Hinode/XRT response functions

Stray Light Correction of the XRT Temperature Response Functions

(7, September, 2015 by Aki Takeda)
(11 Sep,2015 added ratio curves & estimation of open fraction.)
(16 Dec,2019 figures of telescope.)
(23 Feb,2026 added derivation method of open fraction.)

1. Introduction.

What is the XRT temperature response functions?

[Physically ...]
Expected number of photons which will be detected by the CCD (or the number of electrons produced by them) by observing the model plasma (i.e., isothermal plasma with the unit emission measure, e.g., 1 cm^[-5]) through each analysis filter.
[Mathematically ...]
XRT's effective area functions integrated (with respect to wavelength) with the synthesized solar spectra. The former is the spectral response (spectral sensitivity) modified by each analysis filter. The latter is calculated for a given elemental abundance and ionization balance under a certain emission model (e.g., isothermal plasma) of the solar spectra.
```
 
[Temperature response func.] = [Factor(geometrical, etc.)] * [Model Solar Spectra] # [XRT Effective Area]
           (T)                                                       (T, λ)                   (λ)
```

2. XRT's effective area function.

[Effective Area] = [aperture] * [prefilter] * [mirror1] * [mirror2] * [filter1] * [filter2] * [ccdqe] * [contamination]

aperture=2.28 cm^2
filter1=1.0 (FW1=OPEN)
filter2=1.0 (FW2=OPEN)

Effective Area modified partially opened prefilter (without X-ray filters).

3. Modified response functions.

After multiplying the FW1 and FW2 responses, take convolution with the model solar spectra calculated based on Chianti version 7.1.3.
Here we assume the Open Fraction having the value of 0.45 and 0.95 (see Section 5 for derivation).

Open/Al-mesh	Open/Ti-poly

Al-poly/Open	Thin-Be/Open

Open/thick-Al	Open/thick-Be

4. Modification of the Filter Ratio.

Al-poly/Al-mesh	Ti-poly/Al-mesh

thin-Be/Al-poly	thick-Be/thick-Al

5. Estimation of the "Open Fraction" of the prefilter.

G-band images taken with VLS(visible light shutter) Open or Close can be used to estimate the amount of stray light coming through the open area of the prefilter.

VLI transmission from the Blue Book section 2.5.1.

The VLI transmission should not be the peak value (0.026) but the averaged value (0.020) over the band width (since Nov-2025). In addition, the effective area of G-band optics was initially assumed as 25mm*25mm*3.14, from the size of G-band lens (having 50mm diameter). However, the actual value should be smaller because of the way it is mounted in a long housing tube. The new value of VLI effective area is 20mm*20mm*3.14 (since May-2026).

Sample case of phase 1 (10-Jan-2013)

G-band normal image: I_vls_open = Is * (25*25*3.14) * 0.026 * 0.4932
⇒[correction]⇒ G-band normal image: I_vls_open = Is * (20*20*3.14) * 0.020 * 0.4932
Stray light component: I_vls_close = Is * (open area) * 0.4932

VLS_open image : [normal G-band image] overlapped with [stray light image]
VLS_close image : [stray light image] only.

[Total intensity of VLS_open image] = 1.0820e+11 (DN/sec)
[Total intensity of VLS_close image] = 4.8259e+10 (DN/sec)
[Total intensity of normal G-band image] = 5.9941e+10 (DN/sec)


	Ratio of total image intensity : [VLS_close]/[VLS_open] = 4.8259e+10/1.0820e+11 = 0.446 [stray light comp.]/[norm. G-band] = 4.8259/5.9941 = 0.8051

[open area ratio] = [open area (mm^2)]/[XRT effective area (228 mm^2)]
[open area ratio] = [4.826e10 * 0.00026 * 1963.5] / [228 * 5.994e10] = 0.001802
[open area ratio] ⇒ [4.826e10 * 0.00020 * 1963.5] / [228 * 5.994e10] = 0.001386 (applied since 10-Nov-2025)
[open area ratio] ⇒ [4.826e10 * 0.00020 * 1256.6] / [228 * 5.994e10] = 0.0008875 (applied since 31-May-2026)

