The segmented primary mirror telescope under the co-phasing condition can meet the observation requirements of high resolution. However, co-phase errors are always present, which seriously affects the imaging quality. The precise phase modulation requires that the root mean square error of wavefront is less than 𝜆 ⁄ 40. Therefore, the high-precision detection of tip-tilt error between the segments is one of the key technologies to realize the co-phase imaging. In this paper, we propose a simple and efficient tip-tilt error detection method based on single Convolution Neural Network (CNN). Without any preprocessing, the light intensity distribution images on the focal plane are used as the data set for training CNN. And a high-performance CNN model is built to learn the mapping between the tip-tilt errors and light intensity distribution images. After training, CNN can accurately capture the tip-tilt errors by inputting a single image of the light intensity distribution. The simulation model of a three-segment telescope system is established to test the accuracy and robustness of the method. Test results show that the method can achieve high-precision detection of tip-tilt error in a large detection range. This method can achieve a detection range of [-3𝜆,3𝜆] with an accuracy of 7.820×10-3𝜆RMS. The method is robust to the piston error and CCD noise: the tolerance of CCD noise is 5 dB and the tolerance of piston error is [-0.48 𝜆,0.48 𝜆]. This method is simple and does not require complex hardware. It can be widely applied in segmented and deployable primary mirror telescopes.
KEYWORDS: Phase transfer function, Optical transfer functions, Mirrors, Point spread functions, Telescopes, James Webb Space Telescope, Error analysis, Wavefronts, Image segmentation, Segmented mirrors
Astronomical observation requires more distant and fainter object with a better resolution, so that the larger primary mirror telescope is needed to ensure the better resolution and light energy collection. However, the diameter of monolithic primary mirror is limited due to the manufacturing and logistics limitations. The segmented primary mirror is taken as an alternative solution to break the limitation. The segmented primary mirror must be co-phased to accomplish a diffraction-limited imaging. In this paper, we put forward a new method to measure the tip/tilt errors between the segments in whole aperture simultaneously based on analyzing the intensity distribution and Fourier optics principle. We set a mask with sparse multi-sub-pupils configuration on the segments′ conjugate plane. A point source is taken as the object of the segmented telescope, the pattern focused on the CCD is recorded as the point spread function (PSF). Then, the Fourier transform is performed for the PSF and we can obtain the optical transfer function (OTF) which is composed of the modulation and phase transfer functions (MTF and PTF). Tip/tilt errors can be extracted from the PTF side-lobes. Simulation and preliminary experiments have been done to validate the feasibility of the method. The accuracy of the method is 6.344x10-16λ(λ=632.8nm) RMS when the tip/tilt error is less than 0.4λ, and when the tip/tilt error is in the range of [0.4λ, 2.4λ], the accuracy is 8.5x10-15λ RMS. We also analyze the disturbance factor of the method in the simulation, including the piston error, the noise of the signal processing system, the surface shape error of the segments, etc. Furthermore, a preliminary experiment is built up to verify the three segmented system. This method has a higher detection efficiency and a lower hardware requirement which only needs a mask with sparse sub-aperture configuration.
To achieve a diffraction-limited imaging, the piston errors between the segments of the segmented primary mirror telescope should be reduced to λ/40 RMS. The piston detection method using convolutional neural network (CNN) is an advanced technology with high precision and simplicity. However, such methods based on the deep learning strategy usually have generalization problems, that is, the network prediction precision will inevitably decrease if there is a certain difference between the test image and training set used in the network. This will directly affect the scope of application of the method. In this letter, we propose a CNN-based high-precision piston detection method and analyze its robustness. The point spread function (PSF) images acquired under the wide-spectrum light source are used to construct the dataset to overcome 2π ambiguity. In addition, a set of neural networks system including the classification CNN and the regression CNN with good generalization ability is designed to extract the piston value directly from the PSF image. Under the ideal condition, the piston detection precision can reach about 8.4 X 10-4 λοRMS in the capture range of the interference length of the operating light. Finally, we focus on testing the effect degree of the main disturbance factors in the actual system on the accuracy of the method, such as surface error, residual tip-tilt error, and CCD noise, so as to evaluate the robustness of the method. This method is robust and does not require complex hardware. It can be widely applied in segmented and deployable primary mirror telescopes. We believe that the study in this letter will contribute to the applications of the CNN-based technique for piston sensing.
