Design and performance characterization of a quartz crystal micro-retarder array

Recently, micro-retarder arrays consisting of patterned liquid crystal polymer or sub-wavelength grating arrays with four different orientations are widely used in division of focal planeï1/4DOFPï1/4‰Stokes polarimeters. However, due to thermal sensitivity of liquid crystal, real-Time calibration of the instruments is required to achieve high-precision detection under non-isothermal conditions. Sub-wavelength grating arrays require sophisticated process, and the study of the influence of grating structure errors on measurement accuracy has been rarely reported. To overcome these limitations, we design a quartz crystal micro-retarder array for DOFP full-Stokes polarimeter, which is composed of identical units with different retardances at four neighboring pixels. The retardance errors introduced by the errors of the substrate thickness (t) and etching depth (d) of the micro-retarder array are analyzed. Furthermore, the relationship among the measurement error, the instrument matrix error of Stokes polarimeter, and polarization state of incident light is established. Hereby, the influence of retardance error on the measurement error corresponding to incident light of different polarization state is analyzed. To reduce the measurement error of Stokes parameters to less than 0.02, the tolerances of t and d should be less than 0.11 μm and 0.09 μm, respectively. The micro-retarder array on quartz crystal is fabricated according to our design and tolerances analysis. Finally, the retardance characteristics of the micro-retarder arrays are characterized by the high accuracy (0.1%) Mueller polarimeter developed in house.