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Aberration correction based on wavefront sensorless adaptive optics in membrane diffractive optical telescope
Optics Communications 451 (2019) 220–225
Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Aberration correction based on wavefront sensorless adaptive optics in membrane diffractive optical telescope Licheng Zhu a,b,c , Lianghua Wen a,b,c , Ping Yang a,b , Zhenghua Guo a,b,c , Wei Yang a,b , Bing Xu a,b ,∗, Chunlin Guan a,b a
Key laboratory on Adaptive Optics, Chinese Academy of Sciences, Chengdu 610209, China Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China c University of Chinese Academy of Sciences, Beijing 100049, China b
ARTICLE
INFO
Keywords: Membrane diffractive optical telescope Adaptive optics Aberration correction Extended target imaging
ABSTRACT The membrane diffractive optical telescopes are one of areas of active research of large aperture optical telescopes. However, due to the processing technology of thin membrane mirror, the changes of temperature and humidity, etc., the imaging performance of membrane diffractive optical telescope is degraded sharply and it is difficult to reach the design target. Adaptive optics (AO) technology is a potential solution to improve the imaging performance of this telescope. Our work is the first time to correct system aberration of hundred millimeter-level aperture membrane diffractive optical telescope based on AO technology. The point target and extended target imaging experiment of the telescope with WFSless AO system in the laboratory are accomplished. The experimental results demonstrate the effectiveness of AO correction in improving the imaging performance of membrane diffractive optical telescope. Especially when there are unexpected aberrations introduced in the telescope, such as disturbances caused by assembly and operation, AO correction will be an important guarantee for the telescope to maintain good imaging performance.
1. Introductiion Optical imaging systems are used in remote sensing and deep space detection. In order to achieve high spatial resolution, the optical imaging system generally needs to have a larger aperture mirror. Therefore, some new optical imaging systems including single large aperture reflector telescope [1–3], large segmented mirror telescope [4], large aperture membrane diffractive optical telescopes [5–10] and so on have been studied in recent decades. However, as apertures increasing in size, the surface figure of primary mirror of single large aperture telescope becomes increasingly difficult in processing and maintaining, besides, it is also difficult to launch and deploy due to the large volume and mass. The segmented mirror provided a feasible solution to the problem of launch, but the complexity of the imaging system is increasing sharply due to high quality requirement of stitched optical mirrors. The primary collector of diffractive optical telescopes is a transmissive membrane with a focusing diffraction pattern. The membrane is thin, small mass, and easy to be duplicated and integrated. Furthermore, the foldable features of the membrane significantly reduce the size of the system before the space deployment. Therefore, the large aperture membrane diffractive optical telescope has become an area of active research in large aperture and light-mass imaging system.
Since the idea of using Fresnel zone plate as a lightweight highresolution telescope was put forward by Chensnokov and Vasileisky in the International Space Optical conference [11], the focus of research on large aperture membrane diffractive imaging system has gradually shifted to the manufacture and ground demonstration of telescope prototype [5,6,11]. In 2010, as a direct successor to the Eyeglass program, the Membrane Optical Imager Real-time Exploitation (MOIRE) program was sponsored by DARPA [12], which aimed to develop the key technology of persistent and real-time video imaging system with lightweight, deployable structures and low-cost in geosynchronous orbit. The ground demonstration of a single diffractive optical element had been completed and a scene image was successfully captured in 2014. However, the imaging resolution of the theoretical design was not achieved. The researchers concluded that the degraded image was mainly related to unavoidable structural errors and deformation errors of membrane material which caused by photoresist-coating processing and change of moisture expansion coefficient of materials [13]. Additionally, the system optical error will be generated by the instability of the structure during the telescope deployment and working. Therefore, the various wavefront aberrations caused by the above factors are introduced in imaging system, which eventually lead to low spatial
∗ Correspondence to: Box 350, Shuangliu, Chengdu, Sichuan, China. E-mail address: [email protected] (B. Xu).
https://doi.org/10.1016/j.optcom.2019.06.063 Received 22 April 2019; Received in revised form 18 June 2019; Accepted 24 June 2019 Available online 26 June 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
L. Zhu, L. Wen, P. Yang et al.
Optics Communications 451 (2019) 220–225
resolution imaging and become one of the key problems for membrane diffractive optical telescopes in application. In order to achieve the diffraction-limited spatial resolution of membrane diffractive optical telescopes, it is necessary to correct the wavefront aberrations effectively. The annual report of the MOIRE program mentioned that the adaptive optics (AO) technique would be adopted in the follow-up research to correct wavefront aberrations. AO was proposed to correct various wavefront aberrations, which was widely used for ground-based astronomical telescopes [14–16]. Remarkably, the effectiveness of aberration correction for the Fresnel zone plates by AO was firstly verified in a practical system recently [17]. However, there is neither report about the application of AO to the whole membrane diffractive optical telescope at present, nor the correction experiment for the extended target imaging. In this paper, considering the wavefront aberration is quasistatic without atmosphere turbulence in the laboratory, so the control bandwidth of AO system is relatively relaxed. Furthermore, for AO correction of extended target imaging, the Shack–Hartmann wavefront sensor and the specific correlation algorithms are needed [18,19], while the wavefront sensorless adaptive optics (WFSless AO) has simple principle and compact structure, which is more consistent with the correction requirements of point target and extended target. Accordingly, the point target and extended target correction experiments of the membrane diffractive optical telescope in the laboratory are carried out. The imaging system improvements after WFSless AO correction are demonstrated by far-field intensity and the modulation transform function (MTF) of telescope. The correction effect of extended imaging is demonstrated by the image resolution. This paper is organized as follows. In Section 2, the WFSless AO technique is briefly introduced, and the image quality metrics and SPGD algorithm used in this paper are described in detail. The correction experiments of wavefront aberrations are completed in Section 3. The experimental results are also analyzed and discussed in Section 3. Finally, the conclusions of experiments are presented in Section 4.
