Estimation of the degree of asphericity of a glass sphere using a vectorial shearing interferometer

The degree of asphericity is estimated by determining the average radius of curvature in different sections, at various points on the surface of a sphere, and the deviation from it. We employ the vectorial shearing interferometer (VSI) as the instrument to determine the radius of curvature from two subapertures of the transparent glass sphere. We incorporate the sphere as a thick lens into the interferometric setup, illuminating it with an expanded beam. The spherical aberration, introduced by the sphere in the wave front, depends on the local sphere radius, on the refraction index of the glass, and on the cone angle of the source. The wave front aberrated by the sphere impinges on the VSI. Here, the wave front is divided in two in amplitude, it is sheared vectorially, and it is superimposed with itself. The fringe pattern is formed in the intersection of the wave fronts. The shape of the resulting fringe pattern is directly related to spherical aberration. We estimate qualitatively the degree of asphericity, comparing the phase gradients in different sections of the sphere. Here, we report on the experimental setup to test the asphericity, the results with different vectorial shearing (magnitude and direction). Finally, we perform a comparison with the theoretical predictions.