Design and analysis of a pair of prisms for widening the imaging range of an optical system

We demonstrate that a pair of wedge prisms with opposite angular dispersion can be designed to have zero spherical aberration, zero coma, and zero astigmatism and be simultaneously achromatic in convergent rays, and the system can easily reach the diffraction limit and be utilized in precise three-dimensional imaging, special optical testing, etc., for widening the imaging range. Aberration equations of a pair of thin wedge prisms in paraxial optics are first derived, from which a special solution is obtained by making a few presuppositions. Then three initial structures are built to verify our inference. The near-zero Zernike standard coefficients and tiny rms radii of the image spots given by OpticStudio prove that the derived equations hold. After that the refractive indices of two prisms are both tested, where the testing results show that prisms with high-refractive indices are more capable of compensating monochromatic aberrations. With the aid of Monte-Carlo analysis method, tolerance analysis is carried on with the worst cases of the three optimized systems. The results show that a pair of wedge prisms with the opposite angular dispersion can effectively work within the diffraction limit even if the optical manufacturing and assembly errors are large. In the end, the system design limitations are given, and we suggest that the working F-number of the eyepiece should preferably be larger than 8.0.