FOV Dependence of XRT Irradiance

8-Sep-2022 prepared by Aki Takeda
28-Dec-2022 : added section 7.
Link to the latest version.


(Quiet Sun)	(Active Sun)

1. Motivation

This page investigates how XRT's limited FOV affects the derived XRT irradiance, i.e., full-Sun integrated Te, EM, and soft X-ray irradiance.

The current XRT irradiance study is performed by collecting the intensity from the Sun included within 1.1 solar radiai. However, the Sun's emission obviously extends over the outer area. The purpose of this study is to estimate how much energy is uncounted by the limited FOV.

2. Special Observation of high corona (2022/07/16)

In order to observe the higher corona with XRT, whose full FOV is 2040"x2040", we observe the NE-quadrant of the Sun with Al_mesh, Al_poly and thin_Be filters using multiple exposures, as listed in XOB#1CE4. The observation was performed on 2022/07/16, which is in the XRT stray light phase 5. Therefore, we made an additional observation to obtain the stray light component (XOB#1CDC) at the same pointing as the high corona (-530 530) to correct Al_mesh and Al_poly images.

XOB#1CE4 for high NE-corona obs. [click to enlarge]

XOB#1CDC for stray light measurements.

3. Image preparation

Regular XRT synoptic composite images are made of 3 different exposures (short, medium and long). In this special observation, however, multiple long exposures were obtained to improve S/N of the high altitude area. The multiple long exposure images were first all summed up then used for the usual composite image processing.

The stray light component was then subtracted from the Al_mesh and Al_poly composite images, while for thin_Be filter the stray light component is still negligible.

Al_mesh composite image Al_poly composite image thin_Be composite image

Al_mesh stray light img subtracted Al_poly stray light img subtracted ---

NOTE:

Slight arc-shaped enhancement of intensity is observed at around 1.5 Rs in Al_mesh and Al_poly images. It is a ghost pattern appeared due to off-pointing. It is not removed by stray light subtraction, because it is caused by the X-ray optics, not due to visible light contamination. It was confirmed that this ghost pattern does not affect the current analysis.
The same pointing coordinates (-530,530) was requested for the coronal images and the corresponding stray light images, but the actual pointing achieved is affected by the offset between Hinode satellite and XRT telescope, which fluctuates with time. Below is the achived values later determined through the Sun Sensor (UFSS) data anlysis.
```
XRT pointing in Heliocentric coordinates (in arcsec).
coronal image (2022/07/16):     (-555.8, 551.3)
stray light image (2022/07/19): (-555.9, 549.1)
```

4. Data analysis

4.1 : Collect signals of a quater of the Sun

We collect the total intensity of the corona included in the NE-quadrant of the Sun. The mask having the shape of quater-disk was applied to collect intensity included only in the NE-quadrant area.

Total intensity of the corona included in the varying size of FOV.
[click image to enlarge]

The ratio of the collected intensities by the FOV size, 1.0, 1.1, 1.2 and 1.3 Rs relative to the maxmum size (1.7 Rs).

-----------------------------------------------------------------
Filter                    FOV radius (in Rs)  
               1.0         1.1         1.2         1.3       1.7
-----------------------------------------------------------------
Al_mesh:     0.810241    0.944704    0.973690    0.984621    1.0
Al_poly:     0.837398    0.953268    0.977095    0.986408    1.0
thin_Be:     0.901706    0.976902    0.987773    0.992324    1.0
-----------------------------------------------------------------

4.2 : Calculate Te and EM

The coronal intensities collected in the varying size of FOV are used to calculate electron temperature and emission measure with the Fileter Ratio Method.

Total intensity of the corona included in the varying size of FOV.
[click image to enlarge]

results with previous calibration results with previous calibration

The ratio of the Te calculated for the FOV size, 1.0, 1.1, 1.2 and 1.3 Rs relative to that for the maxmum size (1.7 Rs).

-----------------------------------------------------------------
Filter pair               FOV radius (in Rs)                     
               1.0         1.1         1.2         1.3       1.7
-----------------------------------------------------------------
Apol/Alms:   1.03637     1.00847     1.00307     1.00160     1.0
tnBe/Alms:   1.05122     1.01428     1.00604     1.00326     1.0
tnBe/Apol:   1.05492     1.01665     1.00731     1.00400     1.0
-----------------------------------------------------------------

The ratio of the EM calculated for the FOV size, 1.0, 1.1, 1.2 and 1.3 Rs relative to that for the maxmum size (1.7 Rs).

