Shadow Imaging of Geosynchronous Satellites

Transcription

1 Shadow Imaging of Geosynchronous Satellites AFOSR Workshop, Maui Dennis Douglas Bobby Hunt David Sheppard Integrity Applications Incorporated Sept 17 th, 2016 United States Air Force Office of Scientific Research (AFOSR) Grant FA C-0035 Dr. Stacie Williams

2 Outline Top Level Basic Research Objectives Part I: Overview of Shadow Imaging Part II: Basic Research Objectives and Progress Part II-a: Shadow Science and Simulation Part II-b: Shadow Image Processing Part II-c: Shadow Prediction Part III: Summary and Path Forward

3 Part I Overview of Shadow Imaging

4 Motivation and Significance Space Situational Awareness Based Resolved imaging of LEO satellites is routinely performed LEO satellite orbits at range of 160 km to 2000 km Ground based telescopes 1 m aperture using AO/MFBD/speckle imaging techniques Resolved imaging of GEO satellites is not practical using conventional imaging techniques GEO satellite orbits at range of ~ 36,000 km from Earth surface at the equator Ground based telescopes can detect solar illuminated GEO satellites but lack resolved imaging capability due to the extended range Brief history of shadow observations from stellar occultations Shadow observations are routinely performed by the professional and amateur astronomical community (Kuiper belt objects, asteroids, exoplanet detection) 1D The extension of shadow imaging to GEO satellites has been examined only to a limited degree and has not been demonstrated to date Only two published papers exist prior to 2014 that specifically address shadow imaging as a means of obtaining resolved images of GEO satellites (Burns, et al 2005 & Luu, et al 2008)

5 Classical Spatial Resolution Limits At GEO Distance of 36,000 km AEOS / Starfire Keck TMT

6 2D GEO Shadow Observation

7 Far Field Near Field GEO Shadows are Typically in the Fresnel Region and Traverse the Earth at High Velocities GEO distance bound by solid and dashed lines N f = a2 λz

8 Part II-a Shadow Science and Simulation Development

9 Simulation Step 1 True Ground Irradiance Spectral Binning

10 Simulation Step 2 Measurement Inferred Ground Irradiance

11 Baseline Simulation Parameters

12 Satellite Model and Varied Parameters for Simulation Cases

13 Ground Irradiance Map Zoomed View: 100x100 m 28x28 m W/m 2 W/m 2 28 m 28 m 28 m 28 m

14 Signal to Noise Ratio Profile through Center Row

15 Part II-b Shadow Image Reconstruction

16 Reconstruction Step 1 Multi Step Fresnel Integral version of Gerchberg Saxton Phase Retrieval Algorithm Multi-Step Fresnel Multi-Step Inverse Fresnel

17 Reconstruction Step 2 Sum Wavelength Block Reconstructions

18 Reconstructed Images All Simulation Cases: Zoomed to 28x28 m High SNR (mv=8, D=0.4m) Low SNR (mv=11, D=0.4m) High SNR (mv=8, D=0.8m)

19 Enlarged Display of Sim Cases 3A and 3B With and Without Star Phase Compensation

20 Resolution Limits For Each Simulation Case 0.4 m Apertures 0.8 m Apertures

21 Part II-c Shadow Prediction Macroscopic Density Maps & Localized Shadow Tracks

22 Shadow Prediction Process Proper Motion of Stars and Satellite Positions Known Step 1 Earth Spheroid Intersection Calculation Step 2 Refraction Calculation Step 3 Displacement Calculation Step 4 Site Location Calculation Step 1 Step 2 Step 3 Step 4 No Atmosphere Vector from occulted star to satellite normalized to unit length Pucinelli algorithm provides intersection with the spheroid directly WGS-84 Earth model Compute height of reduced atmosphere Compute index of refraction of air (P, T, λ) Compute refraction at the upper atmosphere boundary using Cassini s equation This is an exact geometric solution Vallado sensor boresight calculations are used (11.3) Solving for Range Angle Λ max Λ min Spherical earth assumption reasonable for very small displacements Computations are localized with site distance from center of earth Angular displacement converted to distance on the earth surface Displacement is in the azimuth direction to the satellite from the observer Latitude and longitude are computed of new site are computed

23 Macroscopic Shadow Density Map Night of Jan 19 th, 2016: Shadow Tracks for Single GEO Satellite = Galaxy3C Elevation Look Angle >= 15 o Stellar Visual Magnitude Range m v = [2,8] This is a 2-D histogram with bin sizes 1 X 1 degrees Lat/Lon. Each bin count has been normalized by the area of its quadrangle on the earth ellipsoid. This is for one 24-hour period.

24 Macroscopic Shadow Density Map Night of Jan 19 th, 2016: Shadow Tracks for Single GEO Satellite = Galaxy3C Elevation Look Angle >= 15 o Stellar Visual Magnitude Range m v = [2,10] This is a 2-D histogram with bin sizes 1 X 1 degrees Lat/Lon. Each bin count has been normalized by the area of its quadrangle on the earth ellipsoid. This is for one 24-hour period.

