Abstract

We propose a microlens array (MLA) construction method based on sub-channel optimal design and splicing, and an integrated projection imaging analysis method by using ray tracing and image warping. Our stop mask greatly improves imaging quality and eliminates crosstalk. We realize various projection distances, required projection imaging dimensions, and design optimization of sub-lens structures, providing freedom and possibility for MLA structure design requirements. Optical system chief ray tracing and sub-image generation is combined by using radial basis function forward image warping. Imaging distortion and overlap misalignment from short focal projection, multi-aperture offset, and complicated surfaces are perfectly corrected. Sub-image warping pixel mapping facilitates real-time replacement of projected images. We conduct substantial MLA integration imaging designs and precision analysis of different sub-aperture sizes, MLA sizes, and projection distances.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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2018 (1)

2017 (1)

2014 (3)

Z. Zhuang, Y. Chen, F. Yu, and X. Sun, “Field curvature correction method for ultrashort throw ratio projection optics design using an odd polynomial mirror surface,” Appl. Opt. 53(22), E69–E76 (2014).
[Crossref] [PubMed]

J. F. Algorri, V. Urruchi, J. M. Sánchez-Pena, and J. M. Otón, “An Autostereoscopic Device for Mobile Applications Based on a Liquid Crystal Microlens Array and an OLED Display,” J. Disp. Technol. 10(9), 713–720 (2014).
[Crossref]

X. Liu and H. Li, “The progress of light field 3-D displays,” Inf. Disp. 30(6), 6–14 (2014).
[Crossref]

2013 (4)

2012 (2)

2011 (3)

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast 57(2), 362–371 (2011).
[Crossref]

B. Yang, K. Lu, W. Zhang, and F. Dai, “Design of a free-form lens system for short distance projection,” Proc. SPIE 8128, 81280E (2011).
[Crossref]

B. Fornberg, E. Larsson, and N. Flyer, “Stable computations with Gaussian radial basis functions,” SIAM J. Sci. Comput. 33(2), 869–892 (2011).
[Crossref]

2010 (1)

2009 (2)

D. Wu, Q. D. Chen, L. G. Niu, J. Jiao, H. Xia, J. F. Song, and H. B. Sun, “100% fill-factor aspheric microlenses arrays (AMLA) with sub-20 nm precision,” IEEE Photonics Technol. Lett. 21(20), 1535–1537 (2009).
[Crossref]

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref] [PubMed]

2008 (3)

R. Voelkel and K. J. Weible, “Laser beam homogenizing: limitations and constraints,” Proc. SPIE 7102, 71020J (2008).
[Crossref]

F. Muñoz, P. Benítez, and J. C. Miñano, “High-order aspherics: the SMS nonimaging design method applied to imaging optics,” Proc. SPIE 7100, 71000K (2008).

J. H. Park, G. Baasantseren, N. Kim, G. Park, J. M. Kang, and B. Lee, “View image generation in perspective and orthographic projection geometry based on integral imaging,” Opt. Express 16(12), 8800–8813 (2008).
[Crossref] [PubMed]

2007 (1)

2006 (2)

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25(3), 924–934 (2006).
[Crossref]

U. D. Zeitner and E. B. Kley, “Advanced lithography for microoptics,” Proc. SPIE 6290, 629009 (2006).
[Crossref]

2005 (1)

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

2004 (3)

2003 (2)

M. V. Kunnavakkam, F. M. Houlihan, M. Schlax, J. A. Liddle, P. Kolodner, O. Nalamasu, and J. A. Rogers, “Low-cost, low-loss microlens arrays fabricated by soft-lithography replication process,” Appl. Phys. Lett. 82(8), 1152–1154 (2003).
[Crossref]

J. S. Jang, F. Jin, and B. Javidi, “Three-dimensional integral imaging with large depth of focus by use of real and virtual image fields,” Opt. Lett. 28(16), 1421–1423 (2003).
[Crossref] [PubMed]

2002 (1)

H. Wu, T. W. Odom, and G. M. Whitesides, “Reduction photolithography using microlens arrays: applications in gray scale photolithography,” Anal. Chem. 74(14), 3267–3273 (2002).
[Crossref] [PubMed]

1995 (1)

D. Ruprecht and H. Muller, “Image warping with scattered data interpolation,” IEEE Comput. Graph. Appl. 15(2), 37–43 (1995).
[Crossref]

Adams, A.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25(3), 924–934 (2006).
[Crossref]

Algorri, J. F.

