Tutorial I : Standard Example of Forward-Fitting

1
(No Transcript)
2
(No Transcript)
3
(No Transcript)
4
(No Transcript)
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
Tutorial I Standard Example of
Forward-Fitting
ohis_image() o-gtset,image_algorithmforwardfit
o-gtset,image_dim64,64 o-gtset,pixel_size2,2 o
-gtset,energy_band6,300 o-gtset,time_range0,4
o-gtset,det_index_maskbyte(0,1,1,1,1,1,1,1,1) o-
gtset,n_gaussians2 o-gtset,n_par4 (spherical
gaussians) o-gtset,n_par6 (elliptical
gaussians) o-gtset,n_par7 (curved
gaussians) imo-gtgetdata() o-gtplot
http//www.lmsal.com/aschwand/hessi_imaging/hessi
_fwdfit_tutorial1.html
9
(No Transcript)
10
Output parameters of forward-fitting procedure
po-gtget() print,,p.n_gaussians e.g. 2 (number
of gaussian components) print,p.n_par
e.g. 4 (numbe of free parameters per
component) print,p.chi_ff ...
C-statistic of 9 detectors, e.g.
0.00,0.78,1.01,1.07,1.
12,1.13,0.91,1.15,1.12 print,p.chiav_ff
average of C-statistics from non-zero
detectors, e.g. C1.04 print,p.phot_sec
incidnet photon rate, e.g. R959
photons/sec print,p.peak_flux gaussian
amplitude, e.g. A4.77 photons/sec/cm2 print,p.c
oeff_ff(,0) coefficients of first source,
e.g. 1.00,1.19,-11.34,-11.69 print,p.coeff_ff
(,1) coefficients of second source, e.g.
0.99,1.34,0.69,0.73
11
Tutorial II Initial Guess Optimization
o-gtset,pixel_size4,4 o-gtset,image_dim64,64
o-gtset,pixel_size1,1 o-gtset,image_dim64,64
Unresolved double source
Resolved double source
http//www.lmsal.com/aschwand/hessi_imaging/hessi
_fwdfit_tutorial2.html
12
Tutorial III Number of Source Components
Strategy - Start with single component
- If chi-square (C-statistic) Cgt1.05
increase number of components
incrementally until chi-square in range
C0.951.05
http//www.lmsal.com/aschwand/hessi_imaging/hessi
_fwdfit_tutorial3.html
13
o-gtset,n_gaussians1
o-gtset,n_gaussians2
14
o-gtset,n_gaussians3
15
On the Photometric Accuracy of RHESSI Imaging
and Spectroscopy
Markus J. Aschwanden T.Metcalf, Sam Krucker,
J.Sato, A.Conway, G.Hurford, E.Schmahl
Solar Physics, 219, 149-158, (2004) CD-ROM
supplement http//www.lmsal.com/aschwand/eprints/
2003_photo/
16

• TESTS
• Spectral Photometry
• Image Photometry
• Background
• Positions
• Amplitudes and Widths
• Halo/Core flux ratios
• Spatially-resolved spectra
• Grid selectrion
• Pixel-size
• Field-of-view
• Time intervals

17
2) Image photometry
18
Image fluxes photons / s cm2
Ratio of Image fluxes to SPEX fluxes
F_image/F_SPEX
19
Result Total fluxes in images agree with total
fluxes in SPEX within a few percents (except
MEM-Vis 60)
20
3) Background Components
21
(No Transcript)
22
Results 1) Total fluxes in images agree with
total fluxes in SPEX within a few percents
(except MEM-Vis 60) 2) Pixon and Forward-fit
show (unexplained) background component
(15) in excess of preflare background (1)
23
4) Positional accuracy
24
Results 1) Total fluxes in images agree with
total fluxes in SPEX within a few percents
(except MEM-Vis 60) 2) Pixon and Forward-fit
show (unexplained) background component
(15) in excess of preflare background (1) 3)
Positional accuracy 0.5 pixels (0.5) 400 km
25
5) Amplitude Widths

