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The multi-object spectrograph (MOS) has been the benchmark for the currentgeneration of astronomical spectrographs, valued for its ability to acquire thespectra of hundreds of objects simultaneously. In the last two decades, thedigital micromirror device (DMD) has shown potential in becoming the centralcomponent of the MOS, being used as a programmable slit array. We have designeda seeing-limited DMD-based MOS covering a spectral range of 0.4 to 0.7 $\mu$m,with a field of view (FOV) of $10.5^\prime \times 13.98^\prime$ and a spectralresolution of $R\sim1000$. This DMD-MOS employs all-spherical refractiveoptics, and a volume phase holographic (VPH) grism as the dispersive elementfor high throughput. In this paper, we present the optical design andoptimization process of this DMD-MOS, as well as a preliminary wavelengthcalibration procedure for hyperspectral data reduction. Using simulated data ofthe DMD-MOS, a procedure was developed to measure hyperspectral imagingdistortion and to construct pixel-to-wavelength mappings on the detector. Aninvestigation into the relationships between DMD micromirrors and detectorpixels was conducted. This DMD-MOS will be placed on a 0.5 m diameter telescopeas an exploratory study for future DMD-based MOS systems.

Optical Design and Wavelength Calibration of a DMD-based Multi-Object Spectrograph