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Sheared-beam imaging technique is a non-conventional imaging method which can be used to image remote objects through atmospheric turbulence without needing any adaptive optics. In this imaging technique, the target is coherently illuminated by three laser beams which are laterally sheared at the transmitter plane and arranged into an L shape. In addition, each beam is modulated by a slight frequency shift. The speckle intensity signals scattered from the target are received by a detector array, and then the image of target can be reconstructed by computer algorithm. By far, most of studies in this field have focused on two-dimensional imaging. In real conditions, however, the surface of targets we are concerned about reveals that different depths introduce various phase delays in the scattering signal from target. This delay causes the phase-shift errors to appear between the ideal target Fourier spectrum and the Fourier spectrum received by detector array. Finally, this would result in poor image quality and low resolution. In this study, a three-dimensional target imaging model is established based on the two-dimensional target imaging model. The influence of modulated beat frequency between sheared beam and reference beam is studied on the objects with depth information, and the result shows that large beat frequency may have an adverse effect on reconstructed images. The simulation we have developed for this three-dimensional imaging model uses three targets with different shapes. Each target is divided into several sub-blocks, and we set different depth values (within 10 m) for these blocks. Then beat frequencies are increased from 5 Hz to about 1 MHz, respectively. At each pair of frequencies, the reconstructed image is recorded. Srehl ratio is used as the measure of the imaging quality. Computer simulation results show that the Srehl ratio of reconstructed images descends with the increase of beat frequency, which is fully consistent with the theory of three-dimensional target imaging proposed before. Meanwhile, we find that the depth distribution of target also has an effect on imaging quality. As for actual space targets, the maximum depth is usually not more than 10 m. Compared with the influence caused by beat frequencies, the effect produced by depth distribution is negligible. Therefore when a space target is imaged, beat frequencies play the major role in reconstructing high-quality image. The results presented in this paper indicate that in order to achieve better imaging quality in the practical application, it is necessary to select the smallest beat frequency according to the detector performance and keep the candidate frequencies away from the low-frequency noise of the detector.
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Keywords:
- sheared-beam imaging /
- speckle imaging /
- depth of target /
- phase delay
[1] Li X Y, Gao X, Tang J, Feng L J 2015 Acta Photon. Sin. 44 0611002 (in Chinese)[李希宇, 高昕, 唐嘉, 冯灵洁2015光子学报44 0611002]
[2] Fienup J R 2010 Imaging Systems Tucson, Arizona, USA, June 7-8, 2010 IMD2
[3] Hutchin R A 2012 US Patent 20120162631[2012-06-28]
[4] Hutchin R A 2012 US Patent 20120292481[2012-11-22]
[5] Bush K A, Barnard C C, Voelz D G 1996 Proc. SPIE 2828 362