-----------------------------------------------------------------
Filter pair               FOV radius (in Rs)  
               1.0         1.1         1.2         1.3       1.7
-----------------------------------------------------------------
Apol/Alms:   0.752963    0.934299    0.970927    0.983164    1.0
tnBe/Alms:   0.716275    0.923520    0.964119    0.979329    1.0
tnBe/Apol:   0.738689    0.919990    0.961549    0.977696    1.0
-----------------------------------------------------------------

4.3 : Calculate soft X-ray irradiance (5-60A)

Isothermal coronal spectrum is calculated from the derived Te and EM using Chianti atomic DB ver 10.0. The irradiance is obtained by integrating the spectral energy for the wavelength range of 5 to 60A, for which XRT filters used in this study have the best response.

Soft X-ray irradiance calculatded for the varying size of FOV.
[click image to enlarge]

with previous calibration

The ratio of the XRT irradiance (5-60A) calculated for the FOV size, 1.0 to 1.3 Rs relative to that for the maxmum size (1.7 Rs).

-----------------------------------------------------------------
Filter pair               FOV radius (in Rs)  
               1.0         1.1         1.2         1.3       1.7
-----------------------------------------------------------------
Apol/Alms:   0.764553    0.937850    0.974617    0.986902    1.0
tnBe/Alms:   0.731757    0.928466    0.964119    0.979329    1.0
tnBe/Apol:   0.762626    0.925620    0.967432    0.977696    1.0
-----------------------------------------------------------------

5. Data analysis 2 --- 2-D approach

Instead of using total coronal intensities collected from the FOV of varying size, in this section we use the 2-D information of the observed corona to derive the Te, EM and irradiance averaged over the FOV.

5.1 : Calculate 2-D Te and EM

A pair of coronal images are first binned by 4x4 pixels for the better S/N per pixel then used to obtain 2D maps of Te and EM. The FOV mask is applied on each of the map, then EM-weighted Te average and the total EM within the FOV are calclated respectively. Images below are the EM-maps obtained from 3 different filter pairs with the maximum FOV mask being applied. Note that the EM maps using thin_Be filter have limited available area because the areas with low S/N were eliminated from the Te and EM calculation due to large uncertainty.

[click image to enlarge]

EM-weighted average of Te and total EM within the varying FOV from 2D maps of Te and EM from 3 different filter ratios.
[click image to enlarge]

The EM-weighted averaged Te for the FOV size, 1.0 to 1.3 Rs relative to that for the maxmum size (1.7 Rs).

-----------------------------------------------------------------
Filter pair               FOV radius (in Rs)
               1.0         1.1         1.2         1.3       1.7
-----------------------------------------------------------------
Apol/Alms:   1.036766    1.009585    1.003554    1.001787    1.0
tnBe/Alms:   1.045464    1.006318    1.000000    1.000000    1.0
tnBe/Apol:   1.053373    1.007706    1.000000    1.000000    1.0
-----------------------------------------------------------------

The total EM included in the FOV size, 1.0 to 1.3 Rs relative to that for the maxmum size (1.7 Rs).

-----------------------------------------------------------------
Filter pair               FOV radius (in Rs)
               1.0         1.1         1.2         1.3       1.7
-----------------------------------------------------------------
Apol/Alms:   0.762972    0.929118    0.967767    0.981841    1.0
tnBe/Alms:   0.784352    0.972834    1.000000    1.000000    1.0
tnBe/Apol:   0.779435    0.970815    1.000000    1.000000    1.0
-----------------------------------------------------------------

5.2 : Calculate 2-D irradiance (5-60A)

The 2D-irradiance map is obtained by calculating the irradiance of the isothermal corona for each pixel of 2D-Te map and corresponding pixel of EM map. The quarter disk mask image is applied to the irradiance map and the total irradiance included in the open area is calculated.

[click image to enlarge]

The XRT irradiance included in the FOV size, 1.0, 1.1, 1.2, and 1.3 Rs relative to that for the maxmum size (1.7 Rs).