• Total flux per feature is well-conserved, F a
  x w2
• Amplitudes are reciprocal to widths squared, a
  1/w2
• Depending on convergence behavior (MEM-Sato,
  MEM-Vis)

26
The Image algorithms differ in the reconstructed
source morphology
27
Results 1) Total fluxes in images agree with
total fluxes in SPEX within a few percents
(except MEM-Vis 60) 2) Pixon and Forward-fit
show (unexplained) background component
(15) in excess of preflare background (1) 3)
Positional accuracy 0.5 pixels (0.5) 400
km 4) Amplitudes scale reciprocally to widths
squared, Fa x w2 ? Compare image fluxes
only per feature (never amplitudes)
28
6) Halo/Core Flux Ratios

• Forward-Fit and Pixon have photons confined in
  core
• CLEAN produces enlarged sources due to
  convolution
• with point spread function (Clean beam) and
  addition of residuals
• MEM does not converge and produces large halos
• MEM-Vis does not converge for time-variable
  sources and
• overresolves sources under such circumstances

29
7) Spatially Resolved Spectra
Fitting two-component (thermal nonthermal
powerlaw) model spectrum To image fluxes in 8
energy bins
30
(No Transcript)
31
? Nonthermal flux f_nth and powerlaw slope a
agree within a few
32
(No Transcript)
33
Results 1) Total fluxes in images agree with
total fluxes in SPEX within a few percents
(except MEM-Vis 60) 2) Pixon and Forward-fit
show (unexplained) background component
(15) in excess of preflare background (1) 3)
Positional accuracy 0.5 pixels (0.5) 400
km 4) Amplitudes scale reciprocally to widths
squared, Fa x w2 ? Compare image fluxes
only per feature (never amplitudes)! 5) Spectral
flux and powerlaw slope agree with SPEX few
34
8) Grid Selection

• Reconstructed source size adjusts to the spatial
  resolution
• of the finest used grid (except MEM-Vis)

