Abstract

When all the parts of the wavefront imaging system are kept static after wavefront measuring, the target’s images are blurry, because the depth of field (DOF) of the system affects the imaging quality. In this paper, the method for extending the DOF of the wavefront imaging system through an integrated architecture of a liquid-crystal microlens array (LCMLA) powered by electricity and a common photosensitive array, is presented. The DOF can be extended remarkably only by stitching together several sub-images of the LCMLA. The problem that the wavefronts and imaging results are insensitive to the objective depth is also solved. Optimal driving voltage signals are found out according to Sobel mean gradient to efficiently calibrate the depth of objective space in order to quantitatively measure the depth. The approach indicates a viable way to effectively extend the DOF of imaging micro-systems and to measure the geometrical depth of targets at the same time.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (5)

V. Marx, “Microscopy: hello, adaptive optics,” Nat. Methods 14(12), 1133–1136 (2017).
[Crossref] [PubMed]

N. Ji, “Adaptive optical fluorescence microscopy,” Nat. Methods 14(4), 374–380 (2017).
[Crossref] [PubMed]

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Y. Lei, Q. Tong, Z. Xin, D. Wei, X. Zhang, J. Liao, H. Wang, and C. Xie, “Three dimensional measurement with an electrically tunable focused plenoptic camera,” Rev. Sci. Instrum. 88(3), 033111 (2017).
[Crossref] [PubMed]

H. B. de Aguiar, S. Gigan, and S. Brasselet, “Polarization recovery through scattering media,” Sci. Adv. 3(9), e1600743 (2017).
[Crossref] [PubMed]

2016 (4)

2015 (6)

Y. J. Wang, X. Shen, Y. H. Lin, and B. Javidi, “Extended depth-of-field 3D endoscopy with synthetic aperture integral imaging using an electrically tunable focal-length liquid-crystal lens,” Opt. Lett. 40(15), 3564–3567 (2015).
[Crossref] [PubMed]

Y. Lei, Q. Tong, X. Zhang, H. Sang, A. Ji, and C. Xie, “An electrically tunable plenoptic camera using a liquid crystal microlens array,” Rev. Sci. Instrum. 86(5), 053101 (2015).
[Crossref] [PubMed]

H. Kwon, Y. Kizu, Y. Kizaki, M. Ito, M. Kobayashi, R. Ueno, K. Suzuki, and H. Funaki, “A gradient index liquid crystal microlens array for light-field camera applications,” IEEE Photonics Technol. Lett. 27(8), 836–839 (2015).
[Crossref]

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9(9), 563–571 (2015).
[Crossref] [PubMed]

A. Finkbeiner, “Laser focus: by firing lasers into the sky, Claire Max has transformed the capabilities of current–and future—telescopes,” Nature 517(7535), 430–433 (2015).
[Crossref] [PubMed]

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6(1), 7276 (2015).
[Crossref] [PubMed]

2014 (5)

J. R. Crepp, “Improving planet-finding spectrometers,” Science 346(6211), 809–810 (2014).
[Crossref] [PubMed]

N. Ji, “The practical and fundamental limits of optical imaging in mammalian brains,” Neuron 83(6), 1242–1245 (2014).
[Crossref] [PubMed]

S. Xu, Y. Li, Y. Liu, J. Sun, H. Ren, and S. T. Wu, “Fast-response liquid crystal microlens,” Micromachines (Basel) 5(2), 300–324 (2014).
[Crossref]

S. Kang and X. Zhang, “Liquid crystal microlens with dual apertures and electrically controlling focus shift,” Appl. Opt. 53(2), 244–248 (2014).
[Crossref] [PubMed]

R. Bao, C. Cui, S. Yu, H. Mai, X. Gong, and M. Ye, “Polarizer-free imaging of liquid crystal lens,” Opt. Express 22(16), 19824–19830 (2014).
[Crossref] [PubMed]

2013 (5)

2012 (3)

C. Perwass and L. Wietzke, “Single-lens 3D camera with extended depth-of-field,” Proc. SPIE 8291, 829108 (2012).
[Crossref]

T. Georgiev and A. Lumsdaine, “The multifocus plenoptic camera,” Proc. SPIE 8299, 829908 (2012).
[Crossref]

R. Davies and M. Kasper, “Adaptive Optics for Astronomy,” Annu. Rev. Astron. Astrophys. 50(1), 305–351 (2012).
[Crossref]

2011 (2)

J. Y. Jo, P. Chen, R. J. Sichel, S. J. Callori, J. Sinsheimer, E. M. Dufresne, M. Dawber, and P. G. Evans, “Nanosecond dynamics of ferroelectric/dielectric superlattices,” Phys. Rev. Lett. 107(5), 055501 (2011).
[Crossref] [PubMed]

H. Ishii, T. Nakajima, Y. Takahashi, and T. Furukawa, “Ultrafast Polarization Switching in Ferroelectric Polymer Thin Films at Extremely High Electric Fields,” Appl. Phys. Express 4(3), 1027–1032 (2011).
[Crossref]

2009 (1)

O. Vincent and O. Folorunso, “A descriptive algorithm for sobel image edge detection,” Proc. Info. Sci. IT Edu. Conf. 40, 97–107 (2009).

1974 (1)

Aggoun, A.

Arnold, D. B.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Bao, R.

