X-Ray and Gamma-Ray Imaging with Rotating Modulation Collimators

1. X-Ray and Gamma-Ray Imagingwith Rotating Modulation Collimators Gordon Hurford Space Sciences Lab UC Berkeley 30 Nov 2004

2. Outline • Basic collimator principles • Design and performance issues in an astrophysical context • RMC principles and performance • Illustrated by RHESSI • Adaptation to terrestrial applications

3. General Design Issues for Astrophysics • Limited mass, telemetry • Few source photons • Significant background • Need for robust design

4. Spectroscopic Design Issues • Energy range • Background and spectral characteristics • Energy resolution goals • non-critical • continuum spectroscopy Nominal Solar Flare Spectrum • isolate specific lines • line spectroscopy

5. Some Imaging Design Issues • Sensitivity • Angular resolution • Need to resolve sources ? • Need to accurately locate sources ? • Source complexity • Source contrast

6. Typical Detector Options

7. Imaging Technologies at X-ray and Gamma-ray Energies • Focusing optics • Compton Cameras • Coded masks • Modulation collimators

8. Single Pinhole - Camera Obscura • Direct imaging • Angular resolution ~aperture / separation • Needs detector spatial resolution ~aperture • Low effective area ~aperture ^ 2

9. Coded Masks • Coded mask makes a shadow of a point source on detector • Good sensitivity (Eff. area ~50% of frontal area) • Detector spatial resolution ~aperture size • Limits angular resolution to many arcminutes or degrees • Widely used in non-solar astronomy (e.g. Integral, SWIFT) • Can have flat sidelobe response • Less sensitive to extended sources

10. Types of Modulation Collimators • Excluding coarse collimators used only to limit field of view • Modulation collimators • Time modulation – encodes image as time variations in detected photons • Spatial modulation – encodes image as spatial distribution of detected photons • Direct or indirect imaging • Number of grids • Single grid modulator • Bigrid collimator • Multiple grids

11. Spatial Modulation INCIDENT ANGLE • Bigrid collimator has a periodic angular response • Resolution = ½ grid period / grid separation • Field of view = grid diameter / grid separation • Intermediate grids can suppress ‘sidelobes’

12. HXIS / SMM (1980) • Multigrid collimator with 10 aligned grids • 900 subcollimators pointing to adjacent 8 x 8 arcsec pixels • Direct imaging • Very low sensitivity

13. Imaging Collimator (2) n+1 slats n slats • Bigrid collimator with slightly different pitch in front and rear grids • Creates a large-scale Moire pattern whose peak position is very sensitive to incident photon direction • Moire pattern can be measured by a detector with low spatial resolution (determined by collimator size, not grid pitch) • Good sensitivity (25% of collimator area) • Viable option for 3-axis stabilized spacecraft • Variant on this was used successfully by Yohkoh / HXT

14. Time Modulation DIRECTION • Relative motion between source and collimator modulates the detected flux as a function of time • Detector need not have any spatial resolution. • Relatively high sensitivity (effective area ~ ¼ collimator area) • No longer a direct imaging system. • Motion can be random, rocking or rotational.

15. Rotating Modulation Collimators • Typically a bigrid collimator which rotates about an axis pointed near the source of interest • Usually implemented on rotating spacecraft, but balloon-borne mechanically rotated systems have also been developed. • Used in early x-ray astronomy to discover and locate ‘point sources’ with ~degree resolution • Current RMC’s (e.g. RHESSI) can image multicomponent, multiscale sources with 2 arcsecond resolution

16. RMC Schematic • Bigrid collimator rotates about an axis near source • Detected count rates are modulated in time Count rate vs. time

17. RMC Response Reference point source Weaker source Different azimuth Larger radial offset Larger source Extended source Real source

18. RMC Properties • Distance of source from axis of rotation and RMC resolution determine modulation frequency • RMC modulates sources smaller than its resolution • Modulation amplitude can can be used to infer source size • Source structure determines amplitude and phase of modulation. • Detector need not have spatial resolution •  Can be simpler and/or optimized for spectral resolution • Need robust algorithms to reconstruct image from modulated count rates.

19. Back Projection Algorithm • CONCEPT • Calculate a ‘probability map’ of photon’s origin on the Sun for each detected count. • Add probability maps for all photons • Apply a flat fielding correction • RESULT • Map represents a convolution of true map and point response function • PROPERTIES • Relatively fast • Very robust • No a priori assumptions about source geometry • Real sources have significant circular sidelobes. • Can be directly interpreted only in simple situations

20. Single photon 10 deg rotation 90 deg rotation Multiple rotations Grids 3 – 8 Clean

21. Other Reconstruction Algorithms • Clean • Maximum Entropy • PIXONS • Forward Fitting • etc. • Given reasonable assumptions about source geometry, the algorithms ask: • “What source geometry would reproduce the observed modulated count rates?”

