VIEWGRAPHS

• How does HESSI imaging work ?
• The image reconstruction task
• HESSI imaging topics
• Editorial comments on HESSI imaging
• Ed Schmahl: - imaging in practice

• Response of an individual subcollimator
• Average count rate is proportional to source intensity
• Modulates sources whose diameter < collimator FWHM
• Modulation frequency and phase depends on source location and pitch
• Linear response to multiple sources
• Over a small rotational interval, modulation measures one Fourier Component of source
• Equivalent to one baseline in a radio interferometer
• Grid rotation is equivalent to earth rotation synthesis
• Can use full set of image reconstruction tools developed for radio astronomy
• Over a half-rotation, one subcollimator is a telescope with Bessel Function,

  PSF ~ Jo(2pi * r / ang_PITCH) +…

• Data set represents a set of counts measured in a large number of successive, short time bins.
• Modulation pattern for each time bin is a map of the grid-pair transmission probability for a photon from the m’th pixel.

User: Selects imaging parameters

Time
Energy
Subcollimators
Imaging algorithm
Imaging parameters
Etc

Hessi_image:

Locates data base
Reads event tags
Selects events based on user criteria
Bins events into short time bins
Locates or performs aspect solution
Associates (x,y,roll) aspect with each time bin
Associates live time with each time bin
Associates grid calibration with each time bin
Combines, aspect, grid calibration, etc into ‘phase’ for each time bin
Result is a ‘calibrated photon list’
Optionally, convert to visibilities
Uses selected algorithm
Displays and stores resulting image.

User: Manipulate display of resulting image

User: Iterate or repeat with other imaging parameters, etc.

• Polar coordinates
• Used internally for core computations.
• Exploits inherent symmetries.
• Major saving in computation time.
• Results converted back to rectangular coordinates.
• Ref. Ed Schmahl’s web site.
• Universal Modulation Patterns
• Provides a very efficient way or representing and applying instantaneous subcollimator response.
• Major savings in storage and computation time.
• Grid response is represented by a Fourier series,
• Analytically, grid response is a complicated function, dependent on location and energy.
• Fourier parameters vary slowly with energy, and offset location.
• Parameters are average transmission, modulation amplitude and phase.
• Fundamental, 2^nd and 3^rd harmonics are potentially relevant.

• Goal is to make aspect solution transparent to user.
• Aspect solution will either be calculated as needed or retrieved from a database
• Basic aspect solution software is working, but needs more bells and whistles
• Aspect simulation software is coming soon…
• End-to-end test through hardware (including hardware) was successful
• Currently, pointing behavior is built into photon simulations and taken out with a 'virtual' aspect solution

• Calibration types
• Detector calibration
• Dead-time calibration
• Grid calibration
• Aspect system calibration
• Attenuator calibration
• Imager Calibration Status
• Grids, aspect and attenuators were fully calibrated at the subsystem level
• Calibration data will be installed in SSW data bases
• Goal is to understand instrument response at the ~1% level
• Inflight Calibration
• Assumes grid, aspect and attenuator parameters are independent of time, energy and flare.
• Redundancies in data to be used to refine aspect, grid and attenuator parameters.
• Aspect component positions
• Roll calibration using Crab pulsar
• Grid parameters using flare data redundancies
• Attenuator parameters using discontinuities at attenuator changes.
• Improved calibration data base can be applied retroactively
• Imager performance will improve with time.

• High spectral resolution and imaging spectroscopy are drivers for photometric accuracy.
• Goal is ~1% photometry in optimum circumstances.
• Map units will correspond to photons / pixel / cm^2 (or equivalent).
• Integrate over a source component to extract photons/cm^2
• Back Projection
• For a point source, peak in map indicates summed incident fluence
• Underestimates flux by ~10% (to be fixed)
• For multiple or extended sources, this is not a good choice since ‘hand corrections’ are required.
• Used at present to support testing.

• Snapshot imaging
• Largely untested up to now
• Backprojection works at subsecond intervals.
• Visibilities
• Calculated internally
• Not yet made conveniently accessible
• Format will be table of Time, U, V, Amplitude, Phase, (Errors, Flags, tbd)
• Conversion to AIPS-compatible format is under consideration
• Spectral calibration
• Imaging uses only the diagonal elements of the spectral response matrix.
• Imaging Spectroscopy
• Based on multi-image comparison
• Best option will be feature based rather than pixel-based
• Will be a significant reduction is spectral quality
• Needs good photometry
• Manual capability now
• Goal by launch is semi-automated, feature based.

