Matthew C. H. Leung
A multi-object spectrograph (MOS) is an instrument that can acquire the spectra of hundreds of astrophysical objects simultaneously, saving on observing time since more data can be acquired. In the recent years, a component called the digital micromirror device (DMD) has shown potential in becoming a programmable slit mask in MOS systems, offering advantages over existing multi-object selection methods such as repositionable optical fibres or custom-machined slit masks. A DMD is an array of many tiny mirrors that can be individually programmed to tilt along an axis. Specific micromirrors can be programmed to reflect incoming light from objects of interest into a dispersive element, and the resulting spectra is acquired. We have designed a seeing-limited DMD-MOS covering a spectral range of 0.4-0.7 μm with a spectral resolution of 1000, which can be used to determine the redshifts of galaxies. Due to stray light from the DMD and the system’s wide field of view, the optical design and the hyperspectral data reduction process of this DMD-MOS are complex. Moreover, depending on the field position of the object of interest, the distortion of the resulting spectra on the imaging detector will vary nonlinearly and needs to be determined. A detailed analysis and optimization was completed for this DMD-MOS to characterize and verify its performance. Using simulated performance data of light rays launched into the DMD-MOS, a model was created to determine the pixel-to-wavelength mapping of the imaging detector. Our model corrects distortion and can help astronomers process hyperspectral data in real-time during data acquisition. This process’ low latency means that it can also be used in other applications, such as Remote Sensing. This DMD-MOS will be placed on a 16 inch telescope as an exploratory study for future DMD-based MOS systems.
In our DMD-MOS, incoming light from a telescope is firstly focused onto the plane of the DMD (Figure 3). Micromirrors in the OFF configuration reflect incoming light into a “camera channel” for object selection. Micromirrors in the ON configuration act like slits in a conventional spectrograph, and reflect incoming light into a “spectral channel”. This light then passes through a collimator, is dispersed by a volume phase holographic grism, and is then focused by some camera optics onto an imaging detector (Figure 4). An analysis of the system was conducted, using tools such as spot diagrams (Figure 5), and the DMD-MOS meets the design requirements. Incoming light can be sufficiently focused by the optical elements and resolved by the detector, while no rays are cut off.
Depending on the field position of an object of interest, the distortion of the resulting spectra on the image plane (detector) varies nonlinearly and needs to be corrected. A wavelength fit was determined for this DMD-MOS to map points from the DMD plane, to corresponding points on the detector, for some wavelength, using simulated data. One million rays were launched into the DMD-MOS in a Monte Carlo style simulation with the DMD having 20 ON micromirrors along its centreline, and rays having 13 wavelengths (Figure 6). The resulting positions (spots/points) of the rays when they land on the detector were determined. Then, for each wavelength, the k-means clustering algorithm was used to cluster points corresponding to rays from the same micromirror, and the centroids for each cluster were obtained. The centroids’ positions were fitted with a quadratic function, representing smile distortion (shift in the spectra at some wavelength). Keystone distortion (shift in the spectra along the spatial direction) was fitted with a cubic function. The coefficients of these two functions varied with wavelength, and were approximated by polynomial relationships. Two resulting equations were obtained, so that given some point on the DMD along its centreline, the spectrograph’s magnification, and a wavelength value: the corresponding point on the detector can be determined with a maximum error of 0.022 mm at the minimum wavelength (0.4 μm).
Next, we will generalize this wavelength fit to the entire FOV of the DMD-MOS. More rays will be used for future simulations to reduce the fit error. After a generalized fit is determined, we hope to extend this fit procedure and this DMD-MOS instrument to other applications, such as Remote Sensing. This DMD-MOS will be placed on a 16 inch telescope at the University of Toronto, and will be used as an exploratory study for future DMD-based MOS systems.