Abstract

There has been great interest in researching and implementing effective technologies for the capture, processing, and display of 3D images. This broad interest is evidenced by widespread international research and activities on 3D technologies. There is a large number of journal and conference papers on 3D systems, as well as research and development efforts in government, industry, and academia on this topic for broad applications including entertainment, manufacturing, security and defense, and biomedical applications. Among these technologies, integral imaging is a promising approach for its ability to work with polychromatic scenes and under incoherent or ambient light for scenarios from macroscales to microscales. Integral imaging systems and their variations, also known as plenoptics or light-field systems, are applicable in many fields, and they have been reported in many applications, such as entertainment (TV, video, movies), industrial inspection, security and defense, and biomedical imaging and displays. This tutorial is addressed to the students and researchers in different disciplines who are interested to learn about integral imaging and light-field systems and who may or may not have a strong background in optics. Our aim is to provide the readers with a tutorial that teaches fundamental principles as well as more advanced concepts to understand, analyze, and implement integral imaging and light-field-type capture and display systems. The tutorial is organized to begin with reviewing the fundamentals of imaging, and then it progresses to more advanced topics in 3D imaging and displays. More specifically, this tutorial begins by covering the fundamentals of geometrical optics and wave optics tools for understanding and analyzing optical imaging systems. Then, we proceed to use these tools to describe integral imaging, light-field, or plenoptics systems, the methods for implementing the 3D capture procedures and monitors, their properties, resolution, field of view, performance, and metrics to assess them. We have illustrated with simple laboratory setups and experiments the principles of integral imaging capture and display systems. Also, we have discussed 3D biomedical applications, such as integral microscopy.

© 2018 Optical Society of America

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  119. D. Nam, J.-H. Lee, Y.-H. Cho, Y.-J. Jeong, H. Hwang, and D.-S. Park, “Flat panel light-field 3-D display: concept, design, rendering, and calibration,” Proc. IEEE 105, 876–891 (2017).
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  120. A. Stern, Y. Yitzhaky, and B. Javidi, “Perceivable light fields: matching the requirements between the human visual system and autostereoscopic 3-D displays,” Proc. IEEE 102, 1571–1587 (2014).
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  121. B. Javidi and A. M. Tekalp, “Emerging 3-D imaging and display technologies,” Proc. IEEE 105, 786–788 (2017).
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2018 (3)

D. E. Smalley, E. Nygaard, K. Squire, J. Van Wagoner, J. Rasmussen, S. Gneiting, K. Qaderi, J. Goodsell, W. Rogers, M. Lindsey, K. Costner, A. Monk, M. Pearson, B. Haymore, and J. Peatross, “A photophoretic-trap volumetric display,” Nature 553, 486–490 (2018).
[Crossref]

S. Ebrahimi, M. Dashtdar, E. Sanchez-Ortiga, M. Martinez-Corral, and B. Javidi, “Stable and simple quantitative phase-contrast imaging by Fresnel biprism,” Appl. Phys. Lett. 112, 113701 (2018).
[Crossref]

G. Scrofani, J. Sola-Pikabea, A. Llavador, E. Sanchez-Ortiga, J. C. Barreiro, G. Saavedra, J. Garcia-Sucerquia, and M. Martinez-Corral, “FIMic: design for ultimate 3D-integral microscopy of in-vivo biological samples,” Biomed. Opt. Express 9, 335–346 (2018).
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2017 (20)

K. Kwon, M. Erdenebat, Y. Lim, K. Joo, M. Park, H. Park, J. Jeong, H. Kim, and N. Kim, “Enhancement of the depth-of-field of integral imaging microscope by using switchable bifocal liquid-crystalline polymer micro lens array,” Opt. Express 25, 30503–30512 (2017).
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J.-Y. Son, H. Lee, B.-R. Lee, and K.-H. Lee, “Holographic and light-field imaging as future 3-D displays,” Proc. IEEE 105, 789–804 (2017).
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J. Arai, E. Nakasu, T. Yamashita, H. Hiura, M. Miura, T. Nakamura, and R. Funatsu, “Progress overview of capturing method for integral 3-D imaging displays,” Proc. IEEE 105, 837–849 (2017).
[Crossref]

B. Javidi, X. Shen, A. S. Markman, P. Latorre-Carmona, A. Martinez-Uso, J. M. Sotoca, F. Pla, M. Martinez-Corral, and G. Saavedra, “Multidimensional optical sensing and imaging system (MOSIS): from macroscales to microscales,” Proc. IEEE 105, 850–875 (2017).
[Crossref]

M. Yamaguchi, “Full-parallax holographic light-field 3-D displays and interactive 3-D touch,” Proc. IEEE 105, 947–959 (2017).
[Crossref]

D. Nam, J.-H. Lee, Y.-H. Cho, Y.-J. Jeong, H. Hwang, and D.-S. Park, “Flat panel light-field 3-D display: concept, design, rendering, and calibration,” Proc. IEEE 105, 876–891 (2017).
[Crossref]