Betzig, E.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6(1), 7276 (2015).
[Crossref] [PubMed]

Booth, M. J.

Brasselet, S.

H. B. de Aguiar, S. Gigan, and S. Brasselet, “Polarization recovery through scattering media,” Sci. Adv. 3(9), e1600743 (2017).
[Crossref] [PubMed]

Buffington, A.

Callori, S. J.

J. Y. Jo, P. Chen, R. J. Sichel, S. J. Callori, J. Sinsheimer, E. M. Dufresne, M. Dawber, and P. G. Evans, “Nanosecond dynamics of ferroelectric/dielectric superlattices,” Phys. Rev. Lett. 107(5), 055501 (2011).
[Crossref] [PubMed]

Chen, M.

Chen, P.

J. Y. Jo, P. Chen, R. J. Sichel, S. J. Callori, J. Sinsheimer, E. M. Dufresne, M. Dawber, and P. G. Evans, “Nanosecond dynamics of ferroelectric/dielectric superlattices,” Phys. Rev. Lett. 107(5), 055501 (2011).
[Crossref] [PubMed]

Chen, Y.

Y. Chen, D. Xu, S. T. Wu, S. Yamamoto, and Y. Haseba, “A low voltage and submillisecond-response polymer-stabilized blue phase liquid crystal,” Appl. Phys. Lett. 102(14), 141116 (2013).
[Crossref]

Chitnis, A.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Christensen, R.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Crepp, J. R.

J. R. Crepp, “Improving planet-finding spectrometers,” Science 346(6211), 809–810 (2014).
[Crossref] [PubMed]

Cui, C.

Davies, R.

R. Davies and M. Kasper, “Adaptive Optics for Astronomy,” Annu. Rev. Astron. Astrophys. 50(1), 305–351 (2012).
[Crossref]

Dawber, M.

J. Y. Jo, P. Chen, R. J. Sichel, S. J. Callori, J. Sinsheimer, E. M. Dufresne, M. Dawber, and P. G. Evans, “Nanosecond dynamics of ferroelectric/dielectric superlattices,” Phys. Rev. Lett. 107(5), 055501 (2011).
[Crossref] [PubMed]

de Aguiar, H. B.

H. B. de Aguiar, S. Gigan, and S. Brasselet, “Polarization recovery through scattering media,” Sci. Adv. 3(9), e1600743 (2017).
[Crossref] [PubMed]

Dempsey, W. P.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Dufresne, E. M.

J. Y. Jo, P. Chen, R. J. Sichel, S. J. Callori, J. Sinsheimer, E. M. Dufresne, M. Dawber, and P. G. Evans, “Nanosecond dynamics of ferroelectric/dielectric superlattices,” Phys. Rev. Lett. 107(5), 055501 (2011).
[Crossref] [PubMed]

Evans, P. G.

J. Y. Jo, P. Chen, R. J. Sichel, S. J. Callori, J. Sinsheimer, E. M. Dufresne, M. Dawber, and P. G. Evans, “Nanosecond dynamics of ferroelectric/dielectric superlattices,” Phys. Rev. Lett. 107(5), 055501 (2011).
[Crossref] [PubMed]

Fiebig, S.

Finkbeiner, A.

A. Finkbeiner, “Laser focus: by firing lasers into the sky, Claire Max has transformed the capabilities of current–and future—telescopes,” Nature 517(7535), 430–433 (2015).
[Crossref] [PubMed]

Fischer, R.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Folorunso, O.

O. Vincent and O. Folorunso, “A descriptive algorithm for sobel image edge detection,” Proc. Info. Sci. IT Edu. Conf. 40, 97–107 (2009).

Funaki, H.

H. Kwon, Y. Kizu, Y. Kizaki, M. Ito, M. Kobayashi, R. Ueno, K. Suzuki, and H. Funaki, “A gradient index liquid crystal microlens array for light-field camera applications,” IEEE Photonics Technol. Lett. 27(8), 836–839 (2015).
[Crossref]

Furukawa, T.

H. Ishii, T. Nakajima, Y. Takahashi, and T. Furukawa, “Ultrafast Polarization Switching in Ferroelectric Polymer Thin Films at Extremely High Electric Fields,” Appl. Phys. Express 4(3), 1027–1032 (2011).
[Crossref]

Georgiev, T.

T. Georgiev and A. Lumsdaine, “The multifocus plenoptic camera,” Proc. SPIE 8299, 829908 (2012).
[Crossref]

Gigan, S.

H. B. de Aguiar, S. Gigan, and S. Brasselet, “Polarization recovery through scattering media,” Sci. Adv. 3(9), e1600743 (2017).
[Crossref] [PubMed]

Gong, X.

Hahne, C.

Harvey, B. K.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6(1), 7276 (2015).
[Crossref] [PubMed]

Haseba, Y.

Y. Chen, D. Xu, S. T. Wu, S. Yamamoto, and Y. Haseba, “A low voltage and submillisecond-response polymer-stabilized blue phase liquid crystal,” Appl. Phys. Lett. 102(14), 141116 (2013).
[Crossref]

Hong, A.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Horstmeyer, R.

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9(9), 563–571 (2015).
[Crossref] [PubMed]

Ishii, H.

