Abstract

Two-dimensional arrays of microlenses can be used in wearable display applications as numerical aperture expanders or exit-pupil expanders (EPEs) to increase the size of the display exit pupil. A novel EPE approach that uses two microlens arrays (MLAs) is presented. The approach is based on cascading two identical microlens arrays spaced precisely at one focal-length distance with submicrometer registration tolerances relative to each other. The ideal MLA for this application requires a 100% fill factor, sharp seams between microlenses, and a perfect spherical profile. We demonstrate a dual-MLA-based EPE that produces excellent exit-pupil uniformity and better than 90% diffraction efficiency for all three wavelengths in a color-display system. Two-MLA registration is performed with submicrometer precision by use of far-field alignment techniques. Fourier optics theory is used to derive the analytical formulas, and physical optics beam propagation is used for numerical computations. Three MLA fabrication technologies, including gray-scale lithography, photoresist reflow, and isotropic etching, are evaluated and compared for an EPE application.

© 2005 Optical Society of America

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References

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  1. H. Urey, “Retinal scanning displays,” in Encyclopedia of Optical Engineering,R. Driggers, ed., (Marcel Dekker, 2003), Vol. 3, pp. 2445–2457.
  2. H. Urey, “Diffractive exit-pupil expander for display applications,” Appl. Opt. 40, 5840–5851 (2001).
    [CrossRef]
  3. K. D. Powell, H. Urey, “A novel approach to exit pupil expansion for wearable displays,” in Helmet- and Head-Mounted Displays VII,C. E. Rash, C. E. Reese, eds., Proc. SPIE4711, 235–248 (2002).
    [CrossRef]
  4. I. Harder, M. Lano, N. Lindlein, J. Schwider, “Homogenization and beam shaping with microlens arrays,” in Photon Management,F. Wyrowski, ed., Proc. SPIE5456, 99–107 (2004).
    [CrossRef]
  5. H. Urey, K. D. Powell, “Microlens array-based exit pupil expander for full color display applications,” in Photon Management,F. Wyrowski, ed., Proc. SPIE5456, 227–236 (2004).
    [CrossRef]
  6. H. Urey, “Spot size, depth of focus, and diffraction ring intensity formulas for truncated Gaussian beams,” Appl. Opt. 43, 620–625 (2004).
    [CrossRef] [PubMed]
  7. M. Brown, M. Bowers, “High energy, near diffraction limited output from optical parametric oscillators using unstable resonators,” in Solid State Lasers VI,R. Scheps, ed., Proc. SPIE2986, 113–122 (1997).
    [CrossRef]
  8. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (Wiley, 1994).
  9. H. Sankur, E. Motamedi, “Microoptics development in the past decade,” in Micromachining Technology for Micro-Optics,S. H. Lee, E. G. Johnson, eds., Proc. SPIE4179, 30–55.
  10. M. T. Gale, M. Rossi, J. Petersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
    [CrossRef]
  11. T. Hessler, “Continuous-relief diffractive optical elements: design, fabrication, and applications,” Ph.D. dissertation (University of Neuchatel, 1998).
  12. F. T. O’Neill, J. T. Sheridan, “Photoresist reflow method of microlens production. Part I: Background and experiments,” Optik (Jena) 113, 391–404 (2002).
  13. A. Schilling, R. Merz, C. Ossmann, H. P. Herzig, “Surface profiles of reflow microlenses under the influence of surface tension and gravity,” Opt. Eng. 39, 2171–2176 (2000).
    [CrossRef]

2004 (1)

2002 (1)

F. T. O’Neill, J. T. Sheridan, “Photoresist reflow method of microlens production. Part I: Background and experiments,” Optik (Jena) 113, 391–404 (2002).