B. Javidi and A. M. Tekalp, “Emerging 3-D imaging and display technologies,” Proc. IEEE 105, 786–788 (2017).
[Crossref]

H. Hiura, K. Komine, J. Arai, and T. Mishina, “Measurement of static convergence and accommodation responses to images of integral photography and binocular stereoscopy,” Opt. Express 25, 3454–3468 (2017).
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L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
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A. Klein, T. Yaron, E. Preter, H. Duadi, and M. Fridman, “Temporal depth imaging,” Optica 4, 502–506 (2017).
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T. Nöbauer, O. Skocek, A. J. Pernía-Andrade, L. Weilguny, F. Martínez Traub, M. I. Molodtsov, and A. Vaziri, “Video rate volumetric Ca2+ imaging across cortex using seeded iterative demixing (SID) microscopy,” Nat. Methods 14, 811–818 (2017).
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Y. Lv, H. Ma, Q. Sun, P. Ma, Y. Ning, and X. Xu, “Wavefront sensing based on partially occluded and extended scene target,” IEEE Photon. J. 9, 7801508 (2017).

S. Komatsu, A. Markman, A. Mahalanobis, K. Chen, and B. Javidi, “Three-dimensional integral imaging and object detection using long-wave infrared imaging,” Appl. Opt. 56, D120–D126 (2017).
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P. A. Coelho, J. E. Tapia, F. Pérez, S. N. Torres, and C. Saavedra, “Infrared light field imaging system free of fixed-pattern noise,” Sci. Rep. 7, 13040 (2017).
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N. Bedard, T. Shope, A. Hoberman, M. A. Haralam, N. Shaikh, J. Kovacevic, N. Balram, and I. Tosic, “Light field otoscope design for 3D in vivo imaging of the middle ear,” Biomed. Opt. Express 8, 260–272 (2017).
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J. Liu, D. Claus, T. Xu, T. Keßner, A. Herkommer, and W. Osten, “Light field endoscopy and its parametric description,” Opt. Lett. 42, 1804–1807 (2017).
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R. S. Decker, A. Shademan, J. D. Opfermann, S. Leonard, P. C. W. Kim, and A. Krieger, “Biocompatible near-infrared three-dimensional tracking system,” IEEE Trans. Biomed. Eng. 64, 549–556 (2017).

S. Nagelberg, L. D. Zarzar, N. Nicolas, K. Subramanian, J. A. Kalow, V. Sresht, D. Blankschtein, G. Barbastathis, M. Kreysing, T. M. Swager, and M. Kolle, “Reconfigurable and responsive droplet-based compound micro-lenses,” Nat. Commun. 8, 14673 (2017).
[Crossref]

J. F. Algorri, N. Bennis, V. Urruchi, P. Morawiak, J. M. Sanchez-Pena, and L. R. Jaroszewicz, “Tunable liquid crystal multifocal microlens array,” Sci. Rep. 7, 17318 (2017).
[Crossref]

M. Martinez-Corral, A. Dorado, J. C. Barreiro, G. Saavedra, and B. Javidi, “Recent advances in the capture and display of macroscopic and microscopic 3D scenes by integral imaging,” Proc. IEEE 105, 825–836 (2017).
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2016 (4)

2015 (8)

A. Hassanfiroozi, Y. Huang, B. Javidi, and H. Shieh, “Hexagonal liquid crystal lens array for 3D endoscopy,” Opt. Express 23, 971–981 (2015).
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A. Llavador, E. Sánchez-Ortiga, J. C. Barreiro, G. Saavedra, and M. Martínez-Corral, “Resolution enhancement in integral microscopy by physical interpolation,” Biomed. Opt. Express 6, 2854–2863 (2015).
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X. Lin, J. Wu, G. Zheng, and Q. Dai, “Camera array based light field microscopy,” Biomed. Opt. Express 6, 3179–3189 (2015).
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M. Martinez-Corral, P.-Y. Hsieh, A. Doblas, E. Sánchez-Ortiga, G. Saavedra, and Y.-P. Huang, “Fast axial-scanning widefield microscopy with constant magnification and resolution,” J. Disp. Technol. 11, 913–920 (2015).
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A. Schwarz, J. Wang, A. Shemer, Z. Zalevsky, and B. Javidi, “Lensless three-dimensional integral imaging using a variable and time multiplexed pinhole array,” Opt. Lett. 40, 1814–1817 (2015).
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J. P. Lüke, F. Rosa, J. G. Marichal-Hernández, J. C. Sanluís, C. Domínguez Conde, and J. M. Rodríguez-Ramos, “Depth from light fields analyzing 4D local structure,” J. Disp. Technol. 11, 900–907 (2015).
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P. Vilmi, S. Varjo, R. Sliz, J. Hannuksela, and T. Fabritius, “Disposable optics for microscopy diagnostics,” Sci. Rep. 5, 16957 (2015).
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T.-H. Jen, X. Shen, G. Yao, Y.-P. Huang, H.-P. Shieh, and B. Javidi, “Dynamic integral imaging display with electrically moving array lenslet technique using liquid crystal lens,” Opt. Express 23, 18415–18421 (2015).
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2014 (8)

M. Martinez-Corral, A. Dorado, H. Navarro, G. Saavedra, and B. Javidi, “3D display by smart pseudoscopic-to-orthoscopic conversion with tunable focus,” Appl. Opt. 53, E19–E26 (2014).
[Crossref]

