Improving The Performance Of Co-phasing Error Detection Based On Dispersed Fringe Sensor

With the increasing demand for astronomical telescope,the astronomical community has put forward higher requirements for the resolution of large-scale optical telescopes.According to the optical principle of diffraction imaging,the resolving power of the telescope is directly proportional to the optical aperture of the main mirror,and the telescope aperture that meets the requirements of astronomical observation has reached or even exceeds 10 m,if the telescope continues the traditional single-aperture primary mirror The design plan will inevitably bring great difficulties to the manufacture and application of large-caliber primary mirrors.In response to this problem,researchers have proposed using a "spliced" main mirror(Segmented Mirror)composed of multiple sub-mirrors to meet the ever-increasing caliber requirements of optical telescopes.One of the important difficulties faced by the spliced primary mirror is how to achieve the co-phase detection accuracy of the nm level between the sub-mirrors.In particular,how to measure the “piston error” between the sub-mirrors has become a widespread concern in the international optical engineering community.Some researchers have proposed a Dispersed Fringe Sensing(DFS)as a detection method for piston error.This method has a more reliable structure,a wider detection range than the quadratic pyramid method,Shack-Hartmann method,and other methods.The advantages of high precision are currently the most promising method of piston error detection.In this paper,the co-phasing error detection methods based on dispersed fringe sensors are studied.Three kinds of co-phasing error detection methods based on dispersive fringe images,including least-square curve fitting method,main peak displacement extraction method and frequency sidelobe displacement extraction method are studied theoretically.In details,an optical model based on the work principle of dispersed fringe sensor was established,and the process of three kinds of co-phasing error detection for dispersed fringe images were simulated and analyzed.For the problem that the detection range is limited by the visibility of the dispersed fringe image,various factor are analyzed,including the view field of the light source,the wavelength,the diffraction aperture parameters,the angle between diffractive and dispersion directions,and the dispersive ability of dispersed fringe sensor.A method is proposed to improve the visibility of the fringes by using a combination of a long-wavelength light source,the rectangular aperture diffraction and a prism-grating lens with high dispersion ability.Aiming at the problem that the detection accuracy depends on the calibration of dispersive fringe images,a method for calibration of dispersive fringe images based on peak position extraction by envelope fitting and scanning of un-segmented domain aperture diffraction-dispersion image is proposed.The inherent mechanism of how the three kinds of co-phasing error detection methods based on dispersed fringe images are affected by image calibration are studied,and the effect of calibration error are corrected.This reduces the sensitivity to image calibration errors and improves the detection accuracy of the three detection methods to varying degrees.In particular,methods for multiple-band acquisition of fringe windowing,multi-band signal acquisition of fringe windowing,and multi-band Fourier transform of fringe windowing are respectively proposed,which are used to improve the detection accuracy of the least-square curve fitting method,main peak displacement extraction method and frequency sidelobe displacement extraction method,respectively.Combining the three detection methods,in the presence of Gaussian white noise,the accuracy of the co-phasing error detection can be reached to ?/10,and the detection range covers ±100 ?m.When there are obvious image calibration errors,the detection accuracy of the correction method can still be maintained at ?/10 and the RMS of the calibration method for the dispersive fringe center position is less than 0.03 pixels.Finally,a dispersed fringe sensor was designed and a segmented mirror co-phasing experiment platform was set up.When the segmented mirrors achieve the condition of confocal and co-phasing,the co-phasing error detection process based on the dispersed fringe image,the calibration method of the dispersed fringe image,and the error effect correction method of calibration were verified.The RMS of centering calibration method of dispersed fringe is less than 0.08 degrees.Combined with three kinds of co-phasing error extraction algorithms,the detection accuracy is better than ?/5,when the detection value is ±100?m.If there is obvious image calibration error,the detection accuracy of the correction method is better than one wavelength.For a co-phasing error within a wavelength,the detection accuracy is better than ?/10.When there is a significant image calibration error,the detection accuracy of the correction method can still be maintained.Experimental results show that the method proposed in this paper can effectively increase the co-phasing error detection of anti-jamming capability based on dispersed fringe sensors and improve the detection performance.It is of great significance to the development of dispersed fringe sensing technology.