Abstract

A large open aperture in an optical system can capture high-resolution images but yields a shallow depth of field. To overcome this issue, we investigated a low-cost, readily available method for retrofitting microscopy imaging systems to achieve 3D focus scanning in this study. Specifically, a procedure for fabricating variable focus spinners with dissimilar plates was introduced, and a sequence of 12 images was captured in different focal planes. The image scale and phase were corrected, and the in-focus pixels were abstracted by employing the Laplacian operator. Finally, an all-in-focus sharp image was generated, and a depth map was obtained.

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

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References

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  6. B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
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  7. H. Ren, S. Xu, and S.-T. Wu, “Liquid crystal pump,” Lab Chip. 13, 100–105 (2013).
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  8. T. Zhan, Y.-H. Lee, and S.-T. Wu, “High-resolution additive light field near-eye display by switchable pancharatnam–berry phase lenses,” Opt. Express 26, 4863–4872 (2018).
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2018 (1)

2017 (3)

Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in pancharatnam–berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3, 79–88 (2017).
[Crossref]

L. Wang, H. Oku, and M. Ishikawa, “Paraxial ray solution for liquid-filled variable focus lenses,” Jpn. J. Appl. Phys. 56, 122501 (2017).
[Crossref]

L. Wang, T. Hayakawa, and M. Ishikawa, “Dielectric-elastomer-based fabrication method for varifocal microlens array,” Opt. express 25, 31708–31717 (2017).
[Crossref] [PubMed]

2014 (1)

2013 (2)

L. Wang, H. Oku, and M. Ishikawa, “Variable-focus lens with 30 mm optical aperture based on liquid–membrane–liquid structure,” Appl. Phys. Lett. 102, 131111 (2013).
[Crossref]

H. Ren, S. Xu, and S.-T. Wu, “Liquid crystal pump,” Lab Chip. 13, 100–105 (2013).
[Crossref]

2010 (1)

2009 (1)

H. Oku and M. Ishikawa, “High-speed liquid lens with 2 ms response and 80.3 nm root-mean-square wavefront error,” Appl. Phys. Lett. 94, 221108 (2009).
[Crossref]

2006 (3)

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103, 6100–6104 (2006).
[Crossref] [PubMed]

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature 442, 551 (2006).
[Crossref] [PubMed]

M. A. Muquit, T. Shibahara, and T. Aoki, “A high-accuracy passive 3d measurement system using phase-based image matching,” IEICE Trans. Fundamentals 89, 686–697 (2006).
[Crossref]

2003 (1)

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundamentals 86, 1925–1934 (2003).

2000 (1)

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
[Crossref]

1996 (1)

B. S. Reddy and B. N. Chatterji, “An fft-based technique for translation, rotation, and scale-invariant image registration,” IEEE Trans. Image Process. 5, 1266–1271 (1996).
[Crossref] [PubMed]

1994 (1)

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Pattern Anal. Mach. Intell 16, 824–831 (1994).
[Crossref]

Agarwal, A. K.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature 442, 551 (2006).
[Crossref] [PubMed]

Aoki, T.

M. A. Muquit, T. Shibahara, and T. Aoki, “A high-accuracy passive 3d measurement system using phase-based image matching,” IEICE Trans. Fundamentals 89, 686–697 (2006).
[Crossref]

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundamentals 86, 1925–1934 (2003).

Äyräs, P.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103, 6100–6104 (2006).
[Crossref] [PubMed]

Beebe, D. J.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature 442, 551 (2006).
[Crossref] [PubMed]

Berge, B.

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
[Crossref]

Chatterji, B. N.

B. S. Reddy and B. N. Chatterji, “An fft-based technique for translation, rotation, and scale-invariant image registration,” IEEE Trans. Image Process. 5, 1266–1271 (1996).
[Crossref] [PubMed]

Dong, L.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature 442, 551 (2006).
[Crossref] [PubMed]

Gauza, S.

Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in pancharatnam–berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3, 79–88 (2017).
[Crossref]

Giridhar, M.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103, 6100–6104 (2006).
[Crossref] [PubMed]

Gou, F.

Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in pancharatnam–berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3, 79–88 (2017).
[Crossref]

Greivenkamp, J. E.

J. E. Greivenkamp, Field guide to geometrical optics vol. 1 (SPIE Publications, Washington, 2004).
[Crossref]

Haddock, J. N.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103, 6100–6104 (2006).
[Crossref] [PubMed]

Hayakawa, T.

