Demonstration of resolving power λ/Δλ &gt; 10,000 for a space-based x-ray transmission grating spectrometer

Ralf K. Heilmann; Jeffery Kolodziejczak; Alexander R. Bruccoleri; Jessica A. Gaskin; Mark L. Schattenburg

doi:10.1364/AO.58.001223

Applied Optics
Vol. 58,
Issue 5,
pp. 1223-1238
(2019)
•https://doi.org/10.1364/AO.58.001223

Demonstration of resolving power λ/Δλ > 10,000 for a space-based x-ray transmission grating spectrometer

Ralf K. Heilmann, Jeffery Kolodziejczak, Alexander R. Bruccoleri, Jessica A. Gaskin, and Mark L. Schattenburg

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Ralf K. Heilmann, Jeffery Kolodziejczak, Alexander R. Bruccoleri, Jessica A. Gaskin, and Mark L. Schattenburg, "Demonstration of resolving power λ/Δλ > 10,000 for a space-based x-ray transmission grating spectrometer," Appl. Opt. 58, 1223-1238 (2019)

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- Diffraction and Gratings
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About this Article
History
- Original Manuscript: October 11, 2018
- Revised Manuscript: December 18, 2018
- Manuscript Accepted: December 26, 2018
- Published: February 6, 2019

Abstract

We present measurements of the resolving power of a soft x-ray spectrometer consisting of 200 nm period lightweight, alignment-insensitive critical-angle transmission (CAT) gratings and a lightweight slumped-glass Wolter-I focusing mirror pair. We measure and model contributions from source, mirrors, detector pixel size, and grating period variation to the natural linewidth spectrum of the Al- $K_{α_{1} α_{2}}$ doublet. Measuring up to the 18th diffraction order, we consistently obtain small broadening due to gratings corresponding to a minimum effective grating resolving power $R_{g} > 10, 000$ with 90% confidence. Upper limits are often compatible with $R_{g} = \infty$ . Independent fitting of different diffraction orders, as well as ensemble fitting of multiple orders at multiple wavelengths, gives compatible results. Our data leads to uncertainties for the Al- $K_{α}$ doublet linewidth and line separation parameters two to three times smaller than values found in the literature. Data from three different gratings are mutually compatible. This demonstrates that CAT gratings perform in excess of the requirements for the Arcus Explorer mission and are suitable for next-generation space-based x-ray spectrometer designs with resolving power five to 10 times higher than the transmission grating spectrometer onboard the Chandra X-ray Observatory.

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Cross-Dispersion Range Arcsec (pixels)	Line FWHM Arcsec	Half Power Width Arcsec	Flux Fraction in Range %
$< 3.16 (< 10.5)$	$0.40 \pm 0.01$	$0.27 \pm 0.01$	15
3.16–9.48 (10.5–31.5)	$0.61 \pm 0.03$	$0.41 \pm 0.02$	36
9.48–15.80 (31.5–52.5)	$1.23 \pm 0.12$	$0.84 \pm 0.08$	33

$α_{1}$		$α_{2}$		Ref.
$λ$	$Γ$	$λ$	$Γ$	Ref.
0.8339527	$0.4 \pm 0.1$	0.8341843	$0.4 \pm 0.1$	[7] (1994)
$\pm 0.0000056$		$\pm 0.0000056$
0.833934		0.834173		[41] (1967)
$\pm 0.000009$		$\pm 0.000009$
0.83393				[42] (1964)
$\pm 0.00006$
	$0.42 \pm 0.02$		$0.42 \pm 0.02$	[43] (2001)
	$0.43 \pm 0.04$		$0.43 \pm 0.04$	[44] (1979)

Model Constants	Nominal Values	Description
$Γ_{α 1} = Γ_{α 2}$	236 fm, 0.42 eV	$Al K_{α 1}$ , $K_{α 2}$ Lorentzian FWHM
$λ_{α 2} - λ_{α 1}$	232 fm (0.413 eV)	$Al K_{α 1}$ , $K_{α 2}$ separation

Parameter	Table 5(a–f)	Table 6(a,b)	Description
$Q_{0}$	var	var	Signal floor
$n$	var	var	18th order Al normalization
$f_{G}$	var	var	Gaussian FWHM for 18th order
$L$	1.0	var	Fraction of nominal Al- $K α$ natural linewidth
$S$	1.0	var	Fraction of nominal Al- $K α_{1, 2}$ line separation
$x_{0}$	var	var	18th order Al- $K α_{1}$ peak $x$ position

