Abstract

Imaging or beam-steering systems employing a periodic array of microlenses or micromirrors suffer from diffraction problems resulting from the destructive interference of the beam segments produced by the array. Simple formulas are derived for beam steering with segmented apertures that do not suffer from diffraction problems because of the introduction of a moving linear phase shifter such as a prescan lens before the periodic structure. The technique substantially increases the resolution of imaging systems that employ microlens arrays or micromirror arrays. Theoretical, numerical, and experimental results demonstrating the high-resolution imaging concept using microlens arrays are presented.

© 2006 Optical Society of America

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References

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  1. H. Urey, in Encyclopedia of Optical Engineering, R.G.Driggers, ed. (Marcel Dekker, 2003), pp. 2445-2457.
  2. E. A. Watson, Opt. Eng. 32, 2665 (1993).
    [CrossRef]
  3. J. Duparre and R. Göring, Appl. Opt. 42, 3992 (2003).
    [CrossRef] [PubMed]
  4. H. Urey and K. Powell, Appl. Opt. 44, 4930 (2005).
    [CrossRef] [PubMed]
  5. F. Nikolajeff, S. Haard, and B. Curtis, Appl. Opt. 36, 8481 (1997).
    [CrossRef]
  6. H. Miyajima, K. Murakami, and M. Katashiro, IEEE J. Sel. Top. Quantum Electron. 10, 514 (2004).
    [CrossRef]
  7. E. A. Watson and A. Miller, in Proc. SPIE 2687, 60 (1996).
    [CrossRef]
  8. J. Duparre, D. Radtke, and P. Dannberg, Appl. Opt. 43, 4854 (2004).
    [CrossRef] [PubMed]
  9. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  10. H. Urey, Appl. Opt. 43, 620 (2004).
    [CrossRef] [PubMed]

2005 (1)

2004 (3)

2003 (1)

1997 (1)

1996 (1)

E. A. Watson and A. Miller, in Proc. SPIE 2687, 60 (1996).
[CrossRef]

1993 (1)

E. A. Watson, Opt. Eng. 32, 2665 (1993).
[CrossRef]

Curtis, B.

Dannberg, P.

Duparre, J.

Goodman, J. W.

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

Göring, R.

Haard, S.

Katashiro, M.

H. Miyajima, K. Murakami, and M. Katashiro, IEEE J. Sel. Top. Quantum Electron. 10, 514 (2004).
[CrossRef]

Miller, A.

E. A. Watson and A. Miller, in Proc. SPIE 2687, 60 (1996).
[CrossRef]

Miyajima, H.

H. Miyajima, K. Murakami, and M. Katashiro, IEEE J. Sel. Top. Quantum Electron. 10, 514 (2004).
[CrossRef]

Murakami, K.

H. Miyajima, K. Murakami, and M. Katashiro, IEEE J. Sel. Top. Quantum Electron. 10, 514 (2004).
[CrossRef]

Nikolajeff, F.

Powell, K.

Radtke, D.

Urey, H.

H. Urey and K. Powell, Appl. Opt. 44, 4930 (2005).
[CrossRef] [PubMed]

H. Urey, Appl. Opt. 43, 620 (2004).
[CrossRef] [PubMed]

H. Urey, in Encyclopedia of Optical Engineering, R.G.Driggers, ed. (Marcel Dekker, 2003), pp. 2445-2457.

Watson, E. A.

E. A. Watson and A. Miller, in Proc. SPIE 2687, 60 (1996).
[CrossRef]

E. A. Watson, Opt. Eng. 32, 2665 (1993).
[CrossRef]

Appl. Opt. (5)

IEEE J. Sel. Top. Quantum Electron. (1)

H. Miyajima, K. Murakami, and M. Katashiro, IEEE J. Sel. Top. Quantum Electron. 10, 514 (2004).
[CrossRef]

Opt. Eng. (1)

E. A. Watson, Opt. Eng. 32, 2665 (1993).
[CrossRef]

Proc. SPIE (1)

E. A. Watson and A. Miller, in Proc. SPIE 2687, 60 (1996).
[CrossRef]

Other (2)

H. Urey, in Encyclopedia of Optical Engineering, R.G.Driggers, ed. (Marcel Dekker, 2003), pp. 2445-2457.

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

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Figures (6)

Fig. 1
Fig. 1

Ray-tracing view of the microlens beam steering system. r 1 and r 2 are the displacements of the PSL and the MMLA.

Fig. 2
Fig. 2

Physical optics view of the three-MLA block system after the PSL. Scan angle and OPD between beam segments is marked after each element. (Dummy phase shifters have no net effect in the system.)

Fig. 3
Fig. 3

Propagation of a collimated beam through a three-microlens channel when (a) L1 is displaced by r 1 and (b) the incident beam is tilted with angle α.

Fig. 4
Fig. 4

Simulated PSF for different amounts of the PSL and the MMLA displacements ( r 1 and r 2 ) and the resultant beam tilt angles α and β. (a), (c), and (d) illustrate constructive beam interference (phase condition is met), and (b) illustrates destructive interference (phase condition is not met).

Fig. 5
Fig. 5

Experimental results for the MMLA and the PSL’s motion: (a) all lenses on axis, (b) only the MMLA is moved to steer beam by half-diffraction angle (phase condition not met); (c) both the PSL and the MMLA are moved to steer the beam by half-diffraction angle (phase condition met).

Fig. 6
Fig. 6

Experimental results of the line scans: (a) MMLA motion produces only discrete addressing, (b) PSL and the MMLA move synchronously and the phase condition is met at all times and continuous addressing is achieved (imperfections in the line are due to slight misalignment of the setup).

Tables (1)

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Table 1 System Features and Resolution a

Equations (6)

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α = r 1 f PSL , β = r 2 f MLA .
θ T = α + β ,
OPD T = 2 δ 1 + δ 2 = ( 2 α + β ) d .
O P D n λ , n = 0 , ± 1 , ± 2 .
r 1 = ( θ T n λ d ) f PSL , r 2 = ( θ T + r 1 f PSL ) f MLA .
N R = 2 θ max D K λ = D K f # MLA λ ,

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