Fig. 1. The schematic of WFSless AO system.
Fig. 2. Schematic diagram of membrane diffractive optical telescope.
2. Theoretical basis Fig. 3. The imaging effect of original system (long exposure) and optical layout of experiment.
2.1. WFSless AO technique The WFSless AO technique does not need real-time wavefront measurement. The wavefront corrector is directly controlled by feedback according to an image quality metric of the far-field image to compensate the wavefront aberration. The schematic of the WFSless AO system is shown in Fig. 1. The incident wavefront with various wavefront aberrations is reflected by the deformable mirror (DM), and then focused on the focal plane through a lens. The far-field intensity is sampled by a CCD camera. By generating perturbations on the DM, the change of relative image quality metric of far-field intensity is calculated. Based on the positive correlation between the metric and the residual aberration, the scope and amplitude of the perturbations on DM are optimized according to the change of metric, so that the image quality metric is improved finally and residual aberration approaches to the local minimum value. In Fig. 1, the incident wavefront aberration is 𝛷(𝑥, 𝑦) and the DM’s correction aberration is 𝛹 (𝑥, 𝑦), the expected control objective is to minimize the residual aberration 𝑅 (𝑥, 𝑦) = 𝛷 (𝑥, 𝑦) − 𝛹 (𝑥, 𝑦), during iterations.
aberration 𝑅(𝑥′ , 𝑦′ ) and the I (x, y) at the far-field image plane can be expressed by [20]: [( )2 ( )2 ] | | 𝑗𝑘 𝑥′ − 𝑦 + 𝑦′ − 𝑦 | | [ ( ′ ′ )] | | 𝐼 (𝑥, 𝑦) = | 𝐴 ⋅ exp 𝑗𝑅 𝑥 , 𝑦 ⋅ 𝑒𝑥𝑝 𝑑𝑥′ 𝑑𝑦′ | , |∬ | 2𝑧 | | | | (1) where (x, y) is the coordinate of far-field image plane, the focal length of the lens is z, k = 2𝜋∕𝜆, 𝜆 is the wavelength of imaging light. When there are no aberrations (𝑅(𝑥′ , 𝑦′ ) = 0) the image is an Airy pattern. Accordingly, the image quality metric (J ) selected in this paper is the image sharpness function of the far-field intensity which is normalized to adapt to the possible situation of intensity fluctuation of the far-field intensity [21]. With the optimal image quality metric, the aberrated PSF of system will be corrected effectively. 𝐽=
2.2. Image quality metric
∬ 𝐼(𝑥, 𝑦)2 𝑑𝑥𝑑𝑦 (∬ 𝐼(𝑥, 𝑦)𝑑𝑥𝑑𝑦)2
,
(2)
2.3. SPGD algorithm
In point target imaging, the PSF of system is an image of a point source located on the optical axis with amplitude A, which is equivalent to the far-field intensity distribution I (x, y). The PSF of the imaging system will be distorted when there is aberration in the system. Therefore, according to Fourier optics, the relationship between the residual
In this paper, the Stochastic Parallel Gradient Descent (SPGD) algorithm [22] was implemented to directly control the voltage signals u = {u1, u2, . . . , u140} of 140 actuators of DM according to changes of 221
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Optics Communications 451 (2019) 220–225
Fig. 4. The experiment of the diffractive optical telescope system with adaptive optics correction. Table 1 Parameters of the membrane diffractive optical telescope.
image quality metric(𝛥J). The actuator control signals for next iteration can be determined by: = 𝑢𝑖(𝑘) + 𝛼𝛥𝐽 (𝑘) 𝛥𝑢(𝑘) 𝑢(𝑘+1) 𝑖 , 𝑖
(3)
(𝑘) (𝑘) (𝑘) 𝛥𝑢(𝑘) 𝑖 = 𝛥𝑢1 , 𝛥𝑢1 , … , 𝛥𝑢140 ,
(4)
𝛥𝐽
(𝑘)
=𝐽
(𝑘)
(𝑢 + 𝛥𝑢) − 𝐽
(𝑘)
(𝑢 − 𝛥𝑢) ,
(5)
where the k represents iteration number, 𝛼 is a gain coefficient which can be used to adjust the size of the control parameter corrections. The 𝛥u is random perturbations with fixed amplitude, and the 𝛥J means the gradient estimation in k iteration. It should be noted the telescope has multiple diffraction orders of imaging light due to its binary optical structure, which results in low signal-to-noise ratio. For instance, in the two steps Fresnel zone plate, the theoretical diffraction efficiency of −1 order is 40.5% which is equal to that of +1 order, therefore, the stray light that is not used for diffraction imaging will be superimposed on the imaging plane, which will eventually lead to image quality degradation, as shown in Fig. 3(a). Accordingly, in point target imaging experiment, a diaphragm is used between the telescope and secondary mirror, which allows the order of greatest diffraction efficiency to pass through but blocks other orders, so that we can shield the effect of other diffraction orders on imaging. The optical layout of the experiment is shown in Fig. 3(b).
Parameters
Value
Effective aperture Field (2𝜔) Operating wavelength Effective focal length Diffraction efficiency Total length of optical path
80 mm 0.4◦ 0.48 ∼ 0.65 μm 371.3 mm 30% 1101.49 mm
is 3.5 μm, one diaphragm, a computer control system and a CCD camera. The collimated light is used for simulating the imaging light of an infinite point target, which passes through the telescope and converges into imaging spot at the end of telescope firstly. Then, the convergent light is narrowed and collimated for matching the aperture of DM, the diaphragm is arranged in the mirror group to remove other orders imaging lights. The far-field spot is sampled by focusing the corrected collimated light, and sampled by CCD camera. The image quality metric and feedback signal are calculated by the computer control system, and the DM is controlled by feedback signal synchronously. The aberration correction experiment of membrane diffractive optical telescope is carried out based on the SPGD algorithm by WFSless AO system. The far-field intensity are sampled and recorded in real time. In order to verify the correction capability of WFSless AO system, the artificial wavefront aberration is also added by the DM, which can simulate other system optical error introduced by external factors.