25 Total Night Occultations Vs. Time Lots of Shadows in a Single Night for GEO Satellite Galaxy 3C Night of Jan 19 th, 2016 Night Day Night Visual Magnitude The horizontal axis spans a 24-hour period with 0.5 second time steps. Includes a minimum observer elevation look angle of 15 degrees. Lots of Shadows from Single GEO Satellite

26 Localized Nominal Shadow Tracks Assumes no Astrometric Uncertainties Shadow tracks over 2 x 2 km area in Kihei, HI for the of night of Jan. 19th, 2016 from GEO satellite YAMAL 300K Red dots are computed shadow locations at a 0.1 s time step. The blue lines are interpolated Imagery is from the USGS Orthographic 1-foot database The viewing elevation angle is limited to be greater than 15 degrees Star magnitudes from [2,10] considered 25 shadow GEO satellite tracks in this scenario

27 Astrometric Errors Influence on Ground Shadow Track Uncertainty Two shadow tracks from upper right of previous slide Monte Carlo of each shadow ground track position using 100 trials Lower track uses a stellar position uncertainty of 9 mas, yielding a shadow track uncertainty of =2 m Upper track uses a stellar position uncertainty of 110 mas, yielding a shadow track uncertainty of =24 m

28 GEO Occultation Events over a Year Temporal Morphology Attributed to View Angle with Respect to Galactic Plane Orientation GEO Satellite Galaxy 3C x-axis: 1 sec time steps Animation in 10 days steps Star mags [2,8] Elevation angle >15 deg

29 Part III Summary and Path Forward

30 Summary and Future Research Shadow Simulation Supports diverse observing scenarios Implement deep turbulence models Implement additional detector technology (RULLI, LANL N-Cam, standard types) Optimize collection parameters based on observing scenario Shadow Image Processing Fresnel integral version of G-S algorithm Sub meter resolution readily attainable given sufficient SNR Poisson Maximum Likelihood Estimation (PMLE) for optimal reconstruction Shadow prediction Global shadow density maps Localized shadow track prediction Extend to multiple satellites (density maps and localized track views) Implement soon to be released Gaia star catalog (less astrometric error for stars) Further quantify collection opportunity versus system mobility Capture GEO satellite shadow using single aperture Thank You: United States Air Force Office of Scientific Research (AFOSR) grant FA C-0035 Dr. Stacie Williams

31 Backup Slides

32 Satellite Plane Propagation Planes and Distances Satellite to Top of Atmosphere Vacuum Top of Atmosphere to Ground 10 Phase Screens Applied

33 Developments in Previously Published work on GEO Satellite Shadow Imaging Burns, et al. Sizes of GEO satellites and distance are consistent with Fresnel region diffraction pattern on Earth using visible wavelengths Gerchberg-Saxton phase retrieval algorithm can be used to reconstruct the satellite image from diffraction pattern Probability of a GEO satellite shadow crossing a linear array of collection apertures is significantly increased if the collection system is placed on a mobile platform that moves along the north/south direction Luu, et al. Spectrally resolved shadow imaging introduced to increase spatial resolution Wavelength binning instead of single wide band collection Each bin reconstructed independently then stacked for final image Shadow imaging shown to be very resilient to atmospheric turbulence

34 Exposure Time Determined by Transit Time over Single Collection Aperture Collected Light is Binned into Spectral Blocks Given total spectral range: a b Single binned spectral block width: K Number of Spectral Blocks: J = ( b - a) / K Single Spectral Block: j Λ 1 Det 1 Single Collection Aperture Λ 2 Det 2 Λ 3 Det 3 Λ J Det J

35 Development of End-to-End Shadow Imaging Simulation Capability Source Star Attributes Brightness Angular extent GEO Satellite Geometry Symmetry and feature sizes Environmental Parameters Atmospheric attenuation/refraction/dispersion/turbulence Light Collection Parameters Diameter of each individual collection aperture Spatial sampling of shadow collection Spectral binning associated with each collection aperture GM-APD Measurement Parameters Photon detection efficiency Noise: dark count rate and afterpulsing Timing errors in synchronization An end-to-end simulation was constructed to quantify the impact of each of these factors using a rigorous treatment of the GM-APD measurement process

36 Sampling in Propagation Planes Fixed Grid Spacing Sampling criteria using Fresnel transfer propagation kernel

37 Equatorial Coordinates for Tycho-2 Stars Right Ascension and Declination

38 Density of Stars in the Sky Equatorial and Galactic Coordinate Systems

39 Brightness of Tycho-2 Stars V Magnitude

40 Angular Extent of Largest Stars in the Sky Vast majority of stars

41 Fresnel Impulse Response Function Fresnel Transfer Function used as Light Propagation Kernel Fresnel Transfer Function (Angular Spectrum) Equivalent Analytic Implementations Transfer Function Method used in Numerical Propagation Propagation of polychromatic light

