Deterministic microlens diffuser for Lambertian scatter

Transcription

1 Deterministic microlens diffuser for Lambertian scatter Tasso R. M. Sales, Donald J. Schertler, and Stephen Chakmakjian RPC Photonics, Inc. 330 Clay Road, Rochester, New York Phone: Fax: /30/2006 1

2 Topics Lambertian diffusers Engineered diffusers Single-surface solution Dual-surface solution Summary 8/30/2006 2

3 Lambertian diffusers Cosine intensity pattern Used for calibration purposes Most common example: opal glass Opal glass has low transmission efficiency, ~20% There is no other known diffuser technology capable of implementing the cosθ scatter, typical of Lambertian diffusers θ I(θ) ~ cosθ 8/30/2006 3

4 Engineered Diffusers Refractive, microlens-based diffuser Achromatic Each scatter center individually designed and fabricated Microlens specification and spatial distribution randomized to eliminate repetitive patterns and interference effects in the scatter Control of scatter distribution and intensity profiles Robust to fabrication errors 8/30/2006 4

5 Engineered Diffusers - Examples Holographic diffuser Engineered Diffuser Uniform bandlimited scatter *Laser light, 633nm 8/30/2006 5

6 Engineered Diffusers - Examples.I u4247-s1-a1d NOA61 Rectangle Vert 632, (+/- 12.1), (+/- 15.9) Square pattern 8/30/2006 6

7 Engineered Diffusers - Examples.II Circular pattern 8/30/2006 7

8 Control of Intensity Profiles and energy distribution Square Aztec pyramid Annulus 10 5 Rectangle Narrow rectangle 0-5 Line /30/ Measured 2D Profiles

9 Measured opal-glass scatter Measured efficiency ~20% Cosine Opal glass 8/30/2006 9

10 Lambertian Scatter with Engineered Diffusers θ Single-surface solution Dual-surface solution 8/30/

11 Single-surface solution Lens sag: s () r = R + R 2 r 2 ( κ + 1) r 2 θ I(θ) Basic design process: Select microlenses with R and κ such that scatter is flat with angle θ Angular spread of each microlens is ±θ 0 Probability distribution of θ 0 is such that total scatter adds up to desired cosine scatter 8/30/

12 Solutions with flat scatter For small θ 0 there is always a flat scatter solution with κ -1 R = 18.9mm, κ = -1, D = 100µm As θ 0 increases the optimum κ is in the range of -0.6 to -1 R = 27.1mm, κ = -0.83, D = 100µm 8/30/

13 Histogram of slopes for single-surface solution Single-surface solution requires strong slopes to produce Lambertian scatter *Ensemble of 200 lenses 8/30/

14 Fabrication of Engineered Diffusers Resist-coated wafer Modulated intensity Beam scans surface Single-point laserwriting SEM of a single micro-lens Finite-size Gaussian beam 50 microns Development yields resist master Cross section of photoresist master 8/30/

15 Dual-surface solution Difficult to produce slope angles needed for the single-surface solution Bypass requirement of strong slope angles demanded by single-surface solution with two weaker diffusers Utilize two identical diffusers with small air gap No need for alignment 8/30/

16 Dual-surface solution: Presented at the SPIE 2006 Annual Meeting Single diffuser scatter Assume scatter from each diffuser takes the form: I ( θ ) p π θ cos, θ θ0 = 2 θ0 0, otherwise Assume total scatter given by convolution of scatter from individual diffusers: I 90 ( θ ) = I ( φ) I ( θ φ) dφ Select θ 0 to maximize efficiency Calculated deviation from cosine scatter for θ 0 = 60º as a function of power p 8/30/

17 Optimum single-surface solution I ( θ ) p π θ cos, θ θ0 = 2 θ0 0, otherwise θ 0 = 60º and p = 0.6 Simple convolution model not correct for oblique wideangle scatter Optimum parameters determined experimentally 8/30/

18 Lambertian Scatter with Engineered Diffusers : Dual-surface Solution Measured efficiency ~70% 8/30/

19 Summary g Engineered Diffusers implement arbitrary intensity profiles and energy distribution g Single-surface Engineered Diffuser solution exists but difficult to produce currently g Proposed dual-surface Engineered Diffuser solution two identical diffusers g Each diffuser component has a bandlimited cosine-power scatter shape g Fabricated dual-diffuser solution has efficiency of about 70% (~ 3 times the measured efficiency of opal glass) 8/30/