H. Ishii, T. Nakajima, Y. Takahashi, and T. Furukawa, “Ultrafast Polarization Switching in Ferroelectric Polymer Thin Films at Extremely High Electric Fields,” Appl. Phys. Express 4(3), 1027–1032 (2011).
[Crossref]

Ito, M.

H. Kwon, Y. Kizu, Y. Kizaki, M. Ito, M. Kobayashi, R. Ueno, K. Suzuki, and H. Funaki, “A gradient index liquid crystal microlens array for light-field camera applications,” IEEE Photonics Technol. Lett. 27(8), 836–839 (2015).
[Crossref]

Javidi, B.

Ji, A.

J. Lin, Q. Tong, Y. Lei, Z. Xin, X. Zhang, A. Ji, H. Sang, and C. Xie, “An arrayed liquid crystal Fabry–Perot infrared filter for electrically tunable spectral imaging detection,” IEEE Sens. J. 16(8), 2397–2403 (2016).
[Crossref]

Y. Lei, Q. Tong, X. Zhang, H. Sang, A. Ji, and C. Xie, “An electrically tunable plenoptic camera using a liquid crystal microlens array,” Rev. Sci. Instrum. 86(5), 053101 (2015).
[Crossref] [PubMed]

Ji, N.

N. Ji, “Adaptive optical fluorescence microscopy,” Nat. Methods 14(4), 374–380 (2017).
[Crossref] [PubMed]

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6(1), 7276 (2015).
[Crossref] [PubMed]

N. Ji, “The practical and fundamental limits of optical imaging in mammalian brains,” Neuron 83(6), 1242–1245 (2014).
[Crossref] [PubMed]

Jo, J. Y.

J. Y. Jo, P. Chen, R. J. Sichel, S. J. Callori, J. Sinsheimer, E. M. Dufresne, M. Dawber, and P. G. Evans, “Nanosecond dynamics of ferroelectric/dielectric superlattices,” Phys. Rev. Lett. 107(5), 055501 (2011).
[Crossref] [PubMed]

Kang, S.

Kasper, M.

R. Davies and M. Kasper, “Adaptive Optics for Astronomy,” Annu. Rev. Astron. Astrophys. 50(1), 305–351 (2012).
[Crossref]

Kizaki, Y.

H. Kwon, Y. Kizu, Y. Kizaki, M. Ito, M. Kobayashi, R. Ueno, K. Suzuki, and H. Funaki, “A gradient index liquid crystal microlens array for light-field camera applications,” IEEE Photonics Technol. Lett. 27(8), 836–839 (2015).
[Crossref]

Kizu, Y.

H. Kwon, Y. Kizu, Y. Kizaki, M. Ito, M. Kobayashi, R. Ueno, K. Suzuki, and H. Funaki, “A gradient index liquid crystal microlens array for light-field camera applications,” IEEE Photonics Technol. Lett. 27(8), 836–839 (2015).
[Crossref]

Kobayashi, M.

H. Kwon, Y. Kizu, Y. Kizaki, M. Ito, M. Kobayashi, R. Ueno, K. Suzuki, and H. Funaki, “A gradient index liquid crystal microlens array for light-field camera applications,” IEEE Photonics Technol. Lett. 27(8), 836–839 (2015).
[Crossref]

Kwon, H.

H. Kwon, Y. Kizu, Y. Kizaki, M. Ito, M. Kobayashi, R. Ueno, K. Suzuki, and H. Funaki, “A gradient index liquid crystal microlens array for light-field camera applications,” IEEE Photonics Technol. Lett. 27(8), 836–839 (2015).
[Crossref]

Lei, Y.

Y. Lei, Q. Tong, Z. Xin, D. Wei, X. Zhang, J. Liao, H. Wang, and C. Xie, “Three dimensional measurement with an electrically tunable focused plenoptic camera,” Rev. Sci. Instrum. 88(3), 033111 (2017).
[Crossref] [PubMed]

J. Lin, Q. Tong, Y. Lei, Z. Xin, X. Zhang, A. Ji, H. Sang, and C. Xie, “An arrayed liquid crystal Fabry–Perot infrared filter for electrically tunable spectral imaging detection,” IEEE Sens. J. 16(8), 2397–2403 (2016).
[Crossref]

Q. Tong, Y. Lei, Z. Xin, X. Zhang, H. Sang, and C. Xie, “Dual-mode photosensitive arrays based on the integration of liquid crystal microlenses and CMOS sensors for obtaining the intensity images and wavefronts of objects,” Opt. Express 24(3), 1903–1923 (2016).
[Crossref] [PubMed]

Y. Lei, Q. Tong, X. Zhang, H. Sang, A. Ji, and C. Xie, “An electrically tunable plenoptic camera using a liquid crystal microlens array,” Rev. Sci. Instrum. 86(5), 053101 (2015).
[Crossref] [PubMed]

Li, Y.

S. Xu, Y. Li, Y. Liu, J. Sun, H. Ren, and S. T. Wu, “Fast-response liquid crystal microlens,” Micromachines (Basel) 5(2), 300–324 (2014).
[Crossref]

Liao, J.

