Abstract

We present a new optical system for a combiner-type head-up display (HUD) without any asymmetrical elements by employing a confocal, off-axis, two-hyperboloid mirror as an aberration corrector. From an off-axial aberration analysis, we initially obtain an off-axis two-mirror system corrected for linear astigmatism and spherical aberration by configuring its parameters to satisfy the confocal condition. In addition, to compensate the down angle in the HUD, the image display plane is tilted to satisfy the Scheimpflug condition. This design approach enables us to easily balance the residual aberrations without asymmetrical components, which results in an excellent starting design. The final optical system for an HUD has a virtual image of 7.3 in at 2 m away from an eye box having an area of 130×50  mm2.

© 2019 Optical Society of America

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References

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  1. A. Hofmann, J. Unterhinninghofen, H. Ries, and S. Kaiser, “Double tailoring of freeform surfaces for off-axis aplanatic systems,” Proc. SPIE 8550, 855014 (2012).
    [Crossref]
  2. B. H. Kim and S. C. Park, “Optical system design for a head-up display using aberration analysis of an off-axis two-mirror system,” J. Opt. Soc. Korea 20, 481–487 (2016).
    [Crossref]
  3. P. Ott, “Optic design of head-up displays with freeform surfaces specified by NURBS,” Proc. SPIE 7100, 71000Y (2008).
    [Crossref]
  4. J. Dong, H. Chen, Y. Zhang, S. Chen, and P. Guo, “Miniature anastigmatic spectrometer design with a concave toroidal mirror,” Appl. Opt. 55, 1537–1543 (2016).
    [Crossref]
  5. K. W. Brown and A. Prata, “A design procedure for classical offset dual reflector antennas with circular apertures,” IEEE Trans. Antennas Propag. 42, 1145–1153 (1994).
    [Crossref]
  6. J. U. Lee, Y. Kim, S. H. Kim, Y. Kim, and H. Kim, “Optical design of an image-space telecentric two-mirror system for wide-field line imaging,” Curr. Opt. Photon. 1, 344–350 (2017).
  7. W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008), Chap. 4.
  8. M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Chap. 18.
  9. C. Hahlweg, W. Zhao, and H. Rothe, “Fourier planes vs. Scheimpflug principle in microscopic and scatterometric devices,” Proc. SPIE 8127, 812708 (2011).
    [Crossref]
  10. J. M. Sasian, “Image plane tilt in optical systems,” Opt. Eng. 31, 527–533 (1992).
    [Crossref]
  11. S. Chang and A. Prata, “Geometrical theory of aberrations near the axis in classical off-axis reflecting telescopes,” J. Opt. Soc. Am. A 22, 2454–2464 (2005).
    [Crossref]
  12. S. Chang, “Linear astigmatism of confocal off-axis reflective imaging systems with N-conic mirrors and its elimination,” J. Opt. Soc. Am. A 32, 852–859 (2015).
    [Crossref]
  13. D. J. Schroeder, Astronomical Optics (Academic, 1999), Chap. 3.
  14. http://continental-head-up-display.com/ .
  15. Z. Qin, F. C. Lin, Y. P. Huang, and H. P. D. Shieh, “Maximal acceptable ghost images for designing a legible windshield-type vehicle head-up display,” IEEE Photon. J. 9, 1–12 (2017).
    [Crossref]
  16. I. Singh, A. Kumar, H. S. Singh, and O. P. Nijhawan, “Optical design and performance evaluation of a dual-beam combiner head-up display,” Opt. Eng. 35, 813–819 (1996).
    [Crossref]

2017 (2)

Z. Qin, F. C. Lin, Y. P. Huang, and H. P. D. Shieh, “Maximal acceptable ghost images for designing a legible windshield-type vehicle head-up display,” IEEE Photon. J. 9, 1–12 (2017).
[Crossref]

J. U. Lee, Y. Kim, S. H. Kim, Y. Kim, and H. Kim, “Optical design of an image-space telecentric two-mirror system for wide-field line imaging,” Curr. Opt. Photon. 1, 344–350 (2017).

