Abstract

Many light field displays are fundamentally different from other displays in that they do not have quantized pixels, quantized angular outputs, or a physical screen position, which can make definitions and characterization problematic. We have determined that it is more appropriate to express the spatial resolution in terms of spatial cutoff frequency rather than a physical distance as in the case of a display with actual quantized pixels. This concept is then extended to also encompass angular resolution. The technique exploits the fact that when spatial resolution of a sinusoidal grating pattern is halved, its contrast ratio is reduced by a known proportion. An improved model, based on an earlier design concept, has been developed. It not only can be used to measure spatial and angular cutoff frequencies, but also can enable comprehensive characterization of the display. This model provides fast, simple measurement with good accuracy. It does not use special equipment or require time-consuming subjective evaluations. Using the model to characterize images in a rapid, accurate manner validates the effectiveness of this technique.

© 2018 Optical Society of America

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References

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  1. R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Comput. Sci. Tech. Rep. CSTR 2, 1–11 (2005).
  2. A. Gershun, “The light field,” Stud. Appl. Math. 18, 51–151 (1939).
    [Crossref]
  3. A. Loukianitsa and A. N. Putilin, “Stereodisplay with neural network image processing,” Proc. SPIE 4660, 207–211 (2002).
    [Crossref]
  4. A. Loukianitsa, A. Yarovoy, and K. Kanashin, “Tri-stack 3D LCD monitor,” Proc. SPIE 5664, 241–246 (2005).
    [Crossref]
  5. G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Trans. Graph. 31, 1–11 (2012).
    [Crossref]
  6. D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
    [Crossref]
  7. T. Balogh, “Method and apparatus for displaying three-dimensional images,” U.S. patent6,201,565 (March 13, 2001).
  8. K. Nagano, A. Jones, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “An autostereoscopic projector array optimized for 3D facial display,” in ACM SIGGRAPH 2013 Emerging Technologies (ACM, 2013), p. 3.
  9. R. Rykowski and J. Lee, “Novel technology for view angle performance measurement,” in IMID/IDMC (2008), pp. 41–42.
  10. SID, “The Information Display Measurements Standard” (2012).
  11. A. Boev, R. Bregovic, and A. Gotchev, “Visual-quality evaluation methodology for multiview displays,” Displays 33, 103–112 (2012).
    [Crossref]
  12. P. T. Kovács, A. Boev, R. Bregović, and A. Gotchev, “Quality measurements of 3D light-field displays,” in International Workshop on Video Processing and Quality metrics for Consumer Electronics (VPQM), Chandler, Arizona, USA (2014).
  13. E. Langendijk, K. Hinnen, and C. Varekamp, “Comparison of goggle-free 3D display technologies,” in SID Mid-Europe Chapter Spring Meeting (2004).
  14. S. Wang, M. Sun, P. Surman, J. Yuan, and X. W. Sun, “P-79: Maximizing the 2D viewing field of a computational two-layer light field 3D display,” in SID Symposium Digest of Technical Papers (Wiley, 2015), Vol. 46, pp. 1440–1443.
  15. S. Wang, K. S. Ong, P. Surman, J. Yuan, Y. Zheng, and X. W. Sun, “Quality of experience measurement for light field 3D displays on multilayer LCDs,” J. Soc. Inf. Disp. 24, 726–740 (2016).
    [Crossref]
  16. R. Sekuler, S. M. Anstis, O. J. Braddick, T. Brandt, J. A. Movshon, and G. Orban, “The perception of motion,” J. Exp. Psychol. Hum. Percept. Perform. 16, 693–705 (1990).
    [Crossref]
  17. M. E. V. Valkenburg, Network Analysis (Prentice Hall, 1955).
  18. H. S. Carslaw, Introduction to the Theory of Fourier’s Series and Integrals (1930).
  19. R. Barros, O. Galvão, W. McIlvane, S. Soraci, and K. Murata-Soraci, “Visual information processing,” in Visual Information Processing (Academic, 2003), pp. 205–230.