• Basic Capabilities
• On board solid-state recorder has 4 Gbyte capacity (1 photon = 4 bytes)
• Downlink capability is ~1 Gbyte/day/station (6 x 10 minute passes)
• Data volume dominated by background, except for very large flares
• Maximum data rate ~25000 counts/s/detector segment
• Large flare could easily fill memory and have substantial dead time.
• Use of a second ground station (Wallops) during periods of activity increases downlink capability by ~75%
• Attenuators to control rates
• Two aluminum attenuators (thin and thick).
• Simultaneous insertion for all detectors.
• Controlled by on-board software, based on data rates and adjustable parameters.
• One-time override mechanism to reduce effects of malfunction.
• Disabled in default position for first few weeks/months
• Decimation to control data volume in front segment.
• Discards every fixed fraction of photons below preset energy.
• Four steps of decimation
• Effects compensated in analysis (except for statistics)
• Fast rate mode to provide some imaging capability at high rates.
• At high input rates, transmitted photon rates decrease due to deadtime.
• Fast rate mode is triggered automatically to transmit binned rates in 4 energy channels.
• Detector-dependent time resolution is sufficient to permit imaging in broad spectral bands.
• Detector rear segment is largely unaffected by high rates.

• Detectors view Sun through rotating grids.
• Transmission of grids depends on
• Grid
• Time
• Energy
• Source location relative to pointing axis.
• Distorts spectra
• Spectral corrections depend on approximate location of source
• Spectral corrections are straightforward, for spectroscopy with integration times that are multiples of half-rotation time.
• Important check
• When correctly calibrated, each detector should yield identical, independent spectra.

Grids introduce significant artifacts into light curves on three time scales.

• Modulation time scales (~1 to ~500 milliseconds)
• Timescale depends on grid pitch and source radial offset from pointing axis
• Periodic at twice rotation rate
• Due to internal shadowing in grids
• Time of maximum depends on grid orientation direction from source to pointing axis
• Amplitude of slow modulation depends on energy, source offset, and grid pitch:thickness ratio
• Periodic at rotation rate
  • Due to shadowing in grids, combined with grid tilt
  • Correction of slow variations is straightforward, but requires knowledge of approximate position of source
  • Correction for modulation is possible only for the summed response over several grids.
  • Demodulation’ will be an analysis option.
  • Timescales for modulation for various grids do not overlap
  • Result will be a single lightcurve, (as a function of energy) valid on all timescales.

• Counting statistics
• Statistical s/n in the peak of a BPmap is s ~ 2 * SQRT(total counts)
• Complexity of image (simpler is better)
• Fraction of total counts in feature of interest (a smaller fraction is more susceptible to systematic calibration errors)
• Special circumstances
• Importance of dead time
• Fast-rate mode
• Attenuator changes
• Special source locations (relative to pointing axis or imaging field of view)
• Suspicious symmetries (arcs relative to pointing axis or strong image sources)
• Characteristics of aspect solution
• Known hardware anomalies
• Known software anomalies
• Unusual symmetries
• Unusual source variability
• Believability of feature

• Reimage with:
• different algorithms
• different FOV
• pixel size
• image center
• subcollimator combinations
• energy range
• energy bin sizes
• time ranges
• calibration parameters
• odd/even half-rotations

• Apply redundancy tests
• Compare spectra/lightcurves from different detectors
• Check rotational symmetry of light curve

• Trace back the feature to:
• Fourier components
• Observed modulation curves

• Simulate and analyze similar sources

• Strengths
• Nominal performance requirements (angular- and energy-resolution, imaging spectroscopy
• Image location
• Colocation at different energies
• Energy calibration
• Photometry (usually)
• Dynamically adaptable to a wide range of image scales
• Dynamically adaptable to large range of source strengths
• Limitations
• Limited image complexity (Will NOT provide TRACE-like images!)
• Limited dynamic range within an individual image (goal ~100:1 in favorable cases)
• Extended sources can be invisible
• All sources contribute to noise of each source feature.
• Limiting Factors
• Statistics
• May dominate for weak flares, short integrations, narrow energy windows
• Image complexity
• May be important for spatially complex cases
• Systematic errors – In other cases, limitation may be set by
• Knowledge of instrument response
• Algorithm limitations

Consider HESSI as an imager which you can configure.

• Variables you control:
• Integration time
• Energy range
• Choice/weighting of subcollimators
• Software algorithms and parameters
• Factors to consider:
• Science objective
• Imaging, spectra or light curves
• Spatial scales
• Energy
• Characteristics of flare

Performance of imager will be sensitive to your choices.

We will all be on a steep learning curve.

We should plan on doing easy science first.