J. F. Algorri, V. Urruchi, J. M. Sánchez-Pena, and J. M. Otón, “An Autostereoscopic Device for Mobile Applications Based on a Liquid Crystal Microlens Array and an OLED Display,” J. Disp. Technol. 10(9), 713–720 (2014).
[Crossref]

Ares, M.

Baasantseren, G.

Bauer, A.

Benítez, P.

F. Muñoz, P. Benítez, and J. C. Miñano, “High-order aspherics: the SMS nonimaging design method applied to imaging optics,” Proc. SPIE 7100, 71000K (2008).

Bräuer, A.

Cakmakci, O.

Caum, J.

Chang, S.

Chao, C. K.

H. Yang, C. K. Chao, M. K. Wei, and C. P. Lin, “High fill-factor microlens array mold insert fabrication using a thermal reflow process,” J. Micromech. Microeng. 14(8), 1197–1204 (2004).
[Crossref]

Chen, Q. D.

D. Wu, Q. D. Chen, L. G. Niu, J. Jiao, H. Xia, J. F. Song, and H. B. Sun, “100% fill-factor aspheric microlenses arrays (AMLA) with sub-20 nm precision,” IEEE Photonics Technol. Lett. 21(20), 1535–1537 (2009).
[Crossref]

Chen, Y.

Cheng, D.

Dai, F.

B. Yang, K. Lu, W. Zhang, and F. Dai, “Design of a free-form lens system for short distance projection,” Proc. SPIE 8128, 81280E (2011).
[Crossref]

Dannberg, P.

Deng, Q.

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

Dodgson, N. A.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast 57(2), 362–371 (2011).
[Crossref]

Dong, X.

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

Du, C.

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

Duparré, J.

Favalora, G. E.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast 57(2), 362–371 (2011).
[Crossref]

Feng, Z.

Fischer, S.

Flyer, N.

B. Fornberg, E. Larsson, and N. Flyer, “Stable computations with Gaussian radial basis functions,” SIAM J. Sci. Comput. 33(2), 869–892 (2011).
[Crossref]

Footer, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25(3), 924–934 (2006).
[Crossref]

Fornberg, B.

B. Fornberg, E. Larsson, and N. Flyer, “Stable computations with Gaussian radial basis functions,” SIAM J. Sci. Comput. 33(2), 869–892 (2011).
[Crossref]

Froese, B. D.

Gong, M.

Han, Y.

Holliman, N. S.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast 57(2), 362–371 (2011).
[Crossref]

Horowitz, M.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25(3), 924–934 (2006).
[Crossref]

Houlihan, F. M.

M. V. Kunnavakkam, F. M. Houlihan, M. Schlax, J. A. Liddle, P. Kolodner, O. Nalamasu, and J. A. Rogers, “Low-cost, low-loss microlens arrays fabricated by soft-lithography replication process,” Appl. Phys. Lett. 82(8), 1152–1154 (2003).
[Crossref]

Huang, L.

Jang, J. S.

Javidi, B.

Jiao, J.

D. Wu, Q. D. Chen, L. G. Niu, J. Jiao, H. Xia, J. F. Song, and H. B. Sun, “100% fill-factor aspheric microlenses arrays (AMLA) with sub-20 nm precision,” IEEE Photonics Technol. Lett. 21(20), 1535–1537 (2009).
[Crossref]

Jin, F.

Jin, G.

Kang, J. M.

Kim, N.

Kley, E. B.

U. D. Zeitner and E. B. Kley, “Advanced lithography for microoptics,” Proc. SPIE 6290, 629009 (2006).
[Crossref]

Kolodner, P.

