Analysis and Experiment of Encoding Errors for MOEMS Micro Mirror Spectrometer

Abstract Micro mirror arrays used in the novel spectrometer to achieve the modulation of Hadamard transformation (HT) and spectrum detection by a single detector can also be considered as a blazed grating. During the modulation, spectrum can not be completely reflected by micro mirror array s on the “on” state. While on the “off” state, there will be still light incidence into detector, since the way of light modulation by mirror arrays is diffraction rather than reflection. This will then cause encoding errors. To diminish these encoding errors, a blazed grating model for mirror arrays is proposed. In this paper, both encoding error and compensation are analyzed for the algorithm of HT. Firstly, establish a theoretic model of micro mirror arrays modulation, and calculate the light field distribution based on the Fraunhofer diffraction theory. Then use MathCAD software and Matlab software to simulate and correct the HT encoding errors. Finally, some experimental tests have been done on the Micro mirror sp ectrometer system. The “on” state errors caused by micro mirror can be eliminated by dividing the background or rectifying the HT mask encoding. However, the “off” state errors can only be eliminated by constructing a comp ensation HT matrix. Both the “on” and “off” state errors are coexisted in the real situation. Exp eriment not only can reduce the encoding errors, but also increase signal-to-noise ratio.