## Design and optimization of microlens array based high resolution beam steering system

Optics Express, Vol. 15, Issue 8, pp. 4523-4529 (2007)

http://dx.doi.org/10.1364/OE.15.004523

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### Abstract

High-resolution imaging and beam steering using 3 microlens arrays (MLA) is demonstrated. Small lateral displacement of one microlens array is sufficient for large angle beam steering. A prescan lens is added to the system to overcome the discrete addressing problem associated with microlens scanning systems. A hybrid method that uses both geometrical ray tracing optimization and physical optics simulation is introduced for the design and optimization of the MLA system. Feasibility of 1880×1880 resolution using *f*/2 aspherical MLAs and 752×752 resolution using *f*/5 spherical MLAs are demonstrated assuming 100μm microlens pitch and 2mm clear aperture. The system is compact and suitable for endoscopic imaging and agile steering of large beams.

© 2007 Optical Society of America

## 1. Introduction

*f*/2 aspherical MLAs. Major contribution of this paper is in the demonstration of diffraction-limited 2-point resolution performance using

*f*/2 lenses and beam steering angles as large as +/-0.25rad. Such high-resolution can be achieved using small arrays and small deflections, thus, high-speed beam steering is possible. While the paper is focused on angular beam steering, high resolution imaging can be accomplished by simply adding a large field-of-view focusing lens after the afocal telescopic system.

*f*/2 and

*f*/5 aspherical and

*f*/5 spherical MLAs are reported. The results are compared with the experimental system utilizing

*f*/5 spherical MLAs in Section 5.

## 2. System analysis

2. A. Akatay, C. Ataman, and H. Urey, “High-resolution beam steering using microlens arrays,” Opt. Lett. **31**, 2861–2863 (2006). [CrossRef] [PubMed]

*d*is the MLA pitch,

*D*is the clear aperture size,

*α(x)*is the phase appearing on each microlens channel and equal to the sum of the wavefront aberration,

*ϕ(x)*, and a linear tilt term due to the MMLA displacement.

*D*is equal to

*N.d*, where

*N*is the array size in one dimension.

*A(x)*is the amplitude distribution function across each MLA, and

*a*≤

*d*is the beamlet diameter at the output of each MLA channel as defined in Fig. 1. The field distribution at the image plane -the point spread function (PSF), is obtained by the Fourier transform of the

*t(x)*:

*I*

_{1}) and a train of narrow sinc functions (

*I*

_{2}), as shown in Fig. 2. If there are no aberrations (i.e.

*ϕ*(

*x*)=0), and the irradiance distribution across each microlens is uniform (i.e.,

*a*=

*d*and

*A(x)*= 1), the Fourier transform simplifies to sinc[(

*d*/

*λ*)sin

*θ*], and the zeros of

*I*

_{1}overlaps with the higher order diffraction peaks of

*I*

_{2}and would yield irradiance zeros at those points. In case of aberrations and/or non-uniform irradiance distribution across each microlens of MLA3, the envelope Sinc function denoted by

*I*

_{1}widens and higher order diffraction peaks of

*I*

_{2}appears in the PSF, as illustrated in Fig. 2. When the system has small amount of aberrations, almost all of the optical energy is distributed inside the main lobe of

*I*

_{1}(e.g., within the 0

^{th}and +/-1

^{st}order diffraction lobes of

*I*

_{2}) and the energy outside the main lobe is negligible. In general,

*A(x)*can be assumed uniform and the aberrations can be calculated as wavefront deviation from a reference wavefront.

^{th}order Sinc function in

*I*

_{2}, which can be taken as

*λ*/

*D*. It is interesting to note that as long a s the aberration function is periodic, the 0

^{th}order diffraction spot size, thus the angular resolution of the system, remain the same independent of the aberrations and the microlens fill-factor. The width of a single diffraction order always remain proportional to

*λ*/

*D*, thus remain diffraction limited. However, distribution of energy to different diffraction orders is affected by the aberrations, reducing the contrast of the imaging system, but not the two-point resolution. This is a unique property and important advantage of MLA scanning systems compared to scanning with mirrors or spatial phase modulators [4, 5

5. J. Sun, L. Liu, Y. Maojin, and W. Lingyu, “Study of the transmitter antenna gain for intersatellite laser communications” Opt. Eng. **45**, 58001–58006 (2006). [CrossRef]