C.-W. Chen, M. Cho, Y.-P. Huang, and B. Javidi, “Improved viewing zones for projection type integral imaging 3D display using adaptive liquid crystal prism array,” J. Disp. Technol. 10, 198–203 (2014).
[Crossref]

H. Navarro, M. Martínez-Corral, G. Saavedra, A. Pons, and B. Javidi, “Photoelastic analysis of partially occluded objects with an integral-imaging polariscope,” J. Disp. Technol. 10, 255–262 (2014).
[Crossref]

H. Hua and B. Javidi, “A 3D integral imaging optical see-through head-mounted display,” Opt. Express 22, 13484–13491 (2014).
[Crossref]

A. Markman, J. Wang, and B. Javidi, “Three-dimensional integral imaging displays using a quick-response encoded elemental image array,” Optica 1, 332–335 (2014).
[Crossref]

J. M. Jabbour, B. H. Malik, C. Olsovsky, R. Cuenca, S. Cheng, J. A. Jo, Y.-S. L. Cheng, J. M. Wright, and K. C. Maitland, “Optical axial scanning in confocal microscopy using an electrically tunable lens,” Biomed. Opt. Express 5, 645–652 (2014).
[Crossref]

A. Stern, Y. Yitzhaky, and B. Javidi, “Perceivable light fields: matching the requirements between the human visual system and autostereoscopic 3-D displays,” Proc. IEEE 102, 1571–1587 (2014).
[Crossref]

S. Park, J. Yeom, Y. Jeong, N. Chen, J.-Y. Hong, and B. Lee, “Recent issues on integral imaging and its applications,” J. Inf. Disp. 15, 37–46 (2014).
[Crossref]

2013 (4)

2012 (5)

A. G. York, S. H. Parekh, D. D. Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9, 749–754 (2012).
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E. Sánchez-Ortiga, C. J. R. Sheppard, G. Saavedra, M. Martínez-Corral, A. Doblas, and A. Calatayud, “Subtractive imaging in confocal scanning microscopy using a CCD camera as a detector,” Opt. Lett. 37, 1280–1282 (2012).
[Crossref]

K. Wakunami, M. Yamaguchi, and B. Javidi, “High resolution 3-D holographic display using dense ray sampling from integral imaging,” Opt. Lett. 37, 5103–5105 (2012).
[Crossref]

Y. Kim, J. Kim, K. Hong, H.-K. Yang, J.-H. Jung, H. Choi, S.-W. Min, J.-M. Seo, J.-M. Hwang, and B. Lee, “Accommodative response of integral imaging in near distance,” J. Disp. Technol. 8, 70–78 (2012).
[Crossref]

D. J. Brady, M. E. Gehm, R. A. Stack, D. L. Marks, D. S. Kittle, D. R. Golish, E. M. Vera, and S. D. Feller, “Multiscale gigapixel photography,” Nature 486, 386–389 (2012).
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2011 (5)

K. Muller, P. Merkle, and T. Wiegand, “3-D video representation using depth maps,” Proc. IEEE 99, 643–656 (2011).
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P. A. Santi, “Light sheet fluorescence microscopy: a review,” J. Histochem. Cytochem. 59, 129–138 (2011).
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M. Tanimoto, M. Tehrani, T. Fujii, and T. Yendo, “Free-viewpoint TV,” IEEE Signal Process. Mag. 28(1), 67–76 (2011).
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J. Hong, Y. Kim, H.-J. Choi, J. Hahn, J.-H. Park, H. Kim, S.-W. Min, N. Chen, and B. Lee, “Three-dimensional display technologies of recent interest: principles, status, and issues,” Appl. Opt. 50, H87–H115 (2011).
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B. F. Grewe, F. F. Voigt, M. van’t Hoff, and F. Helmchen, “Fast two-layer two-photon imaging of neural cell populations using an electrically tunable lens,” Biomed. Opt. Express 2, 2035–2046 (2011).
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2010 (2)

X. Xiao, M. Daneshpanah, M. Cho, and B. Javidi, “3D integral imaging using sparse sensors with unknown positions,” J. Disp. Technol. 6, 614–619 (2010).
[Crossref]

H. Navarro, R. Martínez-Cuenca, A. Molina-Martín, M. Martínez-Corral, G. Saavedra, and B. Javidi, “Method to remedy image degradations due to facet braiding in 3D integral imaging monitors,” J. Disp. Technol. 6, 404–411 (2010).
[Crossref]

2009 (2)

M. Martinez-Corral and G. Saavedra, “The resolution challenge in 3D optical microscopy,” Prog. Opt. 53, 1–67 (2009).
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M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235, 144–162 (2009).
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2008 (1)

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
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2007 (1)

I. Moon and B. Javidi, “Three-dimensional identification of stem cells by computational holographic imaging,” J. R. Soc. Interface 4, 305–313 (2007).
[Crossref]

2006 (2)

B. Javidi, I. Moon, and S. Yeom, “Three-dimensional identification of biological microorganism using integral imaging,” Opt. Express 14, 12096–12108 (2006).
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M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
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2005 (2)

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
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R. Ng, “Fourier slice photography,” ACM Trans. Graph. 24, 735–744 (2005).
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2004 (6)

2003 (2)

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier, and integral photography plates,” Opt. Eng. 42, 3326–3333 (2003).
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J. S. Jang and B. Javidi, “Large depth-of-focus time-multiplexed three-dimensional integral imaging by use of lenslets with non-uniform focal lengths and aperture sizes,” Opt. Lett. 28, 1924–1926 (2003).
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2002 (3)

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2000 (1)

M. G. L. Gustafsson, “Surpassing the lateral resolution by a factor of two using structured illumination microscopy,” J. Microsc. 198, 82–87 (2000).
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1991 (1)

E. H. Adelson and J. R. Bergen, “The plenoptic function and the elements of early vision,” Comput. Models Visual Process. 1, 3–20 (1991).