Higuchi, T.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundamentals 86, 1925–1934 (2003).

Honkanen, S.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103, 6100–6104 (2006).
[Crossref] [PubMed]

Ishikawa, M.

L. Wang, T. Hayakawa, and M. Ishikawa, “Dielectric-elastomer-based fabrication method for varifocal microlens array,” Opt. express 25, 31708–31717 (2017).
[Crossref] [PubMed]

L. Wang, H. Oku, and M. Ishikawa, “Paraxial ray solution for liquid-filled variable focus lenses,” Jpn. J. Appl. Phys. 56, 122501 (2017).
[Crossref]

L. Wang, H. Oku, and M. Ishikawa, “An improved low-optical-power variable focus lens with a large aperture,” Opt. Express 22, 19448–19456 (2014).
[Crossref] [PubMed]

L. Wang, H. Oku, and M. Ishikawa, “Variable-focus lens with 30 mm optical aperture based on liquid–membrane–liquid structure,” Appl. Phys. Lett. 102, 131111 (2013).
[Crossref]

H. Oku and M. Ishikawa, “High-speed liquid lens with 2 ms response and 80.3 nm root-mean-square wavefront error,” Appl. Phys. Lett. 94, 221108 (2009).
[Crossref]

H. Oku and M. Ishikawa, “High-speed liquid lens for computer vision,” in Proceedings of IEEE International Conference on Robotics and Automation, (IEEE, 2010), pp. 2643–2648.

Jiang, H.

L. Dong, A. K. Agarwal, D. J. Beebe, and H. Jiang, “Adaptive liquid microlenses activated by stimuli-responsive hydrogels,” Nature 442, 551 (2006).
[Crossref] [PubMed]

Kippelen, B.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103, 6100–6104 (2006).
[Crossref] [PubMed]

Kobayashi, K.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundamentals 86, 1925–1934 (2003).

Lee, Y.-H.

T. Zhan, Y.-H. Lee, and S.-T. Wu, “High-resolution additive light field near-eye display by switchable pancharatnam–berry phase lenses,” Opt. Express 26, 4863–4872 (2018).
[Crossref] [PubMed]

Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in pancharatnam–berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3, 79–88 (2017).
[Crossref]

Li, G.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103, 6100–6104 (2006).
[Crossref] [PubMed]

Liu, G.

Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in pancharatnam–berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3, 79–88 (2017).
[Crossref]

Liu, Y.

Mathine, D. L.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103, 6100–6104 (2006).
[Crossref] [PubMed]

Meredith, G. R.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103, 6100–6104 (2006).
[Crossref] [PubMed]

Muquit, M. A.

M. A. Muquit, T. Shibahara, and T. Aoki, “A high-accuracy passive 3d measurement system using phase-based image matching,” IEICE Trans. Fundamentals 89, 686–697 (2006).
[Crossref]

Nakagawa, Y.

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Pattern Anal. Mach. Intell 16, 824–831 (1994).
[Crossref]

Nayar, S. K.

S. K. Nayar and Y. Nakagawa, “Shape from focus,” IEEE Trans. Pattern Anal. Mach. Intell 16, 824–831 (1994).
[Crossref]

Oku, H.

L. Wang, H. Oku, and M. Ishikawa, “Paraxial ray solution for liquid-filled variable focus lenses,” Jpn. J. Appl. Phys. 56, 122501 (2017).
[Crossref]

L. Wang, H. Oku, and M. Ishikawa, “An improved low-optical-power variable focus lens with a large aperture,” Opt. Express 22, 19448–19456 (2014).
[Crossref] [PubMed]

L. Wang, H. Oku, and M. Ishikawa, “Variable-focus lens with 30 mm optical aperture based on liquid–membrane–liquid structure,” Appl. Phys. Lett. 102, 131111 (2013).
[Crossref]

H. Oku and M. Ishikawa, “High-speed liquid lens with 2 ms response and 80.3 nm root-mean-square wavefront error,” Appl. Phys. Lett. 94, 221108 (2009).
[Crossref]

H. Oku and M. Ishikawa, “High-speed liquid lens for computer vision,” in Proceedings of IEEE International Conference on Robotics and Automation, (IEEE, 2010), pp. 2643–2648.

Peng, F.

Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in pancharatnam–berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3, 79–88 (2017).
[Crossref]

Peseux, J.

B. Berge and J. Peseux, “Variable focal lens controlled by an external voltage: An application of electrowetting,” Eur. Phys. J. E 3, 159–163 (2000).
[Crossref]

Peyghambarian, N.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103, 6100–6104 (2006).
[Crossref] [PubMed]

Reddy, B. S.

