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Nov 15, 2013 (4 years and 5 months ago)

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Inverse Problems in Solar Imaging
Spectroscopy

-

Future Applications

G.J. Hurford

Space Sciences Lab

University of California, Berkeley

Vienna 20 July 2009

Outline

Physics
-
based arguments to show that
the algorithms discussed by previous
speakers are relevant to field as a whole
(as opposed to just a specific mission.)

Illustrate this with 3 future applications of
the double inversion techniques.

Role of RHESSI Inversion Algorithms

Convert Fourier
-
based imaging data as a function
of energy to spatial maps of physical parameters

Convert incomplete visibility data to maps

At each spatial location, convert spectral data

into physical parameters

Why does solar hard x
-
ray imaging use visibilities ?

High energy physics

t
wo diagnostics for
accelerated solar electrons

Hard x
-
rays

Radio

Solar observations require ~ arcsecond resolution

Focusing optics is not feasible in this x
-
ray regime

Use collimation techniques

Solar range of angular scales + need for sensitivity

Bigrid collimators

Basic x
-
ray imaging observable is visibilities

High Resolution Radio Imaging

At radio wavelengths

Diffraction

Antenna diameter needed for
~arcsecond imaging is prohibitively large

e.g. 100m diameter antenna

has only 140 arcsec resolution

at 5 GHz but need ~4 arcsec.

use interferometry

Measuring Fourier Components:

The Radio Interferometer Analog

Mathematical equivalence 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

Interferometry

RMC Comparison

Interferometry

RMC’s

Spatial period

wavelength / baseline

Grid pitch / separation

uv points

N(N
-
1)/2 (antennas)

VLA

351

N (RMCs)

RHESSI

9

Synthesis

Earth rotation (24 h)

S/c rotation (4 s)

Visibility
-
based imaging is required for
imaging high energy solar electrons

In both cases, basic observables are visibilities
(u,v,f)

Diagnostics require spectroscopy

Inhomogeneous source structure

imaging spectroscopy

Summary

FACTORS

Physics of emission processes

hard x
-
rays and radio observations

Angular Size scales of solar phenomena

Physics of detection processes

visibility
-
based imaging

Emission processes convolve physical parameters with energy

Spatial non
-
uniformity of solar phenomena

Visibility
-
based imaging spectroscopy is fundamental
to the study of high
-
energy solar electrons

Spatial reconstruction

Spectral deconvolution

Future Applications (1)

BETTER IMAGING + POLARIMETRY

RHESSI imaging was limited by
measurements at only 9 spatial frequencies

uv plane

No imaging polarimetry

No information on directivity of electrons

(e.g. electron beams?)

GRIPS

G
amma
-
R
ay
I
maging
P
olarimeter for
S
olar flares

P.I. Bob Lin, UCB

Multi
-
pitch rotating
modulator

Spectrometer/polarimeter

with 0.5mm spatial resolution

Energy range

~20 keV to >~10 MeV

Angular resolution

12.5 to 162 arcsec

First balloon flight:
spring 2012

8 m boom length

Detector provides time, energy,
location

and
a
polarization signature

of each photon

Two Perspectives on GRIPS Imaging

Each photon identifies a set of
‘probability stripes’ on Sun from which it
could have originated

Observations of many photons

image

1 3 10

30 100 1000

Time sequence of counts beneath each
mask location/orientation measures one
visibility

Continuous set of gid pitches
measures solid annulus in uv plane

uv plane

Radial profile
of PSF

GRIPS

RHESSI algorithms can be applied directly

Much better image quality

Polarization adds new dimension to
spectral deconvolution

Direct information on
accelerated electrons is lost
in propagation effects

Future Improvements (2)

BETTER VANTAGE POINT

Observations from close to Sun

enable direct comparison to
accelerated electrons

Solar Orbiter
ESA

2017 launch

0.22 au perihelion

Magnetic coupling of Sun to heliosphere

How do you measure visibilities with a stationary collimator?

Grids are stationary

Top and bottom grids have
slightly different pitch

Location and amplitude of
Moire pattern

visibility

Grids are moving

Top and bottom grids have
identical pitch

Time and amplitude of count
rate variations

visibility

2 subcollimators with grids phase shifted by ¼ pitch

(plus an integrated flux measurement)

amplitude and phase of Fourier component.

Telescope Tube

Rear Grids

CZT Detectors

Electronics Box

Front Grids

Spectrometer/Telescope

for

Imaging X
-
rays

(STIX)

P.I. Arnold Benz, ETHZ

Solar Orbiter / STIX

Algorithms directly applicable

Challenges:

Sparse coverage in UV plane

limited image quality

Robustness of algorithms

(automated analysis of 2000 images/hour x 5+ years)

Future Applications (3)

MICROWAVE IMAGING SPECTROSCOPY

Surface brightness
(=brightness temperature)

spectra

accelerated electron spectral parameters,
ambient density and/or magnetic field

FASR

Frequency
-
Agile Solar Radiotelescope

Tim Bastian, NRAO

0.05 to 21 GHz

1 arcsecond resolution at 20 GHz

Design and development funded by NSF

Pathfinder version could be operational by 2012 at Owens Valley, California

Incoherent Microwave Burst Spectra

Free
-
free Gyrosynchrotron

(Thermal and nonthermal)

Brightness Temperature spectra contain diagnostic information
on magnetic fields, plasma & accelerated electron parameters.

Shape depends on mechanism

Position in Tb

Frequency plane depends on physical parameters

(BUT dependence is non linear)

Observational confirmation

Radio imaging

No need to deconvolve detector frequency response.

N antennas

N(N
-
1)/2 pairs

Cannot exploit earth rotation for burst sources

limited number of observed visibilities

uv plane

Frequency
-
synthesis

Angular resolution =
antenna separation

wavelength

For each antenna pair, each frequency measures a different Fourier component

Many more visibilities

uv plane

Couples spectral deconvolution to spatial deconvolution

Implications for Algorithms

New deconvolution algorithms required

Spectral deconvolution is coupled to
spatial deconvolution

Non
-
linear relation between physical
parameters and spectrum

Summary

Visibility
-
based imaging/spectroscopy of
hard x
-
rays and microwaves is the key
observational tool for studying accelerated
electrons at the Sun.

The success of the next generation of solar
microwave and x
-
ray telescopes is critically
dependent on the solution of spatial/spectral
inverse problems.