基于非均匀采样的高分辨曲面投影计算全息方法
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摘要
曲面投影在显示与光刻领域有着重要的应用价值,为实现高分辨的曲面投影成像,提出了以瑞利-索末菲衍射为基础的非均匀采样相位恢复算法,在设计时准确考虑高空间频率的大角度衍射频谱信息,使得投影图像分辨率获得有效提升;建立了衍射面与成像曲面的离散采样方法,并给出了成像分辨率极限的理论表达式。以"田"字形目标图样在圆柱面成像为例,对建立的相位恢复算法和理论进行了验证,结果表明重现的投影像与目标图形符合良好,分辨率与理论预测一致。
Projection on curved surface has important applications in display and photolithography. A phase retrieval algorithm, using non-uniform sample, was presented for high resolution projection on curved surface based on the Rayleigh-Sommerfeld Integral. The high spatial frequency means large diffraction angle was incorporated into the design, so that the imaging resolution of projection could be improved effectively. The discrete sampling method was established for the diffraction surface and the imaging surface. Then the theoretical equation of limit resolution was given. Finally diffraction optical elements were designed for projection on cylindrical surface with the diffraction pattern of grid, in order to verify the phase retrieval theory. The results show that reconstructed projecting image matches well with the target image, and the resolution is in agreement with theoretical prediction.
Projection on curved surface has important applications in display and photolithography. A phase retrieval algorithm, using non-uniform sample, was presented for high resolution projection on curved surface based on the Rayleigh-Sommerfeld Integral. The high spatial frequency means large diffraction angle was incorporated into the design, so that the imaging resolution of projection could be improved effectively. The discrete sampling method was established for the diffraction surface and the imaging surface. Then the theoretical equation of limit resolution was given. Finally diffraction optical elements were designed for projection on cylindrical surface with the diffraction pattern of grid, in order to verify the phase retrieval theory. The results show that reconstructed projecting image matches well with the target image, and the resolution is in agreement with theoretical prediction.
引文
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[13] Tian Ran, Liu Juan, Li Xin. Design and fabrication of complicated diffractive optical elements on multiple curved surfaces[J]. Optics Express, 2015, 23(26):32917-32925.
[14] Liu Peilin, Liu Juan, Li Xin. Design and fabrication of DOEs on multifreeform surfaces via complex amplitude[J]. Optics Express, 2017, 25(24):30061-30072.
[15] Chang Chenliang, Xia Jun, Wu Jun, et al. Scaled diffraction calculation between tilted planes using nonuniform fast Fourier transform[J]. Optics Express,2014, 22(14):17331-17340.
[16] Chang Chenliang, Wu Jun, Qi Yijun, et al. Simple calculation of a computer-generated hologram for lensless holographic 3D projection using a nonuniform sampled wavefront recording plane[J]. Applied Optics,2016, 55(28):7988-7996.
[17] Li Jing, Wu Peng, Yang Zheng, et al. Design method for the near-field diffractive optical elements with large diffraction angle based on the rayleighsommerfeld fiffraction theory[J]. Acta Photonica Sinica, 2017, 46(11):182-188.(in Chinese)李晶,吴鹏,杨正,等.基于瑞利-索末菲衍射理论的近场大衍射角衍射光学元件的设计[J].光子学报, 2017, 46(11):182-188.
[18] Li Yan, Li Sheng, Gao Minguang, et al. Fourier interpolative sampling algorithm in Fourier transform infrared spectrometer[J]. Infrared and Laser Engineering, 2018, 47(1):0123001.(in Chinese)李妍,李胜,高闽光,等. FTIR光谱仪中傅里叶插值采样方法的研究[J].红外与激光工程, 2018, 47(1):0123001.
[19] Zhang Xiaolei, Zhang Xiangchao, Xiao Hong, et al.Speckle removal in phase reconstruction of digital holography for structured surfaces[J]. Infrared and Laser Engineering, 2016, 45(7):0726002.
[2] Oliver Bimber, Ramesh Raskar. Modern Approaches to Augmented Reality[M]. Boston:ACM Press, 2006:1-86.
[3] Yan Gaobin, Yu Jia, Liu Huiping, et al. Full parallax stereo holography research based on CGH[J]. Infrared and Laser Engineering, 2015, 44(8):2467-2471.(in Chinese)闫高宾,于佳,刘惠萍,等.基于计算全息的全视差合成全息研究[J].红外与激光工程, 2015, 44(8):2467-2471.