1988 (1)

1987 (1)

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M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25, 924–934 (2006).
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B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
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Adelson, E. H.

E. H. Adelson and J. Y. A. Wang, “Single lens stereo with plenoptic camera,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 99–106 (1992).
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E. H. Adelson and J. R. Bergen, “The plenoptic function and the elements of early vision,” Comput. Models Visual Process. 1, 3–20 (1991).

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J. F. Algorri, N. Bennis, V. Urruchi, P. Morawiak, J. M. Sanchez-Pena, and L. R. Jaroszewicz, “Tunable liquid crystal multifocal microlens array,” Sci. Rep. 7, 17318 (2017).
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Andalman, A.

Antipa, N.

Antunez, E.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
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Arai, J.

Arimoto, H.

Bahn, J.-E.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier, and integral photography plates,” Opt. Eng. 42, 3326–3333 (2003).
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Bai, L.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
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Baik, I. S.

H. Kang, S. D. Roh, I. S. Baik, H. J. Jung, W. N. Jeong, J. K. Shin, and I. J. Chung, “A novel polarizer glasses-type 3D displays with a patterned retarder,” in SID International Symposium Digest of Technical Papers (2010), Vol. 41, pp. 1–4.

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R. C. Bolles, H. H. Baker, and D. H. Marimont, “Epipolar-plane image analysis: an approach to determining structure from motion,” Int. J. Comput. Vis. 1, 7–55 (1987).
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Barreiro, J. C.

Barth, A.

B. Wilburn, N. Joshi, V. Vaish, E.-V. Talvala, E. Antunez, A. Barth, A. Adams, M. Horowitz, and M. Levoy, “High performance imaging using large camera arrays,” ACM Trans. Graph. 24, 765–776 (2005).
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Bedard, N.

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J. F. Algorri, N. Bennis, V. Urruchi, P. Morawiak, J. M. Sanchez-Pena, and L. R. Jaroszewicz, “Tunable liquid crystal multifocal microlens array,” Sci. Rep. 7, 17318 (2017).
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E. H. Adelson and J. R. Bergen, “The plenoptic function and the elements of early vision,” Comput. Models Visual Process. 1, 3–20 (1991).

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S. S. Kim, B. H. You, H. Choi, B. H. Berkeley, D. G. Kim, and N. D. Kim, “World’s first 240  Hz TFT-LCD technology for full-HD LCD-TV and its application to 3D display,” in SID International Symposium Digest of Technical Papers (2009), Vol. 40, pp. 424–427.

Blanche, P. A.

S. Tay, P. A. Blanche, R. Voorakaranam, A. V. Tunç, W. Lin, S. Rokutanda, T. Gu, D. Flores, P. Wang, G. Li, P. St Hilaire, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “An updatable holographic three-dimensional display,” Nature 451, 694–698 (2008).
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Blankschtein, D.

S. Nagelberg, L. D. Zarzar, N. Nicolas, K. Subramanian, J. A. Kalow, V. Sresht, D. Blankschtein, G. Barbastathis, M. Kreysing, T. M. Swager, and M. Kolle, “Reconfigurable and responsive droplet-based compound micro-lenses,” Nat. Commun. 8, 14673 (2017).
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R. C. Bolles, H. H. Baker, and D. H. Marimont, “Epipolar-plane image analysis: an approach to determining structure from motion,” Int. J. Comput. Vis. 1, 7–55 (1987).
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H. Chen, V. Sick, M. Woodward, and D. Burke, “Human iris 3D imaging using a micro-plenoptic camera,” in Optics in the Life Sciences Congress, OSA Technical Digest (2017), paper BoW3A.6.

Calatayud, A.

Chai, Y.

L. Cong, Z. Wang, Y. Chai, W. Hang, C. Shang, W. Yang, L. Bai, J. Du, K. Wang, and Q. Wen, “Rapid whole brain imaging of neural activity in freely behaving larval zebrafish (Danio rerio),” eLife 6, e28158 (2017).
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Chen, C.-W.

C.-W. Chen, M. Cho, Y.-P. Huang, and B. Javidi, “Improved viewing zones for projection type integral imaging 3D display using adaptive liquid crystal prism array,” J. Disp. Technol. 10, 198–203 (2014).
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Chen, H.

H. Chen, V. Sick, M. Woodward, and D. Burke, “Human iris 3D imaging using a micro-plenoptic camera,” in Optics in the Life Sciences Congress, OSA Technical Digest (2017), paper BoW3A.6.

