Conditions for perfect focusing multiple point sources with the SMS design method

In this work, we demonstrate how it is possible to sharply image multiple object points. The Simultaneous Multiple Surface (SMS) design method has usually been presented as a method to couple N wave-front pairs with N surfaces, but recent findings show that when using N surfaces, we can obtain M image points when N<M under certain conditions. We present the evolution of SMS method, from its basics, to imaging two object points through one surface, the transition from two to three objet points obtained by increasing the parallelism, and getting to the designs of six surfaces imaging up to eight object points. These designs are limited with the condition that the surfaces cannot be placed at the aperture stop. In the process of maximizing the object points to sharp image, we try to exhaust the degrees of freedom of aspherics and free-forms. We conjecture that maximal SMS designs are very close to a good solution, hence using them as a starting point for the optimization will lead us faster to a final optical system. We suggest here different optimization strategies which combined with the SMS method are proven to give the best solution. Through the example of imaging with the high aspect ratio, we compare the results obtained optimizing the rotational lens and using a combination of SMS method and optimization, showing that the second approach is giving significantly smaller value of overall RMS spot diameter.