[4] Chen Zhu, Jiang Hongzhen, Liu Xu, et al. Measurement of surface defects of optical elements using digital holography[J]. Optics and Precision Engineering, 2017,25(3):576-583.(in Chinese)陈竹,姜宏振,刘旭,等.数字全息术用于光学元件表面缺陷形貌测量[J].光学精密工程, 2017, 25(3):576-583.
[5] Jiang W, Wang J, Dong X. A novel hybrid algorithm for the design of the phase diffractive optical elements for beam shaping[J]. Optics&Laser Technology, 2013, 45(1):37-41.
[6] Pang Hui, Ying Chaofu, Fan Changjiang, et al. Design diffractive optical elements for beam shaping with hybrid algorithm[J]. Acta Photonica Sinica, 2010, 39(6):977-981.(in Chinese)庞辉,应朝福,范长江,等.用于光束整形的衍射光学元件设计的混合算法[J].光子学报, 2010, 39(6):977-981.
[7] Kang Guoguo, Xie Jinghui, Mo Xiaoli, et al. Design of binary optics using improved two-step simulatedannealing algorithm[J]. Acta Photonica Sinica, 2008,37(7):1416-1419.(in Chinese)康果果,谢敬辉,莫晓丽.用改进的两步模拟退火法进行二元光学元件的设计[J].光子学报, 2008, 37(7):1416-1419.
[8] Liu Hua. Gaussian beam shaping diffractive optical element designed by Hankel transformation[J]. Chinese Optics, 2016, 9(2):277-283.(in Chinese)刘华.利用汉克尔变换设计高斯光束整形衍射元件的应用研究[J].中国光学, 2016, 9(2):277-283.
[9] Kim G, Dominguez-caballero J A, Menon R. Design and analysis of multi-wavelength diffractive optics[J].Optics Express, 2012, 20(3):2814-2823.
[10] Qu W, Gu H, Tan Q, et al. Precise design of twodimensional diffractive optical elements for beam shaping[J]. Applied Optics, 2015, 54(21):6521-6525.
[11] Pang H, Yin S, Deng Q, et al. A novel method for the design of diffractive optical elements based on the Rayleigh-Sommerfeld integral[J]. Optics&Lasers in Engineering, 2015, 70(1):38-44.
[12] Zhao Haozhi, Liu Juan, Xiao Ru. Modulation of optical intensity on curved surfaces and its application to fabricate DOEs with arbitrary profile by interference[J].Optics Express, 2013, 21(4):5141-5148.
[13] Tian Ran, Liu Juan, Li Xin. Design and fabrication of complicated diffractive optical elements on multiple curved surfaces[J]. Optics Express, 2015, 23(26):32917-32925.
[14] Liu Peilin, Liu Juan, Li Xin. Design and fabrication of DOEs on multifreeform surfaces via complex amplitude[J]. Optics Express, 2017, 25(24):30061-30072.
[15] Chang Chenliang, Xia Jun, Wu Jun, et al. Scaled diffraction calculation between tilted planes using nonuniform fast Fourier transform[J]. Optics Express,2014, 22(14):17331-17340.
[16] Chang Chenliang, Wu Jun, Qi Yijun, et al. Simple calculation of a computer-generated hologram for lensless holographic 3D projection using a nonuniform sampled wavefront recording plane[J]. Applied Optics,2016, 55(28):7988-7996.
[17] Li Jing, Wu Peng, Yang Zheng, et al. Design method for the near-field diffractive optical elements with large diffraction angle based on the rayleighsommerfeld fiffraction theory[J]. Acta Photonica Sinica, 2017, 46(11):182-188.(in Chinese)李晶,吴鹏,杨正,等.基于瑞利-索末菲衍射理论的近场大衍射角衍射光学元件的设计[J].光子学报, 2017, 46(11):182-188.
[18] Li Yan, Li Sheng, Gao Minguang, et al. Fourier interpolative sampling algorithm in Fourier transform infrared spectrometer[J]. Infrared and Laser Engineering, 2018, 47(1):0123001.(in Chinese)李妍,李胜,高闽光,等. FTIR光谱仪中傅里叶插值采样方法的研究[J].红外与激光工程, 2018, 47(1):0123001.
[19] Zhang Xiaolei, Zhang Xiangchao, Xiao Hong, et al.Speckle removal in phase reconstruction of digital holography for structured surfaces[J]. Infrared and Laser Engineering, 2016, 45(7):0726002.
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