2001 (1)

2000 (1)

A. Schilling, R. Merz, C. Ossmann, H. P. Herzig, “Surface profiles of reflow microlenses under the influence of surface tension and gravity,” Opt. Eng. 39, 2171–2176 (2000).
[CrossRef]

1994 (1)

M. T. Gale, M. Rossi, J. Petersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Bowers, M.

M. Brown, M. Bowers, “High energy, near diffraction limited output from optical parametric oscillators using unstable resonators,” in Solid State Lasers VI,R. Scheps, ed., Proc. SPIE2986, 113–122 (1997).
[CrossRef]

Brown, M.

M. Brown, M. Bowers, “High energy, near diffraction limited output from optical parametric oscillators using unstable resonators,” in Solid State Lasers VI,R. Scheps, ed., Proc. SPIE2986, 113–122 (1997).
[CrossRef]

Gale, M. T.

M. T. Gale, M. Rossi, J. Petersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (Wiley, 1994).

Harder, I.

I. Harder, M. Lano, N. Lindlein, J. Schwider, “Homogenization and beam shaping with microlens arrays,” in Photon Management,F. Wyrowski, ed., Proc. SPIE5456, 99–107 (2004).
[CrossRef]

Herzig, H. P.

A. Schilling, R. Merz, C. Ossmann, H. P. Herzig, “Surface profiles of reflow microlenses under the influence of surface tension and gravity,” Opt. Eng. 39, 2171–2176 (2000).
[CrossRef]

Hessler, T.

T. Hessler, “Continuous-relief diffractive optical elements: design, fabrication, and applications,” Ph.D. dissertation (University of Neuchatel, 1998).

Lano, M.

I. Harder, M. Lano, N. Lindlein, J. Schwider, “Homogenization and beam shaping with microlens arrays,” in Photon Management,F. Wyrowski, ed., Proc. SPIE5456, 99–107 (2004).
[CrossRef]

Lindlein, N.

I. Harder, M. Lano, N. Lindlein, J. Schwider, “Homogenization and beam shaping with microlens arrays,” in Photon Management,F. Wyrowski, ed., Proc. SPIE5456, 99–107 (2004).
[CrossRef]

Merz, R.

A. Schilling, R. Merz, C. Ossmann, H. P. Herzig, “Surface profiles of reflow microlenses under the influence of surface tension and gravity,” Opt. Eng. 39, 2171–2176 (2000).
[CrossRef]

Motamedi, E.

H. Sankur, E. Motamedi, “Microoptics development in the past decade,” in Micromachining Technology for Micro-Optics,S. H. Lee, E. G. Johnson, eds., Proc. SPIE4179, 30–55.

O’Neill, F. T.

F. T. O’Neill, J. T. Sheridan, “Photoresist reflow method of microlens production. Part I: Background and experiments,” Optik (Jena) 113, 391–404 (2002).

Ossmann, C.

A. Schilling, R. Merz, C. Ossmann, H. P. Herzig, “Surface profiles of reflow microlenses under the influence of surface tension and gravity,” Opt. Eng. 39, 2171–2176 (2000).
[CrossRef]

Petersen, J.

M. T. Gale, M. Rossi, J. Petersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Powell, K. D.

H. Urey, K. D. Powell, “Microlens array-based exit pupil expander for full color display applications,” in Photon Management,F. Wyrowski, ed., Proc. SPIE5456, 227–236 (2004).
[CrossRef]

K. D. Powell, H. Urey, “A novel approach to exit pupil expansion for wearable displays,” in Helmet- and Head-Mounted Displays VII,C. E. Rash, C. E. Reese, eds., Proc. SPIE4711, 235–248 (2002).
[CrossRef]

Rossi, M.

M. T. Gale, M. Rossi, J. Petersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Sankur, H.

H. Sankur, E. Motamedi, “Microoptics development in the past decade,” in Micromachining Technology for Micro-Optics,S. H. Lee, E. G. Johnson, eds., Proc. SPIE4179, 30–55.

Schilling, A.

