Abstract

The “Angular Spatial Light Modulator” (ASLM) achieves simultaneous angular and spatial light modulation at a plane by combining Digital Micromirror Device (DMD) based programmable blazed grating beam steering and binary pattern sequencing. The ASLM system multiplies the number of effective output pixels of the DMD for increased spatial and/or angular degrees of freedom, and nearly-doubles the étendue output of the DMD. We implement multiple illumination and projection schemes to demonstrate ASLM-based extended FOV display, light-field projection, and multi-view display. We also implement time-multiplexed pupil segmented illumination to extend the pattern steering to two dimensions.

© 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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2019 (1)

2018 (3)

A. Abeeluck, A. Iverson, H. Goetz, and E. Passon, “High-Performance Displays for Wearable and HUD Applications,” Dig. Tech. Pap. 49(1), 768–771 (2018).

M. Hoffmann, I. N. Papadopoulos, and B. Judkewitz, “Kilohertz binary phase modulator for pulsed laser sources using a digital micromirror device,” Opt. Lett. 43(1), 22–25 (2018).
[Crossref] [PubMed]

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

2017 (2)

B. Smith, B. Hellman, A. Gin, A. Espinoza, and Y. Takashima, “Single chip lidar with discrete beam steering by digital micromirror device,” Opt. Express 25(13), 14732–14745 (2017).
[Crossref] [PubMed]

G. Chen, B. Miller, and Y. Takashima, “Eigenmode multiplexing with SLM for volume holographic data storage,” Proc. SPIE 10384, 1038407 (2017).

2016 (2)

B. E. Miller and Y. Takashima, “Cavity-enhanced eigenmode and angular hybrid multiplexing in holographic data storage systems,” Opt. Express 24(26), 29465–29476 (2016).
[Crossref] [PubMed]

H. Seifert, N. Ranieri, Q. Smithwick, and M. Gross, “Time-multiplexed tiled projection system with improved pixel and spatial resolution,” J. Soc. Inf. Disp. 24(9), 552–562 (2016).
[Crossref]

2014 (3)

2013 (1)

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

2010 (1)

2008 (1)

T. Kanebako and Y. Takaki, “Time-multiplexing display module for high-density directional display,” Proc. SPIE 6803, 68030P (2008).
[Crossref]

2007 (1)

K. Kikuta and Y. Takaki, “Development of SVGA resolution 128-dirctional display,” Proc. SPIE 6490, 64900U (2007).
[Crossref]

2006 (1)

S.-K. Kim, D.-W. Kim, M.-C. Park, Y.-M. Kwon, and J.-Y. Son, “Development of a HMD-type multifocus 3D display system using LEDs,” Proc. SPIE 6392, 63920B (2006).
[Crossref]

2004 (1)

1996 (1)

Abeeluck, A.

A. Abeeluck, A. Iverson, H. Goetz, and E. Passon, “High-Performance Displays for Wearable and HUD Applications,” Dig. Tech. Pap. 49(1), 768–771 (2018).

Adesnik, H.

N. C. Pégard, L. Waller, and H. Adesnik, “Holographic Display and Volumetric Light Sculpting by Dynamic Synthesis of 4d Light Fields,” in Biophotonics Congress: Optics in the Life Sciences Congress 2019 (BODA, BRAIN, NTM, MA, OMP) (Optical Society of America, 2019), paper BM3A.5.

Avci, A.

Baran, U.

S. Holmstrom, U. Baran, and H. Urey, “MEMS laser scanners: a review,” J. Microelectromech. Syst. 23(2), 259–275 (2014).
[Crossref]

Beausoleil, R. G.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Bogaert, L.

Brug, J.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Chen, G.

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

G. Chen, B. Miller, and Y. Takashima, “Eigenmode multiplexing with SLM for volume holographic data storage,” Proc. SPIE 10384, 1038407 (2017).

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y.-S. Kim, D. W. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3K.7.
[Crossref]

Choi, H.

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y.-S. Kim, D. W. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3K.7.
[Crossref]

Chu, D.

De Smet, H.

Dorsch, R.

Espinoza, A.

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

B. Smith, B. Hellman, A. Gin, A. Espinoza, and Y. Takashima, “Single chip lidar with discrete beam steering by digital micromirror device,” Opt. Express 25(13), 14732–14745 (2017).
[Crossref] [PubMed]

Fattal, D.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Ferreira, C.

Fiorentino, M.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Gin, A.

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

B. Smith, B. Hellman, A. Gin, A. Espinoza, and Y. Takashima, “Single chip lidar with discrete beam steering by digital micromirror device,” Opt. Express 25(13), 14732–14745 (2017).
[Crossref] [PubMed]

Goetz, H.

A. Abeeluck, A. Iverson, H. Goetz, and E. Passon, “High-Performance Displays for Wearable and HUD Applications,” Dig. Tech. Pap. 49(1), 768–771 (2018).