## 3. Optical performance metrics for analysis and optimization

*peak-to-sidelobe ratio*, which can be defined as the ratio of the peak intensities of the mainlobe and the sidelobe of the PSF. Similarly, the Strehl ratio (

*V*) which is defined as the ratio of the PSF peak intensity of the aberrated system to that of an unaberrated diffraction-limited system, can be used as a measure for evaluation of the optical energy in the central lobe compare to the energy in the spurious sidelobes. The Strehl ratio of the system can be determined from the area integral of the phase function for the aberrated and the unaberrated cases, which correspond to the ratio of the Fourier transforms evaluated at the zero frequency. If the system is slightly aberrated (

*V*>0.5),

*V*can be expressed as

*V*= 1-(2

*π*σ)

^{2}, [6], where σ is the RMS wavefront error and can be obtained from ray tracing optical design tools such as Zemax™. [7]

## 4. Simulation and optimization of the system

*ϕ(x)*. In case of uniform illumination and where MLAs are identical, the simulation and optimization of the whole system can be reduced to the analysis of a single channel of microlenses. Replication of the single channel wavefront error across the array gives

*ϕ(x)*. In the final step, the wavefront after the MLAs can be constructed using

*ϕ(x)*and propagated to the far-field by a 2D Fourier transformation and scaling. The simulation of the system is illustrated in Fig. 3. The plane wave propagation between the DMLA and the imaging lens is skipped since an optimized imaging lens is assumed.

*d*and ±0.425

*d*and constrained to produce the desired beam steering angles subjected to lens curvature and thickness constraints.

*f*-numbers (

*f*

_{#}) of 2 and 5. Since the wafer thickness can be larger than the focal length for the fast

*f*

_{#}systems, the MMLA curved surface faces the DMLA, even though aberration performance would be better otherwise. Figure 4 shows the optimized wavefront aberration plots in x/y directions across the microlens aperture obtained for various lens profiles for the maximum scan angle case, which is the worst case for this system, i.e. on-axis aberrations are negligible. All cases, except the one using spherical

*f*/2 microlenses produce diffraction limited performance and high Strehl ratio.

*f*/2 aspherical/spherical lenses are shown for two scan positions. Note that the main lobe widths are the same, while the energy shifted to diffraction rings are different, proving that the aberrations do not reduce the two-point resolution of the system but reduce the contrast at low spatial frequencies.

*θ*=

_{d}*λ*/

*d*). Spatial cut-off frequency of the system is equal to

*N*/2 cycles/

*θ*, which corresponds to a resolution of

_{d}*N*pixels in a diffraction-order separation. [9

9. H. Urey, N. Nestorovic, B. Ng, and A. Gross, “Optics Designs and System MTF for Laser Scanning Displays,” Proc. SPIE **3689**, 238–248 (1999). [CrossRef]

*f*/2-spherical configuration, the system performs nearly diffraction limited.

*N*), by the number of diffraction orders (NDO) across the scan line, which is equal to 2

*dθ*/

_{max}*λ*. The result gives the diffraction limited resolution i.e. 2

*Ndθ*/

_{max}*λ*. For

*f*/2 and

*f*/5 systems, the maximum beam steering angles are 0.25 rad and 0.1 rad. If

*λ*=0.532 μm and

*N.d*=

*D*=2mm are assumed, a 2D resolution of 1880×1880 for

*f*/2 aspherical MLAs and 752×752 for

*f*/5 spherical MLAs can be obtained.

## 5. Experimental system

*f*/5 MLAs. The MLAs are illuminated by a beam of size slightly bigger than 600 μm (i.e. 3×3 array), whereas in the simulated system N was 4. The MTF of the experimental system is calculated from the PSF data with a Fourier transformation and scaling [3].

*f*/5 spherical system where focal lengths and distances of MLAs are optimized, the performance observed in the experiment is worse, due to both alignment errors and MLAs being constrained to be identical. Full scan line captures are obtained from the experimental setup, with a long exposure time while the MLAs move. Figure 7(a) shows the discrete spots on the scan line captured while only the MMLA is scanned and Fig.7 (b) shows the full scan line captured while both the MMLA and PSL is scanned concurrently such that the phase condition defined in Ref. [2

2. A. Akatay, C. Ataman, and H. Urey, “High-resolution beam steering using microlens arrays,” Opt. Lett. **31**, 2861–2863 (2006). [CrossRef] [PubMed]

## 6. Conclusion

*f*/2 aspherical MLAs and 752×752 resolution using

*f*/5 spherical MLAs are simulated. Experimental demonstration is successful using

*f*/5 spherical MLAs and 600μm clear aperture. The system is suitable for endoscopic laser camera and agile beam steering applications.

