Modeling the performance of the Hadamard transform spectral imaging technique with SAMOS: a ground-based MEMS spectrograph

The SOAR Adaptive-Module Optical Spectrograph (SAMOS) is a Digital Micromirror Device (DMD) based multi-object spectrograph (MOS) that will be deployed on the 4.1-m SOAR telescope. While the instrument's primary observation mode will be multi-object spectroscopy, the rapidly re-configurable DMD slit mask can also enable integral field spectroscopy with Hadamard Transform Spectral Imaging (HTSI). HTSI is an optical multiplexing technique that produces spatially resolved spectra of extended regions. This technique can be implemented on SAMOS as an additional observation mode without changes to the hardware. In comparison to conventional acquisition of the same data using a long-slit scan of the scene, this technique can achieve higher overall efficiency through its gain in signal-to-noise ratio (SNR). The gain in SNR is highly dependent on nature of noise and errors in the multiplexed signals; measurements in the shot-noise limited regime will not result in a gain in SNR, while the highest gain is obtained in low-signal conditions. Other sources of noise and error can degrade the gain in SNR. To implement an HTSI observing mode with SAMOS, it is critical to evaluate cases for which the technique will be successful. To make these evaluations, we have developed a computer model of the performance of the HTSI technique with SAMOS. The simulation considers the input signal's spectral flux, overall throughput, detector properties of SAMOS, and potential sources of error arising from the ground-based observing conditions. We present results from these models and identify the limiting factors for using the HTSI observation mode with SAMOS.