Analysis and study of the interlaced encoding pixels in Hadamard transform spectral imager based on DMD

The key innovation in Hadamard transform spectral imager (HTSI) introduced recently is the use of digital micro-mirror device (DMD) to encode spectral information. However, because the size of individual micro-mirrors does not match the detector pixel size or for other unavoidable errors in the optical design and the system assembling, an interlaced encoding phenomenon appears on some pixels of the encoded images obtained from the detector. These interlaced encoding pixels are not encoded based on Hadamard transform, so they should be processed specially in spectrum recovery. This paper analyzes the interlaced encoding phenomenon and proposes a positioning method and a decoding method for the interlaced encoding pixels on the encoded images. In our experiment, we direct a beam of laser into our HTSI and fill the entire field of view; by observing the column vector, which is made up of the gray values of a pixel on the encoded images from the detector in sequence, the interlaced encoding pixels can be distinguished easily and a coefficient is obtained simultaneously, which denotes the ratio of the area between the left part and the right part of the interlaced encoding pixel. By substituting the coefficient and the encoded gray values of the interlaced pixel into its encoding equation, we can recover the spectral elements of the interlaced pixel with ease. By comparing the spectral curve of the interlaced encoding pixels recovered by the method mentioned in this paper and the spectral curves of its two adjacent pixels, we find the decoding results are quite effective.