3. Experimental validation 3.1. Introduction of membrane diffractive optical telescope
3.3. Results and discussion The membrane diffractive optical telescope used in this paper is composed of a transmissive membrane, relay lens, achromatic lens and condensing lens. The transmissive membrane is two-level phasetype Fresnel zone plates (FZP) [23] which is made of polyimide film. The imaging process of the membrane diffractive optical telescope is that the imaging beam is firstly collected by the membrane FZP. Then, the chromatic aberration is corrected by the achromatic lens. The corrected beam is finally imaged on the far-field image plane through the condensing lens. The main telescope parameters are shown in Table 1, the prototype of the telescope is shown in Fig. 2.
3.3.1. Point target The far-field focal spot and corresponding three-dimensional focal plane intensity distribution of the original system, before and after closed loop correction are shown in Fig. 5. From Fig. 5(a), we can see that the far-field intensity of original system can achieve to 692 ADU. If we add random aberration in the system by sending random voltages to MEMS DM, the focal spot is diffused, and the maximum value of far-field intensity is only 406 ADU. When the aberration is corrected by WFSless AO with the SPGD algorithms, the maximum value is up to 916 ADU. The results show that the far-field focal spot has been optimized by WFSless AO correction which not only compensates the added aberration, but also improves the original system. The MTF curves of the membrane diffractive optical telescope are calculated and shown in Fig. 6. We can see that there is a remarkable decrease in the MTF when we add random aberration in the imaging system, which means that the wavefront aberration significantly weakens the moderate frequency components of the original telescope
3.2. Experiment arrangement The experiment of a diffractive optical telescope system with adaptive optics correction is shown in Fig. 4. For point target experiment, the system is composed of a 632 nm collimated light, a membrane diffractive optical telescope, a microelectromechanical systems (MEMS) DM with 140 actuators, for which the maximum actuator displacement 222
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Optics Communications 451 (2019) 220–225
Fig. 5. The correction effects of point target. The title ‘‘original’’ is the original system without correction. The ‘‘Aberration’’ represents the system with added aberration. The ‘‘AO corrected’’ stands for the result of WFSless AO correction based on SPGD algorithm.
system, thus causing low average intensity and blurred imaging. However, comparing the MTF curves before and after correction, we can find that the moderate frequency is enhanced apparently after WFSless AO correction. At the same time, the MTF of the system is also higher than the original value. Accordingly, the result shows that the PSF of the imaging system is optimized by WFSless AO correction, so the imaging performance of the telescope is expected to be improved. The original resolution of LR1 is 16 lp/mm. The WFSless AO correction are carried out with the LR1∼LR4 images. The corresponding resolutions increase to 28.5 lp/mm, 32 lp/mm, 35.9 lp/mm and 40.3 lp/mm. The results show that in the corrected imaging regions, the smaller the CCD sizes, the better the correction effects. 3.3.2. Extended target ( ) The incoherent image 𝐼 𝑥𝑖 , 𝑦𝑖 of the extended source is equivalent to the superposition of the images of all point sources forming the object, the essence of which is the convolution of the object intensity ( ) ( ) function 𝐼0 𝑥𝑖 , 𝑦𝑖 and the PSF of imaging system ℎ 𝑥𝑖 , 𝑦𝑖 [24].
Fig. 6. The MTF curves of membrane diffractive optical telescope in three situations. The curve represented by legend ‘‘original’’ is the original MTF of telescope without correction. The ‘‘Aberration’’ represents the MTF of telescope with added aberration. The ‘‘AO corrected’’ stands for the result of MTF curve with WFSless AO correction based on SPGD algorithm.
( ) ( ) ( ) 𝐼 𝑥𝑖 , 𝑦𝑖 = 𝐼0 𝑥𝑖 , 𝑦𝑖 ∗ ℎ 𝑥𝑖 , 𝑦𝑖
Fig. 7. The correction experiment of extended target imaging.
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Optics Communications 451 (2019) 220–225
into plane wave for simulating extended target imaging at infinity. In particular, because the stray light entering the sampling plane of CCD is less and difficult to separate in the extended target imaging, so the influence of stray light is not considered in this experiment, and the corresponding diaphragm used in point target will also be removed. The correction experiment of extended target imaging is shown in Fig. 7. In order to simulate different size of CCD in real application, four kinds of CCD sizes are selected in the correction experiments which are 1024 × 1024, 512 × 512, 256 × 256, and 128 × 128 pixels respectively. We named them local regions of image (LR1∼LR4). The small target images are taken from the central region of the larger target images. The corresponding image quality metrics are calculated under the constant exposure time, and 1000 iteration optimization corrections are carried out. The experimental results are shown in Fig. 8. However, when the deformable mirror voltages are maintained after correcting the small target images (LR2∼LR4) and then imaging the whole extended target (LR1), we find that not all parts of the images have been improved. Compared with the original image, the image qualities of the outer parts of corrected regions are slightly reduced. The smaller corrected regions corresponding to the more obvious degradation effects. Furthermore, we chosen three another LR images which are not in the central region of the original image, named LR5∼LR7. After AO correction, the LR5∼LR7 images also become clear. However, compared with the correction results of LR2∼LR4, the degradations of the outer parts of LR5∼LR7 are more obvious, as shown in Fig. 9. We consider that this is determined by the imaging principle of extended target and the WFSless AO correction scheme. Firstly, the essence of WFSless AO is to correct the aberrated PSF of the imaging system, which ability has been proved in point target experiments. Therefore, the WFSless AO is also capable of correcting aberrations in extended target imaging based on the assume of spatial invariance of imaging system. However, the correction field of view of AO system is small due to the anisoplanatism [26], so that it is difficult to achieve excellent correction effect in wide field of view by a single AO system. But the small LR images are approximately equivalent to the independent isoplanar regions [20]. in which the distortions of PSF are smaller, so the AO system can achieve the better correction effects in the LR images. Of course, there are also some slight degradations of image quality outside the correction regions. This is because the different estimations of PSF between the corrected and uncorrected regions. The small LR images corresponding to the much differences of estimated PSF between the corrected and uncorrected regions. Therefore, there
Fig. 8. The LR1∼LR4 target images and the corresponding correction results.