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A. G. York, S. H. Parekh, D. D. Nogare, R. S. Fischer, K. Temprine, M. Mione, A. B. Chitnis, A. Combs, and H. Shroff, “Resolution doubling in live, multicellular organisms via multifocal structured illumination microscopy,” Nat. Methods 9, 749–754 (2012).
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C.-W. Chen, M. Cho, Y.-P. Huang, and B. Javidi, “Improved viewing zones for projection type integral imaging 3D display using adaptive liquid crystal prism array,” J. Disp. Technol. 10, 198–203 (2014).
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X. Xiao, M. Daneshpanah, M. Cho, and B. Javidi, “3D integral imaging using sparse sensors with unknown positions,” J. Disp. Technol. 6, 614–619 (2010).
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Cho, Y.-H.

D. Nam, J.-H. Lee, Y.-H. Cho, Y.-J. Jeong, H. Hwang, and D.-S. Park, “Flat panel light-field 3-D display: concept, design, rendering, and calibration,” Proc. IEEE 105, 876–891 (2017).
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Choi, H.

Y. Kim, J. Kim, K. Hong, H.-K. Yang, J.-H. Jung, H. Choi, S.-W. Min, J.-M. Seo, J.-M. Hwang, and B. Lee, “Accommodative response of integral imaging in near distance,” J. Disp. Technol. 8, 70–78 (2012).
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J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier, and integral photography plates,” Opt. Eng. 42, 3326–3333 (2003).
[Crossref]

S. S. Kim, B. H. You, H. Choi, B. H. Berkeley, D. G. Kim, and N. D. Kim, “World’s first 240  Hz TFT-LCD technology for full-HD LCD-TV and its application to 3D display,” in SID International Symposium Digest of Technical Papers (2009), Vol. 40, pp. 424–427.

Choi, H.-J.

Choi, Y.-J.

J.-Y. Son, V. V. Saveljev, Y.-J. Choi, J.-E. Bahn, S.-K. Kim, and H. Choi, “Parameters for designing autostereoscopic imaging systems based on lenticular, parallax barrier, and integral photography plates,” Opt. Eng. 42, 3326–3333 (2003).
[Crossref]

Chung, I. J.

H. Kang, S. D. Roh, I. S. Baik, H. J. Jung, W. N. Jeong, J. K. Shin, and I. J. Chung, “A novel polarizer glasses-type 3D displays with a patterned retarder,” in SID International Symposium Digest of Technical Papers (2010), Vol. 41, pp. 1–4.

Claus, D.

Coelho, P. A.

P. A. Coelho, J. E. Tapia, F. Pérez, S. N. Torres, and C. Saavedra, “Infrared light field imaging system free of fixed-pattern noise,” Sci. Rep. 7, 13040 (2017).
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Strictly speaking, telecentricity means that both the entrance and the exit pupils are at infinity. To obtain this condition, the system must be necessarily afocal. However, the use of the word “telecentric” is often extended to systems that are simply afocal.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999), Chap. 4.

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In general, an epipolar image is a 2D slice of plenoptic function with a zero angular value in the direction normal to this slice. However, we use a more restricted definition so that an epipolar image is a 2D slice of plenoptic function in which y′=0 is fixed and ϕ=0.

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The radiance is a radiometric magnitude defined as the radiant flux per unit of area and unit of solid angle, emitted by (or received by, or passing through) a differential surface in a given direction. Irradiance is the integration of the radiance over all the angles.

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Supplementary Material (14)

NameDescription
» Visualization 1       Multi-perspective movie with the elemental images as frames.
» Visualization 2       Display on a flat 2D monitor of different elemental images following the mouse movements.
» Visualization 3       Example of application of the refocusing algorithm, using the elemental images as the input.
» Visualization 4       Multi-perspective movie with the calculated elemental images as frames.
» Visualization 5       Example of application of the refocusing algorithm, using the calculated elemental images as the input.
» Visualization 6       3D monitor displaying the microimages captured with the plenoptic camera.
» Visualization 7       3D monitor displaying the microimages calculated from the directly-captured elemental images.
» Visualization 8       3D monitor displaying the microimages calculated from the directly-captured, but cropped, elemental images.
» Visualization 9       Multi-perspective movie of microscopic sample, with the calculated elemental images as frames.
» Visualization 10       Example of application of the refocusing algorithm, using the calculated elemental images as the input.
» Visualization 11       Multi-perspective movie of microscopic sample, with the calculated elemental images as frames.
» Visualization 12       Multi-perspective movie of microscopic sample, with the calculated elemental images as frames.
» Visualization 13       Example of application of the refocusing algorithm, using the calculated elemental images as the input.
» Visualization 14       Example of application of the refocusing algorithm, using the calculated elemental images as the input.

