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Ptychography provides an extremely robust and highly convergent algorithm to reconstruct the specimen phase with a wide field of view. The resolution and accuracy of ptychography are severely restricted by the uncertainty of the position error that includes the scanning position and axial distance error. In fact, it is difficult to accurately measure the distance between the target plane and entrance pupil of charge-coupled device (CCD) or complementary metal oxide semiconductor, which results in the axial distance error. The axial distance error can blur the reconstructed image, degrade the reconstruction quality and reduce the resolution. In order to analyze the effect of the axial distance error, the model for axial distance error is derived based on the amplitude constraint in CCD and Fresnel diffraction integral. This model indicates that the axial distance error can cause a stretching deformation of the retrieved image, which is similar to the defocusing effect caused by different axial distances in holography. In this paper, we propose a method of correcting the axial distance error by using the image information entropy in an iterative way to obtain the accurate axial distance and retrieve the distinct image. The correction method based on the image information entropy is composed of four parts:the initial calculation, the determination of the direction search, the axial error correction and the reconstruction of the distinct image. The initial calculation part is to ensure that the intensity of the reconstructed object tends to be stable before entering into the other processing parts. The search direction portion is to indicate that the initial axial distance is greater than the actual axial distance, or less than the actual axial distance. The axial error correction section is to calculate the sharpness values of the image at different axial distance, and find the peak position of the sharpness distribution that corresponds to the position of the clearest image. The axial distance can be taken from the peak position. The obtained axial distance is again taken into account in the ptychography algorithm to eliminate the axial distance error and obtain the distinct reconstructed image. In this paper, some simulations are conducted to verify the feasibility of the proposed method. The effect of the axial distance error is analyzed. The image energy variation, the Tamura coefficient and the image information entropy are selected as the image definition evaluation functions in our paper. We compare the distributions of three image definition evaluation functions in the correction process of the axial distance error. It is found that the image information entropy has higher sensitivity than the other image definition evaluation functions. Finally, both simulation and experiment have proved the feasibility of axial distance error correction based on image information entropy.
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Keywords:
- ptychography /
- axial distance error /
- image information entropy
[1] Shen C, Tan J, Wei C, Liu Z 2016 Opt. Express 24 16520
[2] Hirose M, Shimomura K, Suzuki A, Burdet N, Takahashi Y 2016 Opt. Express 24 11917
[3] Kim C, Kim Y, Song C 2016 J. Phys.:Condens. Matter 28 493001
[4] Hruszkewycz S O, Cha W, Andrich P, Anderson C P, Ulvestad A, Harder R, Heremans F J 2017 APL Mater. 5 026105
[5] Rodenburg J M, Faulkner H M L 2004 Appl. Phys. Lett. 85 4795
[6] Rodenburg J M, Hurst A C, Cullis A G 2007 Ultramicroscopy 107 227
[7] Maiden A M, Rodenburg J M, Humphry M J 2010 Opt. Lett. 35 2585
[8] Bunk O, Dierolf M, Kynde S 2008 Ultramicroscopy 108 481