Z. Xin, D. Wei, X. Xie, M. Chen, X. Zhang, J. Liao, H. Wang, and C. Xie, “Dual-polarized light-field imaging micro-system via a liquid-crystal microlens array for direct three-dimensional observation,” Opt. Express 26(4), 4035–4049 (2018).
[Crossref] [PubMed]

Y. Lei, Q. Tong, Z. Xin, D. Wei, X. Zhang, J. Liao, H. Wang, and C. Xie, “Three dimensional measurement with an electrically tunable focused plenoptic camera,” Rev. Sci. Instrum. 88(3), 033111 (2017).
[Crossref] [PubMed]

Lin, J.

J. Lin, Q. Tong, Y. Lei, Z. Xin, X. Zhang, A. Ji, H. Sang, and C. Xie, “An arrayed liquid crystal Fabry–Perot infrared filter for electrically tunable spectral imaging detection,” IEEE Sens. J. 16(8), 2397–2403 (2016).
[Crossref]

Lin, Y. H.

Liu, Y.

S. Xu, Y. Li, Y. Liu, J. Sun, H. Ren, and S. T. Wu, “Fast-response liquid crystal microlens,” Micromachines (Basel) 5(2), 300–324 (2014).
[Crossref]

Lumsdaine, A.

T. Georgiev and A. Lumsdaine, “The multifocus plenoptic camera,” Proc. SPIE 8299, 829908 (2012).
[Crossref]

Mai, H.

Marx, V.

V. Marx, “Microscopy: hello, adaptive optics,” Nat. Methods 14(12), 1133–1136 (2017).
[Crossref] [PubMed]

McCormick, C.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Muller, R. A.

Nakajima, T.

H. Ishii, T. Nakajima, Y. Takahashi, and T. Furukawa, “Ultrafast Polarization Switching in Ferroelectric Polymer Thin Films at Extremely High Electric Fields,” Appl. Phys. Express 4(3), 1027–1032 (2011).
[Crossref]

Ng, R.

R. Ng, “Fourier slice photography,” in Proceedings of ACM SIGGRAPH(2005). 735–744.

Nogare, D. D.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Perwass, C.

C. Perwass and L. Wietzke, “Single-lens 3D camera with extended depth-of-field,” Proc. SPIE 8291, 829108 (2012).
[Crossref]

Pesch, M.

Qing, T.

Rahman, S. A.

Ren, H.

S. Xu, Y. Li, Y. Liu, J. Sun, H. Ren, and S. T. Wu, “Fast-response liquid crystal microlens,” Micromachines (Basel) 5(2), 300–324 (2014).
[Crossref]

H. Ren, S. Xu, and S.-T. Wu, “Polymer-stabilized liquid crystal microlens array with large dynamic range and fast response time,” Opt. Lett. 38(16), 3144–3147 (2013).
[Crossref] [PubMed]

Richie, C. T.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6(1), 7276 (2015).
[Crossref] [PubMed]

Ruan, H.

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9(9), 563–571 (2015).
[Crossref] [PubMed]

Sang, H.

J. Lin, Q. Tong, Y. Lei, Z. Xin, X. Zhang, A. Ji, H. Sang, and C. Xie, “An arrayed liquid crystal Fabry–Perot infrared filter for electrically tunable spectral imaging detection,” IEEE Sens. J. 16(8), 2397–2403 (2016).
[Crossref]

Q. Tong, Y. Lei, Z. Xin, X. Zhang, H. Sang, and C. Xie, “Dual-mode photosensitive arrays based on the integration of liquid crystal microlenses and CMOS sensors for obtaining the intensity images and wavefronts of objects,” Opt. Express 24(3), 1903–1923 (2016).
[Crossref] [PubMed]

Y. Lei, Q. Tong, X. Zhang, H. Sang, A. Ji, and C. Xie, “An electrically tunable plenoptic camera using a liquid crystal microlens array,” Rev. Sci. Instrum. 86(5), 053101 (2015).
[Crossref] [PubMed]

S. Kang, T. Qing, H. Sang, X. Zhang, and C. Xie, “Ommatidia structure based on double layers of liquid crystal microlens array,” Appl. Opt. 52(33), 7912–7918 (2013).
[Crossref] [PubMed]

Sellers, J.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Shen, X.

Shroff, H.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Sichel, R. J.

J. Y. Jo, P. Chen, R. J. Sichel, S. J. Callori, J. Sinsheimer, E. M. Dufresne, M. Dawber, and P. G. Evans, “Nanosecond dynamics of ferroelectric/dielectric superlattices,” Phys. Rev. Lett. 107(5), 055501 (2011).
[Crossref] [PubMed]

Sinsheimer, J.

J. Y. Jo, P. Chen, R. J. Sichel, S. J. Callori, J. Sinsheimer, E. M. Dufresne, M. Dawber, and P. G. Evans, “Nanosecond dynamics of ferroelectric/dielectric superlattices,” Phys. Rev. Lett. 107(5), 055501 (2011).
[Crossref] [PubMed]

Sun, J.

S. Xu, Y. Li, Y. Liu, J. Sun, H. Ren, and S. T. Wu, “Fast-response liquid crystal microlens,” Micromachines (Basel) 5(2), 300–324 (2014).
[Crossref]

Sun, W.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6(1), 7276 (2015).
[Crossref] [PubMed]

Suzuki, K.

H. Kwon, Y. Kizu, Y. Kizaki, M. Ito, M. Kobayashi, R. Ueno, K. Suzuki, and H. Funaki, “A gradient index liquid crystal microlens array for light-field camera applications,” IEEE Photonics Technol. Lett. 27(8), 836–839 (2015).
[Crossref]

Takahashi, Y.

