Abstract

In this paper, we present a kind of dual-mode photosensitive arrays (DMPAs) constructed by hybrid integration a liquid crystal microlens array (LCMLA) driven electrically and a CMOS sensor array, which can be used to measure both the conventional intensity images and corresponding wavefronts of objects. We utilize liquid crystal materials to shape the microlens array with the electrically tunable focal length. Through switching the voltage signal on and off, the wavefronts and the intensity images can be acquired through the DMPAs, sequentially. We use white light to obtain the object's wavefronts for avoiding losing important wavefront information. We separate the white light wavefronts with a large number of spectral components and then experimentally compare them with single spectral wavefronts of typical red, green and blue lasers, respectively. Then we mix the red, green and blue wavefronts to a composite wavefront containing more optical information of the object.

© 2016 Optical Society of America

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References

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  1. R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61(5), 656–660 (1971).
  2. J. G. Allen, A. Jankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation,” Proc. SPIE 739, 124–128 (1988).
    [Crossref]
  3. D. Dayton, J. Gonglewski, B. Pierson, and B. Spielbusch, “Atmospheric structure function measurements with a Shack-Hartmann wave-front sensor,” Opt. Lett. 17(24), 1737–1739 (1992).
    [Crossref] [PubMed]
  4. R. W. Wilson, “SLODAR: measuring optical turbulence altitude with a Shack–Hartmann wavefront sensor,” Mon. Not. R. Astron. Soc. 337(1), 103–108 (2002).
    [Crossref]
  5. J. Liang, B. Grimm, S. Goelz, and J. F. Bille, “Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor,” J. Opt. Soc. Am. A 11(7), 1949–1957 (1994).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  8. C. López-Quesada, J. Andilla, and E. Martín-Badosa, “Correction of aberration in holographic optical tweezers using a Shack-Hartmann sensor,” Appl. Opt. 48(6), 1084–1090 (2009).
    [Crossref] [PubMed]
  9. B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
    [PubMed]
  10. Y. H. Fan, H. Ren, and S. T. Wu, “Electrically switchable Fresnel lens using a polymer-separated composite film,” Opt. Express 13(11), 4141–4147 (2005).
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  11. R. Cudney, L. Ríos, and H. Escamilla, “Electrically controlled Fresnel zone plates made from ring-shaped 180 degree domains,” Opt. Express 12(23), 5783–5788 (2004).
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  12. S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
    [Crossref]
  13. M. Ye, B. Wang, and S. Sato, “Double-layer liquid crystal lens,” Jpn. J. Appl. Phys. 43(No. 3A), L352–L354 (2004).
    [Crossref]
  14. H. Ren and S. T. Wu, “Adaptive liquid crystal lens with large focal length tunability,” Opt. Express 14(23), 11292–11298 (2006).
    [Crossref] [PubMed]
  15. 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]
  16. 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]
  17. 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]
  18. L. Seifert, J. Liesener, and H. J. Tiziani, “The adaptive Shack-Hartmann sensor,” Opt. Commun. 216(4–6), 313–319 (2003).
    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  22. H. Gharavi and M. Mills, “Blockmatching motion estimation algorithms-new results,” IEEE Trans. Circuits Systems 37(5), 649–651 (1990).
    [Crossref]
  23. W. Li and E. Salari, “Successive elimination algorithm for motion estimation,” IEEE Trans. Image Process. 4(1), 105–107 (1995).
    [Crossref] [PubMed]
  24. “Spectral response curve,” in the hardware operating instructions of MVC14KSAC-GE6 camera V1.0.0.0, (Microview, 2012).

2015 (3)

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]

J. Li, Y. Gong, H. Chen, and X. Hu, “Wave-front reconstruction with Hartmann–Shack sensor using a phase-retrieval method,” Opt. Commun. 336, 127–133 (2015).
[Crossref]

2013 (1)

2011 (1)

2009 (1)

2007 (1)

2006 (1)

2005 (1)

2004 (2)

2003 (1)

L. Seifert, J. Liesener, and H. J. Tiziani, “The adaptive Shack-Hartmann sensor,” Opt. Commun. 216(4–6), 313–319 (2003).
[Crossref]

2002 (1)

