1. Optical Vortex Coherence Filter Lt Col Gregory Foo, USAF (Ret) Grover A. Swartzlander, Jr. Optical Sciences Center University of Arizona Tucson, AZ 85721 David Palacios JPL Support US Army Research Office (ARO)

2. Overview Research Objectives Definitions Math Model Experiments Results Applications

3. Research Objectives Assess optical vortex coherent filtering –Is it feasible? –Effects on imaging –Alternative interference filter?

4. Definitions Coherent Light - Uniform phase (e.g. laser) Incoherent Light - Random phase (sunlight) Optical Vortex (OV)- Phase singularity/ defect –Undefined Phase –Zero Amplitude –Localized Destructive Interference Optical Vortex Phase Mask –Transmissive Corkscrew –Forms an OV

5. OV Math Model Helical Wavefront m = 3 E(r, ,z)  A(r,z)exp[ im´( )  exp[  ikz] A(r,z)- Amplitude m´( )  Topological Charge  Phase k  2   kTkT k

6. Mutual Coherence  (r 1, r 2,  ) =  (r 1, t +  )  * (r 2, t )  –(Coherent) 1 >  > 0 (Incoherent) y r1r1 r2r2 x

7.  d= [(m  )/2  (n 0 - 1)], 0    2  ∆d OV Phase Mask Continuous Discrete

8. Laser Filtering Object Lens Beam Splitter Image Phase Mask Laser CCD Camera Z X 330 cm33 cm 0.4 cm ∆z

9. Laser Filtering Mixed CoherenceOV Filtering Low Coherence

10. LASER VORTEX ARRAY DETECTOR VORTEX ELEMENT Sensor Protection

11. OV Point Spread Function High CoherenceLow Coherence Pixel

12. OV Coronagraph ksks kpkp  Vortex Mask x fofo z D

13. OV Coronagraph Calculated Pinhole Star

14. White Light OV Propagation 1 < z < 400 waves

15. Broadband Filtering 6.11>m´>4.15  P/P = 6.7 (10 -4 ) 2.03>m´>1.38  P/P = 3.2(10 -2 )

16. OV Core Properties ~ Point size in the focal plane Core/Beam increases with z Core/beam nearly constant for large z. Phase mask displacement controls size Approaches size of Airy disk Darkness increases with spatial coherence Nulls spatially coherent light

17. OV Applications Sensor Protection Exoplanet Detection Image Processing Optical Communication Optical Tweezers

18. Fourier Propagation exp (im´  )

19. C n Dependence on m

20. OV Propagation Point Source m = 1 0200 waves 1.53 > m´ > 1.34