Matt Heiss Frontiers Poster Abstract

Abstract
In an experiment at Jefferson Laboratory in Newport News, VA, a high-energy photon beam will be used to probe the forces that bind quarks together in the nucleus of an atom. The photon beam is produced by passing high-energy electrons through a thin sheet of diamond. In order for the experiment to succeed, the diamond must be precisely aligned. To guarantee this alignment, the diamond must be extremely flat. Our group has developed a laser interferometer that is capable of measuring this flatness to within twenty nanometers. To reduce cost, this interferometer incorporates a consumer camera with a nonspecified fixed lens apparatus. However, in order to properly analyze the interference pattern that will be recorded, the specific workings of the lens assembly must be determined. As the lens is fixed and cannot be replaced, a mathematical model of the camera must be constructed instead. This model will then be used in tandem with data recorded by the camera in order to examine the light passing through the diamond wafer.

The internals of the lens assembly can be approximated by using the thin-lens approximation in order to simplify the mathematical model of the camera. Initially, a two-dimensional model of the lens system was created and used to create an image of a one-dimensional object. Once the correct behavior of the basic model was verified, it was extended to a full three-dimensional model which generates two-dimensional images from three-dimensional objects. Using this model alongside data recorded experimentally, the precise arrangement of lenses in the camera can be calculated. With the lens assembly understood, any distortions in the image received can be corrected for, allowing us to determine the interference pattern produced by the laser interferometer.

A simple mathematical model of the camera, calibrated to match its inputs and outputs with those of the actual camera, accurately reproduces the behavior and even the interior geometry of the lens assembly, to the extent permitted by the thin-lens approximation. Using this model, we can determine the precise interference pattern created by the laser interferometer, and using this we can precisely calculate the flatness of the target diamond wafer.