Centroids analysis for circle of confusion in reverse Hartmann test

The point spread function（PSF） is investigated in order to study the centroids algorithm in a reverse Hartmann test（RHT） system. Instead of the diffractive Airy disk in previous researches, the intensity of PSF behaves as a circle of confusion（CoC） and is evaluated in terms of the Lommel function in this paper. The fitting of a single spot with the Gaussian profile to identify its centroid forms the basis of the proposed centroid algorithm. In the implementation process, gray compensation is performed to obtain an intensity distribution in the form of a two-dimensional（2D） Gauss function while the center of the peak is derived as a centroid value. The segmental fringe is also fitted row by row with the one-dimensional（1D） Gauss function and reconstituted by averaged parameter values. The condition used for the proposed method is determined by the strength of linear dependence evaluated by Pearson＇s correlation coefficient between profiles of Airy disk and CoC. The accuracies of CoC fitting and centroid computation are theoretically and experimentally demonstrated by simulation and RHTs. The simulation results show that when the correlation coefficient value is more than 0.9999, the proposed centroid algorithm reduces the root-mean-square error（RMSE） by nearly one order of magnitude, thus achieving an accuracy of - 0.01 pixel or better performance in experiment. In addition, the 2D and 1D Gaussian fittings for the segmental fringe achieve almost the same centroid results, which further confirm the feasibility and advantage of the theory and method.

Improving coherent averaging line spectrum detection with phase interpolation and compensation

For the purpose of resolving the problem of performance deterioration introduced by inaccurate phase compensation in existing coherent averaging line spectrum detectors, a modified coherent detector is proposed. The three point interpolation in frequency domain is applied to obtain accurate estimate of phase difference between segments when the segmented length is not an integral multiple of the signal period. Then the segmented data are multiplied by a complex coefficient to remove the phase difference and synchronize the phases of all the segments before coherent averaging. Theoretical analysis shows that there will be a gain of 3.9 dB at most by using the modified detector. The detection performance of the incoher- ent averaging power spectrum detector （AVGPR）, the phase coherent averaging detector, the modified coherent averaging detector are compared with each other by computer simulations. The results coincide basically with the theoretical analysis, which show the superiority of the modified detector to the former two detectors.