2016 (2)

2015 (1)

2012 (1)

A. Hofmann, J. Unterhinninghofen, H. Ries, and S. Kaiser, “Double tailoring of freeform surfaces for off-axis aplanatic systems,” Proc. SPIE 8550, 855014 (2012).
[Crossref]

2011 (1)

C. Hahlweg, W. Zhao, and H. Rothe, “Fourier planes vs. Scheimpflug principle in microscopic and scatterometric devices,” Proc. SPIE 8127, 812708 (2011).
[Crossref]

2008 (1)

P. Ott, “Optic design of head-up displays with freeform surfaces specified by NURBS,” Proc. SPIE 7100, 71000Y (2008).
[Crossref]

2005 (1)

1996 (1)

I. Singh, A. Kumar, H. S. Singh, and O. P. Nijhawan, “Optical design and performance evaluation of a dual-beam combiner head-up display,” Opt. Eng. 35, 813–819 (1996).
[Crossref]

1994 (1)

K. W. Brown and A. Prata, “A design procedure for classical offset dual reflector antennas with circular apertures,” IEEE Trans. Antennas Propag. 42, 1145–1153 (1994).
[Crossref]

1992 (1)

J. M. Sasian, “Image plane tilt in optical systems,” Opt. Eng. 31, 527–533 (1992).
[Crossref]

Bass, M.

M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Chap. 18.

Brown, K. W.

K. W. Brown and A. Prata, “A design procedure for classical offset dual reflector antennas with circular apertures,” IEEE Trans. Antennas Propag. 42, 1145–1153 (1994).
[Crossref]

Chang, S.

Chen, H.

Chen, S.

Dong, J.

Guo, P.

Hahlweg, C.

C. Hahlweg, W. Zhao, and H. Rothe, “Fourier planes vs. Scheimpflug principle in microscopic and scatterometric devices,” Proc. SPIE 8127, 812708 (2011).
[Crossref]

Hofmann, A.

A. Hofmann, J. Unterhinninghofen, H. Ries, and S. Kaiser, “Double tailoring of freeform surfaces for off-axis aplanatic systems,” Proc. SPIE 8550, 855014 (2012).
[Crossref]

Huang, Y. P.

Z. Qin, F. C. Lin, Y. P. Huang, and H. P. D. Shieh, “Maximal acceptable ghost images for designing a legible windshield-type vehicle head-up display,” IEEE Photon. J. 9, 1–12 (2017).
[Crossref]

Kaiser, S.

A. Hofmann, J. Unterhinninghofen, H. Ries, and S. Kaiser, “Double tailoring of freeform surfaces for off-axis aplanatic systems,” Proc. SPIE 8550, 855014 (2012).
[Crossref]

Kim, B. H.

Kim, H.

Kim, S. H.

Kim, Y.

Kumar, A.

I. Singh, A. Kumar, H. S. Singh, and O. P. Nijhawan, “Optical design and performance evaluation of a dual-beam combiner head-up display,” Opt. Eng. 35, 813–819 (1996).
[Crossref]

Lee, J. U.

Lin, F. C.

Z. Qin, F. C. Lin, Y. P. Huang, and H. P. D. Shieh, “Maximal acceptable ghost images for designing a legible windshield-type vehicle head-up display,” IEEE Photon. J. 9, 1–12 (2017).
[Crossref]

Nijhawan, O. P.

I. Singh, A. Kumar, H. S. Singh, and O. P. Nijhawan, “Optical design and performance evaluation of a dual-beam combiner head-up display,” Opt. Eng. 35, 813–819 (1996).
[Crossref]

Ott, P.

P. Ott, “Optic design of head-up displays with freeform surfaces specified by NURBS,” Proc. SPIE 7100, 71000Y (2008).
[Crossref]

Park, S. C.

Prata, A.

S. Chang and A. Prata, “Geometrical theory of aberrations near the axis in classical off-axis reflecting telescopes,” J. Opt. Soc. Am. A 22, 2454–2464 (2005).
[Crossref]

K. W. Brown and A. Prata, “A design procedure for classical offset dual reflector antennas with circular apertures,” IEEE Trans. Antennas Propag. 42, 1145–1153 (1994).
[Crossref]

Qin, Z.