H. Ishii, T. Nakajima, Y. Takahashi, and T. Furukawa, “Ultrafast Polarization Switching in Ferroelectric Polymer Thin Films at Extremely High Electric Fields,” Appl. Phys. Express 4(3), 1027–1032 (2011).
[Crossref]

Tong, Q.

Y. Lei, Q. Tong, Z. Xin, D. Wei, X. Zhang, J. Liao, H. Wang, and C. Xie, “Three dimensional measurement with an electrically tunable focused plenoptic camera,” Rev. Sci. Instrum. 88(3), 033111 (2017).
[Crossref] [PubMed]

J. Lin, Q. Tong, Y. Lei, Z. Xin, X. Zhang, A. Ji, H. Sang, and C. Xie, “An arrayed liquid crystal Fabry–Perot infrared filter for electrically tunable spectral imaging detection,” IEEE Sens. J. 16(8), 2397–2403 (2016).
[Crossref]

Q. Tong, Y. Lei, Z. Xin, X. Zhang, H. Sang, and C. Xie, “Dual-mode photosensitive arrays based on the integration of liquid crystal microlenses and CMOS sensors for obtaining the intensity images and wavefronts of objects,” Opt. Express 24(3), 1903–1923 (2016).
[Crossref] [PubMed]

Y. Lei, Q. Tong, X. Zhang, H. Sang, A. Ji, and C. Xie, “An electrically tunable plenoptic camera using a liquid crystal microlens array,” Rev. Sci. Instrum. 86(5), 053101 (2015).
[Crossref] [PubMed]

Ueno, R.

H. Kwon, Y. Kizu, Y. Kizaki, M. Ito, M. Kobayashi, R. Ueno, K. Suzuki, and H. Funaki, “A gradient index liquid crystal microlens array for light-field camera applications,” IEEE Photonics Technol. Lett. 27(8), 836–839 (2015).
[Crossref]

Velisavljevic, V.

Vincent, O.

O. Vincent and O. Folorunso, “A descriptive algorithm for sobel image edge detection,” Proc. Info. Sci. IT Edu. Conf. 40, 97–107 (2009).

Wang, H.

Z. Xin, D. Wei, X. Xie, M. Chen, X. Zhang, J. Liao, H. Wang, and C. Xie, “Dual-polarized light-field imaging micro-system via a liquid-crystal microlens array for direct three-dimensional observation,” Opt. Express 26(4), 4035–4049 (2018).
[Crossref] [PubMed]

Y. Lei, Q. Tong, Z. Xin, D. Wei, X. Zhang, J. Liao, H. Wang, and C. Xie, “Three dimensional measurement with an electrically tunable focused plenoptic camera,” Rev. Sci. Instrum. 88(3), 033111 (2017).
[Crossref] [PubMed]

Wang, K.

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6(1), 7276 (2015).
[Crossref] [PubMed]

Wang, Y. J.

Waterman, C.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Wei, D.

Z. Xin, D. Wei, X. Xie, M. Chen, X. Zhang, J. Liao, H. Wang, and C. Xie, “Dual-polarized light-field imaging micro-system via a liquid-crystal microlens array for direct three-dimensional observation,” Opt. Express 26(4), 4035–4049 (2018).
[Crossref] [PubMed]

Y. Lei, Q. Tong, Z. Xin, D. Wei, X. Zhang, J. Liao, H. Wang, and C. Xie, “Three dimensional measurement with an electrically tunable focused plenoptic camera,” Rev. Sci. Instrum. 88(3), 033111 (2017).
[Crossref] [PubMed]

Wietzke, L.

C. Perwass and L. Wietzke, “Single-lens 3D camera with extended depth-of-field,” Proc. SPIE 8291, 829108 (2012).
[Crossref]

Winter, P.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Wu, S. T.

S. Xu, Y. Li, Y. Liu, J. Sun, H. Ren, and S. T. Wu, “Fast-response liquid crystal microlens,” Micromachines (Basel) 5(2), 300–324 (2014).
[Crossref]

Y. Chen, D. Xu, S. T. Wu, S. Yamamoto, and Y. Haseba, “A low voltage and submillisecond-response polymer-stabilized blue phase liquid crystal,” Appl. Phys. Lett. 102(14), 141116 (2013).
[Crossref]

Wu, S.-T.

Wu, Y.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Xie, C.

Z. Xin, D. Wei, X. Xie, M. Chen, X. Zhang, J. Liao, H. Wang, and C. Xie, “Dual-polarized light-field imaging micro-system via a liquid-crystal microlens array for direct three-dimensional observation,” Opt. Express 26(4), 4035–4049 (2018).
[Crossref] [PubMed]

Y. Lei, Q. Tong, Z. Xin, D. Wei, X. Zhang, J. Liao, H. Wang, and C. Xie, “Three dimensional measurement with an electrically tunable focused plenoptic camera,” Rev. Sci. Instrum. 88(3), 033111 (2017).
[Crossref] [PubMed]

Q. Tong, Y. Lei, Z. Xin, X. Zhang, H. Sang, and C. Xie, “Dual-mode photosensitive arrays based on the integration of liquid crystal microlenses and CMOS sensors for obtaining the intensity images and wavefronts of objects,” Opt. Express 24(3), 1903–1923 (2016).
[Crossref] [PubMed]