The aberrated PSF causes the imaging system to have reduced spatial resolution. Consequently, it is available to improve the spatial resolution of imaging system by correcting the aberrated PSF. We extend the WFSless AO correction to the imaging of extended sources, and analyze the correction effect of the WFSless AO system for wavefront aberrations. Since the image sharpness function used in Section 2.2 is also suitable for image quality evaluation of extended targets [25], the same image quality metric as point target will be used in the correction experiment of extended targets. The extended target experiment can be carried out by replacing the collimated light in the point target experiment with the extended light source and using the identification plate (USAF 1951) as the extended target. The positive lens is used to convert divergent spherical wave
Fig. 9. The full-target images corrected by LR images. (The correction regions are in the red boxes, the regions with better imaging effect are shown in the yellow boxes, and the orange arrows point to the regions with image degradation).. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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will be more obvious degradation effects in the outer parts of the small LR images. Secondly, the central region of the extended target image is closer to the optical axis of the imaging system. In this paraxial approximation region, the imaging system is to be approximately spatial invariant, so the PSF distortion in the central region is smaller. In contrast, the PSF distortions are more serious in the regions which are far away from the center parts of original image. Therefore, the PSF estimations in the edge regions are not as accurate as that in the center regions. Consequently, the degradations of the outer parts of LR5∼LR7 are more serious than LR2∼LR4.
[3] M. Clampin, Overview and status of the james webb space telescope observatory, Iau Special Session, Vol. 1, 2012. [4] M. Nagashima, B.N. Agrawal, Active control of adaptive optics system in a large segmented mirror telescope, Internat. J. Systems Sci. 45 (2014) 159–175. [5] R.A. Hyde, Eyeglass. 1. Very large aperture diffractive telescopes, Appl. Opt. 38 (1999) 4198–4212. [6] R.A. Hyde, S.N. Dixit, M.C. Rushford, Eyeglass: a very large aperture diffractive space telescope, in: Highly Innovative Space Telescope Concepts, 2002, 2002, pp. 28–39. [7] M. Dearborn, B. Isch, T. Johnson, A. Macdonald, E. Peek, C. Lomanno, C. Sheffield, E. Swenson, FalconSAT-7—A Deployable Solar Telescope, 2014. [8] Paul D. Atcheson, et al., MOIRE: initial demonstration of a transmissive diffractive membrane optic for large lightweight optical telescopes, in: Space Telescopes and Instrumentation 2012: Optical, Infrared, and Millimeter Wave, International Society for Optics and Photonics, 2012. [9] L. Koechlin, M. Yadallee, T. Raksasataya, A. Berdeu, New progress on the fresnel imager for UV space astronomy, Astrophys. Space Sci. 354 (2014) 147–153. [10] H.P. Stahl, T.M. Henrichs, Update to single-variable parametric cost models for space telescopes, Opt. Eng. 49 (073006-) (2010) 073006–073013. [11] Y.M. Chesnokov, A.S. Vasilevsky, Space-Based Very High Resolution Telescope based on amplitude zone plate at in conf. of space optics, (Toulouse Labege, France, 1997). [12] J.L. Domber, P. Atcheson, J. Kommers, MOIRE: Ground test bed results for a large membrane telescope, in: AIAA SciTech Forum, Spacecraft Structures Conference, Vol. 1510, 2014, pp. 1–17. [13] R. Hansen, Developing lightweight optics for space, Sci. Tech. Rev. (2013). [14] D.G. Sandler, T.K. Barrett, D.A. Palmer, R.Q. Fugate, W.J. Wild, Use of a neural network to control an adaptive optics system for an astronomical telescope, Nature 351 (1991) 300–302. [15] P. Wizinowich, D.S. Acton, C. Shelton, P. Stomski, J. Gathright, K. Ho, W. Lupton, K. Tsubota, O. Lai, C. Max, First Light Adaptive Optics Images from the Keck II Telescope: A New Era of High Angular Resolution Imagery, Vol. 112, Publications of the Astronomical Society of the Pacific, 2000, pp. 315–319. [16] J. Kubby, Applications of MEMS in segmented mirror space telescopes, in: Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7931, 2011, pp. 568–573. [17] W. Lianghua, P. Yang, Y. Kangjian, C. Shanqiu, W. Shuai, L. Wenjing, B. Xu, Synchronous model-based approach for wavefront sensorless adaptive optics system, Opt. Express 25 (2017) 20584. [18] L.A. Poyneer, Scene-based shack-hartmann wave-front sensing: analysis and simulation, Appl. Opt. 42 (2003) 5807–5815. [19] P.A. Knutsson, M. Ownerpetersen, C. Dainty, Extended object wavefront sensing based on the correlation spectrum phase, Opt. Express 13 (2005) 9527–9536. [20] J.W. Goodman, Introduction to Fourier Optics (2004). [21] R.A. Muller, A. Buffington, Real time correction of atmospherically degraded telescope images through sharpening, JOSA 64 (1974) 1200–1210. [22] M.A. Vorontsov, V.P. Sivokon, Stochastic parallel-gradient-descent technique for high-resolution wave-front phase-distortion correction, J. Opt. Soc. Amer. A 15 (1998) 2745–2758. [23] Y. Zhang, J. Chen, X. Yea, Multilevel phase fresnel zone plate lens as a near-field optical element, Opt. Commun. 269 (2007) 271–273. [24] Y. Huizhen, S. Oleg, V. Michel, Model-based wavefront sensorless adaptive optics system for large aberrations and extended objects, Opt. Express 23 (2015) 24587–24601. [25] L.P. Murray, J.C. Dainty, J. Coignus, F. Felberer, Wavefront correction of extended objects through image sharpness maximisation, Proc. Spie 5823 (2013) 40–47. [26] D.L. Fried, Anisoplanatism in adaptive optics, J. Opt. Soc. Amer. 72 (1982) 52–61.
