## Investigation of Designated Eye Position and Viewing Zone for a two-view autostereoscopic display |

Optics Express, Vol. 22, Issue 4, pp. 4751-4767 (2014)

http://dx.doi.org/10.1364/OE.22.004751

Acrobat PDF (3572 KB)

### Abstract

Designated eye position (DEP) and viewing zone (VZ) are important optical parameters for designing a two-view autostereoscopic display. Although much research has been done to date, little empirical evidence has been found to establish a direct relationship between design and measurement. More rigorous studies and verifications to investigate DEP and to ascertain the VZ criterion will be valuable. We propose evaluation metrics based on equivalent luminance (EL) and binocular luminance (BL) to figure out DEP and VZ for a two-view autostereoscopic display. Simulation and experimental results prove that our proposed evaluation metrics can be used to find the DEP and VZ accurately.

© 2014 Optical Society of America

## 1. Introduction

1. N. A. Dodgson, “Analysis of the viewing zone of the Cambridge autostereoscopic display,” Appl. Opt. **35**(10), 1705–1710 (1996). [CrossRef] [PubMed]

2. N. A. Dodgson, “Analysis of the viewing zone of multi-view autostereoscopic displays,” Proc. SPIE **4660**, 254–265 (2002). [CrossRef]

*et al*. [3, 4

4. A. Yuuki, S. Uehara, K. Taira, G. Hamagishi, K. Izumi, T. Nomura, K. Mashitani, A. Miyazawa, T. Koike, T. Horikoshi, S. Miyazaki, N. Watanabe, Y. Hisatake, and H. Ujike, “Influence of 3-D cross-talk on qualified viewing spaces in two- and multi-view autostereoscopic displays,” J. Soc. Info. Disp. **18**(7), 483–493 (2010).

*et al.*[5–7

7. H. Yamamoto, T. Kimura, S. Matsumoto, and S. Suyama, “Viewing-Zone Control of Light-Emitting Diode Panel for Stereoscopic Display and Multiple Viewing Distances,” J. Disp. Technol. **6**(9), 359–366 (2010). [CrossRef]

*et al.*[8] defined the viewing freedom as crosstalk lower than 10% area. Pierre Boher,

*et al*. [9] considered the perceived crosstalk for both eyes and proposed “combined 3D contrast” to define the viewing space. Those previous studies deal with VZ from different perspectives, and those results show that there is no general consensus on what the VZ basis is. The limiting or restrictive criterion of the VZ was not made explicit. In our previous studies [10, 11] we proposed a method to find out DEP when the designed optimal viewing distance (OVD) is given and also a geometric method to study VZ around the designed OVD [12

12. W. H. Chang, K. C. Huang, Y. H. Chou, H. Y. Lin, and K. Lee, “A Novel Evaluation Method for 3D Display Viewing-Zone,” Proc. SID, 1279–1282 (2012). [CrossRef]

## 2. Methods

### 2.1 Design principle for a two-view autostereoscopic display

_{D}and P

_{B}are the pitch of sub-pixel on image screen and that of parallax barrier, respectively. The distance from display to barrier is defined as f, the distance from barrier to an observer is defined as Z, and the inter-pupil distance (IPD) is marked as P

_{E}. First, according to the convergent rule for a monocular condition that every sub-pixel image designed for the specified eye would converge at the same point, and the point is defined as the designated eye position (DEP) [11] as shown in Fig. 1. Therefore, the distance between two DEPs for the right and left eyes should be designed equal to IPD. A convergent relationship between P

_{D}and Z can be shown in Eq. (1) [10]:Second, according to the binocular consideration for each specified view, the other relationship between the IPD and P

_{D}is written in Eq. (2):From Eqs. (1) and (2), we can derive the designer’s formulas for a two-view autostereoscopic display as shown in Eqs. (3) and (4): and Z is also called as the optimal/optimum viewing distance (OVD).