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), p. 27.

Greivenkamp, J. E.

J. E. Greivenkamp, Field Guide to Geometrical Optics (SPIE Press, 2004).

Gross, M.

H. Seifert, N. Ranieri, Q. Smithwick, and M. Gross, “Time-multiplexed tiled projection system with improved pixel and spatial resolution,” J. Soc. Inf. Disp. 24(9), 552–562 (2016).
[Crossref]

Hellman, B.

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

B. Smith, B. Hellman, A. Gin, A. Espinoza, and Y. Takashima, “Single chip lidar with discrete beam steering by digital micromirror device,” Opt. Express 25(13), 14732–14745 (2017).
[Crossref] [PubMed]

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y.-S. Kim, D. W. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3K.7.
[Crossref]

Hoffmann, M.

Holmstrom, S.

S. Holmstrom, U. Baran, and H. Urey, “MEMS laser scanners: a review,” J. Microelectromech. Syst. 23(2), 259–275 (2014).
[Crossref]

Iverson, A.

A. Abeeluck, A. Iverson, H. Goetz, and E. Passon, “High-Performance Displays for Wearable and HUD Applications,” Dig. Tech. Pap. 49(1), 768–771 (2018).

Jang, J. S.

Jang, J.-Y.

Javidi, B.

Judkewitz, B.

Kanebako, T.

T. Kanebako and Y. Takaki, “Time-multiplexing display module for high-density directional display,” Proc. SPIE 6803, 68030P (2008).
[Crossref]

Kang, E.

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

Kikuta, K.

K. Kikuta and Y. Takaki, “Development of SVGA resolution 128-dirctional display,” Proc. SPIE 6490, 64900U (2007).
[Crossref]

Kim, D. W.

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y.-S. Kim, D. W. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3K.7.
[Crossref]

Kim, D.-W.

S.-K. Kim, D.-W. Kim, M.-C. Park, Y.-M. Kwon, and J.-Y. Son, “Development of a HMD-type multifocus 3D display system using LEDs,” Proc. SPIE 6392, 63920B (2006).
[Crossref]

Kim, E.-S.

Kim, S.-K.

S.-K. Kim, D.-W. Kim, M.-C. Park, Y.-M. Kwon, and J.-Y. Son, “Development of a HMD-type multifocus 3D display system using LEDs,” Proc. SPIE 6392, 63920B (2006).
[Crossref]

Kim, Y.-S.

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y.-S. Kim, D. W. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3K.7.
[Crossref]

Kwon, Y.-M.

S.-K. Kim, D.-W. Kim, M.-C. Park, Y.-M. Kwon, and J.-Y. Son, “Development of a HMD-type multifocus 3D display system using LEDs,” Proc. SPIE 6392, 63920B (2006).
[Crossref]

Lee, B.-G.

Li, K.

Lohmann, A.

Mendlovic, D.

Meuret, Y.

Miller, B.

G. Chen, B. Miller, and Y. Takashima, “Eigenmode multiplexing with SLM for volume holographic data storage,” Proc. SPIE 10384, 1038407 (2017).

Miller, B. E.

Nakamura, J.

Papadopoulos, I. N.

Park, M.-C.

S.-K. Kim, D.-W. Kim, M.-C. Park, Y.-M. Kwon, and J.-Y. Son, “Development of a HMD-type multifocus 3D display system using LEDs,” Proc. SPIE 6392, 63920B (2006).
[Crossref]

Passon, E.

A. Abeeluck, A. Iverson, H. Goetz, and E. Passon, “High-Performance Displays for Wearable and HUD Applications,” Dig. Tech. Pap. 49(1), 768–771 (2018).

Pégard, N. C.

N. C. Pégard, L. Waller, and H. Adesnik, “Holographic Display and Volumetric Light Sculpting by Dynamic Synthesis of 4d Light Fields,” in Biophotonics Congress: Optics in the Life Sciences Congress 2019 (BODA, BRAIN, NTM, MA, OMP) (Optical Society of America, 2019), paper BM3A.5.

Peng, Z.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Ranieri, N.

H. Seifert, N. Ranieri, Q. Smithwick, and M. Gross, “Time-multiplexed tiled projection system with improved pixel and spatial resolution,” J. Soc. Inf. Disp. 24(9), 552–562 (2016).
[Crossref]

Rodriguez, J.

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y.-S. Kim, D. W. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3K.7.
[Crossref]

Roelandt, S.

Seifert, H.

H. Seifert, N. Ranieri, Q. Smithwick, and M. Gross, “Time-multiplexed tiled projection system with improved pixel and spatial resolution,” J. Soc. Inf. Disp. 24(9), 552–562 (2016).
[Crossref]

Shin, D.

Smith, B.