M. V. Kunnavakkam, F. M. Houlihan, M. Schlax, J. A. Liddle, P. Kolodner, O. Nalamasu, and J. A. Rogers, “Low-cost, low-loss microlens arrays fabricated by soft-lithography replication process,” Appl. Phys. Lett. 82(8), 1152–1154 (2003).
[Crossref]

Kunnavakkam, M. V.

M. V. Kunnavakkam, F. M. Houlihan, M. Schlax, J. A. Liddle, P. Kolodner, O. Nalamasu, and J. A. Rogers, “Low-cost, low-loss microlens arrays fabricated by soft-lithography replication process,” Appl. Phys. Lett. 82(8), 1152–1154 (2003).
[Crossref]

Larsson, E.

B. Fornberg, E. Larsson, and N. Flyer, “Stable computations with Gaussian radial basis functions,” SIAM J. Sci. Comput. 33(2), 869–892 (2011).
[Crossref]

Lee, B.

Levoy, M.

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref] [PubMed]

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25(3), 924–934 (2006).
[Crossref]

Li, H.

Liang, R.

Liddle, J. A.

M. V. Kunnavakkam, F. M. Houlihan, M. Schlax, J. A. Liddle, P. Kolodner, O. Nalamasu, and J. A. Rogers, “Low-cost, low-loss microlens arrays fabricated by soft-lithography replication process,” Appl. Phys. Lett. 82(8), 1152–1154 (2003).
[Crossref]

Lin, C. P.

H. Yang, C. K. Chao, M. K. Wei, and C. P. Lin, “High fill-factor microlens array mold insert fabrication using a thermal reflow process,” J. Micromech. Microeng. 14(8), 1197–1204 (2004).
[Crossref]

Liu, P.

Liu, X.

Liu, Y.

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

Lu, K.

B. Yang, K. Lu, W. Zhang, and F. Dai, “Design of a free-form lens system for short distance projection,” Proc. SPIE 8128, 81280E (2011).
[Crossref]

Luo, Y.

McDowall, I.

M. Levoy, Z. Zhang, and I. McDowall, “Recording and controlling the 4D light field in a microscope using microlens arrays,” J. Microsc. 235(2), 144–162 (2009).
[Crossref] [PubMed]

Miñano, J. C.

F. Muñoz, P. Benítez, and J. C. Miñano, “High-order aspherics: the SMS nonimaging design method applied to imaging optics,” Proc. SPIE 7100, 71000K (2008).

Muller, H.

D. Ruprecht and H. Muller, “Image warping with scattered data interpolation,” IEEE Comput. Graph. Appl. 15(2), 37–43 (1995).
[Crossref]

Muñoz, F.

F. Muñoz, P. Benítez, and J. C. Miñano, “High-order aspherics: the SMS nonimaging design method applied to imaging optics,” Proc. SPIE 7100, 71000K (2008).

Nalamasu, O.

M. V. Kunnavakkam, F. M. Houlihan, M. Schlax, J. A. Liddle, P. Kolodner, O. Nalamasu, and J. A. Rogers, “Low-cost, low-loss microlens arrays fabricated by soft-lithography replication process,” Appl. Phys. Lett. 82(8), 1152–1154 (2003).
[Crossref]

Ng, R.

M. Levoy, R. Ng, A. Adams, M. Footer, and M. Horowitz, “Light field microscopy,” ACM Trans. Graph. 25(3), 924–934 (2006).
[Crossref]

Niu, L. G.

D. Wu, Q. D. Chen, L. G. Niu, J. Jiao, H. Xia, J. F. Song, and H. B. Sun, “100% fill-factor aspheric microlenses arrays (AMLA) with sub-20 nm precision,” IEEE Photonics Technol. Lett. 21(20), 1535–1537 (2009).
[Crossref]

Odom, T. W.

H. Wu, T. W. Odom, and G. M. Whitesides, “Reduction photolithography using microlens arrays: applications in gray scale photolithography,” Anal. Chem. 74(14), 3267–3273 (2002).
[Crossref] [PubMed]

Otón, J. M.

