基于相位恢复的二维图像彩色再现
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摘要
携带物体信息的衍射光波中包含了振幅和相位信息,现有相机只能记录光强信息,振幅信息在光束传播过程中抗噪能力差,易丢失,因而相位信息的恢复有着重要的意义。利用光强传输方程和基于Gerchberg-Saxton(GS)的角谱迭代算法,研究了二维图像的相位信息恢复问题。首先利用两幅二维图像,分别模拟像面位置光波复振幅的振幅信息和相位信息。然后利用角谱传递函数计算了光路中两个离焦面位置的复振幅分布。将三面光强分布直接代入光强传输方程,因多次近似只能得到粗略的相位分布,将其作为基于GS角谱迭代算法中的初始相位可加快收敛速度,得到更精确的相位分布,相位误差均方根值低至10-8。最后,结合图像的RGB通道,通过角谱传递函数和计算所得相位,利用三面光强分布,实现了像面附近的彩色图像再现。
The light waves diffracted from objects contain the amplitude and phase information. The light intensity information can be recorded easily by current cameras, however, the amplitude information has the worse ability to resist noise and is easily to lose in the process of beam propagation,so the recovery of phase information is of great significance. Through the transport of intensity equation and the angular spectrum iteration algorithm based on Gerchberg-Saxton(GS), the retrieval of phase information in two-dimensional images was studied. Firstly, two images were used to simulate the amplitude and phase information of the light wave at the position of the imaging plane. Then the complex amplitude distribution on two defocused planes in the imaging optical path were calculated taking advantage of the angular spectrum transfer function. The light intensities of three different parallel planes can only get rough phase by the transport of intensity equation due to the multiple approximations. The rough result were then used as the initial phase values in the GS angular spectrum iterative algorithm to speed up the convergence of iteration and finally obtain the more accurate phase distribution. The root mean square of the phase error in iteration is as low as 10-8 in the Matlab simulation. By applying the method to three different colors and then combining them together, the phase and intensity of color images on any planes can be obtained by only detecting the intensities on three different planes.
The light waves diffracted from objects contain the amplitude and phase information. The light intensity information can be recorded easily by current cameras, however, the amplitude information has the worse ability to resist noise and is easily to lose in the process of beam propagation,so the recovery of phase information is of great significance. Through the transport of intensity equation and the angular spectrum iteration algorithm based on Gerchberg-Saxton(GS), the retrieval of phase information in two-dimensional images was studied. Firstly, two images were used to simulate the amplitude and phase information of the light wave at the position of the imaging plane. Then the complex amplitude distribution on two defocused planes in the imaging optical path were calculated taking advantage of the angular spectrum transfer function. The light intensities of three different parallel planes can only get rough phase by the transport of intensity equation due to the multiple approximations. The rough result were then used as the initial phase values in the GS angular spectrum iterative algorithm to speed up the convergence of iteration and finally obtain the more accurate phase distribution. The root mean square of the phase error in iteration is as low as 10-8 in the Matlab simulation. By applying the method to three different colors and then combining them together, the phase and intensity of color images on any planes can be obtained by only detecting the intensities on three different planes.
引文
[1]于美文.光全息学及其应用[M].北京:北京理工大学出版社,1996.
[2]DEUTSCH B,HILLENBRAND R,NOVOTNY L.Nearfield amplitude and phase recovery using phase-shifting interferometry[J].Optics Express,2008,16(2):494-501.
[3]TEAGUE M R.Deterministic phase retrieval:a Green’s function solution[J].Journal of the Optical Society of America,1983,73(11):1434-1441.
[4]GERCHBERG R W,SAXTON W O.A practical algorithm for the determination of phase from image and diffraction plane pictures[J].Optik,1972,35(2):237-250.
[5]YANG G Z,GU B Y,DONG B Z.Theory of the amplitude-phase retrieval in any linear transform system and its applications[J].International Journal of Modern Physics B,1993,7(18):3153-3224.
