theoretically and verified experimentally. Finally, the dual hologram is utilized to test steep aspherics, and some practical advances of the dual hologram are mentioned.

Interferometric testing with computer-generated holograms: aberration balancing method and error analysis

When testing aspheric surfaces with a computer-generated hologram, some problems should be considered. In this paper, first, we compare two types of hologram: Lohmann and interference. The phase error in the Lohmann type hologram is estimated, and a method of compensating the error is described. Second, we discuss the relation between the shape of the required wavefront and the number of resolution cells of the hologram. Since testing smaller f number optical elements increases the required number of resolution cells of the hologram, we propose the aberration balancing method to reduce the number of resolution cells. The optimum values of the defocus aberration are calculated. Especially, it is shown that the number of resolution cells in the hologram is capable of being reduced to 25%. Third, we discuss the error due to incorrect hologram size and due to misalignment of the optical system when the aberration balancing method is applied. Finally, an experimental example for testing an aspheric mirror 150 mm in diameter and 300 mm in focal length is given.

Interferometric Testing of Aspheric Surfaces with Computer-Generated Holograms

Interferometric Testing of Aspheric Surfaces with Computer-Generated Holograms

Synthetic Holography for Optical Testing

—Computer Generated Holograms (CGH’s) have been used for the testing of aspherical surfaces. The CGH acts as a reference element in an interferometric configuration. The CGH’s may be generated either by coding both amplitude and phase or by coding only the phase of the wavefront. It may be safely assumed that the wavefronts encountered during testing are of uniform amplitude and hence the methods using only phase coding for the generation of the hologram are of more relevance to testing. We have modified the procedure by Birch et al for generating CGH. This modified procedure along with the concept of aberration balancing extends the capability of the CGH; even steep aspherics can be tested. The CGH’s have been generated for the wavefront from a plano-convex lens both for its axial and off-axial positions. The results of the experiments indicate that the CGH and provide a reference wavefront to an accuracy better than λ/10. An analysis of the errors introduced during fabrication and use of the CGH has been presented.

Some Improvements in Computer Hologram for Testing Aspheric Surface

In order to produce an accurate aspheric surface, it is necessary to know the exact shape of that surface in the process of polishing. For this purpose, we have developed an interferometer using computer generated holograms. Experiments were made on that apparatus with three kinds of computer generated holograms. They are 1) interferogram, 2) Lohmann type hologram and 3) inclined bar type hologram. A software has been developed to draw interferogram, but generally computer time to draw it was larger than that to obtain a Lohmann type hologram. The deterioration of the interference pattern when using a Lohmann type hologram could be remedied by using a proposed “inclined bar” type hologram to some extent. Therefore, the inclined bar type hologram is more practical for the purpose of testing an aspheric surface.

Interferometric Testing of Aspheric Surfaces with Computer-Generated Holograms

Interferometric Testing of Aspheric Surfaces with Computer-Generated Holograms

Testing of Aspherical Surfaces with Newton Fringes

The shape of any aspherical surface with rotational symmetry can be very easily found with great accuracy using Newton fringes formed against a spherical test plate.To make it possible, a special mathematical procedure is devised for use with a special measuring system here described.

Hologram-interferometry-A Geometrical Approach

Real time hologram-interferometry is applied to the testing of optical aspheric surfaces. It is shown that, in this particular case, holograminterferometry can be explained by the use of geometrical rather than diffraction optics. Real time hologram-interferometry is shown as a generalization of classical and moiré interferometry, and also of geometrical tests. For this purpose, the concept of the ‘self-adaptive reversed Ronchi test’ is introduced. It is suggested, without experimental confirmation, that the same concepts can be used also in the more general case of diffusing objects.

A Method for Testing Aspheric Surfaces

This paper describes a method for the testing of aspheric surfaces during the process of manufacture. By using an auxiliary lens, a null test is obtained, thus enabling the aspheric curve to be examined for slope errors and quality of polishing. Results for the particular lens concerned indicate that the test can be applied to a considerable range of aspheric surfaces.