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[13] He X L, Liu C, Wang J C 2014 Acta Phys. Sin. 63 034208(in Chinese)[何小亮, 刘诚, 王继成2014 63 034208]
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[17] Shenfield A, Rodenburg J M 2011 Appl. Phys. 109 124510
[18] Maiden A M, Humphry M J, Sarahan M C, Kraus B, Rodenburg J M 2012 Ultramicroscopy 120 64
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[20] Zhang F C, Peterson I, Vila-Comamala J, Diaz A, Berenguer F, Bean R, Chen B, Menzel A K, Robinson I, Rodenburg J M 2013 Opt. Express 21 13592
[21] Sun J S, Chen Q, Zhang Y Z, Zuo C 2016 Opt. Express 7 1336
[22] Shimobaba T, Kakue T, Okada N, Endo Y, Hirayama R, Hiyama D, Ito T 2014 Opt. Commun. 331 189
[23] Liu C, Pan X C, Zhu J Q 2013 Acta Phys. Sin. 62 184204 (in Chinese)[刘诚, 潘兴臣, 朱健强2013 62 184204]
[24] Wang H Y, Liu C, Pan X C, Cheng J, Zhu J Q 2014 Chin. Opt. Lett 12 010501
[25] Wang Y W, Liu X L, Xie H 2006 Opt. Precis. Engineer. 14 1063 (in Chinese)[王义文, 刘献礼, 谢晖2006光学精密工程14 1063]
[26] Zhang L X, Sun H Y, Guo H C 2013 Acta Photon. Sin. 42 605 (in Chinese)[张来线, 孙华燕, 郭惠超2013光子学报42 605]
[27] Zhu Z T, Li S F, Chen H P 2004 Opt. Precis. Engineer. 12 537 (in Chinese)[朱铮涛, 黎绍发, 陈华平2004光学精密工程12 537]
[28] Memmolo P, Distante C, Paturzo M, Finizio A, Ferraro P, Javidi B 2011 Opt. Lett. 201136 1945
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[1] Shen C, Tan J, Wei C, Liu Z 2016 Opt. Express 24 16520
[2] Hirose M, Shimomura K, Suzuki A, Burdet N, Takahashi Y 2016 Opt. Express 24 11917
[3] Kim C, Kim Y, Song C 2016 J. Phys.:Condens. Matter 28 493001
[4] Hruszkewycz S O, Cha W, Andrich P, Anderson C P, Ulvestad A, Harder R, Heremans F J 2017 APL Mater. 5 026105
[5] Rodenburg J M, Faulkner H M L 2004 Appl. Phys. Lett. 85 4795
[6] Rodenburg J M, Hurst A C, Cullis A G 2007 Ultramicroscopy 107 227
[7] Maiden A M, Rodenburg J M, Humphry M J 2010 Opt. Lett. 35 2585
[8] Bunk O, Dierolf M, Kynde S 2008 Ultramicroscopy 108 481
[9] Wang Y L, Shi Y S, Li T, Gao Q K, Xiao J, Zhang S G 2013 Acta Phys. Sin. 62 234201 (in Chinese)[王雅丽, 史祎诗, 李拓, 高乾坤, 肖俊, 张三国2013 62 234201]
[10] Wang H Y, Liu C, Pan X C 2014 Chin. Opt. Lett. 12 010501
[11] Wang B S, Gao S M, Wang J C 2013 Acta Opt. Sin. 33 0611001(in Chinese)[王宝升, 高淑梅, 王继成2012光学学报33 0611001]
[12] Liu C, Walther T, Rodenburg J M 2009 Ultramicroscopy 109 1263
[13] He X L, Liu C, Wang J C 2014 Acta Phys. Sin. 63 034208(in Chinese)[何小亮, 刘诚, 王继成2014 63 034208]
[14] Rodenburg J M 2008 Adv. Imag. Elect. Phys. 150 87
[15] Maiden A M, Rodenburg J M 2009 Ultramicroscopy 109 1256
[16] Guizar-Sicairos M, Fienup J R 2008 Opt. Express. 16 7264
[17] Shenfield A, Rodenburg J M 2011 Appl. Phys. 109 124510
[18] Maiden A M, Humphry M J, Sarahan M C, Kraus B, Rodenburg J M 2012 Ultramicroscopy 120 64
[19] Beckers M, Senkbeil T, Gorniak T, Giewekemeyer K, Salditt T, Rosenhahn A 2013 Ultramicroscopy 126 44
[20] Zhang F C, Peterson I, Vila-Comamala J, Diaz A, Berenguer F, Bean R, Chen B, Menzel A K, Robinson I, Rodenburg J M 2013 Opt. Express 21 13592
[21] Sun J S, Chen Q, Zhang Y Z, Zuo C 2016 Opt. Express 7 1336
[22] Shimobaba T, Kakue T, Okada N, Endo Y, Hirayama R, Hiyama D, Ito T 2014 Opt. Commun. 331 189
[23] Liu C, Pan X C, Zhu J Q 2013 Acta Phys. Sin. 62 184204 (in Chinese)[刘诚, 潘兴臣, 朱健强2013 62 184204]
[24] Wang H Y, Liu C, Pan X C, Cheng J, Zhu J Q 2014 Chin. Opt. Lett 12 010501
[25] Wang Y W, Liu X L, Xie H 2006 Opt. Precis. Engineer. 14 1063 (in Chinese)[王义文, 刘献礼, 谢晖2006光学精密工程14 1063]
[26] Zhang L X, Sun H Y, Guo H C 2013 Acta Photon. Sin. 42 605 (in Chinese)[张来线, 孙华燕, 郭惠超2013光子学报42 605]
[27] Zhu Z T, Li S F, Chen H P 2004 Opt. Precis. Engineer. 12 537 (in Chinese)[朱铮涛, 黎绍发, 陈华平2004光学精密工程12 537]
[28] Memmolo P, Distante C, Paturzo M, Finizio A, Ferraro P, Javidi B 2011 Opt. Lett. 201136 1945
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