Fit ID	CDB	ROI pixels	$f_{G}$ pixels	$R_{g}$ (90% l.l.) from $Δ χ^{2}$	$R_{g}$ (90% l.l.) from fit	$χ^{2}$	DOF	$P (χ^{2})$
(a)	0	143	$0 + 2.8$	15600	-	125.0	135	0.28
(b)	$0, \pm 1$	143	$0 + 1.8$	24500	-	133.6	135	0.48
(c)	$0, \pm 1, \pm 2$	143	$0 + 2.0$	21500	-	126.0	135	0.30
(d)	0	27	$3.3 \pm 1.8$	9100	8700	20.55	19	0.64
(e)	$0, \pm 1$	27	$2.1 \pm 1.5$	12600	12200	16.76	19	0.39
(f)	$0, \pm 1, \pm 2$	27	$2.6 \pm 1.2$	12100	12200	17.62	19	0.45

Fit ID	(a)	(b)	(c)	(d)	(e)	(f)	(g)	(h)	(i)
Order	18	18	14	14	10	10	7	18-14-10	18-14-10
CDB	$0, \pm 1$	$0, \pm 1, \pm 2$	$0, \pm 1$	$0, \pm 1, \pm 2$	$0, \pm 1$	$0, \pm 1, \pm 2$	$0, \pm 1$	$0, \pm 1$	$0, \pm 1, \pm 2$
phot/1000	22.2	31.8	10.2	14.8	7.3	10.8	9.	39.7	57.4
$f_{G}$	2.58	2.03	2.64	1.93	2.07	1.96	2.39	2.86	2.02
$σ_{G}$	1.67	1.71	1.27	1.40	1.40	1.27	0.70	1.14	1.32
$R_{g}$ (best fit)	18900	24000	14300	19600	13100	13800	7900	17000	24100
$R_{g}$ (90% l.l. from fit)	9100	10000	8000	8900	6200	6700	5300	10300	11600
$R_{g}$ (90% l.l. from $Δ χ^{2}$ )	9800	11500	–	–	–	–	–	10400	12400
$R_{g}$ (95% l.l. from fit)	8300	9000	7400	8100	5600	6100	5000	9600	10600
$R_{g}$ (95% l.l. from $Δ χ^{2}$ )	9500	10800	–	–	–	–	–	10000	11800
$L$	0.955	0.98	0.993	0.993	1.05	1.01	0.965	0.991	0.992
$σ_{L}$ from fit	0.034	0.027	0.035	0.03	0.06	0.051	0.055	0.023	0.019
$σ_{L}$ from $Δ χ^{2}$	0.04	$+ 0.02$ , $- 0.04$	–	–	–	–	–	0.03	0.02
$S$	0.995	0.974	0.959	0.971	0.921	0.911	0.931	0.969	0.969
$σ_{S}$	0.014	0.011	0.018	0.015	0.027	0.024	0.029	0.011	0.008
$χ^{2}$	107.6	95.5	141.9	133.7	63.0	61.4	42.8	329.0	311.6
DOF	107	107	123	119	56	53	48	292	287
$P (χ^{2} \| DOF)$	0.53	0.22	0.88	0.83	0.76	0.80	0.31	0.93	0.85

Fit ID	Table 6(b)	Table 6(i)	(c)	(d)
Order	18	$Al - {18, 14, 10}$	$Al - {18, 14, 10}, Mg - 12$	$Al - {18, 14, 10}, Mg - 12$
CDB	$0, \pm 1, \pm 2$	$0, \pm 1, \pm 2$	$0, \pm 1$	$0, \pm 1, \pm 2$
$R_{g}$ (best fit)	24000	24100	16400	23200
$R_{g}$ (90% l.l. from fit)	10000	11600	10400	11700
$R_{g}$ (90% l.l. from $Δ χ^{2}$ )	11500	12400	12700	12300
$R_{g}$ (95% l.l. from fit)	9000	10600	9700	10700
$R_{g}$ (95% l.l. from $Δ χ^{2}$ )	10800	11800	11800	11700

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Applied Optics