The RHESSI Imaging The RHESSI Imaging ConceptConcept

Rick PernakRick PernakLaboratory for Solar and Space PhysicsLaboratory for Solar and Space Physics

Goddard Space Flight CenterGoddard Space Flight CenterAndAnd

The Catholic University of AmericaThe Catholic University of America

RHESSIRHESSI

NASA SMEX missionNASA SMEX missionDesigned to observe solar flares in X-rays Designed to observe solar flares in X-rays

and Gamma Raysand Gamma RaysUnprecedented ResolutionUnprecedented Resolution

SpatialSpatialSpectralSpectralTemporalTemporal

Launch: February 5, 2002Launch: February 5, 2002

InstrumentInstrument

Rotating Modulation Collimator (RMC)Rotating Modulation Collimator (RMC) 9 Subcollimators, Grids, and Detectors9 Subcollimators, Grids, and Detectors 2 sets of grids2 sets of grids

X-ray ImagingX-ray Imaging

Difficult to focus X-rays (or Gamma Rays) Difficult to focus X-rays (or Gamma Rays) because of such a short wavelengthbecause of such a short wavelength

Focusing Optics not feasibleFocusing Optics not feasibleNeed to block X-rays and cast shadowsNeed to block X-rays and cast shadowsUse collimator-based Fourier-transform Use collimator-based Fourier-transform

imagingimaging

Detector and Incident PhotonsDetector and Incident Photons

Modulation ProfilesModulation Profiles

Imaging SoftwareImaging Software

From data (modulation profiles and/or From data (modulation profiles and/or visibilities), have the desired information to visibilities), have the desired information to construct an imageconstruct an image

Current algorithms: Back Projection, Current algorithms: Back Projection, Clean, Pixon, MEM, Forward FitClean, Pixon, MEM, Forward Fit

Back ProjectionBack Projection

Workhorse of RHESSI imagingWorkhorse of RHESSI imaging ““Simplest” image reconstruction procedureSimplest” image reconstruction procedure Constructs “probability maps” of incident Constructs “probability maps” of incident

photonsphotons

How Back Projection WorksHow Back Projection Works

CleanClean

First used in Radio ImagingFirst used in Radio Imaging An extension of Back-ProjectionAn extension of Back-Projection Most-publishedMost-published

1.1. Iterative algorithmIterative algorithm2.2. Treats extended sources as superposition of Treats extended sources as superposition of

point sourcespoint sources3.3. Picks out brightest pixelsPicks out brightest pixels4.4. Convolves with Clean beamConvolves with Clean beam5.5. Adds residualsAdds residuals

PixonPixon

Most reliable algorithm (theoretically) in Most reliable algorithm (theoretically) in terms of photometryterms of photometry

Arranges pixels in map, creates its own Arranges pixels in map, creates its own modulation profile and tries to match the modulation profile and tries to match the data (data (χχ22 check) check)

The tradeoff is efficiencyThe tradeoff is efficiency

VisibilitiesVisibilities

Radio-based conceptRadio-based concept Essentially an Essentially an

amplitude and a amplitude and a phasephase

Created from Created from modulation profilesmodulation profiles

Analogous to radio Analogous to radio interferometer interferometer visibilitiesvisibilities

Mathematical Approach to Mathematical Approach to VisibilitiesVisibilities

Each detector has a pitch, k, which is used Each detector has a pitch, k, which is used to construct visibilitiesto construct visibilities

UV points based on pitch and phase angleUV points based on pitch and phase angleVisibilities based on UV points and spatial Visibilities based on UV points and spatial

coordinatescoordinates

MEMMEM

Maximum Entropy MethodMaximum Entropy MethodAnother Radio-based imaging methodAnother Radio-based imaging methodRHESSI MEM programs: MEM_VIS, RHESSI MEM programs: MEM_VIS,

MEM_SATO, MEM_NJITMEM_SATO, MEM_NJITEntropy term: log of the map fluxEntropy term: log of the map flux

Bayesian: S = H - (Bayesian: S = H - (λλ**χχ22))Cornwell/Evans: S = H – Cornwell/Evans: S = H – ββ**χχ2 - 2 - αα*F*F

H = H = ΣΣ F Fijij*log(F*log(Fijij))

MEM_NJITMEM_NJIT

MEM_SATO, MEM_VIS not successfulMEM_SATO, MEM_VIS not successfulBoth used counts/modulation profilesBoth used counts/modulation profilesMEM_NJIT is visibility-based, designed by MEM_NJIT is visibility-based, designed by

New Jersey Institute of TechnologyNew Jersey Institute of TechnologyStarting to be used more and more by Starting to be used more and more by

RHESSI researchersRHESSI researchers

Forward FittingForward Fitting

““Guess” at parameters of an eventGuess” at parameters of an eventGenerate map that is consistent with dataGenerate map that is consistent with dataUseable with modulation profiles, but new Useable with modulation profiles, but new

software uses visibilitiessoftware uses visibilities

Qualitative ComparisonQualitative Comparison

Scientific StudiesScientific Studies

Using MEM_NJIT and Forward Fitting:Using MEM_NJIT and Forward Fitting:Asymmetries in Flux and Source SizeAsymmetries in Flux and Source SizeEnergy dependence in the asymmetriesEnergy dependence in the asymmetries