4. Conclusion Above all, in this paper, the WFSless AO is applied for aberration correction in membrane diffractive telescope. The conventional SPGD algorithm is adopted to control the DM for compensating wavefront aberration. As a result, the maximum far-field intensity of point target imaging is improved from 692 ADU to 916 ADU, and the MTF of telescope is optimized, the moderate frequency is enhanced apparently by WFSless AO correction. In addition, the correction experiments of extended imaging in different field of view have been carried out. The method shows the well correction effects in the extended target imaging. Although the imaging field of view is small, the correction frequency and effect can be significantly improved by using the central LR images at the expense of a certain resolution of the edge image. This work is the first time to correct the extended target imaging of hundred millimeter-level aperture membrane diffractive optical telescope based on adaptive optics. In our subsequent research, the new parallel algorithm and image quality metric will be tested to further accelerate the correction process of extended target imaging in wide field of view. Acknowledgments This work was supported by National Natural Science Foundation of China (Grant No. 60978049), Youth Innovation Promotion Association, China, Scientists of Chinese Academy of Sciences (Grant No. 2012280), High Resolution Light Imaging Camera System Technology in Geostationary Orbit, China (Grant No. 2016YFB0500204). References [1] S.E. Kendrick, H.P. Stahl, Large aperture space telescope mirror fabrication trades, in: Space Telescopes and Instrumentation 2008: Optical, Infrared, and Millimeter, International Society for Optics and Photonics, 2008, 70102G-70102G-70112. [2] M. Postman, C.M. Mountain, R. Soummer, W. Traub, K.R. Stapelfeldt, W.R. Oegerle, T.T. Hyde, H.P. Stahl, Advanced technology large-aperture space telescope: science drivers and technology developments, Opt. Eng. 51 (2012) 1007.
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Contents lists available at ScienceDirect
Optics Communications journal homepage: www.elsevier.com/locate/optcom
Aberration correction based on wavefront sensorless adaptive optics in membrane diffractive optical telescope Licheng Zhu a,b,c , Lianghua Wen a,b,c , Ping Yang a,b , Zhenghua Guo a,b,c , Wei Yang a,b , Bing Xu a,b ,∗, Chunlin Guan a,b a
Key laboratory on Adaptive Optics, Chinese Academy of Sciences, Chengdu 610209, China Institute of Optics and Electronics, Chinese Academy of Sciences, Chengdu 610209, China c University of Chinese Academy of Sciences, Beijing 100049, China b
ARTICLE
INFO
Keywords: Membrane diffractive optical telescope Adaptive optics Aberration correction Extended target imaging
ABSTRACT The membrane diffractive optical telescopes are one of areas of active research of large aperture optical telescopes. However, due to the processing technology of thin membrane mirror, the changes of temperature and humidity, etc., the imaging performance of membrane diffractive optical telescope is degraded sharply and it is difficult to reach the design target. Adaptive optics (AO) technology is a potential solution to improve the imaging performance of this telescope. Our work is the first time to correct system aberration of hundred millimeter-level aperture membrane diffractive optical telescope based on AO technology. The point target and extended target imaging experiment of the telescope with WFSless AO system in the laboratory are accomplished. The experimental results demonstrate the effectiveness of AO correction in improving the imaging performance of membrane diffractive optical telescope. Especially when there are unexpected aberrations introduced in the telescope, such as disturbances caused by assembly and operation, AO correction will be an important guarantee for the telescope to maintain good imaging performance.
1. Introductiion Optical imaging systems are used in remote sensing and deep space detection. In order to achieve high spatial resolution, the optical imaging system generally needs to have a larger aperture mirror. Therefore, some new optical imaging systems including single large aperture reflector telescope [1–3], large segmented mirror telescope [4], large aperture membrane diffractive optical telescopes [5–10] and so on have been studied in recent decades. However, as apertures increasing in size, the surface figure of primary mirror of single large aperture telescope becomes increasingly difficult in processing and maintaining, besides, it is also difficult to launch and deploy due to the large volume and mass. The segmented mirror provided a feasible solution to the problem of launch, but the complexity of the imaging system is increasing sharply due to high quality requirement of stitched optical mirrors. The primary collector of diffractive optical telescopes is a transmissive membrane with a focusing diffraction pattern. The membrane is thin, small mass, and easy to be duplicated and integrated. Furthermore, the foldable features of the membrane significantly reduce the size of the system before the space deployment. Therefore, the large aperture membrane diffractive optical telescope has become an area of active research in large aperture and light-mass imaging system.
Since the idea of using Fresnel zone plate as a lightweight highresolution telescope was put forward by Chensnokov and Vasileisky in the International Space Optical conference [11], the focus of research on large aperture membrane diffractive imaging system has gradually shifted to the manufacture and ground demonstration of telescope prototype [5,6,11]. In 2010, as a direct successor to the Eyeglass program, the Membrane Optical Imager Real-time Exploitation (MOIRE) program was sponsored by DARPA [12], which aimed to develop the key technology of persistent and real-time video imaging system with lightweight, deployable structures and low-cost in geosynchronous orbit. The ground demonstration of a single diffractive optical element had been completed and a scene image was successfully captured in 2014. However, the imaging resolution of the theoretical design was not achieved. The researchers concluded that the degraded image was mainly related to unavoidable structural errors and deformation errors of membrane material which caused by photoresist-coating processing and change of moisture expansion coefficient of materials [13]. Additionally, the system optical error will be generated by the instability of the structure during the telescope deployment and working. Therefore, the various wavefront aberrations caused by the above factors are introduced in imaging system, which eventually lead to low spatial
∗ Correspondence to: Box 350, Shuangliu, Chengdu, Sichuan, China. E-mail address: [email protected] (B. Xu).
https://doi.org/10.1016/j.optcom.2019.06.063 Received 22 April 2019; Received in revised form 18 June 2019; Accepted 24 June 2019 Available online 26 June 2019 0030-4018/© 2019 Elsevier B.V. All rights reserved.
