In astronomy, the images are sometimes undersampled. In the previous research works, image reconstructions have to be employed to recover the lost information from a set of undersampled images to achieve a high-resolution image using dithering or drizzle methods, which increase the complexity of alignment processes and make the real-time correction impossible. In this paper, the telescope is aligned by changing the positions of the secondary mirror using sharpness function method combined with the stochastic parallel gradient descent algorithm based on both well-sampled and undersampled images without image reconstructions. To improve the accuracy and robustness of the alignment, a new metric called relative root mean square error is proposed. Both numerical simulations and experiments are implemented, and the alignment precisions are measured by wavefront residual errors using Shack-Hartmann wavefront sensors. The results show that the correction processes can converge stably and quickly whether the images are well-sampled or undersampled. In experiments, the average wavefront error is 0.0595 λ for undersampled images and 0.0548 λ for well-sampled images after the telescope alignment, indicating that the misalignments are well compensated for both well-sampled and undersampled images.

/pdf/telescopes-alignment-using-the-sharpness-function-method-4dnv6hixt5.pdf

Telescopes Alignment Using the Sharpness Function Method Based on Undersampled Images

The optical alignment of telescopes is essential to satisfy the high request of image quality. One of the most easy and efficient approaches to correct the misalignments is based on the far-field images in the focal plane by maximizing sharpness metrics. To analyze the aberrations corresponding to different fields and various working conditions of telescopes, the image segmentation becomes an indispensable process. After image segmentation, aberrations can be studied in detail. What’s more, it can also simplify the calculation. In this paper, OTSU method based on one-dimension histogram is adopted to segment the telescope images. First, images corresponding to different fields of the telescope in both designed and misaligned working conditions are simulated. Second, these images are segmented by the OTSU method to obtain a series of binary images. To verify the anti-noise capability of this method, noise images are simulated by adding Gaussian noise with different standard deviations. These noise images are also segmented by OTSU method. Then, edge checks are carried out to compare the segmentation results of noiseless images with noise images. The results indicate that for noiseless images and noise images simulated in designed working condition, the segmentation processes are accurately, while for noise images simulated in misaligned working condition, the segmentation results are influenced by noise.

Telescope images segmentation with OTSU method

To satisfy the demands of high image quality and resolutions, telescope alignment is indispensable. In this paper, a wavefront sensorless method based on a modified stochastic parallel gradient descent algorithm (SPGD) called the adaptive moment estimation SPGD (Adam SPGD) algorithm is proposed. Simulations are carried out using a four-mirror telescope, whose aperture is 6 m and fields of view are Φ2°. Three misalignments are shown as examples. Positions of the secondary mirror and third mirror are employed to compensate aberrations. The results show that merit functions and energy distributions of corrected images match with the designed ones. The mean RMS of residual wavefront errors is smaller than λ/14 (λ = 0.5 μm), indicating that the misalignments are well compensated. The results verify the effectiveness of our method. 

Telescope Alignment Method Using a Modified Stochastic Parallel Gradient Descent Algorithm

Image definition will be influenced by alignment errors of mirrors in an optical system consisting of hyperbolic, parabolic or ellipse mirrors. The major factors of alignment errors are gravity, wind loads and heat exchange for some optical systems like ground-based telescopes, while vibration and temperature gradient for systems like space telescopes. Larger telescopes are more sensitive to these error sources, which becomes the concerns of researchers. So the alignment errors of mirrors must be corrected in time to keep systems working in best condition. In order to solve the problem, many methods are proposed based on the detection of wave-front errors using wave-front sensors like Hartmann-Shack. However, wave-front sensors may not be used or cause optical systems to be more complicated. For example, multi-fields must be tested when telescope is working. On the one hand, if a wave-front sensor is used, it must be moved around imaging plane, on the other hand, if more wave-front sensors are used, system must be more complicated. So a new method is discussed for alignment error correction by evaluating the quality of spot diagrams based on the using of stochastic parallel gradient descent (SPGD) algorithm. The method considers the performance metric like spot diagram radius as a function of control parameters and then uses the SPGD optimization algorithm to improve the performance metric. The control parameters include positions of mirrors. The iteration process must be used in the right way to control position parameters. If it is not considered, a problem may come up that positions of spot diagrams may be influenced by the iteration. Furthermore, spot diagrams will probably disappear from detectors. Then the radii of spot diagrams are not correct. So a better way is put forward by the combination of de-center and tilt of mirrors. The way ensures that the position error produced by de-center and tilt are compensated for. A formula is provided in this paper to give the relationship between them. Based on the analysis, an optical system is designed to verify the conclusion. The SPGD algorithm is achieved by computer programming and the position of the mirror is controlled by a hexapod. Firstly, the problem is verified that the spot diagram will disappear from the detector with a normal iteration process. Then the new way is implemented. In the iteration process, the spot diagram is always in the center of the detectors. In order to prove the feasibility of the method, three different alignment errors are tested and all of them each give an Airy disk finally. The experiment can provide reference for engineering practice.

Experimental research of alignment error correction by aspheric mirror based on the function of imaging quality

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Experimental research of alignment error correction by aspheric mirror based on the function of imaging quality