Detection and closed-loop control of piston errors for a Fizeau imaging interferometer.

In the Fizeau imaging interferometer testbed we recently built, the optical path difference (OPD; i.e., piston error) among three sub-telescopes should be corrected for phased imaging to enhance the spatial resolution. This study presents the detection of the OPD via a dispersed fringe sensor (DFS) method and its closed-loop control. The retrieval of the OPD from a dispersed fringe map is a fast-Fourier-transform-based DFS method, which indicates in theory that the OPD has a linear relationship with the displacement of the secondary peaks in the Fourier spectrum of the dispersed fringe map. Then the design and alignment of the OPD detection module are presented, as well as the OPD compensation module with a two-level motion stage. A unique benefit of the fast-Fourier-transform-based DFS is high time efficiency for closed-loop control; for a window of $32 \times 128 ;{\rm pixels}$32×128pixels, a 932 Hz computation rate was achieved by dedicated electrical hardware, which is significant for the distributed satellite formation-flying platform. The experiments validated (1) that the detection range of the DFS is more than $\pm {160};\unicode{x00B5}{\rm m}$±160µm, (2) that the OPD has a fine-line relationship with the secondary peak displacement, (3) the feasibility of the DFS method used for closed-loop control, and (4) that an OPD control precision of 0.0593 µm RMS is achieved.