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Optics Communications 451 (2019) 220–225
resolution imaging and become one of the key problems for membrane diffractive optical telescopes in application. In order to achieve the diffraction-limited spatial resolution of membrane diffractive optical telescopes, it is necessary to correct the wavefront aberrations effectively. The annual report of the MOIRE program mentioned that the adaptive optics (AO) technique would be adopted in the follow-up research to correct wavefront aberrations. AO was proposed to correct various wavefront aberrations, which was widely used for ground-based astronomical telescopes [14–16]. Remarkably, the effectiveness of aberration correction for the Fresnel zone plates by AO was firstly verified in a practical system recently [17]. However, there is neither report about the application of AO to the whole membrane diffractive optical telescope at present, nor the correction experiment for the extended target imaging. In this paper, considering the wavefront aberration is quasistatic without atmosphere turbulence in the laboratory, so the control bandwidth of AO system is relatively relaxed. Furthermore, for AO correction of extended target imaging, the Shack–Hartmann wavefront sensor and the specific correlation algorithms are needed [18,19], while the wavefront sensorless adaptive optics (WFSless AO) has simple principle and compact structure, which is more consistent with the correction requirements of point target and extended target. Accordingly, the point target and extended target correction experiments of the membrane diffractive optical telescope in the laboratory are carried out. The imaging system improvements after WFSless AO correction are demonstrated by far-field intensity and the modulation transform function (MTF) of telescope. The correction effect of extended imaging is demonstrated by the image resolution. This paper is organized as follows. In Section 2, the WFSless AO technique is briefly introduced, and the image quality metrics and SPGD algorithm used in this paper are described in detail. The correction experiments of wavefront aberrations are completed in Section 3. The experimental results are also analyzed and discussed in Section 3. Finally, the conclusions of experiments are presented in Section 4.
Fig. 1. The schematic of WFSless AO system.
Fig. 2. Schematic diagram of membrane diffractive optical telescope.
2. Theoretical basis Fig. 3. The imaging effect of original system (long exposure) and optical layout of experiment.
2.1. WFSless AO technique The WFSless AO technique does not need real-time wavefront measurement. The wavefront corrector is directly controlled by feedback according to an image quality metric of the far-field image to compensate the wavefront aberration. The schematic of the WFSless AO system is shown in Fig. 1. The incident wavefront with various wavefront aberrations is reflected by the deformable mirror (DM), and then focused on the focal plane through a lens. The far-field intensity is sampled by a CCD camera. By generating perturbations on the DM, the change of relative image quality metric of far-field intensity is calculated. Based on the positive correlation between the metric and the residual aberration, the scope and amplitude of the perturbations on DM are optimized according to the change of metric, so that the image quality metric is improved finally and residual aberration approaches to the local minimum value. In Fig. 1, the incident wavefront aberration is 𝛷(𝑥, 𝑦) and the DM’s correction aberration is 𝛹 (𝑥, 𝑦), the expected control objective is to minimize the residual aberration 𝑅 (𝑥, 𝑦) = 𝛷 (𝑥, 𝑦) − 𝛹 (𝑥, 𝑦), during iterations.
aberration 𝑅(𝑥′ , 𝑦′ ) and the I (x, y) at the far-field image plane can be expressed by [20]: [( )2 ( )2 ] | | 𝑗𝑘 𝑥′ − 𝑦 + 𝑦′ − 𝑦 | | [ ( ′ ′ )] | | 𝐼 (𝑥, 𝑦) = | 𝐴 ⋅ exp 𝑗𝑅 𝑥 , 𝑦 ⋅ 𝑒𝑥𝑝 𝑑𝑥′ 𝑑𝑦′ | , |∬ | 2𝑧 | | | | (1) where (x, y) is the coordinate of far-field image plane, the focal length of the lens is z, k = 2𝜋∕𝜆, 𝜆 is the wavelength of imaging light. When there are no aberrations (𝑅(𝑥′ , 𝑦′ ) = 0) the image is an Airy pattern. Accordingly, the image quality metric (J ) selected in this paper is the image sharpness function of the far-field intensity which is normalized to adapt to the possible situation of intensity fluctuation of the far-field intensity [21]. With the optimal image quality metric, the aberrated PSF of system will be corrected effectively. 𝐽=
2.2. Image quality metric
∬ 𝐼(𝑥, 𝑦)2 𝑑𝑥𝑑𝑦 (∬ 𝐼(𝑥, 𝑦)𝑑𝑥𝑑𝑦)2
,
(2)
2.3. SPGD algorithm
In point target imaging, the PSF of system is an image of a point source located on the optical axis with amplitude A, which is equivalent to the far-field intensity distribution I (x, y). The PSF of the imaging system will be distorted when there is aberration in the system. Therefore, according to Fourier optics, the relationship between the residual
In this paper, the Stochastic Parallel Gradient Descent (SPGD) algorithm [22] was implemented to directly control the voltage signals u = {u1, u2, . . . , u140} of 140 actuators of DM according to changes of 221
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Fig. 4. The experiment of the diffractive optical telescope system with adaptive optics correction. Table 1 Parameters of the membrane diffractive optical telescope.