[6]WOODS S C,GREENAWAY A H.Wave-front sensing by use of a Green's function solution to the intensity transport equation[J].Journal of the Optical Society of America A,2003,20(3):508-512.
[7]GUREYEV T E,ROBERTS A,NUGENT K A.Phase retrieval with the transport-of-intensity equation:matrix solution with use of Zernike polynomials[J].Journal of the Optical Society of America A,1995,12(9):1932-1941.
[8]ZUO C,CHEN Q,HUANG L,et al.Phase discrepancy analysis and compensation for fast Fourier transform based solution of the transport of intensity equation[J].Optics Express,2014,22(14):17172-17186.
[9]郭俊虎.相干光光强恢复相位的方法研究[D].武汉:华中科技大学,2011.
[10]吴海燕.非干涉光场的相位恢复算法研究[D].合肥:安徽大学,2012.
[11]肖峻.亥姆霍兹定理在求解静电场边值问题中的应用[J].电气电子教学学报,2006,28(4):55-57.
[12]唐荣安,洪学仁,徐红萍,等.傅里叶变换基本性质的物理诠释[J].物理与工程,2016,26(2):51-53.
[13]郭怡明,张方,宋强,等.一种混合迭代算法在大离焦距离TIE相位恢复中的应用[J].光学学报,2016,36(9):0912001.
[14]黄利新,姚新,蔡冬梅,等.一种快速高精度的相位恢复迭代法[J].中国激光,2010,37(5):1218-1221.
[15]李俊昌.衍射计算及数字全息[M].北京:科学出版社,2014:26-32.
[2]DEUTSCH B,HILLENBRAND R,NOVOTNY L.Nearfield amplitude and phase recovery using phase-shifting interferometry[J].Optics Express,2008,16(2):494-501.
[3]TEAGUE M R.Deterministic phase retrieval:a Green’s function solution[J].Journal of the Optical Society of America,1983,73(11):1434-1441.
[4]GERCHBERG R W,SAXTON W O.A practical algorithm for the determination of phase from image and diffraction plane pictures[J].Optik,1972,35(2):237-250.
[5]YANG G Z,GU B Y,DONG B Z.Theory of the amplitude-phase retrieval in any linear transform system and its applications[J].International Journal of Modern Physics B,1993,7(18):3153-3224.
[6]WOODS S C,GREENAWAY A H.Wave-front sensing by use of a Green's function solution to the intensity transport equation[J].Journal of the Optical Society of America A,2003,20(3):508-512.
[7]GUREYEV T E,ROBERTS A,NUGENT K A.Phase retrieval with the transport-of-intensity equation:matrix solution with use of Zernike polynomials[J].Journal of the Optical Society of America A,1995,12(9):1932-1941.
[8]ZUO C,CHEN Q,HUANG L,et al.Phase discrepancy analysis and compensation for fast Fourier transform based solution of the transport of intensity equation[J].Optics Express,2014,22(14):17172-17186.
[9]郭俊虎.相干光光强恢复相位的方法研究[D].武汉:华中科技大学,2011.
[10]吴海燕.非干涉光场的相位恢复算法研究[D].合肥:安徽大学,2012.
[11]肖峻.亥姆霍兹定理在求解静电场边值问题中的应用[J].电气电子教学学报,2006,28(4):55-57.
[12]唐荣安,洪学仁,徐红萍,等.傅里叶变换基本性质的物理诠释[J].物理与工程,2016,26(2):51-53.
[13]郭怡明,张方,宋强,等.一种混合迭代算法在大离焦距离TIE相位恢复中的应用[J].光学学报,2016,36(9):0912001.
[14]黄利新,姚新,蔡冬梅,等.一种快速高精度的相位恢复迭代法[J].中国激光,2010,37(5):1218-1221.
[15]李俊昌.衍射计算及数字全息[M].北京:科学出版社,2014:26-32.