2016 (1)

S. Wang, K. S. Ong, P. Surman, J. Yuan, Y. Zheng, and X. W. Sun, “Quality of experience measurement for light field 3D displays on multilayer LCDs,” J. Soc. Inf. Disp. 24, 726–740 (2016).
[Crossref]

2012 (2)

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Trans. Graph. 31, 1–11 (2012).
[Crossref]

A. Boev, R. Bregovic, and A. Gotchev, “Visual-quality evaluation methodology for multiview displays,” Displays 33, 103–112 (2012).
[Crossref]

2010 (1)

D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
[Crossref]

2005 (2)

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Comput. Sci. Tech. Rep. CSTR 2, 1–11 (2005).

A. Loukianitsa, A. Yarovoy, and K. Kanashin, “Tri-stack 3D LCD monitor,” Proc. SPIE 5664, 241–246 (2005).
[Crossref]

2002 (1)

A. Loukianitsa and A. N. Putilin, “Stereodisplay with neural network image processing,” Proc. SPIE 4660, 207–211 (2002).
[Crossref]

1990 (1)

R. Sekuler, S. M. Anstis, O. J. Braddick, T. Brandt, J. A. Movshon, and G. Orban, “The perception of motion,” J. Exp. Psychol. Hum. Percept. Perform. 16, 693–705 (1990).
[Crossref]

1939 (1)

A. Gershun, “The light field,” Stud. Appl. Math. 18, 51–151 (1939).
[Crossref]

Anstis, S. M.

R. Sekuler, S. M. Anstis, O. J. Braddick, T. Brandt, J. A. Movshon, and G. Orban, “The perception of motion,” J. Exp. Psychol. Hum. Percept. Perform. 16, 693–705 (1990).
[Crossref]

Balogh, T.

T. Balogh, “Method and apparatus for displaying three-dimensional images,” U.S. patent6,201,565 (March 13, 2001).

Barros, R.

R. Barros, O. Galvão, W. McIlvane, S. Soraci, and K. Murata-Soraci, “Visual information processing,” in Visual Information Processing (Academic, 2003), pp. 205–230.

Boev, A.

A. Boev, R. Bregovic, and A. Gotchev, “Visual-quality evaluation methodology for multiview displays,” Displays 33, 103–112 (2012).
[Crossref]

P. T. Kovács, A. Boev, R. Bregović, and A. Gotchev, “Quality measurements of 3D light-field displays,” in International Workshop on Video Processing and Quality metrics for Consumer Electronics (VPQM), Chandler, Arizona, USA (2014).

Bolas, M.

K. Nagano, A. Jones, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “An autostereoscopic projector array optimized for 3D facial display,” in ACM SIGGRAPH 2013 Emerging Technologies (ACM, 2013), p. 3.

Braddick, O. J.

R. Sekuler, S. M. Anstis, O. J. Braddick, T. Brandt, J. A. Movshon, and G. Orban, “The perception of motion,” J. Exp. Psychol. Hum. Percept. Perform. 16, 693–705 (1990).
[Crossref]

Brandt, T.

R. Sekuler, S. M. Anstis, O. J. Braddick, T. Brandt, J. A. Movshon, and G. Orban, “The perception of motion,” J. Exp. Psychol. Hum. Percept. Perform. 16, 693–705 (1990).
[Crossref]

Brédif, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Comput. Sci. Tech. Rep. CSTR 2, 1–11 (2005).

Bregovic, R.

A. Boev, R. Bregovic, and A. Gotchev, “Visual-quality evaluation methodology for multiview displays,” Displays 33, 103–112 (2012).
[Crossref]

P. T. Kovács, A. Boev, R. Bregović, and A. Gotchev, “Quality measurements of 3D light-field displays,” in International Workshop on Video Processing and Quality metrics for Consumer Electronics (VPQM), Chandler, Arizona, USA (2014).

Busch, J.

K. Nagano, A. Jones, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “An autostereoscopic projector array optimized for 3D facial display,” in ACM SIGGRAPH 2013 Emerging Technologies (ACM, 2013), p. 3.

Carslaw, H. S.

H. S. Carslaw, Introduction to the Theory of Fourier’s Series and Integrals (1930).

Debevec, P.

K. Nagano, A. Jones, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “An autostereoscopic projector array optimized for 3D facial display,” in ACM SIGGRAPH 2013 Emerging Technologies (ACM, 2013), p. 3.

Duval, G.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Comput. Sci. Tech. Rep. CSTR 2, 1–11 (2005).

Galvão, O.

R. Barros, O. Galvão, W. McIlvane, S. Soraci, and K. Murata-Soraci, “Visual information processing,” in Visual Information Processing (Academic, 2003), pp. 205–230.