R. W. Wilson, “SLODAR: measuring optical turbulence altitude with a Shack–Hartmann wavefront sensor,” Mon. Not. R. Astron. Soc. 337(1), 103–108 (2002).
[Crossref]

2001 (2)

1997 (1)

1995 (1)

W. Li and E. Salari, “Successive elimination algorithm for motion estimation,” IEEE Trans. Image Process. 4(1), 105–107 (1995).
[Crossref] [PubMed]

1994 (1)

1992 (1)

1990 (1)

H. Gharavi and M. Mills, “Blockmatching motion estimation algorithms-new results,” IEEE Trans. Circuits Systems 37(5), 649–651 (1990).
[Crossref]

1988 (1)

J. G. Allen, A. Jankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation,” Proc. SPIE 739, 124–128 (1988).
[Crossref]

1979 (1)

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[Crossref]

1971 (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61(5), 656–660 (1971).

Allen, J. G.

J. G. Allen, A. Jankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation,” Proc. SPIE 739, 124–128 (1988).
[Crossref]

Andilla, J.

Ares, J.

Arines, J.

Bará, S.

Bille, J. F.

Byer, R. L.

Chen, H.

J. Li, Y. Gong, H. Chen, and X. Hu, “Wave-front reconstruction with Hartmann–Shack sensor using a phase-retrieval method,” Opt. Commun. 336, 127–133 (2015).
[Crossref]

Climent, V.

Clubley, D.

Cudney, R.

Cudney, R. S.

Dayton, D.

Durán, V.

Escamilla, H.

Fan, Y. H.

Fejer, M. M.

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]

Gharavi, H.

H. Gharavi and M. Mills, “Blockmatching motion estimation algorithms-new results,” IEEE Trans. Circuits Systems 37(5), 649–651 (1990).
[Crossref]

Goelz, S.

Gong, Y.

J. Li, Y. Gong, H. Chen, and X. Hu, “Wave-front reconstruction with Hartmann–Shack sensor using a phase-retrieval method,” Opt. Commun. 336, 127–133 (2015).
[Crossref]

Gonglewski, J.

Grimm, B.

Gustafson, E. K.

Hennawi, J.

Hu, X.

J. Li, Y. Gong, H. Chen, and X. Hu, “Wave-front reconstruction with Hartmann–Shack sensor using a phase-retrieval method,” Opt. Commun. 336, 127–133 (2015).
[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]

Jankevics, A.

J. G. Allen, A. Jankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation,” Proc. SPIE 739, 124–128 (1988).
[Crossref]

Jaroszewicz, Z.

Ji, A.

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]

Kang, S.

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]

Lancis, J.

Lei, Y.

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, J.

J. Li, Y. Gong, H. Chen, and X. Hu, “Wave-front reconstruction with Hartmann–Shack sensor using a phase-retrieval method,” Opt. Commun. 336, 127–133 (2015).
[Crossref]

Li, W.

W. Li and E. Salari, “Successive elimination algorithm for motion estimation,” IEEE Trans. Image Process. 4(1), 105–107 (1995).
[Crossref] [PubMed]

Liang, J.

Liesener, J.

L. Seifert, J. Liesener, and H. J. Tiziani, “The adaptive Shack-Hartmann sensor,” Opt. Commun. 216(4–6), 313–319 (2003).
[Crossref]

López-Quesada, C.

Mansell, J. D.

Martín-Badosa, E.

Mills, M.

H. Gharavi and M. Mills, “Blockmatching motion estimation algorithms-new results,” IEEE Trans. Circuits Systems 37(5), 649–651 (1990).
[Crossref]

Pierson, B.

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61(5), 656–660 (1971).

Prado, P.

Reitze, D. H.

Ren, H.

Ríos, L.

Salari, E.

W. Li and E. Salari, “Successive elimination algorithm for motion estimation,” IEEE Trans. Image Process. 4(1), 105–107 (1995).
[Crossref] [PubMed]

Sang, H.

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]

Sato, S.

M. Ye, B. Wang, and S. Sato, “Double-layer liquid crystal lens,” Jpn. J. Appl. Phys. 43(No. 3A), L352–L354 (2004).
[Crossref]

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[Crossref]

Schmutz, L.