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

B. Smith, B. Hellman, A. Gin, A. Espinoza, and Y. Takashima, “Single chip lidar with discrete beam steering by digital micromirror device,” Opt. Express 25(13), 14732–14745 (2017).
[Crossref] [PubMed]

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y.-S. Kim, D. W. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3K.7.
[Crossref]

Smithwick, Q.

H. Seifert, N. Ranieri, Q. Smithwick, and M. Gross, “Time-multiplexed tiled projection system with improved pixel and spatial resolution,” J. Soc. Inf. Disp. 24(9), 552–562 (2016).
[Crossref]

Son, J.-Y.

S.-K. Kim, D.-W. Kim, M.-C. Park, Y.-M. Kwon, and J.-Y. Son, “Development of a HMD-type multifocus 3D display system using LEDs,” Proc. SPIE 6392, 63920B (2006).
[Crossref]

Takaki, Y.

Y. Takaki and J. Nakamura, “Generation of 360-degree color three-dimensional images using a small array of high-speed projectors to provide multiple vertical viewpoints,” Opt. Express 22(7), 8779–8789 (2014).
[Crossref] [PubMed]

T. Kanebako and Y. Takaki, “Time-multiplexing display module for high-density directional display,” Proc. SPIE 6803, 68030P (2008).
[Crossref]

K. Kikuta and Y. Takaki, “Development of SVGA resolution 128-dirctional display,” Proc. SPIE 6490, 64900U (2007).
[Crossref]

Takashima, Y.

J. Rodriguez, B. Smith, E. Kang, B. Hellman, G. Chen, A. Gin, A. Espinoza, and Y. Takashima, “Beam steering by digital micro-mirror device for multi-beam and single-chip lidar,” Proc. SPIE 10757, 107570F (2018).
[Crossref]

G. Chen, B. Miller, and Y. Takashima, “Eigenmode multiplexing with SLM for volume holographic data storage,” Proc. SPIE 10384, 1038407 (2017).

B. Smith, B. Hellman, A. Gin, A. Espinoza, and Y. Takashima, “Single chip lidar with discrete beam steering by digital micromirror device,” Opt. Express 25(13), 14732–14745 (2017).
[Crossref] [PubMed]

B. E. Miller and Y. Takashima, “Cavity-enhanced eigenmode and angular hybrid multiplexing in holographic data storage systems,” Opt. Express 24(26), 29465–29476 (2016).
[Crossref] [PubMed]

J. Rodriguez, B. Hellman, B. Smith, H. Choi, G. Chen, Y.-S. Kim, D. W. Kim, and Y. Takashima, “Multi-order Laser Beam Steering with Digital Micro Mirror Device for High-speed LIDARs,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (Optical Society of America, 2019), paper AW3K.7.
[Crossref]

Thienpont, H.

Tran, T.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Urey, H.

S. Holmstrom, U. Baran, and H. Urey, “MEMS laser scanners: a review,” J. Microelectromech. Syst. 23(2), 259–275 (2014).
[Crossref]

Vo, S.

D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495(7441), 348–351 (2013).
[Crossref] [PubMed]

Waller, L.

N. C. Pégard, L. Waller, and H. Adesnik, “Holographic Display and Volumetric Light Sculpting by Dynamic Synthesis of 4d Light Fields,” in Biophotonics Congress: Optics in the Life Sciences Congress 2019 (BODA, BRAIN, NTM, MA, OMP) (Optical Society of America, 2019), paper BM3A.5.

Yöntem, A. Ö.

Zalevsky, Z.

Dig. Tech. Pap. (1)

A. Abeeluck, A. Iverson, H. Goetz, and E. Passon, “High-Performance Displays for Wearable and HUD Applications,” Dig. Tech. Pap. 49(1), 768–771 (2018).

J. Microelectromech. Syst. (1)

S. Holmstrom, U. Baran, and H. Urey, “MEMS laser scanners: a review,” J. Microelectromech. Syst. 23(2), 259–275 (2014).
[Crossref]

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

J. Soc. Inf. Disp. (1)

H. Seifert, N. Ranieri, Q. Smithwick, and M. Gross, “Time-multiplexed tiled projection system with improved pixel and spatial resolution,” J. Soc. Inf. Disp. 24(9), 552–562 (2016).
[Crossref]

Nature (1)

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Figures (12)