## References and links

1. | J. Duparré, D. Radtke, and P. Dannberg, “Implementation of Field Lens Arrays in Beam-Deflecting Microlens Array Telescopes” Appl. Opt. |

2. | A. Akatay, C. Ataman, and H. Urey, “High-resolution beam steering using microlens arrays,” Opt. Lett. |

3. | J. W. Goodman, |

4. | H. Urey, “Retinal Scanning Displays,” in |

5. | J. Sun, L. Liu, Y. Maojin, and W. Lingyu, “Study of the transmitter antenna gain for intersatellite laser communications” Opt. Eng. |

6. | M. Born and E. Wolf, |

7. | Software for Optical Design; Zemax Development Corporation (2006). |

8. | N. Lindlein, “Simulation of micro-optical systems including microlens arrays,” J. Opt. A: Pure Appl. Opt. 4 , |

9. | H. Urey, N. Nestorovic, B. Ng, and A. Gross, “Optics Designs and System MTF for Laser Scanning Displays,” Proc. SPIE |

10. | N. F. Borrelli, |

11. | A. Akatay, A. Waddie, H. Suyal, M. Taghizadeh, and H. Urey “Comparative performance analysis of 100% fill-factor microlens arrays fabricated by various methods,” Proc. SPIE |

**OCIS Codes**

(050.0050) Diffraction and gratings : Diffraction and gratings

(080.2740) Geometric optics : Geometric optical design

(120.5800) Instrumentation, measurement, and metrology : Scanners

(170.3890) Medical optics and biotechnology : Medical optics instrumentation

(220.4830) Optical design and fabrication : Systems design

(350.3950) Other areas of optics : Micro-optics

**ToC Category:**

Optical Design and Fabrication

**History**

Original Manuscript: January 26, 2007

Revised Manuscript: March 19, 2007

Manuscript Accepted: March 20, 2007

Published: April 3, 2007

**Virtual Issues**

Vol. 2, Iss. 5 *Virtual Journal for Biomedical Optics*

**Citation**

Ata Akatay and Hakan Urey, "Design and optimization of microlens array based high resolution beam steering system," Opt. Express **15**, 4523-4529 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-8-4523

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### References

- J. Duparré, D. Radtke, and P. Dannberg, "Implementation of Field Lens Arrays in Beam-Deflecting Microlens Array Telescopes" Appl. Opt. 43, 4854-4861 (2004). [CrossRef] [PubMed]
- A. Akatay, C. Ataman, and H. Urey, "High-resolution beam steering using microlens arrays," Opt. Lett. 31, 2861-2863 (2006). [CrossRef] [PubMed]
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
- H. Urey, "Retinal Scanning Displays," in Encyclopedia of Optical Engineering, R. Driggers, ed., (Marcel Dekker, 2003), pp. 2445-2457.
- J. Sun, L. Liu, Y. Maojin, and W. Lingyu, "Study of the transmitter antenna gain for intersatellite laser communications" Opt. Eng. 45, 58001- 58006 (2006). [CrossRef]
- M. Born and E. Wolf, Principles of Optics, seventh ed., (Cambridge University Press, 2002)
- Software for Optical Design; Zemax Development Corporation (2006).
- N. Lindlein, "Simulation of micro-optical systems including microlens arrays," J. Opt. A: Pure Appl. Opt. 4, 1-9 (2002).
- H. Urey, N. Nestorovic, B. Ng, and A. Gross, "Optics Designs and System MTF for Laser Scanning Displays," Proc. SPIE 3689, 238-248 (1999). [CrossRef]
- N. F. Borrelli, Microoptics Technology: fabrication and applications of lens arrays and devices, (Marcel Dekker, 1999).
- A. Akatay, A. Waddie, H. Suyal, and M. Taghizadeh, and H. Urey "Comparative performance analysis of 100% fill-factor microlens arrays fabricated by various methods," Proc. SPIE 6185, 1-11 (2006).

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