35
(No Transcript)
36
Results 1) Total fluxes in images agree with
total fluxes in SPEX within a few percents
(except MEM-Vis 60) 2) Pixon and Forward-fit
show (unexplained) background component
(15) in excess of preflare background (1) 3)
Positional accuracy 0.5 pixels (0.5) 400
km 4) Amplitudes scale reciprocally to widths
squared, Fa x w2 ? Compare image fluxes
only per feature (never amplitudes)! 5) Spectral
flux and powerlaw slope agree with SPEX few 6)
Reconstructed source size adjusted to resolution
of finest used grid (in old FF version).
37
9) Pixel size
Reconstructed source size is independent of pixel
size (except for MEM-Vis)
38
(No Transcript)
39
FORWARD-FIT used the spatial resolution of the
finest selected grid as an initial guess, because
the automated algorithm determined the finest
grid based on the criterion of significant
modulation above the photon noise level
w_init 2.23.grid/2 If the user chooses
only coarse grids, the initial guess of the
source size is correspondingly larger. If a too
large source size is chosen as initial guess, the
modulations are relatively small and
FORWARD-FIT tends not to converge. In the new
version, the pixel size is used as an initial
guess of the source size, which is an upper
limit of the true source if not resolved. Pixel
sizes smaller than source are required to enable
convergence.
Hurford et al. 2002, Solar Physics 210 61-86
40
Pitch Grid 9 178 Grid 8 102 Grid 7
59 Grid 6 34 Grid 5 20 Grid 4 11
41
Test of source size convergence with
Forward-fit
(Pixel size 8 ? Initial guess)
64x64 pixel 8
Grid C-statistic Width 2-9 5.67 7.8
? Bad fit (C5.67), no convergence 3-9 2.06 7.8
4-9 2.05 7.9 5-9 2.18 8.1 6-9 2.37 8.7 7-9 2.12 10
.0 8-9 2.46 12.2 9-9 2.71 15.8 ? Source
size increases because of
to coarse
grids The algorithm converges for grid choices
3-9 8-9, but is not Sensitive to source sizes lt
8 (see signal-to-noise ratio in grid 3! )
42
Pixel size 0.5
43
Test of source size convergence with
Forward-fit
(Grid 4-9, Pixel size ? Initial guess of source
size)
64 pixel 0.5
Pixel C-statistic Width 8 2.05 7.9
? convergence, but not sensitive for
wltpixel 6 2.19 6.0 4 2.33 4.3 3 2.40 6.3 2 2.4
0 3.5 1 2.32 3.7 0.5 2.45 2.9 ? source
size converges to w3 The
algorithm converges for all pixel sizes. The
source size asymptotically converges to w3,
once it becomes fully resolved (This corresponds
to the maximum resolution of the finest grid
11/3).
44
Results 1) Total fluxes in images agree with
total fluxes in SPEX within a few percents
(except MEM-Vis 60) 2) Pixon and Forward-fit
show (unexplained) background component
(15) in excess of preflare background (1) 3)
Positional accuracy 0.5 pixels (0.5) 400
km 4) Amplitudes scale reciprocally to widths
squared, Fa x w2 ? Compare image fluxes
only per feature (never amplitudes)! 5) Spectral
flux and powerlaw slope agree with SPEX few 6)
Reconstructed source size adjusted to resolution
of finest used grid 7) Reconstructed source
size is independent of pixel size, if source
size is resolved. If the source is not resolved,
the pixel size is an upper limit of the true
source size.
45
10) Field-of-view
The reconstructyed source size should be
independent of the chosen map field-of-view
46
Results 1) Total fluxes in images agree with
total fluxes in SPEX within a few percents
(except MEM-Vis 60) 2) Pixon and Forward-fit
show (unexplained) background component
(15) in excess of preflare background (1) 3)
Positional accuracy 0.5 pixels (0.5) 400
km 4) Amplitudes scale reciprocally to widths
squared, Fa x w2 ? Compare image fluxes
only per feature (never amplitudes)! 5) Spectral
flux and powerlaw slope agree with SPEX few 6)
Reconstructed source size adjusted to resolution
of finest used grid 7) Reconstructed source
size is independent of pixel size and
field-of-view
47
11) Time Intervals
? MEM does not converge for short time intervals
(low count statistics) ? MEM-VIS converges only
for short time intervals (because it does not
correct for time variability)
48
(No Transcript)
49
Results 1) Total fluxes in images agree with
total fluxes in SPEX within a few percents
(except MEM-Vis 60) 2) Pixon and Forward-fit
show (unexplained) background component
(15) in excess of preflare background (1) 3)
Positional accuracy 0.5 pixels (0.5) 400
km 4) Amplitudes scale reciprocally to widths
squared, Fa x w2 ? Compare image fluxes
only per feature (never amplitudes)! 5) Spectral
flux and powerlaw slope agree with SPEX few 6)
Reconstructed source size adjusted to resolution
of finest used grid 7) Reconstructed source
size is independent of pixel size and
field-of-view 8) MEM-Vis does not correct for
time variability and thus does not converge
for longer time intervals
50
CONCLUSIONS 1) Total fluxes in images agree
with total fluxes in SPEX within a few
percents (except MEM-Vis 60) 2) Pixon and
Forward-fit show (unexplained) background
component (15) in excess of preflare background
(1) 3) Positional accuracy 0.5 pixels (0.5)
400 km 4) Amplitudes scale reciprocally to
widths squared, Fa x w2 ? Compare image
fluxes only per feature (never amplitudes)! 5)
Spectral flux and powerlaw slope agree with SPEX
few 6) Reconstructed source size is
independent of pixel size, if source is
resolved. If the source size is not resolved,
the pixel size is an upper limit. 7) The source
size is independent of the field-of-view 8)
MEM-Vis does not correct for time variability and
thus does not converge for longer time
intervals