J. G. Allen, A. Jankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation,” Proc. SPIE 739, 124–128 (1988).
[Crossref]

Seifert, L.

L. Seifert, J. Liesener, and H. J. Tiziani, “The adaptive Shack-Hartmann sensor,” Opt. Commun. 216(4–6), 313–319 (2003).
[Crossref]

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Shack, R. V.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61(5), 656–660 (1971).

Spielbusch, B.

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]

Tajahuerce, E.

Tiziani, H. J.

L. Seifert, J. Liesener, and H. J. Tiziani, “The adaptive Shack-Hartmann sensor,” Opt. Commun. 216(4–6), 313–319 (2003).
[Crossref]

Tong, Q.

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]

Wang, B.

M. Ye, B. Wang, and S. Sato, “Double-layer liquid crystal lens,” Jpn. J. Appl. Phys. 43(No. 3A), L352–L354 (2004).
[Crossref]

Williams, D. R.

Wilson, R. W.

R. W. Wilson, “SLODAR: measuring optical turbulence altitude with a Shack–Hartmann wavefront sensor,” Mon. Not. R. Astron. Soc. 337(1), 103–108 (2002).
[Crossref]

Wormell, D.

J. G. Allen, A. Jankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation,” Proc. SPIE 739, 124–128 (1988).
[Crossref]

Wu, S. T.

Xie, C.

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]

Ye, M.

M. Ye, B. Wang, and S. Sato, “Double-layer liquid crystal lens,” Jpn. J. Appl. Phys. 43(No. 3A), L352–L354 (2004).
[Crossref]

Yoshida, S.

Zhang, T.

Zhang, X.

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]

Appl. Opt. (3)

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 Trans. Circuits Systems (1)

H. Gharavi and M. Mills, “Blockmatching motion estimation algorithms-new results,” IEEE Trans. Circuits Systems 37(5), 649–651 (1990).
[Crossref]

IEEE Trans. Image Process. (1)

W. Li and E. Salari, “Successive elimination algorithm for motion estimation,” IEEE Trans. Image Process. 4(1), 105–107 (1995).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61(5), 656–660 (1971).

J. Opt. Soc. Am. A (2)

J. Refract. Surg. (1)

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Jpn. J. Appl. Phys. (2)

S. Sato, “Liquid-crystal lens-cells with variable focal length,” Jpn. J. Appl. Phys. 18(9), 1679–1684 (1979).
[Crossref]

M. Ye, B. Wang, and S. Sato, “Double-layer liquid crystal lens,” Jpn. J. Appl. Phys. 43(No. 3A), L352–L354 (2004).
[Crossref]

Mon. Not. R. Astron. Soc. (1)

R. W. Wilson, “SLODAR: measuring optical turbulence altitude with a Shack–Hartmann wavefront sensor,” Mon. Not. R. Astron. Soc. 337(1), 103–108 (2002).
[Crossref]

Opt. Commun. (2)

L. Seifert, J. Liesener, and H. J. Tiziani, “The adaptive Shack-Hartmann sensor,” Opt. Commun. 216(4–6), 313–319 (2003).
[Crossref]

J. Li, Y. Gong, H. Chen, and X. Hu, “Wave-front reconstruction with Hartmann–Shack sensor using a phase-retrieval method,” Opt. Commun. 336, 127–133 (2015).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Proc. SPIE (1)

J. G. Allen, A. Jankevics, D. Wormell, and L. Schmutz, “Digital wavefront sensor for astronomical image compensation,” Proc. SPIE 739, 124–128 (1988).
[Crossref]

Rev. Sci. Instrum. (1)

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]

Other (1)

“Spectral response curve,” in the hardware operating instructions of MVC14KSAC-GE6 camera V1.0.0.0, (Microview, 2012).

