Air Force Research Laboratory Integrity  Service  Excellence Peter N. Crabtree and Patrick J. McNicholl Air Force Research Laboratory 19 Nov 2014 Summary of ICI Analysis Results and Fundamental Resolution Limits for Shadow Imaging

2 Outline Quick review of analysis of intensity interferometry applied to GEO imaging Occultation measurements Long history of astronomical applications More recently considered for sensing manmade objects in GEO (Burns, et al. 2005; and Luu, et al., 2008) Problem formulation & notation Simplify to the tractable 1D knife edge (KE) case Estimate KE location given photon-limited Fresnel diffraction pattern Results for knife edge problem Summary and conclusions

3 Summary of Results from Analysis of Intensity Interferometry or Intensity Correlation Interferometry (ICI)

4 Narrow band hyper-spectral II (HICI) 1 1. HICI concept independently proposed by D. Thompson (LANL) and P. Dao (AFRL). HICI nomenclature due to D. Thompson. HICI optimized SNR analysis including incoherent spread effects by P. McNicholl (AFRL, unpublished).

5 Multi-aperture full spectrum HICI SNR model 1 1. HICI concept independently proposed by D. Thompson (LANL) and P.Dao (AFRL). HICI nomenclature due to D. Thompson. HICI optimized SNR analysis including incoherent spread effects by P. McNicholl (AFRL, unpublished).

6 Highly Optimistic Numerical Estimates/Simulations Conditions Assumed GOES-12: visual magnitude ~ 12 (typical of GEO satellites 4 ) 40.5 cm (~ 16”) apertures, f/10 optics, 50% optical efficiency constant QE = 20% from 400 to 700 nm (alternate: S20) no detector dark counts or sky background noise cross strip (2nd gen) RULLI (  x R ~ 5  m) high dispersive power limit: plate factor ( p )  0 100% fill factor: 40.5 cm sensor spacing N ap = 65 2 = 4225 (alternate: 15 2 = 225) sea level, zenith viewing (MODTRAN), 1 arcsecond seeing benchmark HICI SNR 0 = m Pristine

7 Phase retrieval images from SNR model and simulated HICI data 0.1  rad/3.8 m FWHM PSF Pristine GOES 12 Simulated conventional large aperture with AO 0.2  rad/7.6 m FWHM PSF Resolution quoted for Keck HIO w/data pre-filtering (Wiener-like, width  10) N ap = (65) 2 = 4225 Mat. Cost Scale ~ $1G T ~ 1,015 hrs (QE=0.2) T ~ 6,183 hrs (S20) Simulated hyperspectral intensity correlation interferometry N ap = (15) 2 = 225 Mat. Cost Scale ~ $50M T ~ 19,052 hrs (QE=0.2) T ~ 116,097 hrs (S20) SNR(0) = 10

8 Fundamental Resolution Limits for Stellar Occultation Applied to GEO Objects

Occultation of Chariklo 2 (A Centaur minor planet between Saturn and Uranus) 2. F. Braga-Ribas, et al., “A ring system detected around the Centaur (10199) Chariklo,” Nature 508, 72–75 (03 April 2014).

10 Adaptation of stellar occultation technique to GEO object silhouette imaging 3,4 aperture array Entrance pupil(s) imaged onto a photon counting imager Geometric RSO Silhouette Fresnel Diffracted Ground Shadow corrected zonal photo- electron (PE) position 3. R. H. Burns, et al., “Shadow imaging of GEO satellites,” Proc. SPIE 5896, Unconventional Imaging, 58960C (2005). 4. J. Luu, L. Jiang, and B. Willard, “Shadow imaging efforts at MIT Lincoln Laboratory,” Advanced Maui Optical and Space Surveillance Technologies Conference (2008).

11 Lack of rigorous treatment of shot noise and advantage of wavelength resolving sensors Generated Photo-Electron (PE) Images Assume: GEO occultation of star with solar-like spectrum observed at zenith from sea level Continuous meridional linear array (  40 m) with 0.5 m zonal width No background, dark counts, scintillation, finite star size, …. 30% QE, 10 nm passband at 550 nm center Otherwise idealized photo-electron imaging/timing detector technology

12 Notation stellar spectral irradiance, e.g., (PE/sec/FLU 2 /nm) zonal width/velocity factor, e.g., (sec) effective spectral flux, e.g., (PE/FLU 2 /nm)

13 Notation

14 Poisson Point Process

15 Cramér-Rao Bound for a PPP

16 Hammersley-Chapman-Robins Bound for a PPP 5 5. P. J. McNicholl and P. N. Crabtree, “Statistical bounds and maximum likelihood performance for shot noise limited knife- edge modeled stellar occultation,” Proc. SPIE 9227, Unconventional Imaging and Wavefront Sensing, (2014).

17 Simplify to the Knife Edge Case 1D flux, e.g., (PE/FLU)KE position

18 KE without Diffraction

19 Geosynchronous Object Scaling Example of Knife Edge Results

20 Geosynchronous Object Scaling Example of Knife Edge Results 5 5. P. J. McNicholl and P. N. Crabtree, “Statistical bounds and maximum likelihood performance for shot noise limited knife- edge modeled stellar occultation,” Proc. SPIE 9227, Unconventional Imaging and Wavefront Sensing, (2014).

21 Conclusions

22 Questions?

23 Supplementary material

24 Hanbury Brown and Twiss (HBT) effect

25 Narrow band II SNR due to signal shot noise

26 KE Monochromatic Case

27 Data Window Size and Bandwidth Effects on CR Bound

28 Single Band KE Results vs. Flux

29 Single Band KE Results vs. Spectral Flux

30 N-tuple Band Sensor

31 Single Band vs. Continuously Resolved Spectral Sensor

32 Geosynchronous Object Scaling Example of Knife Edge Results

33 Timeliness