B. S. Reddy and B. N. Chatterji, “An fft-based technique for translation, rotation, and scale-invariant image registration,” IEEE Trans. Image Process. 5, 1266–1271 (1996).
[Crossref] [PubMed]

Ren, H.

H. Ren, S. Xu, and S.-T. Wu, “Liquid crystal pump,” Lab Chip. 13, 100–105 (2013).
[Crossref]

S. Xu, Y. Liu, H. Ren, and S.-T. Wu, “A novel adaptive mechanical-wetting lens for visible and near infrared imaging,” Opt. express 18, 12430–12435 (2010).
[Crossref] [PubMed]

H. Ren and S.-T. Wu, Introduction to adaptive lenses vol. 75 (John Wiley & Sons, New York City, 2012).
[Crossref]

Sasaki, Y.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundamentals 86, 1925–1934 (2003).

Schwiegerling, J.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103, 6100–6104 (2006).
[Crossref] [PubMed]

Shibahara, T.

M. A. Muquit, T. Shibahara, and T. Aoki, “A high-accuracy passive 3d measurement system using phase-based image matching,” IEICE Trans. Fundamentals 89, 686–697 (2006).
[Crossref]

Tabiryan, N. V.

Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in pancharatnam–berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3, 79–88 (2017).
[Crossref]

Takita, K.

K. Takita, T. Aoki, Y. Sasaki, T. Higuchi, and K. Kobayashi, “High-accuracy subpixel image registration based on phase-only correlation,” IEICE Trans. Fundamentals 86, 1925–1934 (2003).

Tan, G.

Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in pancharatnam–berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3, 79–88 (2017).
[Crossref]

Valley, P.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103, 6100–6104 (2006).
[Crossref] [PubMed]

Wang, L.

L. Wang, T. Hayakawa, and M. Ishikawa, “Dielectric-elastomer-based fabrication method for varifocal microlens array,” Opt. express 25, 31708–31717 (2017).
[Crossref] [PubMed]

L. Wang, H. Oku, and M. Ishikawa, “Paraxial ray solution for liquid-filled variable focus lenses,” Jpn. J. Appl. Phys. 56, 122501 (2017).
[Crossref]

L. Wang, H. Oku, and M. Ishikawa, “An improved low-optical-power variable focus lens with a large aperture,” Opt. Express 22, 19448–19456 (2014).
[Crossref] [PubMed]

L. Wang, H. Oku, and M. Ishikawa, “Variable-focus lens with 30 mm optical aperture based on liquid–membrane–liquid structure,” Appl. Phys. Lett. 102, 131111 (2013).
[Crossref]

Weng, Y.

Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in pancharatnam–berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3, 79–88 (2017).
[Crossref]

Williby, G.

G. Li, D. L. Mathine, P. Valley, P. Äyräs, J. N. Haddock, M. Giridhar, G. Williby, J. Schwiegerling, G. R. Meredith, B. Kippelen, S. Honkanen, and N. Peyghambarian, “Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications,” Proc. Natl. Acad. Sci. U.S.A. 103, 6100–6104 (2006).
[Crossref] [PubMed]

Wolberg, G.

G. Wolberg, Digital Image Wrapping vol. 1 (Wiley-IEEE Computer Society Press, Los Alamitos, 1990).

Wu, S.-T.

T. Zhan, Y.-H. Lee, and S.-T. Wu, “High-resolution additive light field near-eye display by switchable pancharatnam–berry phase lenses,” Opt. Express 26, 4863–4872 (2018).
[Crossref] [PubMed]

Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in pancharatnam–berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3, 79–88 (2017).
[Crossref]

H. Ren, S. Xu, and S.-T. Wu, “Liquid crystal pump,” Lab Chip. 13, 100–105 (2013).
[Crossref]

S. Xu, Y. Liu, H. Ren, and S.-T. Wu, “A novel adaptive mechanical-wetting lens for visible and near infrared imaging,” Opt. express 18, 12430–12435 (2010).
[Crossref] [PubMed]

H. Ren and S.-T. Wu, Introduction to adaptive lenses vol. 75 (John Wiley & Sons, New York City, 2012).
[Crossref]

Xu, S.

Zhan, T.