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Figures (41)

Figure 1
Figure 1 Scheme of a telecentric system composed of two converging lenses.
Figure 2
Figure 2 Most popular optical instruments based on telecentricity. (a) Keplerian telescope, and (b) optical microscope.
Figure 3
Figure 3 Scheme of the fast axial-scanning optical microscope.
Figure 4
Figure 4 (a) Aperture stop in a telecentric system, (b) the limit of the field of uniform illumination, (c) the vignetting region, and (d) the field of limit illumination.
Figure 5
Figure 5 Example of field limitation. The image is composed of a central circular region of uniform illumination plus an annular field in which the illumination decreases (vignetting region).
Figure 6
Figure 6 Depth of focus (dof) is the axial range by which the sensor can be displaced and still record a sharp image of an object point. Sharp means that only one pixel is impressed. In good approximation, the depth of field (DoF) is the conjugate of the dof.
Figure 7
Figure 7 Two pictures of the same scene: (a) small DoF and (b) large DoF.
Figure 8
Figure 8 In the simplest configuration, a telecentric optical system is composed of two convex lenses, coupled in afocal manner, plus an aperture stop that is usually a circular aperture.
Figure 9
Figure 9 Two Airy disks, corresponding to the images of two point sources that are placed close to each other. According to Rayleigh criterion of resolution, we illustrate three cases: (a) the images are not resolved, (b) the images are barely resolved, and (c) the images are well resolved.
Figure 10
Figure 10 Three pictures of the oil painting “Gala looking at the Mediterranean Sea,” painted by Salvador Dali. A different effect is obtained when the picture is imaged with: (a) a lens with a low value of the f-number, (b) a lens with a medium value of the f-number; and (c) a lens with a high value of the f-number.
Figure 11
Figure 11 Scheme of a conventional photographic camera. Every pixel collects a cone of rays with the same spatial coordinate but with variable angular content.
Figure 12
Figure 12 (a) Plenoptic field incident onto the image sensor and (b) the captured image.
Figure 13
Figure 13 (a) Integral photography system as proposed by Lippmann and (b) corresponding sampled plenoptic map.
Figure 14
Figure 14 (a) Subset of 7×7 EIs (300×300 pixels each) of the 3D scenes. A movie obtained after composing the EIs of the central row of the integral image is shown in Visualization 1; (b) central EI; and (c) grid of 300×300 microimages (11×11 pixels each) of the 3D scene. The zoomed area is scaled by a factor of 5.
Figure 15
Figure 15 (a) Illustration of the backpropagation algorithm. Any pixel produces a backpropagated ray passing through the center of the corresponding lens. Clearly, backpropagated rays change their spatial coordinates but keep constant their angular coordinates. (b) Sketch of plenoptic map captured by the lens array. (c) Backpropagated (zR>0) plenoptic map obtained by shearing the original plenoptic map. The shearing preserves the angular coordinate. (d) Illustration of the Abel transform necessary for the calculation of the irradiance distribution of the image at the backpropagated distance.
Figure 16
Figure 16 Three images obtained after applying the refocusing algorithm for three different values of zR.
Figure 17
Figure 17 On the left we show a collection of, for example, 3×3 elemental images. Any elemental image is designed by its index (i,j). On the right of this figure, we show the scheme of functioning of the refocusing algorithm for nS=0,1,2,3.
Figure 18
Figure 18 Scheme of the back-projection algorithm. The number of calculated pixels in the refocused images is selected at will.
Figure 19
Figure 19 Sketch of the Fourier slice algorithm.
Figure 20
Figure 20 Illustration of the DoF of refocusing process (DoFRefoc). We are considering in this example the refocusing of a single point source when NH=7. In this case only one pixel per EI is impressed. When the refocused image is calculated at the object plane, all the EIs match and the image is a rectangle with width Δp and height NH. On the right side, we show the refocused image corresponding to ΔnS=2/(NH+1)=1/4. In this case, the refocused image has a pyramid structure with height (NH+1)/2.
Figure 21
Figure 21 Single scheme of a plenoptic camera.
Figure 22
Figure 22 (a) Sampled plenoptic map captured with the plenoptic camera of the previous figure and (b) the plenoptic map at the lens plane. The two maps are related through a rotation by π/2 and a horizontal shearing.
Figure 23
Figure 23 (a) Plenoptic picture capture with the plenoptic camera prototype (zoomed area is scaled by a factor of 4), (b) calculated EIs, (c) central EI, and (d) refocused image at the second jug.
Figure 24
Figure 24 Scheme of integral photography (IP) concept. (a) Image capture stage and (b) 3D display stage, which produces floating 3D images in front of the 2D monitor.
Figure 25
Figure 25 Overview of our experimental integral-imaging 3D display system. We moved the recording device vertically and horizontally to record different perspectives provided by the integral monitor.
Figure 26
Figure 26 (a) 7×7 central EIs already shown in Fig. 16 but resized to 113×113 pixels; (b) the corresponding 113×113 microimages but resized to 15×15 pixels each.
Figure 27
Figure 27 (a) Scheme of a telecentric optical microscope and (b) the integral microscope is obtained by inserting a MLA at the image plane.
Figure 28
Figure 28 (a) Microimages captured directly with the IMic (zoomed area is magnified by a factor of 3), (b) calculated views, (c) the central view (full movie is shown in Visualization 9), and (d) refocused image (full movie is shown in Visualization 10).
Figure 29
Figure 29 Schematic layout of Fourier integral microscopy (FIMic). A collection of EIs is obtained directly. The telecentric relay system is composed of two converging lenses (RL1 and RL2) coupled in an afocal manner.
Figure 30
Figure 30 Seven central elemental images obtained with the bright-field (left) and with the fluorescence (right) setup.
Figure 31
Figure 31 Examples of refocused irradiance distribution. In Visualization 13 and Visualization 14, we show movies corresponding to refocusing tracks ranging up to 0.4 mm.
Figure 32
Figure 32 Scheme for illustration of the spatial-angular coordinates of a ray. For the distances we consider positive the directions that are from left to right and from bottom to top. The angles are measured from the ray to the optical axis and are positive if they follow the counterclockwise direction. Following such criteria, the angles σ1 and σ2 shown in this figure are negative.
Figure 33
Figure 33 Scheme for deduction of the ABCD matrices that describe refraction in (a) the plane diopter and (b) the spherical diopter.
Figure 34
Figure 34 Scheme of refraction through a thick lens.
Figure 35
Figure 35 Image formation through a thin lens.
Figure 36
Figure 36 ABCD matrix between the focal planes.
Figure 37
Figure 37 ABCD matrix between the principal planes of a thick lens. Points N and N are known as the nodal points.
Figure 38
Figure 38 Two examples for the calculation of cardinal parameters of a thick lens. (a) Biconvex lens with r1=13  mm, r2=10  mm, e=10  mm, and n=1.52; (b) plano–convex lens with r1=13  mm, r2=, e=10  mm, and n=1.52.
Figure 39
Figure 39 Scheme for the calculation of the correspondence equations when the axial distances are measured from the focal planes.
Figure 40
Figure 40 Illustration of the wave nature of the light scheme of the experimental setup for the implementation of the Young experiment. The monochromatic wave emitted by a laser is expanded and impinges a diffracting screen composed of two pinholes.
Figure 41
Figure 41 (a) Scheme for the definition of the amplitude transmittance of a thin lens and (b) scheme for the propagation of light waves from the FFP to the BFP of a lens.