### 2.2 Geometric approach

7. H. Yamamoto, T. Kimura, S. Matsumoto, and S. Suyama, “Viewing-Zone Control of Light-Emitting Diode Panel for Stereoscopic Display and Multiple Viewing Distances,” J. Disp. Technol. **6**(9), 359–366 (2010). [CrossRef]

12. W. H. Chang, K. C. Huang, Y. H. Chou, H. Y. Lin, and K. Lee, “A Novel Evaluation Method for 3D Display Viewing-Zone,” Proc. SID, 1279–1282 (2012). [CrossRef]

_{D}, the barrier aperture ratio a

_{B}, the pitch of sub-pixel P

_{D}, the pitch of barrier P

_{B}, the distance between the image screen and barrier f, the number of pairs N in the image screen, and the horizontal screen size W. Similarly, the lines L2 to L4 can be obtained. The formulas of L1 to L4 in x-z plane are listed in Eqs. (9) to (12). A, B, C, and D are intersection points of every two lines. ∆X of VZ is the distance between points C and B in the X coordinate, and points C and B can be solved from Eqs. (9) to (12): Points B and C have the same z coordinate

_{E}>>P

_{D}, P

_{B}~2P

_{D}and 2P

_{D}N = W, and Eq. (16) is reduced toSince (N-1) is roughly equal to N, Eq. (17) becomesand Eq. (3) would beTo substitute Eq. (19) for Z in Eq. (18), we find thatFor both a

_{B}and a

_{D}being less than 1, then (2a

_{B}+ a

_{D})<<(W/P

_{E}), in a practical case, and we finally achieve the quation for ΔZ from Eq. (20)From Eq. (21), we can know that

_{B}and a

_{D}are the only parameters for designers to adjust the VZ for a two-view autostereoscopic display.

### 2.3 Ray tracing approach

^{TM}is applied for ray tracing to simulate the luminance distribution in the space, and the commercial software Matlab

^{TM}is applied for reconstructing the viewing zones from the ray tracing simulation and measured data through our evaluation metric.

*L*

_{R-3}. The italic style character

*L*represents the luminance, the subscript characters R means for the right eye, and the subscript characters 3 means the luminance comes from point 3. Multiple-point luminance that an observer perceived at her or his right eye as shown in Fig. 4(b) is notated as

*L*

_{Req}. The equation of

*L*

_{Req}is expressed in Eq. (22), and we name it as the equivalent luminance (EL), or called total luminance [10], for right eye. EL is an equation to describe the intersection of luminance from the three different points, and EL satisfies the condition of no pixel disappearing which we defined in section 2.2.

### 2.5 Uniformity map

*L*

_{min}and

*L*

_{max}represent the minimum and maximum luminance of the measured points. In the study, the measured points include only the three points as shown in Fig. 3(b). Although the human perception for display uniformity depends on the spatial frequency and background luminance of the test pattern [18

18. C. O. Spring, “Perception of Luminance Uniformity: Comparing Photometric Calculations to Subjective Perceptions of Uniformity,” Master Thesis, University of Colorado (2002), http://www.craigspring.com/images/Lum_Uniform_Thesis_Screen.pdf.

19. EBU – TECH 3320, “User requirements for Video Monitors in Television Production,” https://tech.ebu.ch/docs/tech/tech3320.pdf.

### 2.6 Binocular issue

### 2.7 Refractive index effect

12. W. H. Chang, K. C. Huang, Y. H. Chou, H. Y. Lin, and K. Lee, “A Novel Evaluation Method for 3D Display Viewing-Zone,” Proc. SID, 1279–1282 (2012). [CrossRef]

_{B}) to approach the real situation. The new OVD at the main lobe is then modified as

## 3. Simulation and experiment results

### 3.1 Simulation without considering the refractive index of glasses

^{TM}are used to capture and simulate the raw data of angular luminance profile. Then, Matlab

^{TM}is used to reconstruct the VZ from the raw data. To verify Eq. (15), we build six Lighttools models, in which pitches of sub-pixeles P

_{D}are 0.009 cm, N = 2880, IPD = 6.5 cm, OVD = 146.25 cm, pitch of barrier P

_{B}= 0.017975cm, with six different barrier and pixel aperture ratios (a

_{B}, a

_{D}) being (0.334, 0.5), (0.334, 0.7), (0.334, 0.3), (0.5, 0.3), (0.5, 0.5), and (0.5, 0.7), for model 1 to model 6, respectively. In Figs. 7(a) and 7(b), the

*L*

_{req}is drawn along the x direction at z = 146.25cm. In model 1, the calculated ∆X by using Eq. (15) is 7.59 cm and the simulated ∆X by using Eq. (22) is 7.598 cm, as shown in Fig. 7(a). For model 2, the calculated ∆X is 8.89 cm and the simulated ∆X is 8.798 cm, as shown in Fig. 7(b). The viewing zone formula calculation is consistent with simulation, and we can find that ∆X and pixel aperture ratio are in direct proportion, this trend comply with our viewing zone formula. According to Eq. (15), the crosstalk free VZ condition is to set ∆X equal to IPD, and therefore (2a