T. Zhan, Y.-H. Lee, and S.-T. Wu, “High-resolution additive light field near-eye display by switchable pancharatnam–berry phase lenses,” Opt. Express 26, 4863–4872 (2018).
[Crossref] [PubMed]

Y.-H. Lee, G. Tan, T. Zhan, Y. Weng, G. Liu, F. Gou, F. Peng, N. V. Tabiryan, S. Gauza, and S.-T. Wu, “Recent progress in pancharatnam–berry phase optical elements and the applications for virtual/augmented realities,” Opt. Data Process. Storage 3, 79–88 (2017).
[Crossref]

Appl. Phys. Lett. (2)

L. Wang, H. Oku, and M. Ishikawa, “Variable-focus lens with 30 mm optical aperture based on liquid–membrane–liquid structure,” Appl. Phys. Lett. 102, 131111 (2013).
[Crossref]

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Supplementary Material (2)

NameDescription
» Code 1       Raw images and the Matlab code for computing image gradient.
» Code 2       Raw images and Matlab code for computing all-in-focus image and depth map.

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Figures (7)

Fig. 1
Fig. 1 Illustration of the law of refraction. (a) Basic refraction scenario, where the ratio between the sines of the angles of incidence and refraction is equal to the ratio between the indices of refraction of the two media. (b) A light beam passes through a transparent plate with a certain index of refraction and is refracted twice: when it hits the upper boundary and when it passes through the lower boundary. The final light beam is parallel to the incident beam but is shifted by a certain amount. (c) Extension of the focal length from f1 to f2 by placing Medium 2 in front of a lens, given that N2 > N1.
Fig. 2
Fig. 2 Three screenshots of the Zemax simulation. An ideal lens (set as paraxial lens) was employed on the first surface with a focal length of 100 mm. Only green light was considered, and the refractive index of the BK7 glass on green light was n = 1.5168. (a). The first lens was set as an ideal lens (set as paraxial lens). When the thickness of the glass plate was 0 mm, the original total axial length was 100 mm. (b) When the thickness of the glasses plate was 5 mm, the total axial length became 101.70359 mm. (c) When the thickness of the plate was 11 mm, the total axial length could be extended to 103.74789 mm.
Fig. 3
Fig. 3 Experimental setup. (a) Sketch of the setup of the variable focus imaging system. (b) Photograph of the experimental setup. The variable focus spinner had 12 apertures that were mounted with different transparent plates.
Fig. 4
Fig. 4 Results obtained by using transparent plates of various thicknesses. (a) Six images acquired by using transparent plates with thicknesses of 0, 2, 4, 6, 8, and 10 mm. The movement of the focus point is clearly observable. The 1024 pixels along the blue line marked on the photographs were calculated to determine the focus. (b) Gradients calculated by using all 12 of the obtained images. The region in each plot with higher P–V values corresponds to the in-focus area, so shift of this region from right to left confirms that the focus changed gradually. Matlab code and the raw images could be found in Code 1 [17].
Fig. 5
Fig. 5 Images obtained by changing the plate thickness from 0 mm to 11 mm. (a) Raw image sequence. (b) Images obtained after rescaling, phase correction, and Laplacian edge detection. (c) All-in-focus sharp image generated by merging the in-focus pixels. (d) Depth map produced by using the index numbers of the images, which contained depth information. Matlab code and the raw images could be found in Code 2 [19].
Fig. 6
Fig. 6 Images of a USAF 1951 resolution chart. (a) Image obtained with no plate (thickness = 0 mm). (b) Image obtained with an 11-mm-thick plate inserted.
Fig. 7
Fig. 7 Comparison of the processed all-in-focus result (a) without scale and phase correction and (b) with correction. As shown in (a), when the phases of the images were not aligned, dislocation occurred when stacking the pixels from different layers, such as the area marked in the yellow frame.

Equations (9)

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

sin θ 1 sin θ 2 = N 2 N 1 ,
AB ¯ = t cos θ 2 .
σ = AB ¯ × sin ( θ 1 θ 2 ) .
σ = ( 1 N 1 N 2 × cos θ 1 cos θ 2 ) × t × sin θ 1 .
d = ( 1 N 1 N 2 × cos θ 1 cos θ 2 ) × t .
F = F x i ^ + F y j ^ .
[ x y 1 ] = [ u v 1 ] = [ u v 1 ] [ S u 0 0 0 S v 0 0 0 1 ] ,
[ x y 1 ] = [ u v 1 ] = [ u v 1 ] [ 1 0 0 0 1 0 T u T v 1 ] ,
Laplace ( f ) = 2 f x 2 + 2 f y 2 .