42 Spectral Irradiance of Vega used as Radiometric Basis Data from Space Telescope Science Institute AB magnitude of Vega Spectral irradiance at satellite Electric field amplitude at satellite

43 Angular Extent of Star Applied as Phase Term Continuum of Tilted Plane Waves Tilt Term Star Phase at Satellite Radial Integral of Tilt Term Complex Electric Field at Satellite

44 MODTRAN used for Nominal Atmospheric Transmission Scaled by Airmass per Off Zenith Pointing (approximation) Airmass Scaled atm. transmission

45 Atmospheric Refraction 500 nm Light

46 Atmospheric Dispersion Centered at 500 nm Light

47 Atmospheric Refractive Index Structure Constant versus Altitude Hufnagel-Valley 5/7 Profile

48 Atmospheric Turbulence Applied to Electric Field as Phase Term Atm. coherence length (Fried parameter) Spatial frequency PSD Phase from single atm. layer Phase applied to electric field

49 Notation used to Define Propagation Planes

50 Avalanche Photo Diode Basics Linear and Geiger Modes: Photon Counting Device GM-APD measurement process is inherently different from a CCD or CMOS detector APD: Reverse bias PN junction with strong electric field Photo generated electrons gain sufficient kinetic energy to free other electron through collisions (avalanche effect) Breakdown voltage: balance of electron creation and loss through current Linear mode (LM) operates below the breakdown voltage current is linear with incident light flux GM-APD: Operates above the breakdown voltage electron population grows exponentially (avalanche) Binary operation (avalanche or no avalanche within gate time) Avalanche probability over many samples calculated and used to estimate flux

51 Overview of GM-APD Parameters Dead Time (t d ): Time it takes the GM-APD to be quenched after an avalanche and then returned to nominal geiger mode Gate Time (t g ): Time in which the device is in the nominal steady state and capable of detecting an avalanche event Number of Gates (n g ): Number of measurement windows within the total exposure time Exposure Time (t): The exposure time is the duration of the device measurement and consists of multiple discrete units of t g + t d Photon Detection Efficiency (P d ): Combines the quantum efficiency (QE) and spatially dependent detection efficiency on the active area of the GM- APD pixel Dark Count Rate (N D ): Number of excited electrons that trigger an avalanches without a photon being absorbed Afterpulsing (P ap ): : Probability of the release of a previously "trapped" electron that causes an avalanche within a single gate time

52 Signal to Noise Ratio for GM-APD Actively Quenched Gated Mode Operation Signal photons per gate Background photons per gate Signal photon rate Dark noise detections per gate Effective photons per gate Sky background photon rate

53 Numerical Simulation of GM-APD Measurement Process with No Afterpulsing Probability that single gate has n p photons given by Poisson distribution: Bernoulli trial determines if the i th gate records an avalanche (each gate is independent) Random number generated from binomial distribution Number of recorded avalanches over exposure time Inferred photon fluence Binary measurement of avalanche occurrence within each gate Inferred photon fluence

54 Photon Fluence to GM-APD Pixel Source Star Magnitude and Collection Aperture Diameter Fluence # photons/pixel/s

55 Impact on SNR based on GM-APD Parameters and Photon Fluence

56 Two GM-APD Detector Baselines A = Current Capability, B = Near Future Capability

57 SNR versus Photon Fluence Using Baseline GM-APD Detectors

58 SNR versus Photon Fluence Low Fluence Region with Ideal Detector Comparison

59 Simulation Group 6 Large Angular Extent of Source Star Applied

60 Timing Error Modeled as Displacement in Collection Aperture Position

61 Example of Image Reconstruction based on Number of Wavelength Blocks

62 Aperture Size Impacts Fidelity of Collected Diffraction Pattern Self Normalized Collected Irradiance Shown Satellite Transmission Function Intensity ripples lost as collection aperture size increases

63 Conclusion Set I Shadow Imaging Resolution Limits using a Bright Source Star Sub Meter Resolution Readily Achieved using Small Apertures Very large telescope diameter required to achieve similar capability

64 Conclusion Set II Shadow imaging is shown to be insensitive to satellite shape and geometry Modest atmospheric turbulence is confirmed to have very little impact on shadow imaging performance Timing errors on the order of have small impact on shadow imaging performance. When the timing error reaches a value of resolution is limited to D a A source star with an angular extent of 10 nrad is shown to negatively impact shadow imaging resolution. At 20 nrad the image quality is significantly degraded.

65 Conclusion Set IV SNR Thresholds Single wavelength block SNR < 1 is shown to yield low contrast 1 meter resolvable features Based on results from Simulation Group 8 Reconstructed image corresponds to red SNR line on left plot

66 Conclusion Set V Source Star Brightness Resolvable features of 1 meter readily attained for a source star brightness down to m v = 10. Limit of 1 meter feature size resolvability near m v = 11 Based on results from Simulation Group 8 Resolvable Spatial Feature Size Approximately 873,000 potential source stars with m v 11 Approximately 1,400,000 potential source stars with m v 11.5