KEYWORDS: Optical transfer functions, Modulation transfer functions, Telescopes, Point spread functions, Mirrors, James Webb Space Telescope, Error analysis, Diffraction, Fourier transforms, Fourier optics
Astronomical observation wants more distant and fainter object with a better resolution, larger primary mirror telescopes are needed to improve the diffraction limit and increase the collected light energy, but limited by monolithic primary mirror manufacture, testing, transportation and launch. And segmented telescopes can address these. However, segmented telescopes also introduce co-phasing errors. In this paper, we put forward a new method to measure piston error based on analyzing the intensity distribution and Fourier optics principle. This method can detect the piston error with a high accuracy in a larger capture when the residual tip-tilt error still exists. A point source is taken as the object of the segmented telescope, the pattern focused on the CCD is recorded as the point spread function (PSF). Fourier transform is performed for the PSF. And we can obtain the optical transfer function (OTF) which is composed of the modulation and phase transfer functions (MTF and PTF). Then we derive the relationships between the piston error and the MTF′s side-lobe peaks and we found that tip-tilt error influences the accurate detection of piston error in term of the relationship. Thus, we take the MTF′s side-lobe peaks obtained when only tip-tilt error exists as the normalized factor, then the influences of tip-tilt error is removed. Simulation has been done to validate the feasibility of the method. The results state that this method's capture range is the operating light′s coherence length, the accuracy is 10.0nm RMS, preliminary experimental results also proved the assumption.
We propose a MTF non-redundant distribution method, with which the multi-piston errors of segmented telescope can be detected simultaneously. A mask with a sparse multi-subaperture configuration is set in the exit pupil of the segmented telescope. One subaperture matches to one segment and samples the wave-front reflected by this segment. Coherent diffraction patterns, produced by each pair of the wave-fronts, are recorded as point spread function (PSF). A Fourier transform is performed for the PSF to obtain the optical transfer function (OTF). Then, relationship between the piston error and the amplitudes of the MTF sidelobes is derived. The piston error can be retrieved accurately by this relationship, and the capture range is the coherent length of the operating light. The key to realize a multi-piston errors simultaneous detection using this relationship is to avoid overlap of the MTF sidelobes which formed by each pair of subwaves. We research and derive the MTF model of a mask with a sparse multi-subaperture configuration. According to Fourier optics principle, the MTF distribution of this model is analyzed, and rules for the MTF sidelobes non-redundant distribution are obtained. Simulations have been done to validate the rules. Taking an 18-segment mirror as an example, a mask with a sparse 18 sub-apertures configuration is designed to realize the MTF sidelobes non-redundant distribution. Thus, just need to set a mask with a sparse multi-subaperture configuration in the conjugate plane of the segmented mirror, the piston errors of the full aperture can be retrieved simultaneously.
Segmented and deployable primary mirror telescope is adopted to realize a higher resolution observation. Meanwhile the cophasing error is introduced. The piston error between the segments should be smaller than λ/20 RMS to achieve a diffraction-limited imaging. However the initial piston error is about 200 μm. A high-accurate piston error measurement with a large capture range is needed. We propose a method to simultaneously detect the multi-piston errors between segments with a high accuracy in a large capture range. A mask with a sparse sub-aperture configuration is set in the exit-pupil plane of the telescope to sample the wave from the segments. The relation between the piston error of any two segments and the amplitude of the modulation transfer function (MTF) sidelobes (MTFnph) is derived according to the Fourier optics principle. The piston error can be retrieved by this relation after measuring the MTFnph. Simulation and experiments have been carried out to validate the feasibility of the method. The results state that this method's capture range is the operating light’s coherence length, the accuracy is 0.026λ RMS (λ = 633 nm). The MTF model of a mask with sparse multi-subaperture configuration is established. The arrangement rules, to avoid the sidelobes overlapping, are obtained. The mask with a sparse 18 subaperture configuration is designed, which makes the MTF sidelobes distribution non-redundant. Consequently, just a mask with a sparse multi-subaperture configuration is needed, simultaneous detection of the multi-piston errors can be realized in term of this method.
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