A. Schilling, R. Merz, C. Ossmann, H. P. Herzig, “Surface profiles of reflow microlenses under the influence of surface tension and gravity,” Opt. Eng. 39, 2171–2176 (2000).
[CrossRef]

Schutz, H.

M. T. Gale, M. Rossi, J. Petersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

Schwider, J.

I. Harder, M. Lano, N. Lindlein, J. Schwider, “Homogenization and beam shaping with microlens arrays,” in Photon Management,F. Wyrowski, ed., Proc. SPIE5456, 99–107 (2004).
[CrossRef]

Sheridan, J. T.

F. T. O’Neill, J. T. Sheridan, “Photoresist reflow method of microlens production. Part I: Background and experiments,” Optik (Jena) 113, 391–404 (2002).

Urey, H.

H. Urey, “Spot size, depth of focus, and diffraction ring intensity formulas for truncated Gaussian beams,” Appl. Opt. 43, 620–625 (2004).
[CrossRef] [PubMed]

H. Urey, “Diffractive exit-pupil expander for display applications,” Appl. Opt. 40, 5840–5851 (2001).
[CrossRef]

H. Urey, “Retinal scanning displays,” in Encyclopedia of Optical Engineering,R. Driggers, ed., (Marcel Dekker, 2003), Vol. 3, pp. 2445–2457.

K. D. Powell, H. Urey, “A novel approach to exit pupil expansion for wearable displays,” in Helmet- and Head-Mounted Displays VII,C. E. Rash, C. E. Reese, eds., Proc. SPIE4711, 235–248 (2002).
[CrossRef]

H. Urey, K. D. Powell, “Microlens array-based exit pupil expander for full color display applications,” in Photon Management,F. Wyrowski, ed., Proc. SPIE5456, 227–236 (2004).
[CrossRef]

Appl. Opt. (2)

Opt. Eng. (2)

M. T. Gale, M. Rossi, J. Petersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[CrossRef]

A. Schilling, R. Merz, C. Ossmann, H. P. Herzig, “Surface profiles of reflow microlenses under the influence of surface tension and gravity,” Opt. Eng. 39, 2171–2176 (2000).
[CrossRef]

Optik (Jena) (1)

F. T. O’Neill, J. T. Sheridan, “Photoresist reflow method of microlens production. Part I: Background and experiments,” Optik (Jena) 113, 391–404 (2002).

Other (8)

H. Urey, “Retinal scanning displays,” in Encyclopedia of Optical Engineering,R. Driggers, ed., (Marcel Dekker, 2003), Vol. 3, pp. 2445–2457.

T. Hessler, “Continuous-relief diffractive optical elements: design, fabrication, and applications,” Ph.D. dissertation (University of Neuchatel, 1998).

M. Brown, M. Bowers, “High energy, near diffraction limited output from optical parametric oscillators using unstable resonators,” in Solid State Lasers VI,R. Scheps, ed., Proc. SPIE2986, 113–122 (1997).
[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (Wiley, 1994).

H. Sankur, E. Motamedi, “Microoptics development in the past decade,” in Micromachining Technology for Micro-Optics,S. H. Lee, E. G. Johnson, eds., Proc. SPIE4179, 30–55.

K. D. Powell, H. Urey, “A novel approach to exit pupil expansion for wearable displays,” in Helmet- and Head-Mounted Displays VII,C. E. Rash, C. E. Reese, eds., Proc. SPIE4711, 235–248 (2002).
[CrossRef]

I. Harder, M. Lano, N. Lindlein, J. Schwider, “Homogenization and beam shaping with microlens arrays,” in Photon Management,F. Wyrowski, ed., Proc. SPIE5456, 99–107 (2004).
[CrossRef]

H. Urey, K. D. Powell, “Microlens array-based exit pupil expander for full color display applications,” in Photon Management,F. Wyrowski, ed., Proc. SPIE5456, 227–236 (2004).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Scanned beam display optics including an EPE at the intermediate image plane. FOV, field of view. Insets, left to right: 2-D micro-electromechanical system (MEMS) scanner die, microscope image of a 2-D binary diffraction grating, and view of the expanded exit pupil, which is made up of an array of diffraction orders that are due to the periodic structure of the 2-D diffraction grating.