Gershun, A.

A. Gershun, “The light field,” Stud. Appl. Math. 18, 51–151 (1939).
[Crossref]

Gotchev, A.

A. Boev, R. Bregovic, and A. Gotchev, “Visual-quality evaluation methodology for multiview displays,” Displays 33, 103–112 (2012).
[Crossref]

P. T. Kovács, A. Boev, R. Bregović, and A. Gotchev, “Quality measurements of 3D light-field displays,” in International Workshop on Video Processing and Quality metrics for Consumer Electronics (VPQM), Chandler, Arizona, USA (2014).

Hanrahan, P.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Comput. Sci. Tech. Rep. CSTR 2, 1–11 (2005).

Hinnen, K.

E. Langendijk, K. Hinnen, and C. Varekamp, “Comparison of goggle-free 3D display technologies,” in SID Mid-Europe Chapter Spring Meeting (2004).

Hirsch, M.

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Trans. Graph. 31, 1–11 (2012).
[Crossref]

D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
[Crossref]

Horowitz, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Comput. Sci. Tech. Rep. CSTR 2, 1–11 (2005).

Jones, A.

K. Nagano, A. Jones, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “An autostereoscopic projector array optimized for 3D facial display,” in ACM SIGGRAPH 2013 Emerging Technologies (ACM, 2013), p. 3.

Kanashin, K.

A. Loukianitsa, A. Yarovoy, and K. Kanashin, “Tri-stack 3D LCD monitor,” Proc. SPIE 5664, 241–246 (2005).
[Crossref]

Kim, Y.

D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
[Crossref]

Kovács, P. T.

P. T. Kovács, A. Boev, R. Bregović, and A. Gotchev, “Quality measurements of 3D light-field displays,” in International Workshop on Video Processing and Quality metrics for Consumer Electronics (VPQM), Chandler, Arizona, USA (2014).

Langendijk, E.

E. Langendijk, K. Hinnen, and C. Varekamp, “Comparison of goggle-free 3D display technologies,” in SID Mid-Europe Chapter Spring Meeting (2004).

Lanman, D.

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Trans. Graph. 31, 1–11 (2012).
[Crossref]

D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
[Crossref]

Lee, J.

R. Rykowski and J. Lee, “Novel technology for view angle performance measurement,” in IMID/IDMC (2008), pp. 41–42.

Levoy, M.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Comput. Sci. Tech. Rep. CSTR 2, 1–11 (2005).

Liu, J.

K. Nagano, A. Jones, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “An autostereoscopic projector array optimized for 3D facial display,” in ACM SIGGRAPH 2013 Emerging Technologies (ACM, 2013), p. 3.

Loukianitsa, A.

A. Loukianitsa, A. Yarovoy, and K. Kanashin, “Tri-stack 3D LCD monitor,” Proc. SPIE 5664, 241–246 (2005).
[Crossref]

A. Loukianitsa and A. N. Putilin, “Stereodisplay with neural network image processing,” Proc. SPIE 4660, 207–211 (2002).
[Crossref]

McIlvane, W.

R. Barros, O. Galvão, W. McIlvane, S. Soraci, and K. Murata-Soraci, “Visual information processing,” in Visual Information Processing (Academic, 2003), pp. 205–230.

Movshon, J. A.

R. Sekuler, S. M. Anstis, O. J. Braddick, T. Brandt, J. A. Movshon, and G. Orban, “The perception of motion,” J. Exp. Psychol. Hum. Percept. Perform. 16, 693–705 (1990).
[Crossref]

Murata-Soraci, K.

R. Barros, O. Galvão, W. McIlvane, S. Soraci, and K. Murata-Soraci, “Visual information processing,” in Visual Information Processing (Academic, 2003), pp. 205–230.

Nagano, K.

K. Nagano, A. Jones, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “An autostereoscopic projector array optimized for 3D facial display,” in ACM SIGGRAPH 2013 Emerging Technologies (ACM, 2013), p. 3.

Ng, R.

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Comput. Sci. Tech. Rep. CSTR 2, 1–11 (2005).

Ong, K. S.

S. Wang, K. S. Ong, P. Surman, J. Yuan, Y. Zheng, and X. W. Sun, “Quality of experience measurement for light field 3D displays on multilayer LCDs,” J. Soc. Inf. Disp. 24, 726–740 (2016).
[Crossref]

Orban, G.