Z. Qin, F. C. Lin, Y. P. Huang, and H. P. D. Shieh, “Maximal acceptable ghost images for designing a legible windshield-type vehicle head-up display,” IEEE Photon. J. 9, 1–12 (2017).
[Crossref]

Ries, H.

A. Hofmann, J. Unterhinninghofen, H. Ries, and S. Kaiser, “Double tailoring of freeform surfaces for off-axis aplanatic systems,” Proc. SPIE 8550, 855014 (2012).
[Crossref]

Rothe, H.

C. Hahlweg, W. Zhao, and H. Rothe, “Fourier planes vs. Scheimpflug principle in microscopic and scatterometric devices,” Proc. SPIE 8127, 812708 (2011).
[Crossref]

Sasian, J. M.

J. M. Sasian, “Image plane tilt in optical systems,” Opt. Eng. 31, 527–533 (1992).
[Crossref]

Schroeder, D. J.

D. J. Schroeder, Astronomical Optics (Academic, 1999), Chap. 3.

Shieh, H. P. D.

Z. Qin, F. C. Lin, Y. P. Huang, and H. P. D. Shieh, “Maximal acceptable ghost images for designing a legible windshield-type vehicle head-up display,” IEEE Photon. J. 9, 1–12 (2017).
[Crossref]

Singh, H. S.

I. Singh, A. Kumar, H. S. Singh, and O. P. Nijhawan, “Optical design and performance evaluation of a dual-beam combiner head-up display,” Opt. Eng. 35, 813–819 (1996).
[Crossref]

Singh, I.

I. Singh, A. Kumar, H. S. Singh, and O. P. Nijhawan, “Optical design and performance evaluation of a dual-beam combiner head-up display,” Opt. Eng. 35, 813–819 (1996).
[Crossref]

Smith, W. J.

W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008), Chap. 4.

Unterhinninghofen, J.

A. Hofmann, J. Unterhinninghofen, H. Ries, and S. Kaiser, “Double tailoring of freeform surfaces for off-axis aplanatic systems,” Proc. SPIE 8550, 855014 (2012).
[Crossref]

Zhang, Y.

Zhao, W.

C. Hahlweg, W. Zhao, and H. Rothe, “Fourier planes vs. Scheimpflug principle in microscopic and scatterometric devices,” Proc. SPIE 8127, 812708 (2011).
[Crossref]

Appl. Opt. (1)

Curr. Opt. Photon. (1)

IEEE Photon. J. (1)

Z. Qin, F. C. Lin, Y. P. Huang, and H. P. D. Shieh, “Maximal acceptable ghost images for designing a legible windshield-type vehicle head-up display,” IEEE Photon. J. 9, 1–12 (2017).
[Crossref]

IEEE Trans. Antennas Propag. (1)

K. W. Brown and A. Prata, “A design procedure for classical offset dual reflector antennas with circular apertures,” IEEE Trans. Antennas Propag. 42, 1145–1153 (1994).
[Crossref]

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

J. Opt. Soc. Korea (1)

Opt. Eng. (2)

I. Singh, A. Kumar, H. S. Singh, and O. P. Nijhawan, “Optical design and performance evaluation of a dual-beam combiner head-up display,” Opt. Eng. 35, 813–819 (1996).
[Crossref]

J. M. Sasian, “Image plane tilt in optical systems,” Opt. Eng. 31, 527–533 (1992).
[Crossref]

Proc. SPIE (3)

P. Ott, “Optic design of head-up displays with freeform surfaces specified by NURBS,” Proc. SPIE 7100, 71000Y (2008).
[Crossref]

A. Hofmann, J. Unterhinninghofen, H. Ries, and S. Kaiser, “Double tailoring of freeform surfaces for off-axis aplanatic systems,” Proc. SPIE 8550, 855014 (2012).
[Crossref]

C. Hahlweg, W. Zhao, and H. Rothe, “Fourier planes vs. Scheimpflug principle in microscopic and scatterometric devices,” Proc. SPIE 8127, 812708 (2011).
[Crossref]

Other (4)

W. J. Smith, Modern Optical Engineering, 4th ed. (McGraw-Hill, 2008), Chap. 4.

M. Bass, Handbook of Optics, 3rd ed. (McGraw-Hill, 2009), Chap. 18.

D. J. Schroeder, Astronomical Optics (Academic, 1999), Chap. 3.

http://continental-head-up-display.com/ .