-----------------------------------------------------------------
Filter pair               FOV radius (in Rs)
               1.0         1.1         1.2         1.3       1.7
-----------------------------------------------------------------
Apol/Alms:   0.775731    0.932218    0.968845    0.982374    1.0
tnBe/Alms:   0.801218    0.975571    1.000000    1.000000    1.0
tnBe/Apol:   0.801115    0.974530    1.0000000   1.0000000   1.0
-----------------------------------------------------------------

6. Data analysis 3 --- at Quiet Sun condition

6.1 : Collect coronal intensities within 1.3 Rs

[click image to enlarge]

[click image to enlarge]

The XRT intensities included in the 4-leafed FOV size, 1.0, 1.1 & 1.2 relative to that of the maxmum size (1.3 Rs).

-----------------------------------------------------------------
Filter                    FOV radius (in Rs)
               1.0         1.1         1.2         1.3     
-----------------------------------------------------------------
Al_mesh:     0.662069    0.932009    0.983907      1.0
Al_poly:     0.583695    0.898404    0.974255      1.0
Ti_poly:     0.583140    0.907152    0.973879      1.0
thin_Be:     0.471829    0.809106    0.938594      1.0
-----------------------------------------------------------------

6.2 : Calculate Te and EM

[click image to enlarge]


using Chianti ver.9 instead of ver.10	using Chianti ver.9 instead of ver.10

The ratio of the Te calculated for the FOV size, 1.0, 1.1, and 1.2 Rs relative to that for the maxmum size (1.3 Rs).

-----------------------------------------------------------------
Filter pair                FOV radius (in Rs)
                 1.0         1.1         1.2         1.3
-----------------------------------------------------------------
Apol/Alms:     0.953771    0.985686    0.996086      1.0
Tpol/Alms:     0.947060    0.987906    0.995361      1.0
tnBe/Alms:     0.944312    0.978498    0.994699      1.0
tnBe/Apol:     0.949433    0.975471    0.990896      1.0
-----------------------------------------------------------------

The ratio of the EM calculated for the FOV size, 1.0, 1.1, and 1.2 Rs relative to that for the maxmum size (1.3 Rs).

-----------------------------------------------------------------
Filter pair                FOV radius (in Rs)
                 1.0         1.1         1.2         1.3
-----------------------------------------------------------------
Apol/Alms:     0.670474    0.935276    0.984815      1.0
Tpol/Alms:     0.680297    0.937093    0.985923      1.0
tnBe/Alms:     0.668562    0.935596    0.985187      1.0
tnBe/Apol:     0.691764    0.980017     1.00301      1.0
-----------------------------------------------------------------

6.3 : Calculate XRT Irradiance

[click image to enlarge]

-----------------------------------------------------------------
Filter pair                FOV radius (in Rs)
                 1.0         1.1         1.2         1.3
-----------------------------------------------------------------
Apol/Alms:     0.593938    0.881161    0.956145      1.0
Tpol/Alms:     0.569324    0.905216    0.985923      1.0
tnBe/Alms:     0.580185    0.885690    0.958894      1.0
tnBe/Apol:     0.621636    0.930290    1.00301       1.0
-----------------------------------------------------------------

7. Deriving Radial Intensity Variations

7.1 : 2022/07/16 --- medium active corona

[click image to enlarge]

positions of intensity profile in the Linear-Log plot

Difference of I(r+1) and I(r)

[click image to enlarge]

7.2 : 2009/08/10 --- minimum corona

[click image to enlarge]

position of intensity profile in the Linear-Log plot

extrapolating radial intansity variation by assumig decreasing rate [I(r+1)-I(r)].

Intensity decreasing rate
<1.29 : observed
>1.31 : assumed as reaching zero at 1.43 Rs Radial intensity variation
<1.29 : observed
>1.31 : calculated
generating the integrated signals at higher than 1.3Rs

height ≤ 1.30 : observed
height > 1.30 : calculated
calculate Te and EM.

Temperature Emission Measure
Trying 2D-approach (with 20090812 data)
- for Al_mesh, Al_poly, Ti_poly : area outer than 1.3 Rs is noise.
- for thin_Be : most area is not suitable for TEEM study.

Al_mesh composite image	Al_poly composite image	thin_Be composite image

Al_mesh stray light img subtracted	Al_poly stray light img subtracted	---


results with previous calibration	results with previous calibration

Intensity decreasing rate <1.29 : observed >1.31 : assumed as reaching zero at 1.43 Rs	Radial intensity variation <1.29 : observed >1.31 : calculated

Temperature	Emission Measure