22. 3 Perspectives on RMC Imaging • 1. An inversion problem of reconstructing image from the observed modulated light curve • Back projection • CLEAN • Maximum Entropy, PIXONS, Forward Fitting…. • 2. Optical system with a characteristic Point Response Function • 3. Device for measuring Fourier components of source distribution

23. RMC Point Response Function Single grid (3) Grids 1 - 9 Circular Bessel FunctionSum of9Circular Bessel Functions

24. Measuring Fourier Components:The Radio Interferometer Analog • Mathematical equivalence established between information in a correlated radio signal and a modulated x-ray signal • In both cases, observed amplitude and phase measure a Fourier component of source distribution • Combined Fourier components  reconstructed source image

27. Detectors

28. RHESSI Grids 1 mm 9 grids Pitch range: 35 microns to 2.75 mm Thickness range: 1.2 mm to 3 cm

29. Flaring Arcade of Loops Oct 28, 2004

30. Footpoint Motions HESSI can follow motions of compact sources as a function of time or energy at the subarcsecond level

31. High Resolution Imaging RHESSI blue contours: 25-30 keV with 2.2 arcsec resolution

32. RMC Imaging with Few Photons • 18 minute integration of the 2.223 MeV neutron capture line • Source detected and located with 103 photons

33. Gamma-ray Imaging Oct 28, 2004

34. RMC Measurement of Source Size Gaussian source • Modulation amplitude depends on ratio of source size to collimator resolution. • Measurement of relative modulation amplitude vs. collimator resolution provides a direct measurement of source size.

35. Size Scale of Flare Sources (1)The Role of Albedo • Expect several 10’s of % of solar x-ray flux to be in a large patch of reflected x-rays. • Surface brightness of this albedo is < 1% of of compact primary source. • Conventional imaging systems cannot isolate this component.

36. Size Scale of Flare Sources (2) Isolating the Albedo Component • Mapping gives a good estimate of size scale of compact component. • At high spatial frequencies, size scale is well-fit by a 7 arcsec source. • Presence of albedo component is also clear. • Size determination works in practice, even in presence of a diffuse source component.

37. Limiting Factors for RMC Imaging • Photon statistics (need ~102 to 105 counts, depending on source complexity) • Number of measured spatial frequencies (limits complexity of sources that can be well-characterized) • Systematic errors (knowledge of grid and detector response) • Image quality often expressed in terms of • dynamic range == ratio of brightest to dimmest imagable source • Typical RHESSI dynamic range is 10 to 50 :1 • Expect 100:1 by end of mission.

38. Some Strengths of RMC Imaging • Well suited to high resolution imaging-spectroscopy • Accurate, absolute source locations • Can be sensitive to a wide range of source size scales • Imaging inherently suppresses background • Inherently self-calibration in many respects • Forgiving in terms of mechanical construction

39. RHESSI Aspect and Pointing Requirements Typical pointing ½ deg Angular resolution = 2.2 arcsec Aspect knowledge = 0.4 arcsec Field of view = 1 degree Pointing Requirement = 0.2 degrees • Change in relative source to collimator orientation is fully compensated during analysis by shifting phase of modulation pattern on a photon-by-photon basis • ( = photon-by-photon image motion compensation ) •  Can substitute aspect knowledge for accurate pointing •  Can make long exposures with no loss of resolution •  Implications for terrestrial systems

40. RHESSI Alignment Requirements • Grid displacements parallel to slits do not affect response • Grid displacements perpendicular to slits are compensated by the co-planar aspect system • Only critical requirement is relative twist of upper and lower grids (rms << grid pitch / grid diameter) • 2 arcsecond imaging with 1 arcmin (3) twist tolerance • Metering structure need only be resistant to twist • Moderate misalignments degrade sensitivity, not resolution  mechanically “forgiving” Grid separation = 1.55 m Grid diameter = 90 mm Grid pitch = 35 um FOV = diameter / separation Resolution = ½ pitch / separation

41. RHESSI Self-Calibration • All relevant alignments can be calibrated using in-flight data • Grid slit locations ( to micron level ) • Aspect system parameters ( to subarcsecond level ) • Grid tilt ( to < 1 arcminute ) • Relative Detector Response ( to a few percent )

42. Terrestrial Applications – Distinctive Requirements in collaboration with Norm Madden & Klaus Ziock • Finite focal distance •  different pitch for front and rear grids • Robust, cost-effective design suitable for replication •  should use proven technologies • Timely and reliable output •  Turnkey analysis in close to real time • Deployable • operable by field personnel in less than ideal conditions

43. Example of a Possible Application • Goal • Large area system to distinguish • compact from extended gamma-ray sources

44. Possible Design Concept Variable Resolution Modulator • Mechanically-rotated front grid • Fixed Anger camera plays dual role of rear grid and detector • Peripherally-mounted screw drive provides rotation with continuously variable grid-to-detector separation •  continuous range of resolutions ( ~½ grid pitch / separation ) X X source rotating modulator detector image

45. Simulation

46. PSF of Variable Resolution Modulation ‘Continuous’ Sum of Circular Bessel Functions

47. Imaging Properties • Can readily determine source sizes over a wide range • ( meters to ~20 cm ) • Good imaging properties for more complex sources • Accurate source location capability ( few cm ) • Can image as a function of energy • Image display can be built up in real time

48. Other Properties • High throughput ( ~50% ) • Automatic background discrimination • Works over a range of source – imager distances • Can deal with moving targets • Self-calibrating detector • Limited ability to locate sources in 3D

49. Summary • Properties of RMC’s are well-matched to the observational requirements of high-spectral and high-spatial resolution hard x-ray and gamma-ray imaging. • RHESSI has demonstrated that such RMC’s work in practice. • Some of the concepts and properties may be applicable to terrestrial applications.

50. X-Ray and Gamma-Ray Imagingwith Rotating Modulation Collimators Gordon Hurford Space Sciences Lab UC Berkeley 30 Nov 2004