A differential computation method is presented to improve the precision of calibration for coaxial reverse Hartmann test (RHT). In the calibration, the accuracy of the distance measurement greatly influences the surface shape test, as demonstrated in the mathematical analyses. However, high-precision absolute distance measurement is difficult in the calibration. Thus, a differential computation method that only requires the relative distance was developed. In the proposed method, a liquid crystal display screen successively displayed two regular dot matrix patterns with different dot spacing. In a special case, images on the detector exhibited similar centroid distributions during the reflector translation. Thus, the critical value of the relative displacement distance and the centroid distributions of the dots on the detector were utilized to establish the relationship between the rays at certain angles and the detector coordinates. Experiments revealed the approximately linear behavior of the centroid variation with the relative displacement distance. With the differential computation method, we increased the precision of traditional calibration 10 rad root mean square. The precision of the RHT was increased by approximately 100 nm.
Optical sparse aperture (OSA) imaging systems show great potential to generate higher resolution images than those of equivalent single filled aperture systems. However, due to the sparsity and dispersion of sparse aperture arrays, pupil function is no longer a connected domain, which further attenuates or loses the mid-frequency modulation transfer function (MTF), resulting in lower mid-frequency contrast and blurred images. Therefore, an improved traversal algorithm is proposed to optimize Golay-9 array configurations for compensating the mid-frequency MTF. Its structural parameters include diameters of sub-apertures, relative rotation angles between individual sub-apertures, and radius of concentric circles. Then, these parameters are traversed successively in order. Finally, the influences of the obtained optimized array configurations on the mid-frequency MTF are analyzed in detail, and the image performances are evaluated. The experimental results prove the contrast enhancement. Compared with a Golay-9 array at
F
=
36.5
%
, the maximum MTF increases from 0.1503 to 0.307, and the mid-frequency MTF is boosted from 0.0565 to 0.0767. In addition, the peak signal to noise ratio of the degraded image is promoted from 19.75 dB to 20.63 dB. Both quantitative and qualitative evaluations demonstrate the validity of the proposed method.
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