J. Lin, Q. Tong, Y. Lei, Z. Xin, X. Zhang, A. Ji, H. Sang, and C. Xie, “An arrayed liquid crystal Fabry–Perot infrared filter for electrically tunable spectral imaging detection,” IEEE Sens. J. 16(8), 2397–2403 (2016).
[Crossref]

Y. Lei, Q. Tong, X. Zhang, H. Sang, A. Ji, and C. Xie, “An electrically tunable plenoptic camera using a liquid crystal microlens array,” Rev. Sci. Instrum. 86(5), 053101 (2015).
[Crossref] [PubMed]

S. Kang, X. Zhang, C. Xie, and T. Zhang, “Liquid-crystal microlens with focus swing and low driving voltage,” Appl. Opt. 52(3), 381–387 (2013).
[Crossref] [PubMed]

S. Kang, T. Qing, H. Sang, X. Zhang, and C. Xie, “Ommatidia structure based on double layers of liquid crystal microlens array,” Appl. Opt. 52(33), 7912–7918 (2013).
[Crossref] [PubMed]

Xie, X.

Xin, Z.

Z. Xin, D. Wei, X. Xie, M. Chen, X. Zhang, J. Liao, H. Wang, and C. Xie, “Dual-polarized light-field imaging micro-system via a liquid-crystal microlens array for direct three-dimensional observation,” Opt. Express 26(4), 4035–4049 (2018).
[Crossref] [PubMed]

Y. Lei, Q. Tong, Z. Xin, D. Wei, X. Zhang, J. Liao, H. Wang, and C. Xie, “Three dimensional measurement with an electrically tunable focused plenoptic camera,” Rev. Sci. Instrum. 88(3), 033111 (2017).
[Crossref] [PubMed]

Q. Tong, Y. Lei, Z. Xin, X. Zhang, H. Sang, and C. Xie, “Dual-mode photosensitive arrays based on the integration of liquid crystal microlenses and CMOS sensors for obtaining the intensity images and wavefronts of objects,” Opt. Express 24(3), 1903–1923 (2016).
[Crossref] [PubMed]

J. Lin, Q. Tong, Y. Lei, Z. Xin, X. Zhang, A. Ji, H. Sang, and C. Xie, “An arrayed liquid crystal Fabry–Perot infrared filter for electrically tunable spectral imaging detection,” IEEE Sens. J. 16(8), 2397–2403 (2016).
[Crossref]

Xu, D.

Y. Chen, D. Xu, S. T. Wu, S. Yamamoto, and Y. Haseba, “A low voltage and submillisecond-response polymer-stabilized blue phase liquid crystal,” Appl. Phys. Lett. 102(14), 141116 (2013).
[Crossref]

Xu, S.

S. Xu, Y. Li, Y. Liu, J. Sun, H. Ren, and S. T. Wu, “Fast-response liquid crystal microlens,” Micromachines (Basel) 5(2), 300–324 (2014).
[Crossref]

H. Ren, S. Xu, and S.-T. Wu, “Polymer-stabilized liquid crystal microlens array with large dynamic range and fast response time,” Opt. Lett. 38(16), 3144–3147 (2013).
[Crossref] [PubMed]

Yamamoto, S.

Y. Chen, D. Xu, S. T. Wu, S. Yamamoto, and Y. Haseba, “A low voltage and submillisecond-response polymer-stabilized blue phase liquid crystal,” Appl. Phys. Lett. 102(14), 141116 (2013).
[Crossref]

Yang, C.

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9(9), 563–571 (2015).
[Crossref] [PubMed]

Ye, M.

Yu, S.

Zhang, T.

Zhang, X.

Z. Xin, D. Wei, X. Xie, M. Chen, X. Zhang, J. Liao, H. Wang, and C. Xie, “Dual-polarized light-field imaging micro-system via a liquid-crystal microlens array for direct three-dimensional observation,” Opt. Express 26(4), 4035–4049 (2018).
[Crossref] [PubMed]

Y. Lei, Q. Tong, Z. Xin, D. Wei, X. Zhang, J. Liao, H. Wang, and C. Xie, “Three dimensional measurement with an electrically tunable focused plenoptic camera,” Rev. Sci. Instrum. 88(3), 033111 (2017).
[Crossref] [PubMed]

S. Kang and X. Zhang, “Compound liquid crystal microlens array with convergent and divergent functions,” Appl. Opt. 55(12), 3333–3338 (2016).
[Crossref] [PubMed]

Q. Tong, Y. Lei, Z. Xin, X. Zhang, H. Sang, and C. Xie, “Dual-mode photosensitive arrays based on the integration of liquid crystal microlenses and CMOS sensors for obtaining the intensity images and wavefronts of objects,” Opt. Express 24(3), 1903–1923 (2016).
[Crossref] [PubMed]

J. Lin, Q. Tong, Y. Lei, Z. Xin, X. Zhang, A. Ji, H. Sang, and C. Xie, “An arrayed liquid crystal Fabry–Perot infrared filter for electrically tunable spectral imaging detection,” IEEE Sens. J. 16(8), 2397–2403 (2016).
[Crossref]

