Image Analysis with the DMD in Convergent Path

The digital micromirror device (DMD) which is one kind of Micro-Electro-Mechanical System has been widely adapted for use in lighting projection systems, and some new imaging systems such as high-dynamic range imaging, aperture-coded spectral imaging, or medical imaging. The micromirrors on the DMD surface are non-continuous distribution and capable of tilt relative to individual rotation axis, which is different from the plane mirror. Therefore, when the DMD is applied in a convergence imaging path, there is an optical path difference (OPD) between the off-axis chief ray and the on-axis chief ray, and moreover severe non-symmetric imaging on the focal plane. Based on the geometrical optics and aberration theory, this paper proposes a calculation formula that gives the OPD as a function of the image height, the incident angle, the DMD pixel size and the DMD tilt angle in the convergent imaging path. This formula can give the OPD of the system when the optical axis is vertical to the surface of the DMD in an ideal state, which has great significance to the design and adjustment of optical path using DMD devices.