Fig. 2
Fig. 2

(a) Three-level (two-mask) DOE scanning-electron microscope (SEM) picture. (b) Best theoretical color exit-pupil pattern possible with an eight-level (three-mask) DOE if all fabrication and mask alignment issues are resolved (notice the scaling of the exit-pupil size with each wavelength. The area of the largest circle corresponding to the red laser illumination is approximately twice that of area of the smallest circle corresponding to the blue laser). (c) Experimental exit-pupil pattern produced by the multilevel DOE in (a), showing very poor efficiency and color uniformity.

Fig. 3
Fig. 3

(a) Single-MLA profile. (b) Physical optics beam propagation from a MLA patterned surface toward the far field. (c) Far-field exit-pupil intensity cross section. (d), (e), (f) The same figures as immediately above but for the DMLA.

Fig. 4
Fig. 4

Comparison of diffraction envelope size versus wavelength for (a) a three-color DOE and (b) a DMLA EPE.

Fig. 5
Fig. 5

D-DM LA alignment and bonding setup by far-field alignment techniques.

Fig. 6
Fig. 6

(a) Microfabrication sequence for producing microlenses by gray-scale lithography; (b) desired microlens profile; (c) actual microlens surface profile measured with an atomic-force microscope (AFM). Notice the rounding in the corners and the surface roughness.

Fig. 7
Fig. 7

Simulated profiles for microlenses produced by gray-scale lithography, and the corresponding exit-pupil patterns. Seam radii of 0, 1.5, and 3 μm are shown on the left.

Fig. 8
Fig. 8

Simulated profiles for microlenses produced by photoresist reflow, and the corresponding exit pupil patterns. Top, minimum gap of 0 μm such that flat-gap regions exist only in hexagonal corners. Middle, minimum gap of 2.5 μm. Bottom, minimum gap of 2.5 μm with opaque masking over a flat region, showing excellent performance uniformity.

Fig. 9
Fig. 9

Simulated profiles of microlenses produced by isotropic etching, and the corresponding exit pupil patterns. Flat-top widths of 0, 1.5, and 2.5 μm are shown.

Fig. 10
Fig. 10

DMLA color EPE, yielding a uniformity of better than 20% and an efficiency of better than 90% for all colors.

Equations (9)

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t MLA ( x , y ) = exp [ - i π ( x 2 + y 2 ) / λ f MLA ] rect ( x d , y d ) * * × n m δ ( x - n d , y - m d ) ,
s i j ( x , y ) = h ( x - i d , y - j d ) rect ( x d , y d ) .
t MLA 2 ( x , y ) = 1 j λ f MLA n m FT { s n m ( x , y ) } v = y / λ f MLA u = x / λ f MLA * * δ ( x - n d , y - m d ) .
t exp ( x , y ) = - 1 λ 2 f MLA f ocu n m s n m ( f MLA f ocu x , f MLA f ocu y ) × exp [ - j 2 π λ f ocu ( x n d + y m d ) ] .
D exp = d f ocu / f MLA .
N order ( λ ) = d 2 / λ f MLA .
t exp ( x ) = n = N N exp ( - j 2 π x n d λ f ocu ) = 1 + 2 n = 1 N cos ( 2 π n x d λ f ocu ) .
n = 0 N exp ( j δ n ) = exp ( j N δ / 2 ) { sin [ ( N + 1 ) δ / 2 ] sin ( δ / 2 ) } .
t exp ( x ) = n = - N N exp ( j δ n ) = 2 cos ( N δ / 2 ) { sin [ ( N + 1 ) δ / 2 ] sin ( δ / 2 ) } - 1 ,

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