Y. Lei, Q. Tong, X. Zhang, H. Sang, A. Ji, and C. Xie, “An electrically tunable plenoptic camera using a liquid crystal microlens array,” Rev. Sci. Instrum. 86(5), 053101 (2015).
[Crossref] [PubMed]

S. Kang and X. Zhang, “Liquid crystal microlens with dual apertures and electrically controlling focus shift,” Appl. Opt. 53(2), 244–248 (2014).
[Crossref] [PubMed]

S. Kang, X. Zhang, C. Xie, and T. Zhang, “Liquid-crystal microlens with focus swing and low driving voltage,” Appl. Opt. 52(3), 381–387 (2013).
[Crossref] [PubMed]

S. Kang, T. Qing, H. Sang, X. Zhang, and C. Xie, “Ommatidia structure based on double layers of liquid crystal microlens array,” Appl. Opt. 52(33), 7912–7918 (2013).
[Crossref] [PubMed]

Zheng, W.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Zimmerberg, J.

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

Annu. Rev. Astron. Astrophys. (1)

R. Davies and M. Kasper, “Adaptive Optics for Astronomy,” Annu. Rev. Astron. Astrophys. 50(1), 305–351 (2012).
[Crossref]

Appl. Opt. (5)

Appl. Phys. Express (1)

H. Ishii, T. Nakajima, Y. Takahashi, and T. Furukawa, “Ultrafast Polarization Switching in Ferroelectric Polymer Thin Films at Extremely High Electric Fields,” Appl. Phys. Express 4(3), 1027–1032 (2011).
[Crossref]

Appl. Phys. Lett. (1)

Y. Chen, D. Xu, S. T. Wu, S. Yamamoto, and Y. Haseba, “A low voltage and submillisecond-response polymer-stabilized blue phase liquid crystal,” Appl. Phys. Lett. 102(14), 141116 (2013).
[Crossref]

IEEE Photonics Technol. Lett. (1)

H. Kwon, Y. Kizu, Y. Kizaki, M. Ito, M. Kobayashi, R. Ueno, K. Suzuki, and H. Funaki, “A gradient index liquid crystal microlens array for light-field camera applications,” IEEE Photonics Technol. Lett. 27(8), 836–839 (2015).
[Crossref]

IEEE Sens. J. (1)

J. Lin, Q. Tong, Y. Lei, Z. Xin, X. Zhang, A. Ji, H. Sang, and C. Xie, “An arrayed liquid crystal Fabry–Perot infrared filter for electrically tunable spectral imaging detection,” IEEE Sens. J. 16(8), 2397–2403 (2016).
[Crossref]

J. Opt. Soc. Am. (1)

Micromachines (Basel) (1)

S. Xu, Y. Li, Y. Liu, J. Sun, H. Ren, and S. T. Wu, “Fast-response liquid crystal microlens,” Micromachines (Basel) 5(2), 300–324 (2014).
[Crossref]

Nat. Commun. (1)

K. Wang, W. Sun, C. T. Richie, B. K. Harvey, E. Betzig, and N. Ji, “Direct wavefront sensing for high-resolution in vivo imaging in scattering tissue,” Nat. Commun. 6(1), 7276 (2015).
[Crossref] [PubMed]

Nat. Methods (3)

N. Ji, “Adaptive optical fluorescence microscopy,” Nat. Methods 14(4), 374–380 (2017).
[Crossref] [PubMed]

W. Zheng, Y. Wu, P. Winter, R. Fischer, D. D. Nogare, A. Hong, C. McCormick, R. Christensen, W. P. Dempsey, D. B. Arnold, J. Zimmerberg, A. Chitnis, J. Sellers, C. Waterman, and H. Shroff, “Adaptive optics improves multiphoton super-resolution imaging,” Nat. Methods 14(9), 869–872 (2017).
[Crossref] [PubMed]

V. Marx, “Microscopy: hello, adaptive optics,” Nat. Methods 14(12), 1133–1136 (2017).
[Crossref] [PubMed]

Nat. Photonics (1)

R. Horstmeyer, H. Ruan, and C. Yang, “Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue,” Nat. Photonics 9(9), 563–571 (2015).
[Crossref] [PubMed]

Nature (1)

A. Finkbeiner, “Laser focus: by firing lasers into the sky, Claire Max has transformed the capabilities of current–and future—telescopes,” Nature 517(7535), 430–433 (2015).
[Crossref] [PubMed]

Neuron (1)

N. Ji, “The practical and fundamental limits of optical imaging in mammalian brains,” Neuron 83(6), 1242–1245 (2014).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

J. Y. Jo, P. Chen, R. J. Sichel, S. J. Callori, J. Sinsheimer, E. M. Dufresne, M. Dawber, and P. G. Evans, “Nanosecond dynamics of ferroelectric/dielectric superlattices,” Phys. Rev. Lett. 107(5), 055501 (2011).
[Crossref] [PubMed]

Proc. Info. Sci. IT Edu. Conf. (1)

O. Vincent and O. Folorunso, “A descriptive algorithm for sobel image edge detection,” Proc. Info. Sci. IT Edu. Conf. 40, 97–107 (2009).