_{B}+ a

_{D}) is equal to 1. This diamond-shaped VZ will appear repeatedly along x direction at OVD, and its widths still fit the ∆X and ∆Z formulas. It is worthy of noting that diamond-shaped region will appear repeatedly at around OVD, the reason is that the rays from pixel will pass through the other barrier slits, thus will appear as the other diamond-shaped region at the other locations around OVD. The designed dimond-shaped region is named as the “main lobe”, and the others are called the “side lobes” [10]. As was mentioned above, the viewing zone is defined as the full region that equivalent luminance is not equal to zero. If we consider the widely used definition FWHM (full width at half maximum) to define the area, the viewing region in x direction would be smaller than that defined in Eq. (15) (as shown in Figs. 7(a) and 7(b)). The FWHM results show that the geometric approach is not good enough to describe VZ. As VZ shown in Fig. 2 that the intersection points A and D are not at the same x coordinate, the ∆Z is harder to be defined. Figures 7(c) and 7(d) show the side view at the y-z plane, and ∆Z in main lobes are 45.5 cm and 53.75 cm for (a

_{B}, a

_{D}) = (0.334, 0.5) and (0.334, 0.7), respectively. Tables 1 and 2 show the comparsions between the geometry and the EL metrics. Table 1 shows that calculation using Eq. (15) is consistent with EL metric simulation with 1%~2% error, and the error is defined as the absolute value of ((Calculated result)-(Simulated result))/(Calculated result). Also, Table 2 shows that the calculated ∆Z(1) and ∆Z(2) of main lobes for different formula by using Eqs. (16) and (21), respectively. And a good consistent result with <5% error is achieved for ∆Z(1) in Error ratio (1). Since ∆Z(2) is calculated from ∆X, a larger Error ratio (2) than Error ratio (1) is expected in Table 2.

### 3.2 Simulation with considering refractive index of glasses

_{B}= 1.515, the designed OVD calculated by Eq. (28) is modified as 96.42 cm. The result, as shown in Fig. 14, proves that the designed OVD estimated by Eq. (28) is closed to the predicted location.

### 3.3 Experiment result

_{B}, a

_{D}and VZ in Eq. (15), we built three experiments, in which P

_{D}are 0.010583 cm, N = 800, IPD = 6.5 cm, OVD = 33 cm, P

_{B}= 0.02113cm, W = 16.933 cm, with three different barrier and pixel aperture ratios (a

_{B}, a

_{D}) being (0.334, 0.5), (0.334, 0.7), and (0.5, 0.7) for model 7 to model 9, respectively. Since illumination of VZ is to be observed in this experiment, a design with brighter backlight and shorter OVD would be better for detecting the VZ. In this experiment, we prepared a handmade backlight with 4620 nits (measured by Konica-Minolta CS-200 luminance meter), barrier is printed by MANIA-BARCO silver-writer, and set the designed OVD as 33cm.

_{B}and a

_{D}. The relationship in Eq. (15) could be confirmed in this experiment.

## 4. Conclusion

## Acknowledgments

## References and links

1. | N. A. Dodgson, “Analysis of the viewing zone of the Cambridge autostereoscopic display,” Appl. Opt. |

2. | N. A. Dodgson, “Analysis of the viewing zone of multi-view autostereoscopic displays,” Proc. SPIE |

3. | A. Yuuki, S. Uehara, K. Taira, G. Hamagishi, K. Izumi, T. Nomura, K. Mashitani, A. Miyazawa, T. Koike, T. Horikoshi, and H. Ujike, “Viewing Zones of Autostereoscopic Displays and their Measurement Methods,” Proc. 15th IDW, 1111–1114 (2008). |

4. | A. Yuuki, S. Uehara, K. Taira, G. Hamagishi, K. Izumi, T. Nomura, K. Mashitani, A. Miyazawa, T. Koike, T. Horikoshi, S. Miyazaki, N. Watanabe, Y. Hisatake, and H. Ujike, “Influence of 3-D cross-talk on qualified viewing spaces in two- and multi-view autostereoscopic displays,” J. Soc. Info. Disp. |

5. | H. Yamamoto, M. Kouno, S. Muguruma, Y.Hayaski, Y. Yamamoto, M. Kouno, Y. Shimizum, and N. Nishida, “Optimization of stereoscopic full color LED display using parallax barrier to enlarge viewing areas,” Proc. Asia Display/ IDW, 1303–1306 (2001). |

6. | H. Yamamoto, T. Sato, S. Muguruma, Y. Hayasaki, Y. Nagai, Y. Shimizu, and N. Nishida, “Stereoscopic Full-Color Light Emitting Diode Display Using Parallax Barrier for Different Interpupillary Distances,” Opt. Rev. |