image quality metric(𝛥J). The actuator control signals for next iteration can be determined by: = 𝑢𝑖(𝑘) + 𝛼𝛥𝐽 (𝑘) 𝛥𝑢(𝑘) 𝑢(𝑘+1) 𝑖 , 𝑖
(3)
(𝑘) (𝑘) (𝑘) 𝛥𝑢(𝑘) 𝑖 = 𝛥𝑢1 , 𝛥𝑢1 , … , 𝛥𝑢140 ,
(4)
𝛥𝐽
(𝑘)
=𝐽
(𝑘)
(𝑢 + 𝛥𝑢) − 𝐽
(𝑘)
(𝑢 − 𝛥𝑢) ,
(5)
where the k represents iteration number, 𝛼 is a gain coefficient which can be used to adjust the size of the control parameter corrections. The 𝛥u is random perturbations with fixed amplitude, and the 𝛥J means the gradient estimation in k iteration. It should be noted the telescope has multiple diffraction orders of imaging light due to its binary optical structure, which results in low signal-to-noise ratio. For instance, in the two steps Fresnel zone plate, the theoretical diffraction efficiency of −1 order is 40.5% which is equal to that of +1 order, therefore, the stray light that is not used for diffraction imaging will be superimposed on the imaging plane, which will eventually lead to image quality degradation, as shown in Fig. 3(a). Accordingly, in point target imaging experiment, a diaphragm is used between the telescope and secondary mirror, which allows the order of greatest diffraction efficiency to pass through but blocks other orders, so that we can shield the effect of other diffraction orders on imaging. The optical layout of the experiment is shown in Fig. 3(b).
Parameters
Value
Effective aperture Field (2𝜔) Operating wavelength Effective focal length Diffraction efficiency Total length of optical path
80 mm 0.4◦ 0.48 ∼ 0.65 μm 371.3 mm 30% 1101.49 mm
is 3.5 μm, one diaphragm, a computer control system and a CCD camera. The collimated light is used for simulating the imaging light of an infinite point target, which passes through the telescope and converges into imaging spot at the end of telescope firstly. Then, the convergent light is narrowed and collimated for matching the aperture of DM, the diaphragm is arranged in the mirror group to remove other orders imaging lights. The far-field spot is sampled by focusing the corrected collimated light, and sampled by CCD camera. The image quality metric and feedback signal are calculated by the computer control system, and the DM is controlled by feedback signal synchronously. The aberration correction experiment of membrane diffractive optical telescope is carried out based on the SPGD algorithm by WFSless AO system. The far-field intensity are sampled and recorded in real time. In order to verify the correction capability of WFSless AO system, the artificial wavefront aberration is also added by the DM, which can simulate other system optical error introduced by external factors.
3. Experimental validation 3.1. Introduction of membrane diffractive optical telescope
3.3. Results and discussion The membrane diffractive optical telescope used in this paper is composed of a transmissive membrane, relay lens, achromatic lens and condensing lens. The transmissive membrane is two-level phasetype Fresnel zone plates (FZP) [23] which is made of polyimide film. The imaging process of the membrane diffractive optical telescope is that the imaging beam is firstly collected by the membrane FZP. Then, the chromatic aberration is corrected by the achromatic lens. The corrected beam is finally imaged on the far-field image plane through the condensing lens. The main telescope parameters are shown in Table 1, the prototype of the telescope is shown in Fig. 2.
3.3.1. Point target The far-field focal spot and corresponding three-dimensional focal plane intensity distribution of the original system, before and after closed loop correction are shown in Fig. 5. From Fig. 5(a), we can see that the far-field intensity of original system can achieve to 692 ADU. If we add random aberration in the system by sending random voltages to MEMS DM, the focal spot is diffused, and the maximum value of far-field intensity is only 406 ADU. When the aberration is corrected by WFSless AO with the SPGD algorithms, the maximum value is up to 916 ADU. The results show that the far-field focal spot has been optimized by WFSless AO correction which not only compensates the added aberration, but also improves the original system. The MTF curves of the membrane diffractive optical telescope are calculated and shown in Fig. 6. We can see that there is a remarkable decrease in the MTF when we add random aberration in the imaging system, which means that the wavefront aberration significantly weakens the moderate frequency components of the original telescope
3.2. Experiment arrangement The experiment of a diffractive optical telescope system with adaptive optics correction is shown in Fig. 4. For point target experiment, the system is composed of a 632 nm collimated light, a membrane diffractive optical telescope, a microelectromechanical systems (MEMS) DM with 140 actuators, for which the maximum actuator displacement 222
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Fig. 5. The correction effects of point target. The title ‘‘original’’ is the original system without correction. The ‘‘Aberration’’ represents the system with added aberration. The ‘‘AO corrected’’ stands for the result of WFSless AO correction based on SPGD algorithm.
system, thus causing low average intensity and blurred imaging. However, comparing the MTF curves before and after correction, we can find that the moderate frequency is enhanced apparently after WFSless AO correction. At the same time, the MTF of the system is also higher than the original value. Accordingly, the result shows that the PSF of the imaging system is optimized by WFSless AO correction, so the imaging performance of the telescope is expected to be improved. The original resolution of LR1 is 16 lp/mm. The WFSless AO correction are carried out with the LR1∼LR4 images. The corresponding resolutions increase to 28.5 lp/mm, 32 lp/mm, 35.9 lp/mm and 40.3 lp/mm. The results show that in the corrected imaging regions, the smaller the CCD sizes, the better the correction effects. 3.3.2. Extended target ( ) The incoherent image 𝐼 𝑥𝑖 , 𝑦𝑖 of the extended source is equivalent to the superposition of the images of all point sources forming the object, the essence of which is the convolution of the object intensity ( ) ( ) function 𝐼0 𝑥𝑖 , 𝑦𝑖 and the PSF of imaging system ℎ 𝑥𝑖 , 𝑦𝑖 [24].