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Figures (10)

Fig. 1.
Fig. 1. Layout of single convex hyperboloidal mirror at finite conjugates.
Fig. 2.
Fig. 2. Scheimpflug condition of on-axis lens system.
Fig. 3.
Fig. 3. Spot diagrams of single off-axis hyperboloidal mirror corrected for spherical aberration and satisfying Scheimpflug condition.
Fig. 4.
Fig. 4. Layout of confocal, off-axis, N -mirror imaging system working at finite conjugates. Every consecutive pair of mirrors shares a common focus.
Fig. 5.
Fig. 5. Layout of confocal, off-axis, two-hyperboloid mirror system corrected for spherical aberration and linear astigmatism, and satisfying Scheimpflug condition.
Fig. 6.
Fig. 6. Spot diagrams of confocal, off-axis, two-hyperboloid mirror system corrected for spherical aberration and linear astigmatism, and satisfying Scheimpflug condition.
Fig. 7.
Fig. 7. Optical layout of final designed HUD system.
Fig. 8.
Fig. 8. Spot diagrams of final designed HUD system.
Fig. 9.
Fig. 9. Distortion analysis method of HUD system: (a) five eye positions in eye box, and (b) evaluation method for distortion at each eye position.
Fig. 10.
Fig. 10. Grid distortions of final designed HUD system at (a) center eye position and (b) position 4.

Tables (4)

Tables Icon

Table 1. Initial Data of Confocal Off-Axis Two-Hyperboloid Mirror System for an HUD

Tables Icon

Table 2. Optical Specifications of HUD Optical System

Tables Icon

Table 3. Detailed Mirror Surface Data of Final Designed HUD System (in mm)

Tables Icon

Table 4. Distortion Analysis of Final Designed HUD System at Each Eye Position

Equations (19)

Equations on this page are rendered with MathJax. Learn more.

z 2 a 2 y 2 b 2 = 1 ,
| P F ¯ | | P F ¯ | = 2 a .
l l = 2 a ,
a = l 2 ( 1 + m ) .
d = l sin 2 i 2 sin u ,
e = a 2 + b 2 a = d a ,
a × e d = 0 .
( 1 + m ) e sin u + m sin 2 i = 0 .
m H = l l = e sin u sin 2 i + e sin u .
θ i = arctan ( m tan θ o ) ,
θ i = arctan ( m H tan θ o ) = arctan ( e sin u sin 2 i + e sin u tan θ o ) ,
p = 1 N 1 [ ( 1 + m p ) tan i p q = p + 1 N m q ] + ( 1 + m N ) tan i N = 0 ,
θ i = arctan ( p = 1 N m p × tan θ o ) .
p = 1 N 1 [ ( 1 e p sin u p sin 2 i p + e p sin u p ) tan i p q = p + 1 N ( e q sin u q sin 2 i q + e q sin u q ) ] + ( 1 e N sin u N sin 2 i N + e N sin u N ) tan i N = 0 ,
θ i = arctan [ tan θ o p = 1 N ( e p sin u p sin 2 i p + e p sin u p ) ] .
( 1 e 1 sin u 1 sin 2 i 1 + e 1 sin u 1 ) ( e 2 sin u 2 sin 2 i 2 + e 2 sin u 2 ) tan i 1 + ( 1 e 2 sin u 2 sin 2 i 2 + e 2 sin u 2 ) tan i 2 = 0 ,
θ i = arctan [ ( e 1 sin u 1 sin 2 i 1 + e 1 sin u 1 ) ( e 2 sin u 2 sin 2 i 2 + e 2 sin u 2 ) tan θ o ] = arctan ( m 1 m 2 × tan θ o ) ,
Z = c h 2 1 + 1 ( 1 + K ) c 2 h 2 + A h 4 + B h 6 + C h 8 + D h 10 + E h 12 + F h 14 ,
Horizontal percent distortion :       x D ( % ) = x x o x o × 100 ( % ) , Vertical percent distortion :       y D ( % ) = y y o y o × 100 ( % ) .

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