Tables (1)

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Table 1. List of Acronyms Used in the Paper

Equations (108)

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MF1F2=MF2F2MF1F1=(0f2P20)(0f1P10)=(P1f200P2f1)=(ABCD),
MOO=TF2OMF1F2TOF1=(P1f2z0P2f1z0P1f20P2f1).
z0=M2z0andM=f2f1.
α=Δz0Δz0=M2.
MOFTL=MFTLFTLMLLMFobFobT0Fob=(fTLPobfobz0fLLPob0PTLfob).
z0=fob2PLL,
f#=f1ϕASandNA=sinσ.
f#=f2ϕAS=|M|f#andNA=sinσ=NA|M|.
f#=12NAandf#=12NA.
ρgeo=2Δp|M|,
dof=2f2ϕASΔp=2f#Δp.
DoFgeo=dofM2=2f#Δp|M|=Δp|M|NA.
u1+(x,y)=1λ0f1t˜(xλ0f1,yλ0f1)p(x,y),
u2(x,y)=1λ0f2u˜1+(xλ0f2,yλ0f2)=1λ02f1f2[(λ0f1)2t(λ0f1xλ0f2,λ0f1yλ0f2)p˜(xλ0f2,yλ0f2)]=1|M|t(xM,yM)p˜(xλ0f2,yλ0f2),
PSF(r)=(ϕ2)2Disk(r2λ0f2/ϕ),
ρdif=1.22·λ0·f2ϕ.
ρdif=ρdif|M|=1.22·λ0·f1ϕ=1.22·λ0·f#=0.61·λ0NA,
u0(x,y)=t(x,y)eik0z0λ0z0exp{ik02z0(x2+y2)}.
u2(x,y)=1Mt(xM,yM)[p˜(xλ0f2,yλ0f2)exp{ik02M2z0(x2+y2)}],
DoFdif=λ0NA2=4f#2λ0.
ρ=max{ρgeo,ρdif}=max{2Δp|M|,1.22·λ0·f#},
DoF=DoFgeo+DoFdif=2f#(Δp|M|+2f#λ0)=2f#M2(Δp+2f#λ0).
I(x)=σL(x,σ)dσ.
(xzθz)=(1zR01)(xθ),
I(x;zR)=θL(x+zRθ,θ)dθ,
zR=gNnS,
OnS(p,q)=i,j=(NH1)/2+(NH1)/2Ii,j(pinS,qjnS).
L˜(ux,uθ)=R2L(x,θ)exp{i2π(xux+θuθ)}dxdθ.
(uθux)=(1tanαtanα1)(uθux),
L˜(ux,0)=R2L(x,θ)exp{i2π(xux+θtanαux)}dxdθ.
I(xα)=RL˜(ux,0)exp{i2π(xαux)}dux=R(R2L(x,θ)exp{i2π(xux+θtanαux)}dxdθ)exp{i2π(xαux)}dux=R2L(x,θ)dxdθRexp{i2πux(x+θtanαxα)}dux.
exp{i2πu(xx0)}du=δ(xx0),
f(x)δ(xx0)dx=f(xx0).
I(xα)=R2L(x,θ)δ(x+θtanαxα)dxdθ=RL(xα+θtanα,θ)dθ,
DoFEI=DoFgeo+DoFdif=2f#M2(Δp+2λ0f#),
ρEI=max{ρgeo,ρdif}=max{2Δp|M|,1.22λ0f#|M|}.
ρRefoc[Δp|M|,2Δp|M|].
ΔnS=gNΔzRzR2.
DoFRefoc=ΔzR=2zR2NNH2g,
ρRefoc[1.4  mm,2.8  mm]
DoFRProc=DoFEI=2.9  m;andDoFRefoc=2.2  mm.
(xθ)=(zf01ffz)(xθ),
(xLθL)=(1f+z1fzf)(xθ).
ρgeo=2p|M|.
ρdif=1.22·λ0·f#|M|.
DoFcEI=DoFgeo+DoFdif=4λ0f#2M2(μ22+1),
μ=pρdif.
Mhst=fTLfob,
ρhst=max{2ΔpMhst,0.61·λ0NA},
DoFhst=1NA(ΔpMhst+λ0NA).
(xFθF)=(0fTL1fTL0)(xθ).
ρView=max{2pMhst,ρhst}.
ρView=2μρhst.
DoFView=pMNA+λ0NA2=λ0NA2(μ22+1).