Fig. 6. The MTF curves of membrane diffractive optical telescope in three situations. The curve represented by legend ‘‘original’’ is the original MTF of telescope without correction. The ‘‘Aberration’’ represents the MTF of telescope with added aberration. The ‘‘AO corrected’’ stands for the result of MTF curve with WFSless AO correction based on SPGD algorithm.
( ) ( ) ( ) 𝐼 𝑥𝑖 , 𝑦𝑖 = 𝐼0 𝑥𝑖 , 𝑦𝑖 ∗ ℎ 𝑥𝑖 , 𝑦𝑖
Fig. 7. The correction experiment of extended target imaging.
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into plane wave for simulating extended target imaging at infinity. In particular, because the stray light entering the sampling plane of CCD is less and difficult to separate in the extended target imaging, so the influence of stray light is not considered in this experiment, and the corresponding diaphragm used in point target will also be removed. The correction experiment of extended target imaging is shown in Fig. 7. In order to simulate different size of CCD in real application, four kinds of CCD sizes are selected in the correction experiments which are 1024 × 1024, 512 × 512, 256 × 256, and 128 × 128 pixels respectively. We named them local regions of image (LR1∼LR4). The small target images are taken from the central region of the larger target images. The corresponding image quality metrics are calculated under the constant exposure time, and 1000 iteration optimization corrections are carried out. The experimental results are shown in Fig. 8. However, when the deformable mirror voltages are maintained after correcting the small target images (LR2∼LR4) and then imaging the whole extended target (LR1), we find that not all parts of the images have been improved. Compared with the original image, the image qualities of the outer parts of corrected regions are slightly reduced. The smaller corrected regions corresponding to the more obvious degradation effects. Furthermore, we chosen three another LR images which are not in the central region of the original image, named LR5∼LR7. After AO correction, the LR5∼LR7 images also become clear. However, compared with the correction results of LR2∼LR4, the degradations of the outer parts of LR5∼LR7 are more obvious, as shown in Fig. 9. We consider that this is determined by the imaging principle of extended target and the WFSless AO correction scheme. Firstly, the essence of WFSless AO is to correct the aberrated PSF of the imaging system, which ability has been proved in point target experiments. Therefore, the WFSless AO is also capable of correcting aberrations in extended target imaging based on the assume of spatial invariance of imaging system. However, the correction field of view of AO system is small due to the anisoplanatism [26], so that it is difficult to achieve excellent correction effect in wide field of view by a single AO system. But the small LR images are approximately equivalent to the independent isoplanar regions [20]. in which the distortions of PSF are smaller, so the AO system can achieve the better correction effects in the LR images. Of course, there are also some slight degradations of image quality outside the correction regions. This is because the different estimations of PSF between the corrected and uncorrected regions. The small LR images corresponding to the much differences of estimated PSF between the corrected and uncorrected regions. Therefore, there
Fig. 8. The LR1∼LR4 target images and the corresponding correction results.
The aberrated PSF causes the imaging system to have reduced spatial resolution. Consequently, it is available to improve the spatial resolution of imaging system by correcting the aberrated PSF. We extend the WFSless AO correction to the imaging of extended sources, and analyze the correction effect of the WFSless AO system for wavefront aberrations. Since the image sharpness function used in Section 2.2 is also suitable for image quality evaluation of extended targets [25], the same image quality metric as point target will be used in the correction experiment of extended targets. The extended target experiment can be carried out by replacing the collimated light in the point target experiment with the extended light source and using the identification plate (USAF 1951) as the extended target. The positive lens is used to convert divergent spherical wave
Fig. 9. The full-target images corrected by LR images. (The correction regions are in the red boxes, the regions with better imaging effect are shown in the yellow boxes, and the orange arrows point to the regions with image degradation).. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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will be more obvious degradation effects in the outer parts of the small LR images. Secondly, the central region of the extended target image is closer to the optical axis of the imaging system. In this paraxial approximation region, the imaging system is to be approximately spatial invariant, so the PSF distortion in the central region is smaller. In contrast, the PSF distortions are more serious in the regions which are far away from the center parts of original image. Therefore, the PSF estimations in the edge regions are not as accurate as that in the center regions. Consequently, the degradations of the outer parts of LR5∼LR7 are more serious than LR2∼LR4.
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4. Conclusion Above all, in this paper, the WFSless AO is applied for aberration correction in membrane diffractive telescope. The conventional SPGD algorithm is adopted to control the DM for compensating wavefront aberration. As a result, the maximum far-field intensity of point target imaging is improved from 692 ADU to 916 ADU, and the MTF of telescope is optimized, the moderate frequency is enhanced apparently by WFSless AO correction. In addition, the correction experiments of extended imaging in different field of view have been carried out. The method shows the well correction effects in the extended target imaging. Although the imaging field of view is small, the correction frequency and effect can be significantly improved by using the central LR images at the expense of a certain resolution of the edge image. This work is the first time to correct the extended target imaging of hundred millimeter-level aperture membrane diffractive optical telescope based on adaptive optics. In our subsequent research, the new parallel algorithm and image quality metric will be tested to further accelerate the correction process of extended target imaging in wide field of view. Acknowledgments This work was supported by National Natural Science Foundation of China (Grant No. 60978049), Youth Innovation Promotion Association, China, Scientists of Chinese Academy of Sciences (Grant No. 2012280), High Resolution Light Imaging Camera System Technology in Geostationary Orbit, China (Grant No. 2016YFB0500204). References [1] S.E. Kendrick, H.P. Stahl, Large aperture space telescope mirror fabrication trades, in: Space Telescopes and Instrumentation 2008: Optical, Infrared, and Millimeter, International Society for Optics and Photonics, 2008, 70102G-70102G-70112. [2] M. Postman, C.M. Mountain, R. Soummer, W. Traub, K.R. Stapelfeldt, W.R. Oegerle, T.T. Hyde, H.P. Stahl, Advanced technology large-aperture space telescope: science drivers and technology developments, Opt. Eng. 51 (2012) 1007.
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