R. Sekuler, S. M. Anstis, O. J. Braddick, T. Brandt, J. A. Movshon, and G. Orban, “The perception of motion,” J. Exp. Psychol. Hum. Percept. Perform. 16, 693–705 (1990).
[Crossref]

Putilin, A. N.

A. Loukianitsa and A. N. Putilin, “Stereodisplay with neural network image processing,” Proc. SPIE 4660, 207–211 (2002).
[Crossref]

Raskar, R.

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Trans. Graph. 31, 1–11 (2012).
[Crossref]

D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
[Crossref]

Rykowski, R.

R. Rykowski and J. Lee, “Novel technology for view angle performance measurement,” in IMID/IDMC (2008), pp. 41–42.

Sekuler, R.

R. Sekuler, S. M. Anstis, O. J. Braddick, T. Brandt, J. A. Movshon, and G. Orban, “The perception of motion,” J. Exp. Psychol. Hum. Percept. Perform. 16, 693–705 (1990).
[Crossref]

Soraci, S.

R. Barros, O. Galvão, W. McIlvane, S. Soraci, and K. Murata-Soraci, “Visual information processing,” in Visual Information Processing (Academic, 2003), pp. 205–230.

Sun, M.

S. Wang, M. Sun, P. Surman, J. Yuan, and X. W. Sun, “P-79: Maximizing the 2D viewing field of a computational two-layer light field 3D display,” in SID Symposium Digest of Technical Papers (Wiley, 2015), Vol. 46, pp. 1440–1443.

Sun, X. W.

S. Wang, K. S. Ong, P. Surman, J. Yuan, Y. Zheng, and X. W. Sun, “Quality of experience measurement for light field 3D displays on multilayer LCDs,” J. Soc. Inf. Disp. 24, 726–740 (2016).
[Crossref]

S. Wang, M. Sun, P. Surman, J. Yuan, and X. W. Sun, “P-79: Maximizing the 2D viewing field of a computational two-layer light field 3D display,” in SID Symposium Digest of Technical Papers (Wiley, 2015), Vol. 46, pp. 1440–1443.

Surman, P.

S. Wang, K. S. Ong, P. Surman, J. Yuan, Y. Zheng, and X. W. Sun, “Quality of experience measurement for light field 3D displays on multilayer LCDs,” J. Soc. Inf. Disp. 24, 726–740 (2016).
[Crossref]

S. Wang, M. Sun, P. Surman, J. Yuan, and X. W. Sun, “P-79: Maximizing the 2D viewing field of a computational two-layer light field 3D display,” in SID Symposium Digest of Technical Papers (Wiley, 2015), Vol. 46, pp. 1440–1443.

Valkenburg, M. E. V.

M. E. V. Valkenburg, Network Analysis (Prentice Hall, 1955).

Varekamp, C.

E. Langendijk, K. Hinnen, and C. Varekamp, “Comparison of goggle-free 3D display technologies,” in SID Mid-Europe Chapter Spring Meeting (2004).

Wang, S.

S. Wang, K. S. Ong, P. Surman, J. Yuan, Y. Zheng, and X. W. Sun, “Quality of experience measurement for light field 3D displays on multilayer LCDs,” J. Soc. Inf. Disp. 24, 726–740 (2016).
[Crossref]

S. Wang, M. Sun, P. Surman, J. Yuan, and X. W. Sun, “P-79: Maximizing the 2D viewing field of a computational two-layer light field 3D display,” in SID Symposium Digest of Technical Papers (Wiley, 2015), Vol. 46, pp. 1440–1443.

Wetzstein, G.

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Trans. Graph. 31, 1–11 (2012).
[Crossref]

Yarovoy, A.

A. Loukianitsa, A. Yarovoy, and K. Kanashin, “Tri-stack 3D LCD monitor,” Proc. SPIE 5664, 241–246 (2005).
[Crossref]

Yu, X.

K. Nagano, A. Jones, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “An autostereoscopic projector array optimized for 3D facial display,” in ACM SIGGRAPH 2013 Emerging Technologies (ACM, 2013), p. 3.

Yuan, J.

