Research On Deconvolution Of Differential Optical Transfer Function For Co-phasing Error Sensing Of Segmented Telescope

Increasing the aperture of a telescope is the most effective way to improve its lightcollecting ability and angular resolution.With the increase of aperture,the challenges in the primary mirror processing,support structure,transportation and launch process of a traditional monolithic telescope will arise.The segmented primary mirror structure is proposed by researchers as an effective way to solve these problems,which has become the development trend of large-aperture astronomical telescope.However,the segmented telescopes also face many challenges in the optical system alignment and maintenance process.Some related researches point out that in order to achieve the equivalent imaging quality of a monolithic telescope,it is necessary to ensure the relative position accuracy of primary mirror segments in nano-scale.High precision cophasing error sensing is the precondition and key step to actively adjust the position of each segment and guarantee the imaging quality of a segmented telescope.Differential optical transfer function(dOTF)is an analytic image-based wavefront sensing approach,which is simple in both hardware implementation and mathematical operation.This method can determine the co-phasing errors of all segments,while traditional co-phasing error sensing methods may have the problems of low sensing efficiency and poor reliability,especially when the number of segments is particularly large.It is particularly suitable for the phasing of extra-large segmented space telescopes.However,there is one deep-rooted problem inherent in this method,i.e.,the low co-phasing error sensing accuracy caused by blurred complex pupil field due to convolution.Aiming at this problem,this paper makes thorough research and exploration on improving the accuracy and practicability of dOTF in sensing the cophasing errors of segmented telescopes.This paper mainly includes the following parts:Aiming at the blurring effect due to convolution inherent in the dOTF method,this paper proposes an iteration deconvolution strategy using one dOTF,which repeatedly and iteratively estimates the pupil modification and then implements deconvolution of dOTF in the frequency domain correspondingly according to the prior knowledge of introducing pupil modification by blockage.Meanwhile,a noise-suppression factor is introduced according to the SNR to suppress the effect of noise near the nulls of the dOTF signal,and otherwise the noise will be amplified during the deconvolution process.The deconvolution algorithm of dOTF can obtain good results within several iterations,and improve the sensing accuracy of the co-phasing errors of a segmented telescope.Aiming at the limitation of the iterative accuracy of the proposed iteration deconvolution strategy with one dOTF,this paper proposes a cross-iteration deconvolution strategy,which uses an additional dOTF(using a different pupil modification)to estimate the pupil modification required by the other dOTF repeatedly and cross-iteratively,based on the knowledge that the accuracy of the phase far away from the conjugate center is higher.Then the corresponding pupil modifications are used to implement deconvolution of the very dOTF.Whereafter,the co-phasing error sensing ability of the dOTF with cross-iteration deconvolution strategy in the presence of continuous low-order aberrations is analyzed.The ameliorative dOTF algorithm improves the wavefront sensing accuracy and effectiveness.Aiming at the limitation that the proposed deconvolution methods are only applicable to the dOTF with pupil modification introduced by blockage,this paper has derived the general deconvolution forms of arbitrary pupil modification types(including pupil blockage,phase tilt and phase shift),which reveal the corresponding relationship between pupil modification amount and original complex pupil in the modified area.On this basis,the cross-iteration deconvolution strategy of dOTF with pupil modification introduced by phase tilt and phase shift are verified,respectively.Then,the relationship between the value of phase change and the sensing accuracy is analyzed in this paper through simulation.Aiming at the limitation that the phase only ranges from-0.5π to 0.5π when arctangent function is used to obtain the phase distribution of dOTF,a phase unwrapping algorithm is developed to increase the sensing range to 2π(-π～π),which can also improve the testing range of tilt error to at least 5 wavelengths when only the tilt error is considered.Finally,a feasible experimental scheme is proposed.With the analysis of factors that may affect the experimental results,the experiments on dOTF method and the proposed two kinds of deconvolution strategy of dOTF with pupil modification introduced by blockage are carried out using a single circular lens.Experimental results show that the dOTF method and two kinds of deconvolution strategy of dOTF have feasibility and calculation effectiveness.