7. | H. Yamamoto, T. Kimura, S. Matsumoto, and S. Suyama, “Viewing-Zone Control of Light-Emitting Diode Panel for Stereoscopic Display and Multiple Viewing Distances,” J. Disp. Technol. |

8. | T. Järvenpää and M. Salmimaa, “Optical characterization of autostereoscopic 3-D displays,” J. Soc. Info. Disp. |

9. | P. Boher, T. Leroux, T. Bignon, and V. Collomb-Patton, “A new way to characterize autostereoscopic 3D displays using Fourier optics instrument,” Proc. SPIE7237, (2009). |

10. | K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H. Chen, C. C. Liao, Y. H. Chen, K. Lee, and W. H. Hsu, “A Study of Optimal Viewing Distance in a Parallax Barrier 3D Display,” J. Soc. Info. Disp. |

11. | K. C. Huang, C. L. Wu, C. C. Liao and K. Lee, “3D display measurement for DEP,” IMID Digest. 1018-1021 (2009). |

12. | W. H. Chang, K. C. Huang, Y. H. Chou, H. Y. Lin, and K. Lee, “A Novel Evaluation Method for 3D Display Viewing-Zone,” Proc. SID, 1279–1282 (2012). [CrossRef] |

13. | International Committee for Display Metrology, |

14. | K. C. Huang, C.-H. Tsai, K. J. Lee, and W.-J. Hsueh, “Measurement of Contrast Ratios for 3D Display,” Proc. SPIE |

15. | K. C. Huang, J. C. Yuan, C. H. Tsai, W. J. Hsueh, and N.-Y. Wang, “How crosstalk affects stereopsis in stereoscopic displays,” Proc. SPIE |

16. | K. C. Huang, F. H. Chen, L. Lin, H. Y. Lin, Y. H. Chou, C. C. Liao, Y. H. Chen, and K. Lee, “A crosstalk Model and its Application to Stereoscopic and Autostereoscopic Displays,” J. Soc. Info. Disp. |

17. | K. C. Huang, J. H. C. Yuan, C. H. Tsai, W. J. Hsueh, and N. Y. Wang, “A study of how crosstalk affects stereopsis in stereoscopic displays,” Proc. SPIE |

18. | C. O. Spring, “Perception of Luminance Uniformity: Comparing Photometric Calculations to Subjective Perceptions of Uniformity,” Master Thesis, University of Colorado (2002), http://www.craigspring.com/images/Lum_Uniform_Thesis_Screen.pdf. |

19. | EBU – TECH 3320, “User requirements for Video Monitors in Television Production,” https://tech.ebu.ch/docs/tech/tech3320.pdf. |

20. | K. C. Huang, C. L. Wu, F. H. Chen, L. C. Lin, K. Lee, and H. Y. Lin, “Evaluation Metric for Binocular Luminance Difference,” Proc. China Display/Asia Display, 168–171 (2011). |

**OCIS Codes**

(100.6890) Image processing : Three-dimensional image processing

(110.3000) Imaging systems : Image quality assessment

(120.2040) Instrumentation, measurement, and metrology : Displays

(220.4840) Optical design and fabrication : Testing

**ToC Category:**

Vision, Color, and Visual Optics

**History**

Original Manuscript: November 11, 2013

Revised Manuscript: January 24, 2014

Manuscript Accepted: January 26, 2014

Published: February 21, 2014

**Virtual Issues**

Vol. 9, Iss. 4 *Virtual Journal for Biomedical Optics*

**Citation**

Kuo-Chung Huang, Yi-Heng Chou, Lang-chin Lin, Hoang Yan Lin, Fu-Hao Chen, Ching-Chiu Liao, Yi-Han Chen, Kuen Lee, and Wan-Hsuan Hsu, "Investigation of Designated Eye Position and Viewing Zone for a two-view autostereoscopic display," Opt. Express **22**, 4751-4767 (2014)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-22-4-4751