Proc. SPIE (2)

C. Perwass and L. Wietzke, “Single-lens 3D camera with extended depth-of-field,” Proc. SPIE 8291, 829108 (2012).
[Crossref]

T. Georgiev and A. Lumsdaine, “The multifocus plenoptic camera,” Proc. SPIE 8299, 829908 (2012).
[Crossref]

Rev. Sci. Instrum. (2)

Y. Lei, Q. Tong, X. Zhang, H. Sang, A. Ji, and C. Xie, “An electrically tunable plenoptic camera using a liquid crystal microlens array,” Rev. Sci. Instrum. 86(5), 053101 (2015).
[Crossref] [PubMed]

Y. Lei, Q. Tong, Z. Xin, D. Wei, X. Zhang, J. Liao, H. Wang, and C. Xie, “Three dimensional measurement with an electrically tunable focused plenoptic camera,” Rev. Sci. Instrum. 88(3), 033111 (2017).
[Crossref] [PubMed]

Sci. Adv. (1)

H. B. de Aguiar, S. Gigan, and S. Brasselet, “Polarization recovery through scattering media,” Sci. Adv. 3(9), e1600743 (2017).
[Crossref] [PubMed]

Science (1)

J. R. Crepp, “Improving planet-finding spectrometers,” Science 346(6211), 809–810 (2014).
[Crossref] [PubMed]

Other (3)

C. Hahne, A. Aggoun, and V. Velisavljevic, “The refocusing distance of a standard plenoptic photograph,” in 3DTV-Conference: The True Vision-Capture, Transmission and Display of 3D Video (3DTV-CON), (2015).
[Crossref]

R. Ng, “Fourier slice photography,” in Proceedings of ACM SIGGRAPH(2005). 735–744.

R. Ng, “Digital light field photography,” Ph.D. dissertation (Stanford University, 2006).

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Figures (15)

Fig. 1
Fig. 1 Images acquired by turning off and on the LCMLA and the wavefronts of a model dozer at different depths of the objective space. Distance between the dozer and the LCWIS is 750mm in case-(a), and 850mm in case-(b).
Fig. 2
Fig. 2 (a) Basic structure of the LC device with addressably controlled electrode regions for driving LC molecule reorientation according to the electric field generated by the voltage signals applied across three electrode regions (Vc > Vb), and (b) the LC device fabricated.
Fig. 3
Fig. 3 Testing system for measuring the focusing performance of the LCMLA.
Fig. 4
Fig. 4 Relationship between the focal length of the LCMLA and the rms value of the voltage signal applied over it.
Fig. 5
Fig. 5 Typical characters of our imaging setup: (a) a photograph of a ruler acquired in a conventional imaging mode corresponding to (b) schematic of the imaging operation with the LC device turned off, and (c) schematically showing an arrayed beam convergence with the LCMLA.
Fig. 6
Fig. 6 Photograph of the LCWIS and model targets used in experiments for DOF extension.
Fig. 7
Fig. 7 Direct-imaging results and corresponding enlarged views for different depth position of the yellow model dozer. The dozer was placed at depths of (a) 1550 mm, (b) 1350 mm, and (c) 1150 mm, respectively.
Fig. 8
Fig. 8 Direct-imaging results with the LC device off (column a) and on (column b) along with stitched images formed by sub-images (column c), and their enlarged views for the dozer depth positions of (1) 950mm, (2) 850mm, (3) 750mm, (4) 650mm, (5) 550mm, (6) 450mm, (7) 350mm, and (8) 250mm, respectively.
Fig. 9
Fig. 9 Wavefronts of the model dozer located at different position.
Fig. 10
Fig. 10 Typical imaging characteristics of our setup: (a) When the LCMLA is applied by voltage signal V1, the sharp sub-image array of the target, which is at the position D1 away from the LCWIS, can be obtained by the photosensitive array. (b) Then moving the target to D2 away from the imaging system, the voltage signal should be turned to V2 for outputting sharp results by the photosensitive array used.
Fig. 11
Fig. 11 Direct-imaging results and their enlarged views with the LCMLA applied by different voltage signal, and the gray variation of the same region with different voltage signal.
Fig. 12
Fig. 12 Local results after edge extraction using Sobel operator.
Fig. 13
Fig. 13 Relationship between the depth of the objective space and the voltage signal applied.
Fig. 14
Fig. 14 Direct-imaging results (color) and their enlarged views (gray) of the model dozer corresponding to different voltage signal.
Fig. 15
Fig. 15 Results of performing wavefront imaging with DOF extension and depth measurement. (a) Image obtained directly by the LCWIS without any voltage signal for the LCMLA used, (b) sub-image array output from the LCMLA applied by a voltage signal of 1.6Vrms corresponding to the left target, and another voltage signal of 1.9Vrms corresponding to the right target, (c) clear right or green target image reconstructed by stitching arrayed sub-images and its composite wavefront, (d) clear left or yellow target image reconstructed by the same process above and its composite wavefront.

Tables (3)

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Table 1 Sobel mean gradient with different voltage signal corresponding to the target located at the depth 750mm.

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Table 2 Sobel mean gradient with different voltage signal corresponding to the target located at different depth.

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Table 3 Sobel mean gradient of different voltage signal.

Equations (5)

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D N = f 2 F f 2 +NδF .
δ= f 2 N(Ff)
G x(ij) =[ 1 0 1 2 0 2 1 0 1 ] A ij , G y(ij) =[ 1 2 1 0 0 0 1 2 1 ] A ij
G ij = G x(ij) 2 + G y(ij) 2 .
G= G ij m×n .