Design of lenses to project the image of a pupil in optical testing interferometers.

When an optical surface or lens in an interferometer (Twyman-Green or Fizeau interferometer) is tested, the wave front at the pupil of the element being tested does not have the same shape as at the observation plane, because this shape changes along its propagation trajectory if the wave front is not flat or spherical. An imaging lens must then be used, as reported many times in the literature, to project the image of the pupil of the system being tested over the observation plane. This lens is especially necessary if the deviation of the wave front from sphericity is large, as in the case of testing paraboloidal or hyperboloidal surfaces. We show that the wave front at both positions does not need to have the same shape. The only condition is that the interferograms at both places be identical, which is a different condition. This leads to some considerations that should be taken into account in the optical design of such lenses.

Sub-Nyquist null aspheric testing using a computer-stored compensator.

A novel method to demodulate undersampled interferograms using a computer-stored undersampled compensator is presented. First, the sine and cosine of the computer-stored wave front is correlated with the interferogram that emerges from the asphere under test. Afterward, these two correlation images are used to find the phase map. The detected phase of the correlation fringes is the estimated phase difference between the software compensator and the frame-grabbed interferogram. The prior information required for this method is a good knowledge of the wave front being tested to a few wavelengths of error. Complying with this prior knowledge, the undersampled interferogram under analysis may be easily demodulated. Given that the proposed method is based on the correlation of the frame-grabbed interferogram and the computer-stored one, the method also withstands noise.

Aberrations of sphero-cylindrical ophthalmic lenses.

The authors have presented in two previous articles the graphic solutions resembling Tscherning ellipses, for spherical as well as for aspherical ophthalmic lenses free of astigmatism or power error. These solutions were exact, inasmuch as they were based on exact ray tracing, and not third-order theory as frequently done. In this paper sphero-cylindrical lenses are now analyzed, also using exact ray tracing. The functional dependence of the astigmatism and the power error for these lenses is described extensively.

Tscherning ellipses and ray tracing in ophthalmic lenses.

In this paper the exact shape of the solutions to the equations for lenses free of oblique astigmatism, as well as those free from curvature of field or peripheral focus error, are presented. These solutions, as expected, resemble the Tscherning ellipses, but strongly deformed.

Tscherning ellipses and ray tracing in aspheric ophthalmic lenses.

The effect of conicoid asphericity in one of the surfaces of an ophthalmic lens is examined by means of exact ray tracing. Graphical solutions resembling the Tscherning ellipses are obtained for lenses free of oblique astigmatism as well as for lenses free of peripheral power error or curvature of field.