Journal Club

Bozeman

6 November 2001

Population: 636 800 Ladies: 337 200

Gents: 299 600

SXT image formation process

itrue brightness

distribution

ppoint spread

function

cconvolution of i and p

BLUR

dblurred & noisy

data

d = c + noise

NOISE

cconvolution of i and p

SXT image formation process (continued)

SXT image formation process (continued)

What we know is d. For i, p, c we can only look for approximations.

cross sections

i

d

Deconvolution

To find i from d and p

or

To find p from d and i

i – approximation of image (true brightness distribution)

p – approximation of point spread function

d – data (blurred & noisy)

Blind Deconvolution

i – image (true brightness distribution)

p – point spread function

d – data (blurred & noisy)

Find new estimate

of i from d and p

Find new estimate

of p from d and i

Find new estimate

of I from D and P

Find new estimate

of P from D and I

I, P, D – Fourier transforms of i, d, p

d = convolution of p and i

+ noise

D = product of P and I

+ noise in fouries space

PURPOSE

To determine the approximation of the core part of the SXT PSF from flare observations collected in-flight, in thick aluminum filter.

STEPS TO ACHIVE

• Select appropriate SXT data set

• Find first approximation of the PSF by Steepest Descent Method

• Improve it by Blind Deconvolution

SXT Point Spread Function Model

Two regions

spiky core

extended wings

Large flare image taken on 27 Feb 1992 at 09:51.

Half resolution SXT data.

Wing part of SXT PSF

Core part of SXT PSF

Ground calibration images in Al-K line (White Sands 1991)

Elliptical distortion of SXT PSF (strong in CCD corners)Contours at 0.1, 0.2, 0.4 and 0.8 of maximum value.

To the left, a coverage map of the CCD detector surface by full resolution SXT frames. Gray intensity says how many times a given pixel was captured within a full resolution frame during year 2000. To the right a shaded surface for the coverage map (Log10 scale).

Where SXT Data have been taken during the year 2000

Compact source images selected in thick aluminium filter data (small dots) and WSMR calibration beam positions on CCD surface (crosses).

• Compact • CCD Temperature below –20o C• DC below 50 DN• Taken outside SAA• Global maximum present at least 7 pixels away from image boundaries• Not saturated but maximum value above 1000 DN

Selection of SXT data

Steepest Descent Method

PSF is the sharpest object of photon origins that can be formed on SXT CCD

Find sequence of images placed nearly at the same location on CCD

• • •

Steepest Descent Method (continued)

• • •

• • •

Normalize image signal in certain sub-arrays centered at the peak. (here 15x15 square sub-arrays)

image sequence

sub-array sequencenormalized

Steepest Descent Method (continued)

• • •

Construct PSF approximation by taking at each pixel minimal signal value possible to find in the whole normalized sequence

at respective pixel position.

sub-array sequencenormalized

Calibration Steepest descents

x cross-section y cross-section

Steepest Descent Method – comparison with WSMR calibration data

Initial data preparation for Blind Deconvolution

Construct initial guess for PSF by steepest descent method and put it into an image size array

Select the most compact flare image found in the neighborhood of a

givenCCD pixel

Fourier transformsPSF

SXT flare mage

Re

Re Im

Im

Find new estimate

of I2 from D and P2

Find new estimate

of P1 from D and I1

Impose image constraints

• positivity

• conservation of total counts

Fourier Transform

Inverse Fourier Transform

Impose PSF constraints

• positivity

• normalization

Fourier Transform

Inverse Fourier Transform

I2

i2

i1

I1

P1

p1

p2

P2

Fourier domain constraint

average I1 and I2

Fourier transform of Initial approximation

for PSF

ALGORITHM

RESULTS

Input PSF steepest descents

Restored PSF blind deconvolution

RESULTS

Input SXT data Restored SXT data

RESULTS

Input SXT data Restored SXT data

Conclusions

Blind Deconvolution of the selected SXT flare data can give us:

• Sharper PSF core profile than can be directly obtained from data by steepest descent method

• Peak sharpening in SXT data

• Peak separation in data

• Works fast

What we have done

• Working IDL code

• Good SXT Flare data selected

• First deconvolutions of SXT data performed

Will do next

• Improve the code

• Fit deconvolved PSFs by Moffat functions

• Prepare web site about the project (partly done) to make the code accessible for other users.

• Add the code to Solar Soft package