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

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

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

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General Design Issues for Astrophysics

• Limited mass, telemetry
• Few source photons
• Significant background
• Need for robust design

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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

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Some Imaging Design Issues

• Sensitivity
• Angular resolution
• Need to resolve sources ?
• Need to accurately locate sources ?
• Source complexity
• Source contrast

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Typical Detector Options
Energy Range Energy Resolution Typical Dimension Spatial Resolution
Proportional Counters 2 to 40 keV Moderate Up to 1m 1 mm
CZT 3 to 200 keV Excellent Few cm 1 cm or better
Scintillators 20 keV to 20 MeV Low Up to 10s of cm 1 to 10 cm
Cooled Germanium 3 keV to 20 MeV Excellent Few cm lt1 to 10 cm
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Imaging Technologies at X-ray and Gamma-ray
Energies

• Focusing optics
• Compton Cameras
• Coded masks
• Modulation collimators

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Single Pinhole - Camera Obscura

• Direct imaging
• Angular resolution
  aperture / separation
• Needs detector spatial resolution aperture
• Low effective area
  aperture 2

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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

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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

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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

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HXIS / SMM (1980)

• Multigrid collimator with 10 aligned grids
• 900 subcollimators pointing to adjacent 8 x 8
  arcsec pixels
• Direct imaging
• Very low sensitivity

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Imaging Collimator (2)
n1 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

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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.

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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 RMCs (e.g. RHESSI) can image
  multicomponent, multiscale sources with 2
  arcsecond resolution

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RMC Schematic

• Bigrid collimator rotates about an axis near
  source
• Detected count rates are modulated in time

Count rate vs. time
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RMC Response
Reference point source Weaker source Different
azimuth Larger radial offset Larger
source Extended source Real source
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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.

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Back Projection Algorithm

• CONCEPT
• Calculate a probability map of photons
  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

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Single photon 10 deg
rotation 90 deg rotation
Multiple rotations Grids 3
8 Clean
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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?

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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

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RMC Point Response Function
Single grid (3)
Grids 1 - 9
Circular Bessel Function
Sum of 9 Circular Bessel Functions
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Measuring Fourier ComponentsThe 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

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Detectors
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RHESSI Grids
1 mm
9 grids Pitch range 35 microns to 2.75
mm Thickness range 1.2 mm to 3 cm
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Flaring Arcade of Loops Oct 28, 2004
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Footpoint Motions
HESSI can follow motions of compact sources as a
function of time or energy at the subarcsecond
level
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High Resolution Imaging
RHESSI blue contours 25-30 keV with 2.2
arcsec resolution
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RMC Imaging with Few Photons

• 18 minute integration of the 2.223 MeV neutron
  capture line
• Source detected and located with 103 photons

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Gamma-ray Imaging Oct 28, 2004
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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.

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Size Scale of Flare Sources (1)The Role of Albedo

• Expect several 10s of of solar x-ray flux to
  be in a large patch of reflected x-rays.
• Surface brightness of this albedo is lt 1 of of
  compact primary source.
• Conventional imaging systems cannot isolate
  this component.

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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.

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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 1001 by end of mission.

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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

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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

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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 ltlt 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
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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
  lt 1 arcminute )
• Relative Detector Response ( to a few percent )

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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

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Example of a Possible Application

• Goal
• Large area system to distinguish
• compact from extended gamma-ray sources

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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
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Simulation
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PSF of Variable Resolution Modulation
Continuous Sum of Circular Bessel Functions
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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

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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

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Summary

• Properties of RMCs 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 RMCs work in
  practice.
• Some of the concepts and properties may be
  applicable to terrestrial applications.

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X-Ray and Gamma-Ray Imagingwith Rotating
Modulation Collimators
Gordon Hurford Space Sciences Lab UC
Berkeley 30 Nov 2004
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Grazing Incidence Telescopes

• Advantages
• Direct Imaging
• Excellent background suppression
• Disadvantages
• Limited angular resolution at high energies
  (10s of arcsec)
• Limited energy range (up to 80 keV)
• Widely used at soft x-ray energies (lt 5 keV)
• Well suited to nonsolar applications at high
  energies where background is more critical than
  angular resolution

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