J. F. Algorri, V. Urruchi, J. M. Sánchez-Pena, and J. M. Otón, “An Autostereoscopic Device for Mobile Applications Based on a Liquid Crystal Microlens Array and an OLED Display,” J. Disp. Technol. 10(9), 713–720 (2014).
[Crossref]

Park, G.

Park, J. H.

Parkins, K.

Pockett, L.

N. S. Holliman, N. A. Dodgson, G. E. Favalora, and L. Pockett, “Three-Dimensional Displays: A Review and Applications Analysis,” IEEE Trans. Broadcast 57(2), 362–371 (2011).
[Crossref]

Rodriguez, F.

Rogers, J. A.

M. V. Kunnavakkam, F. M. Houlihan, M. Schlax, J. A. Liddle, P. Kolodner, O. Nalamasu, and J. A. Rogers, “Low-cost, low-loss microlens arrays fabricated by soft-lithography replication process,” Appl. Phys. Lett. 82(8), 1152–1154 (2003).
[Crossref]

Rolland, J. P.

Royo, S.

Ruprecht, D.

D. Ruprecht and H. Muller, “Image warping with scattered data interpolation,” IEEE Comput. Graph. Appl. 15(2), 37–43 (1995).
[Crossref]

Sánchez-Pena, J. M.

J. F. Algorri, V. Urruchi, J. M. Sánchez-Pena, and J. M. Otón, “An Autostereoscopic Device for Mobile Applications Based on a Liquid Crystal Microlens Array and an OLED Display,” J. Disp. Technol. 10(9), 713–720 (2014).
[Crossref]

Schlax, M.

M. V. Kunnavakkam, F. M. Houlihan, M. Schlax, J. A. Liddle, P. Kolodner, O. Nalamasu, and J. A. Rogers, “Low-cost, low-loss microlens arrays fabricated by soft-lithography replication process,” Appl. Phys. Lett. 82(8), 1152–1154 (2003).
[Crossref]

Schreiber, P.

Sieler, M.

Song, J. F.

D. Wu, Q. D. Chen, L. G. Niu, J. Jiao, H. Xia, J. F. Song, and H. B. Sun, “100% fill-factor aspheric microlenses arrays (AMLA) with sub-20 nm precision,” IEEE Photonics Technol. Lett. 21(20), 1535–1537 (2009).
[Crossref]

Sun, H. B.

D. Wu, Q. D. Chen, L. G. Niu, J. Jiao, H. Xia, J. F. Song, and H. B. Sun, “100% fill-factor aspheric microlenses arrays (AMLA) with sub-20 nm precision,” IEEE Photonics Technol. Lett. 21(20), 1535–1537 (2009).
[Crossref]

Sun, X.

Tünnermann, A.

Urruchi, V.

J. F. Algorri, V. Urruchi, J. M. Sánchez-Pena, and J. M. Otón, “An Autostereoscopic Device for Mobile Applications Based on a Liquid Crystal Microlens Array and an OLED Display,” J. Disp. Technol. 10(9), 713–720 (2014).
[Crossref]

Vo, S.

Voelkel, R.

R. Voelkel and K. J. Weible, “Laser beam homogenizing: limitations and constraints,” Proc. SPIE 7102, 71020J (2008).
[Crossref]

Wang, C.

Q. Deng, C. Du, C. Wang, C. Zhou, X. Dong, Y. Liu, and T. Zhou, “Microlens array for stacked laser diode beam collimation,” Proc. SPIE 5636, 666–670 (2005).
[Crossref]

Wang, Y.

Wei, M. K.

H. Yang, C. K. Chao, M. K. Wei, and C. P. Lin, “High fill-factor microlens array mold insert fabrication using a thermal reflow process,” J. Micromech. Microeng. 14(8), 1197–1204 (2004).
[Crossref]

Weible, K. J.

R. Voelkel and K. J. Weible, “Laser beam homogenizing: limitations and constraints,” Proc. SPIE 7102, 71020J (2008).
[Crossref]

Whitesides, G. M.

H. Wu, T. W. Odom, and G. M. Whitesides, “Reduction photolithography using microlens arrays: applications in gray scale photolithography,” Anal. Chem. 74(14), 3267–3273 (2002).
[Crossref] [PubMed]

Wu, D.

