Calibration, sensitivity analysis, and demonstration of a basic polarimeter for artificial satellite observations

Abstract

The Department of Physics at the United States Air Force Academy has a DFM Engineering f/8.2, 16-inch telescope outfitted with a 9-position filter wheel populated with broadband photometric filters (Johnson-Cousins B, V, R, and a blue-blocking exoplanet filter) and a 100 lines per millimeter diffraction grating. As part of their senior capstone project, physics cadets developed a simple, four-channel linear Stokes polarimeter by populating the open slots in the filter wheel with linear polarization filters oriented at 0°, 45°, 90°, and 135° relative to the vertical axis of the imaging camera. Size and weight restrictions on the back of the telescope prohibited the use of more elaborate polarimeters. They also developed the process and procedures to characterize the effect of the telescope optical elements on the polarization of incident light. Using an unpolarized uniform flat light source, along with a polarized film rotated at 10° increments from 0° to 180°, the intensity of the light source was measured as it passed through the entire optical system including the previously mentioned linear polarized filters. The measured intensities were fitted to Malus Law using a least squares method. From this fit, a modified Mueller matrix was created that describes how the telescope’s optical elements, including the polarizing filters, alter the incident light measured by the telescope’s camera. To relate the measured intensities of light to the Stokes parameters of the light reflected from a satellite, a calibration matrix was computed using a pseudoinverse of the modified Mueller matrix. The sensitivity of the pseudoinverse process was analyzed by perturbing input data and measuring the root mean square (RMS) error between the perturbed and ideal matrices. This process for employing the pseudoinverse introduced minimal error into the system as the RMS error for the calibration matrix was within an acceptable error range. The calibration matrix was applied to observations of three different satellites, AMC-15, DirecTV-10, and DirecTV-14, resulting in their measured Stokes parameters, Degree of Linear Polarization, and Angle of Linear Polarization.