Hadamard transform-based calibration method for programmable optical filters based on digital micro-mirror device

Abstract

Digital micromirror device (DMD) based optical filters provide a new avenue for spectral modulation in many research applications. Traditional sequential channel scanning method for the calibration of such filters may suffer from compromised spectral tuning accuracy due to the signal to noise ratio restriction on the minimum pixel number of each channel. In this work, we propose a Hadamard transform based calibration method to address this issue. A DMD-based programmable optical filter is constructed and calibrated using both the sequential scanning method and the proposed method for the subsequent synthesis of three representative filters (i.e., the bandpass filter, Gaussian filter, and principal component based filter). The spectral tuning accuracy is evaluated by calculating the relative root mean square error (RMSE) between the synthesized transmittance spectrum and the target spectrum. The results show that when calibrated with the proposed method, the programmable filter exhibits a consistent decrease in the relative RMSE with an increasing channel number for all filters. The smallest relative RMSE values are therefore achieved when each channel contains only one DMD pixel. In contrast, for the sequential scanning method, the relative RMSE increases dramatically when each channel contains three or fewer DMD pixels. This suggests that our method is superior to the sequential scanning method in spectral tuning accuracy when the signal level is low.