Sample case of phase 2 (10-Jul-2015)


	Ratio of total image intensity : [VLS_close]/[VLS_open] = 1.0767e12/1.1295e12 = 0.953.. [stray light comp.]/[norm. G-band] = 1.0767e12/5.2812e10 = 20.4

[open area ratio] = [1.077e12 * 0.00026 * 1963.5] / [228 * 5.281e10] = 0.04566
[open area ratio] ⇒ [1.077e12 * 0.00020 * 1963.5] / [228 * 5.281e10] = 0.03513 (applied since 10-Nov-2025)
[open area ratio] ⇒ [1.077e12 * 0.00020 * 1256.6] / [228 * 5.281e10] = 0.02248 (applied since 31-May-2026)

Phase 3 and after
- Unable to use the same method due to a large error in G-band measurements (leak components overwhelms normal G-band intensity).
- Use G-band intensity analysis for CCD contam-DB (by K. Yoshimura).
  - G-band intensity ratio [phase_3/phase_2]=2.3
  - G-band intensity ratio [phase_4/phase_3]=1.33
- Derived open frac ratio (for the correction after 31-May-2026).
  - Phase_3 (2017/5/27-): 0.02248 * 2.3 = 0.0517
  - Phase_4 (2018/5/29-): 0.02248 * 2.3 * 1.33 = 0.0688
- After phase_4, the stray light increasing factor is calculated from the difference of Al_mesh images, since G-band images started to show saturation even with the shortest exposure at 1 msec.
  - Phase_5 (2022/6/8-): 0.02248 * 2.3 * 1.33 * 1.10 = 0.0756
  - Phase_6 (2023/5/5-): 0.02248 * 2.3 * 1.33 * 1.10 * 1.23 = 0.0930
  - Phase_7 (2024/5/11-): 0.02248 * 2.3 * 1.33 * 1.10 * 1.23 * 1.22 = 0.1135

6. Software to use the modified response functions.

(idlpro/xrt)
(idlpro/xrt/irrad3 for older versions)

FUNCTION get_pf_openfrac, input
;+
; This routine returns the XRT pre-filter open ratio estimated
;   from the G-band image analysis by Aki Takeda in June-2026.
;
;   open_ratio at phase 1 (after  9-May-2012 12:00) : 0.0009             [cf: 0.001 in ver.20250123]
;   open_ratio at phase 2 (after 14-Jun-2015 12:30) : 0.0225                 [0.033]
;   open_ratio at phase 3 (after 27-May-2017 11:00) : 0.0517 ; 0.0225*2.30   [0.075]
;   open_ratio at phase 4 (after 29-May-2018 00:00) : 0.0688 ; 0.0517*1.33   [0.099]
;   open_ratio at phase 5 (after  8-Jun-2022 12:40) : 0.0756 ; 0.0688*1.10   [0.108]
;   open_ratio at phase 6 (after  5-May-2023 04:30) : 0.0930 ; 0.0756*1.23   [0.135]
;   open_ratio at phase 7 (after 11-May-2024 06:16) : 0.1135 ; 0.0930*1.22   [0.165]
;
; IDL> factor=get_pf_openfrac(XRT_index)
; IDL> factor=get_pf_openfrac('19-feb-2013 12:00')
;
; HISTORY : 18-Oct-2020 : initial version,
;                           get_slcorfact_raw.pro was modified.
;           24-oct-2020 : phase 3 and 4 values optimized by
;                           using G-band monitor image values.
;           12-nov-2020 : phase 2 to 4 values modified according to
;                         the change front blue filter transmission,
;                         from 0.026%(peak) to 0.020%(average).
;            6-sep-2022 : added phase 5 values.
;           13-jun-2023 : added phase 6 values.
;           26-aug-2024 : added phase 7 values.
;           28-nov-2024 : a bug fixed (ofrac_p7 typo).
;           23-jan-2025 : a bug fixed (p6 starting date corrected).
;            6-jun-2026 : reconsideration of G-band optics
;                         effective area (1963.5 --> 1256.6 mm^2).
;-