D. Wu, Q. D. Chen, L. G. Niu, J. Jiao, H. Xia, J. F. Song, and H. B. Sun, “100% fill-factor aspheric microlenses arrays (AMLA) with sub-20 nm precision,” IEEE Photonics Technol. Lett. 21(20), 1535–1537 (2009).
[Crossref]

Wu, H.

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Figures (15)

Fig. 1
Fig. 1 Working principle of integration projection system based on MLA
Fig. 2
Fig. 2 The basic structure of ultra-short throw projection system based on MLA
Fig. 3
Fig. 3 Design and analysis flow chart of MLA projection
Fig. 4
Fig. 4 (a) Initial projection sub-lens. (b) Optimized projection sub-lens. (c) Half-FOV MTF of optimized projection sub-lens. (d) Spot diagram of optimized projection sub-lens.
Fig. 5
Fig. 5 (a) Ray aberrations of optimized projection sub-lens. (b) Field curves of optimized projection sub-lens.
Fig. 6
Fig. 6 Sketch map of a rectangular array arrangement structure of MLA. (a) px and py are the center interval between the adjacent lenses in the MLA, while p is the aperture of the sub-lens. (b) Cross section view of MLA through the central sub-lens of the MLA in the YZ direction and the definition of YDE and ZDE. (c) Cross section view of MLA through the MLA plane and the definition of XDE.
Fig. 7
Fig. 7 Projection area analysis of MLA
Fig. 8
Fig. 8 (a) The sampling FOV points in the shared area. (b) RMS spots analysis of a 1.4-mm sub-aperture 12 × 12 MLA. (c) Analysis of average RMS spots in MLA imaging for different sub-apertures and different number of sub-channels at a projection distance of 500 mm.
Fig. 9
Fig. 9 Average RMS spot size analysis of MLA with different sizes of MLA and projection distance by using the designed sub-aperture size and projection distance.
Fig. 10
Fig. 10 Integrated imaging analysis of MLA with different sub-aperture sizes and different imaging distances in the same MLA size (11 × 11) by using the designed sub-aperture size and projection distance.
Fig. 11
Fig. 11 (a) Uniformly sampled view points on the projection plane. (b) Blue original grid field of view points and the distorted ray tracing points through chief ray tracing of the sub-lens ML (1,1), ML (1,11), ML (11,1), and ML (11,11) in the 11 × 11 MLA.
Fig. 12
Fig. 12 (a) Image (left) and aperture (right) array mask. (b) MLA and light source simulation structure. (c) Projection illuminance simulation result.
Fig. 13
Fig. 13 (a) Hexagon array arrangement MLA structure. (b) Stop mask, sub-image array mask. (c) Projection simulation in LightTools. (d) Illumination simulation results corresponding to a hexagonal array configuration.
Fig. 14
Fig. 14 A proposed multi-layer structure MLA and its illumination simulation.
Fig. 15
Fig. 15 (a) Components of MLA projector. (b) Overall look of MLA projector. (c) Experimental effect.

Tables (1)

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Table 1 Comparison between integrated projector and single-channel projector with the same aperture size

Equations (8)

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[ XDE(i,j) YDE(i,j) ZDE(i,j) ]=[ (i i central ) p x (j j central ) p y cos(α) (j j central ) p y sin(α) ] p x = p y =p [ (i i central )p (j j central )pcos(α) (j j central )psin(α) ]
S= pL f
D [S(N1)p] 2 = [ pL f (N1)p] 2 = [ L F/# (N+1)p] 2
r array (h')= 1 N [ r RMS (h')+ i=2 N r RMS (h'+δ v i ) ]
P ix = p r ¯ RMS
x j '= i=1 n α x,i R i (d)+ p m ( x j , y j )
y j '= i=1 n α y,i R i (d)+ p m ( x j , y j )
R i (d)= ( d 2 +λ r i 2 ) μ/2 = [ ( x j x center_i ) 2 + ( y j y center_i ) 2 +λ r i 2 ] μ/2

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