Fig. 1
Fig. 1 (a) DLP3000 DMD micromirror layout and rotation axes. (b) On-state and (c) off-state micromirrors reflecting light. The color scale shows height above DMD base surface.
Fig. 2
Fig. 2 (a), (b) Phase profiles of two different spatial patterns of micromirrors illuminated at different moments during the micromirror transition. (c), (d) The respective binary patterns projected into different diffraction orders.
Fig. 3
Fig. 3 DMD illumination schemes for (a) conventional binary state projection, (b) ASLM pattern steered output, (c) pupil-segmented illumination for conventional projection, and (d) vertical pupil-segmented illumination and horizontal ASLM pattern steering for a 2D output pupil array. Input and output pupils depicted for a single point, but an extended illumination area is employed so that multiple micromirrors are illuminated. Micromirrors (~10 µm) are not on the same scale as the illumination and projection optics (mm-cm) to demonstrate pupil-driven design forms. For the illustration purpose, only a single micromirror is schematically depicted.
Fig. 4
Fig. 4 (a) ASLM extended FOV display schematic with seven independent diffraction orders and off-state light. All output diffraction orders numbered. DMD shown is the larger structure, not the active area. (b) Experimental setup with higher diffraction orders visible on the spatial filter (i.e., card with the array of green dots) and seven independent binary patterns on an observation screen, each 2 cm in height and spaced by 6-7 cm.
Fig. 5
Fig. 5 (a) ASLM light-field projection schematic capturing three diffraction orders and spatially filtering out other diffraction orders. All diffraction orders numbered. (b) Through-focus of ASLM light-field projection.
Fig. 6
Fig. 6 (a) ASLM 1D multi-view display by 0.1 NA critical illumination with observation screen and two imaging lenses. Single-point illumination is shown to accurately depict independent pupil steering, but extended-area illumination is assumed for diffraction-based pattern steering. All diffraction orders numbered. (b) Photo of the of the observation screen showing five of the diffraction order outputs. The lenses form two angle-dependent patterns of Princess Leia. (c) Close-up views (left) and their respective input binary patterns (right).
Fig. 7
Fig. 7 (a) ASLM 1D multi-view display by 0.1 NA critical illumination with small-aperture camera for direct viewing of the angle-dependent patterns on the surface of the DMD demonstrating a successful angularly and spatially modulated light field at the DMD plane. Single-point illumination is shown to accurately depict independent pupil steering, but extended-area illumination is assumed for diffraction-based pattern steering. All diffraction orders numbered. (b) Photos of the DMD from two different angles with ambient light. The scale bar is only accurate for the vertical dimension in both photos due to the changing viewing angle. Single quadrant illuminated (Section 5.4).
Fig. 8
Fig. 8 (a) ASLM 2D multi-view display by 3-LED pupil segmented Koehler illumination. Each vertically-stacked LED has six independent horizontally steered output diffraction orders for a 3 × 6 array of outputs for direct pattern viewing on the surface of the DMD. Single-point illumination is shown to accurately depict independent pupil steering, but extended-area illumination is assumed for diffraction-based pattern steering. (b) Photos of the 18 angle-dependent patterns, arranged by viewing position corresponding to the 2D output pupil array.
Fig. 9
Fig. 9 Diffraction efficiency and crosstalk measurement experimental setup using a swing arm about the DMD and an active-normalization system of two APDs.
Fig. 10
Fig. 10 (a) Steering efficiency into each diffraction order direction as a function of illumination pulse delay (dictating mirror angle) beyond 215 µs at 62.5 ns increments. (b) Steering efficiency into diffraction order −2 at 2.5 ns increments.
Fig. 11
Fig. 11 DLP3000 DMD geometry viewed from the source direction (30° angle-of-incidence) depicting fill-factor for micromirrors tilted (a) 12° toward source; (b) 12° away from source. (Parity: The source is setup to view the micromirrors 30° to the left.) Height h is measured normal from micromirror base surface (same as Fig. 1(b) and 1(c)).
Fig. 12
Fig. 12 Phased quadrant reset causing quadrant-dependent beam steering efficiency.

Tables (2)

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Table 1 ASLM Projection Schemes and Applications

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Table 2 Measured diffraction efficiency and crosstalk for 532 nm source at 30° angle-of-incidence.

Equations (6)

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sin θ inc sin θ n = 2nλ p .
c n = 1 p 0 p e j ϕ 0 ξ p e j2πn ξ p dξ = e jπ( n+ ϕ 0 2π ) sinc( n+ ϕ 0 2π ),
c n = 1 p 0 p*F F p1D e j ϕ 0 ξ p e j2πn ξ p dξ =F F p1D e jπF F p1D ( n+ ϕ 0 2π ) sinc( F F p1D ( n+ ϕ 0 2π ) ),
F F p1D =F F 1D cos( θ inc + θ mirror ) cos( θ inc ) .
ϕ 0 = 2πF F p1D psin( θ mirror ) λ × 2 2 .
η=F F 1D 2 cos 2 ( θ inc + θ mirror ) cos 2 ( θ inc ) sin c 2 ( F F 1D cos( θ inc + θ mirror ) cos( θ inc ) ( n+ F F 1D psin( θ mirror )cos( θ inc + θ mirror ) λcos( θ inc ) ) ).

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