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### References

- N. A. Dodgson, “Analysis of the viewing zone of the Cambridge autostereoscopic display,” Appl. Opt. 35(10), 1705–1710 (1996). [CrossRef] [PubMed]
- N. A. Dodgson, “Analysis of the viewing zone of multi-view autostereoscopic displays,” Proc. SPIE 4660, 254–265 (2002). [CrossRef]
- A. Yuuki, S. Uehara, K. Taira, G. Hamagishi, K. Izumi, T. Nomura, K. Mashitani, A. Miyazawa, T. Koike, T. Horikoshi, H. Ujike, “Viewing Zones of Autostereoscopic Displays and their Measurement Methods,” Proc. 15th IDW, 1111–1114 (2008).
- A. Yuuki, S. Uehara, K. Taira, G. Hamagishi, K. Izumi, T. Nomura, K. Mashitani, A. Miyazawa, T. Koike, T. Horikoshi, S. Miyazaki, N. Watanabe, Y. Hisatake, H. Ujike, “Influence of 3-D cross-talk on qualified viewing spaces in two- and multi-view autostereoscopic displays,” J. Soc. Info. Disp. 18(7), 483–493 (2010).
- H. Yamamoto, M. Kouno, S. Muguruma, Y.Hayaski, Y. Yamamoto, M. Kouno, Y. Shimizum, and N. Nishida, “Optimization of stereoscopic full color LED display using parallax barrier to enlarge viewing areas,” Proc. Asia Display/ IDW, 1303–1306 (2001).
- H. Yamamoto, T. Sato, S. Muguruma, Y. Hayasaki, Y. Nagai, Y. Shimizu, N. Nishida, “Stereoscopic Full-Color Light Emitting Diode Display Using Parallax Barrier for Different Interpupillary Distances,” Opt. Rev. 9(6), 244–250 (2002). [CrossRef]
- H. Yamamoto, T. Kimura, S. Matsumoto, S. Suyama, “Viewing-Zone Control of Light-Emitting Diode Panel for Stereoscopic Display and Multiple Viewing Distances,” J. Disp. Technol. 6(9), 359–366 (2010). [CrossRef]
- T. Järvenpää, M. Salmimaa, “Optical characterization of autostereoscopic 3-D displays,” J. Soc. Info. Disp. 16(8), 825–833 (2008).
- P. Boher, T. Leroux, T. Bignon, V. Collomb-Patton, “A new way to characterize autostereoscopic 3D displays using Fourier optics instrument,” Proc. SPIE7237, (2009).
- K. C. Huang, Y. H. Chou, L. Lin, H. Y. Lin, F. H. Chen, C. C. Liao, Y. H. Chen, K. Lee, W. H. Hsu, “A Study of Optimal Viewing Distance in a Parallax Barrier 3D Display,” J. Soc. Info. Disp. 21(6), 263–270 (2013).
- K. C. Huang, C. L. Wu, C. C. Liao and K. Lee, “3D display measurement for DEP,” IMID Digest. 1018-1021 (2009).
- W. H. Chang, K. C. Huang, Y. H. Chou, H. Y. Lin, K. Lee, “A Novel Evaluation Method for 3D Display Viewing-Zone,” Proc. SID, 1279–1282 (2012). [CrossRef]
- International Committee for Display Metrology, Information Display Measurements Standard (SID, 2012), Chap 17.
- K. C. Huang, C.-H. Tsai, K. J. Lee, W.-J. Hsueh, “Measurement of Contrast Ratios for 3D Display,” Proc. SPIE 4080, 78–86 (2000). [CrossRef]
- K. C. Huang, J. C. Yuan, C. H. Tsai, W. J. Hsueh, N.-Y. Wang, “How crosstalk affects stereopsis in stereoscopic displays,” Proc. SPIE 5006, 247–253 (2003). [CrossRef]
- K. C. Huang, F. H. Chen, L. Lin, H. Y. Lin, Y. H. Chou, C. C. Liao, Y. H. Chen, K. Lee, “A crosstalk Model and its Application to Stereoscopic and Autostereoscopic Displays,” J. Soc. Info. Disp. 21(6), 249–262 (2013).
- K. C. Huang, J. H. C. Yuan, C. H. Tsai, W. J. Hsueh, N. Y. Wang, “A study of how crosstalk affects stereopsis in stereoscopic displays,” Proc. SPIE 5006, 247–253 (2003). [CrossRef]
- C. O. Spring, “Perception of Luminance Uniformity: Comparing Photometric Calculations to Subjective Perceptions of Uniformity,” Master Thesis, University of Colorado (2002), http://www.craigspring.com/images/Lum_Uniform_Thesis_Screen.pdf .
- EBU – TECH 3320, “User requirements for Video Monitors in Television Production,” https://tech.ebu.ch/docs/tech/tech3320.pdf .
- K. C. Huang, C. L. Wu, F. H. Chen, L. C. Lin, K. Lee, and H. Y. Lin, “Evaluation Metric for Binocular Luminance Difference,” Proc. China Display/Asia Display, 168–171 (2011).

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