We investigate the qualitative aspects of the simultaneous multiple surface (SMS) design method. The SMS method is a powerful and complex tool, whose abilities and limitations we feel are not yet fully understood. Here, we view the SMS method as an iterative dynamical system, consider the physical boundaries on which the method applies and show that in some cases, attractors occur on the boundaries of these regions. One consequence of our viewpoint is numerical evidence of the impossibility of perfectly imaging three points to three points using only two reflectors. Another consequence is that SMS may be viewed as a means for designing a primary component that essentially separates the bundles in such a way that a continuous secondary component exists that images the two separate bundles appropriately. In other words, a clever choice of the primary component decouples the problem.
Optical design in the 19th century was largely empirical, and today design in the geometric realm is often
performed by optimizing a cost function which is defined via ray tracing. A natural question to ask then, is how
to perform optical design using a more direct method, such as solving partial differential equations or variational
problems. We consider the problem of writing down equations to model a single surface (mirror or lens) to
completely control a single bundle of rays. When this is done, with high probability the solution surface will not
be rotationally symmetric, but freeform. Although a bundle may not be completely controllable with a single
surface, approximate solution can be sometimes have applications. In particular, we will show how to compute
the shape of a driver-side mirror that has no blind-spot or distortion.
In previous work, we proposed a method for imaging using micro optical electromechanical (MOEM) mirrors. Our solution was to introduce into the imaging sensor optics a 2-D micro-mirror array. This device provides high resolution images with a wide field of view. In this paper, we provide further simulations that validate the functionality of our system design. In addition, we present our first system prototype that can produce an image with higher resolution and support a wider field of view than the image sensor employed in the system.
We present a means for forming images using micromirror arrays. Using an array of 2D tilt mirrors it is possible to create an image
whose resolution is much higher than the number of mirrors. We
present several types of simulations, including images produced by
graphical ray tracing for linear MEMS array of containing 1 and 2
mirrors, and general NxN configurations.