- Future Applications

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15 Νοε 2013 (πριν από 3 χρόνια και 4 μήνες)

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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.