DoFRefoc=λ0NA2(μ2+1).
ϕFS=pf2fL.
N=f2f1ϕASp,
NAEI=NAN,
ρEIW=0.61λ0NAEI.
ρEINyq=2ΔpfMOf1f2fL.
ρEI=max{N0.61λ0NA,2Δpf2fMOfLf1}.
ρEI=0.61λ0NAN.
DOFEI=λ0N2NA2+ΔpNNAf2fMOfLf1.
DOFEI=54λ0NA2N2.
ρEI=N2μρViewandDOFEI=5N24+2μ2DOFView.
zR=nSΔpf22fob2pf12fL.
σ2=σ1andy2=y1tσ1.
(y2σ2)=(1t01)(y1σ1),
T=(ABCD)=(1t01).
C=n2n1n2r=1fD.
S=(10n2n1n2rn1n2)=(101fDn1n2).
P=(100n1n2).
L=S2·T·S1=(1efD1ennfD1+1fD2efD1fD21enfD2).
1f=nfD1+1fD2efD1fD2=(n1)(1r11r2+en1nr1r2).
Lthin=(101f1),
1f=1fD1+1fD2.
MOO=TLO·Lthin·TOL=(1afaa(1+af)1f1+af).
1a+1a=1f,
MOO=(M=aa01fγ=aa).
MFF=TLF·Lthin·TFL=(1f01)(10P1)(1f01)=(0fP0).
y2=fσ1andσ2=Py1.
MHH=TS2H·L·THS1=(1efD1xHfxH(1efD1)enxH(1+xHfenfD2)1f1+xHfenfD2).
xH=effD1andxH=enffD2,
MHH=(101f1).
MOO=MFO·MFF·MOF=(z/ffzz/f1fz/f).
zz=f2.
M=zf=fz.
f(z,t)=A·cos[2π(zλ0tT)]=A·cos(k0zωt)=A2[ei(k0zωt)+cc],
f(z)=Aeik0z.
f(x,y,z)=Aeik0(xcosα+ycosβ+zcosγ),
f(r)=Aeik0rr=Aeik0x2+y2+z2x2+y2+z2.
f(x,y,z)=Aeik0zz·eik02z(x2+y2).
u(x,y,z)=A(eik0zzeik02z[(xa)2+y2]+eik0zzeik02z[(x+a)2+y2]).
IT(x,y,z)=|u(x,y,z)|2=A2z2cos2(πxλ0z/2a),
u(x,y,z)=+t(x0,y0)eikzzeik2z[(xx0)2+(yy0)2]dx0dy0=t(x,y)h(x,y;z).
g(x,y)=f(x,y)h(x,y)=R2f(x0,y0)h(xx0,yy0)dx0dy0.
h(x,y;z)=eik0zλ0z{ik2z(x2+y2)}.
tL(x,y)=u+(x,y)u(x,y)=exp{ik02f(x2+y2)}.
uL(x,y)=t(x,y)eik0fλ0fexp{ik02f(x2+y2)}=eik0fλ0fexp{ik02f(x2+y2)}×R2t(x0,y0)exp{ik02f(x02+y02)}exp{i2π(xλ0fx0+yλ0fy0)}dx0dy0.
uL(x,y)=eik0fiλ02f2exp{ik02f(x2+y2)}[t˜(xλ0f,yλ0f)exp{ik02f(x2+y2)}],
R2m(x,y)n(x,y)exp{i2π(xu+yv)}dxdy=m˜(u,v)n˜(u,v).
f(xa,ya)h(xa,ya)=a2g(xa,ya).
F{exp[ik02f(x2+y2)]}=iλ0fexp[iπλ0f(u2+v2)],
uL+(x,y)=uL(x,y)tL(x,y)=eik0fiλ02f2[t˜(xλ0f,yλ0f)exp{ik02f(x2+y2)}].
u1(x,y)=uL+(x,y)eik0fλ0fexp{ik02f(x2+y2)}=ei2k0fiλ03f3t˜(xλ0f,yλ0f)exp{ik02f(x2+y2)}exp{ik02f(x2+y2)}=ei2k0fiλ0ft˜(xλ0f,yλ0f).
exp{ik02f(x2+y2)}exp{ik02f(x2+y2)}=λ02f2δ(x,y),
f(x,y)δ(xx0,yy0)=f(xx0,yy0).
δ(xx0,yy0)Fexp{i2π(xλ0fx0+yλ0fy0)}.

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