S. Wang, K. S. Ong, P. Surman, J. Yuan, Y. Zheng, and X. W. Sun, “Quality of experience measurement for light field 3D displays on multilayer LCDs,” J. Soc. Inf. Disp. 24, 726–740 (2016).
[Crossref]

S. Wang, M. Sun, P. Surman, J. Yuan, and X. W. Sun, “P-79: Maximizing the 2D viewing field of a computational two-layer light field 3D display,” in SID Symposium Digest of Technical Papers (Wiley, 2015), Vol. 46, pp. 1440–1443.

Zheng, Y.

S. Wang, K. S. Ong, P. Surman, J. Yuan, Y. Zheng, and X. W. Sun, “Quality of experience measurement for light field 3D displays on multilayer LCDs,” J. Soc. Inf. Disp. 24, 726–740 (2016).
[Crossref]

ACM Trans. Graph. (2)

G. Wetzstein, D. Lanman, M. Hirsch, and R. Raskar, “Tensor displays: compressive light field synthesis using multilayer displays with directional backlighting,” ACM Trans. Graph. 31, 1–11 (2012).
[Crossref]

D. Lanman, M. Hirsch, Y. Kim, and R. Raskar, “Content-adaptive parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization,” ACM Trans. Graph. 29, 163 (2010).
[Crossref]

Comput. Sci. Tech. Rep. CSTR (1)

R. Ng, M. Levoy, M. Brédif, G. Duval, M. Horowitz, and P. Hanrahan, “Light field photography with a hand-held plenoptic camera,” Comput. Sci. Tech. Rep. CSTR 2, 1–11 (2005).

Displays (1)

A. Boev, R. Bregovic, and A. Gotchev, “Visual-quality evaluation methodology for multiview displays,” Displays 33, 103–112 (2012).
[Crossref]

J. Exp. Psychol. Hum. Percept. Perform. (1)

R. Sekuler, S. M. Anstis, O. J. Braddick, T. Brandt, J. A. Movshon, and G. Orban, “The perception of motion,” J. Exp. Psychol. Hum. Percept. Perform. 16, 693–705 (1990).
[Crossref]

J. Soc. Inf. Disp. (1)

S. Wang, K. S. Ong, P. Surman, J. Yuan, Y. Zheng, and X. W. Sun, “Quality of experience measurement for light field 3D displays on multilayer LCDs,” J. Soc. Inf. Disp. 24, 726–740 (2016).
[Crossref]

Proc. SPIE (2)

A. Loukianitsa and A. N. Putilin, “Stereodisplay with neural network image processing,” Proc. SPIE 4660, 207–211 (2002).
[Crossref]

A. Loukianitsa, A. Yarovoy, and K. Kanashin, “Tri-stack 3D LCD monitor,” Proc. SPIE 5664, 241–246 (2005).
[Crossref]

Stud. Appl. Math. (1)

A. Gershun, “The light field,” Stud. Appl. Math. 18, 51–151 (1939).
[Crossref]

Other (10)

T. Balogh, “Method and apparatus for displaying three-dimensional images,” U.S. patent6,201,565 (March 13, 2001).

K. Nagano, A. Jones, J. Liu, J. Busch, X. Yu, M. Bolas, and P. Debevec, “An autostereoscopic projector array optimized for 3D facial display,” in ACM SIGGRAPH 2013 Emerging Technologies (ACM, 2013), p. 3.

R. Rykowski and J. Lee, “Novel technology for view angle performance measurement,” in IMID/IDMC (2008), pp. 41–42.

SID, “The Information Display Measurements Standard” (2012).

M. E. V. Valkenburg, Network Analysis (Prentice Hall, 1955).

H. S. Carslaw, Introduction to the Theory of Fourier’s Series and Integrals (1930).

R. Barros, O. Galvão, W. McIlvane, S. Soraci, and K. Murata-Soraci, “Visual information processing,” in Visual Information Processing (Academic, 2003), pp. 205–230.

P. T. Kovács, A. Boev, R. Bregović, and A. Gotchev, “Quality measurements of 3D light-field displays,” in International Workshop on Video Processing and Quality metrics for Consumer Electronics (VPQM), Chandler, Arizona, USA (2014).

E. Langendijk, K. Hinnen, and C. Varekamp, “Comparison of goggle-free 3D display technologies,” in SID Mid-Europe Chapter Spring Meeting (2004).