[6] Landesman B T, Kindilien P, Pierson R E 1997 Opt. Express 1 312
[7] Landesman B T, Olson D F 1994 Proc. SPIE 2302 14
[8] Voelz D G, Belsher J F, Ulibarri A L, Gamiz V 2002 Proc. SPIE 4489 35
[9] Voelz D G, Gonglewski J D, Idell P S 1993 Proc. SPIE 2029 169
[10] Stahl S M, Kremer R, Fairchild P, Hughes K, Spivey B 1996 Proc. SPIE 2847 150
[11] Goodman J W (Qin K C, Liu P S, Chen J B, Cao Q Z, translated) 2013 Introduction to Fourier Optics (3rd Ed.) (Beijing:Publishing House of Electronics Industry) p54(in Chinese)[古德曼(秦克诚, 刘培森, 陈家碧, 曹其智译) 2013傅里叶光学导论(3版) (北京:电子工业出版社)第54页]
[12] Fairchild P, Payne I 2013 IEEE Aerospace Conference Big Sky Montana, USA, March 2-9, 2013 p1
[13] Idell P S, Gonglewski J D 1990 Opt. Lett. 15 1309
[14] Hutchin R A 1993 Proc. SPIE 2029 161
[15] Cao B, Luo X J, Chen M L, Zhang Y 2015 Acta Phys. Sin. 64 124205 (in Chinese)[曹蓓, 罗秀娟, 陈明徕, 张羽2015 64 124205]
[16] Chen M L, Luo X J, Zhang Y, Lan F Y, Liu H, Cao B, Xia A L 2017 Acta Phys. Sin. 66 024203 (in Chinese)[陈明徕, 罗秀娟, 张羽, 兰富洋, 刘辉, 曹蓓, 夏爱利2017 66 024203]
[17] Liu P S 1987 Fundamentals of Statistical Optics of Speckle (Beijing:Science Press) p7(in Chinese)[刘培森1987散斑统计光学基础(北京:科学出版社)第7页]
[18] Corser B A 1996 M. S. Dissertation (Lubbock:Texas Tech University)
[19] Dong L 2014 Laser Infrared 44 1350 (in Chinese)[董磊2014激光与红外44 1350]
[20] Si Q D, Luo X J, Zeng Z H 2014 Acta Phys. Sin. 63 104203 (in Chinese)[司庆丹, 罗秀娟, 曾志红2014 63 104203]
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[1] Li X Y, Gao X, Tang J, Feng L J 2015 Acta Photon. Sin. 44 0611002 (in Chinese)[李希宇, 高昕, 唐嘉, 冯灵洁2015光子学报44 0611002]
[2] Fienup J R 2010 Imaging Systems Tucson, Arizona, USA, June 7-8, 2010 IMD2
[3] Hutchin R A 2012 US Patent 20120162631[2012-06-28]
[4] Hutchin R A 2012 US Patent 20120292481[2012-11-22]
[5] Bush K A, Barnard C C, Voelz D G 1996 Proc. SPIE 2828 362
[6] Landesman B T, Kindilien P, Pierson R E 1997 Opt. Express 1 312
[7] Landesman B T, Olson D F 1994 Proc. SPIE 2302 14
[8] Voelz D G, Belsher J F, Ulibarri A L, Gamiz V 2002 Proc. SPIE 4489 35
[9] Voelz D G, Gonglewski J D, Idell P S 1993 Proc. SPIE 2029 169
[10] Stahl S M, Kremer R, Fairchild P, Hughes K, Spivey B 1996 Proc. SPIE 2847 150
[11] Goodman J W (Qin K C, Liu P S, Chen J B, Cao Q Z, translated) 2013 Introduction to Fourier Optics (3rd Ed.) (Beijing:Publishing House of Electronics Industry) p54(in Chinese)[古德曼(秦克诚, 刘培森, 陈家碧, 曹其智译) 2013傅里叶光学导论(3版) (北京:电子工业出版社)第54页]
[12] Fairchild P, Payne I 2013 IEEE Aerospace Conference Big Sky Montana, USA, March 2-9, 2013 p1
[13] Idell P S, Gonglewski J D 1990 Opt. Lett. 15 1309
[14] Hutchin R A 1993 Proc. SPIE 2029 161
[15] Cao B, Luo X J, Chen M L, Zhang Y 2015 Acta Phys. Sin. 64 124205 (in Chinese)[曹蓓, 罗秀娟, 陈明徕, 张羽2015 64 124205]
[16] Chen M L, Luo X J, Zhang Y, Lan F Y, Liu H, Cao B, Xia A L 2017 Acta Phys. Sin. 66 024203 (in Chinese)[陈明徕, 罗秀娟, 张羽, 兰富洋, 刘辉, 曹蓓, 夏爱利2017 66 024203]
[17] Liu P S 1987 Fundamentals of Statistical Optics of Speckle (Beijing:Science Press) p7(in Chinese)[刘培森1987散斑统计光学基础(北京:科学出版社)第7页]
[18] Corser B A 1996 M. S. Dissertation (Lubbock:Texas Tech University)
[19] Dong L 2014 Laser Infrared 44 1350 (in Chinese)[董磊2014激光与红外44 1350]
[20] Si Q D, Luo X J, Zeng Z H 2014 Acta Phys. Sin. 63 104203 (in Chinese)[司庆丹, 罗秀娟, 曾志红2014 63 104203]
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