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Figures (17)

Fig. 1
Fig. 1 Key structure and parameters of the LCMLA designed and fabricated by us.
Fig. 2
Fig. 2 Micro-structural schematic of the DMPAs developed by us for performing conventional intensity imaging and corresponding wavefront measurement. (a) No controlling voltage: the DMPAs working in the imaging mode. (b) A voltage signal is applied: the DMPAs working in the wavefront measurement mode. (c) The cross-section view of a single liquid crystal microlens applied by a voltage signal with needed amplitude and duty cycle and waveform.
Fig. 3
Fig. 3 Measurement system for acquiring common optical performances of the LCMLA fabricated by us.
Fig. 4
Fig. 4 Beam converging patterns and the corresponding PSFs of the LCMLA applied by different voltage signal. (a) The beam converging spots and corresponding PSFs of single liquid crystal microlens: red light at different rms voltage state. (b) The beam converging spots and PSFs of spectral lasers processed by a liquid crystal microlens including different wavelength at 4.5 Vrms. (c) Arrayed PSF of red beams processed by partial LCMLA at 4.5 Vrms.
Fig. 5
Fig. 5 Relationship between the focal length of the LCMLA and the rms value of the voltage signal applied.
Fig. 6
Fig. 6 Experimental system for performing dual-mode imaging detection. (a) Several main experimental setups. (b) The liquid crystal device fabricated and the red dashline box indicating the effective zone of the device for carrying out beam processing. (c) A shot of naturally performing measurements.
Fig. 7
Fig. 7 Schematic of measuring the division wavefront map of the beams out from the object.
Fig. 8
Fig. 8 Typical imaging characters leading to construct light wavefront of the object based on the DMPAs developed. (a) Conventional intensity image of a model dozer when the DMPA works in the imaging mode. (b) Low definition intensity image used to shape the wavefront of the model dozer when the DMPA works in the wavefront measurement mode. (c) The constructed wavefront is also presented.
Fig. 9
Fig. 9 Data selection for separating object wavefront based on the spectral response properties of the sensors used.
Fig. 10
Fig. 10 Conventional intensity images of two bricks when the DMPA works in the imaging mode.
Fig. 11
Fig. 11 Low definition intensity image used to shape a white light wavefront and the associated front view of wavefront constructed, and the small inserts indicate the detailed beam distribution characters, which are already adjusted under the conditions of the red frame with a brightness of 60% and a contrast of 75%, and the blue frame with a brightness of 62% and a contrast of 80%.
Fig. 12
Fig. 12 Low definition white light images leading to forming the wavefronts and associated front view of wavefronts constructed, and the low definition spectral images originated from common laser illumination and corresponding front view of wavefronts constructed.
Fig. 13
Fig. 13 The object of model tree.
Fig. 14
Fig. 14 Low definition intensity image acquired at 4.5 Vrms and associated wavefronts. (a) Low definition intensity image of the red light, and the small inserts indicating the detailed beam distribution characters. The green and blue frame are adjusted under a brightness of 70% and a contrast of 80%, and under a brightness of 70% and a contrast of 80%, respectively. (b) Low definition intensity image of the green light. The red and blue frame are adjusted under a brightness of 76% and a contrast of 85%, and under a brightness of 54% and a contrast of 65%, respectively. (c) Low definition intensity image of the blue light. The red and green frame are adjusted under a brightness of 76% and a contrast of 85%, and under a brightness of 56% and a contrast of 65%, respectively. (d) Low definition intensity image of the white light. (e) The wavefront constructed by the low definition intensity images from (a) to (d).
Fig. 15
Fig. 15 The mixing of the spectral wavefronts and then a comparison of the mixed wavefront and the white light wavefront chosen.
Fig. 16
Fig. 16 The mean-absolute-difference of the mixed wavefront to the white light wavefront when r = 0.8.
Fig. 17
Fig. 17 The mean-absolute-difference of different wavefront to the white light wavefront.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

{ tan θ x = Δ x f tan θ y = Δ y f ,
[ Δ x Δ y ] i , j = [ x c x o y c y o ] i , j ,
[ x c y c ] i , j = 1 m = [ M l ] i , j [ M u ] i , j n = [ N l ] i , j [ N u ] i , j I ( m , n ) [ m = [ M l ] i , j [ M u ] i , j n = [ N l ] i , j [ N u ] i , j x ( m , n ) I ( m , n ) m = [ M l ] i , j [ M u ] i , j n = [ N l ] i , j [ N u ] i , j y ( m , n ) I ( m , n ) ] ,
M A D = i = 1 M j = 1 N | W s ( i , j ) r × W t ( i , j ) | M × N ,
G 532 = S G 532 S G G W ,
W m = m × W r + n × W g + ( 1 m n ) × W b ,

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