S. Wang, M. Sun, P. Surman, J. Yuan, and X. W. Sun, “P-79: Maximizing the 2D viewing field of a computational two-layer light field 3D display,” in SID Symposium Digest of Technical Papers (Wiley, 2015), Vol. 46, pp. 1440–1443.

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Figures (18)

Fig. 1.
Fig. 1.

Image of depth object. Snellen “E” pattern on stepped model, where each step from left to right goes 5 mm further back. Maximum resolution is in the fourth column from left (15 mm behind front screen).

Fig. 2.
Fig. 2.

Left: Reference pattern from contrast sensitivity chart superimposed on image. Right: Contrast plots indicating that display performance can be represented as a low-pass filter.

Fig. 3.
Fig. 3.

Ringing. The figure on the left shows the low-pass filter-like characteristic of ringing. Lower right shows the Gibbs phenomenon of ringing in a square wave function.

Fig. 4.
Fig. 4.

Cutoff frequencies. (Left) Spatial cutoff frequency for 560 cs/m. (Right) Angular cutoff frequency for 50 cs/radian.

Fig. 5.
Fig. 5.

Reference sinusoidal grating. This is for 0.637 contrast. In practice, the contrast will be less as black and white levels are not 0, 0, 0 and 255, 255, 255.

Fig. 6.
Fig. 6.

Fourier series. Low-pass filtered square wave approximates to a sinusoidal function & “DC component” as third and higher harmonics can be neglected.

Fig. 7.
Fig. 7.

Contrast. The contrast at the cutoff frequency is 0.637 of the maximum contrast. In this case, the maximum and minimum contrasts are 1 and 0, respectively.

Fig. 8.
Fig. 8.

Depth objects. (Top) Original stepped object. (Lower) New object with sloping surface and logarithmic bar grating.

Fig. 9.
Fig. 9.

Gamma correction. (L) Nonlinear characteristic, matches eye sensitivity to shade differences. (R) Grayscale RGB from increments of 10 in RGB. The gamma value of 2.2 is used to plot the curve.

Fig. 10.
Fig. 10.

Plotting half-resolution boundary. Left: Reference sinusoidal gratings overlaid on image. Right: Plot from contrast matching points.

Fig. 11.
Fig. 11.

“Black” and “white” grayscale levels are found from superimposing gray squares on test area in corner and adjusting for invisibility as shown in this figure.

Fig. 12.
Fig. 12.

Model covers four octaves of spatial frequency (0.5 to 8 mm pitch) and depths from 15 to 15 mm. There are “black” and “white” areas in each corner for calibrating the reference sinusoidal grating.

Fig. 13.
Fig. 13.

Depth object image. Spatial resolution, angular resolution, DOF, and FOV can be determined from the points K, L, M, and N.

Fig. 14.
Fig. 14.

Image depth. The image does not appear in front of the nearest screen to the viewer. The magnification in the z direction is 1.20 (taken from the red mean line). “100” and “200” refer to the distance from the center at 1 m from screen.

Fig. 15.
Fig. 15.

Calibrating reference sinusoidal grating. The maxima and minima of the lower sinusoidal pattern are matched with the grayscale values obtained from the “black/white” levels and the contrast ratio for half spatial resolution.

Fig. 16.
Fig. 16.

Viewing angle. The angle over which the resolution is greater or equal to half the resolution at the center, measured across the central axis.

Fig. 17.
Fig. 17.

Viewing angle. Left: At a viewing angle with best performance, the 1/2 resolution boundary is well defined. Right: Away from the optimum viewing direction, boundary is ill-defined.

Fig. 18.
Fig. 18.

Flow chart showing procedure for finding all parameters, with the exception of the viewing angle.

Tables (4)

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Table 1. Screen Resolution Type, Description, and Units

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Table 2. Fourier Series Coefficients

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Table 3. Parameter Definitions and Units

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Table 4. Summary of Results with Comments

Equations (10)

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f(θ)=4πn=1,3,51nsin(πnθL),
B=YWγ+YBγ2,
A=0.637(YWγ+YBγ)2,
Y=(Asinθ+B)1γ.
R=1000G,
AN=1arctan2GDNDN2G,
AF=1arctan2GDFDF2G,
DOF=DN+DF.
V=arctanDRO+arctanDLO,
CR=(YWYB)γ.