Optimization of graded multilayer designs for astronomical x-ray telescopes

Peter H. Mao; Fiona A. Harrison; David L. Windt; Finn E. Christensen

doi:10.1364/AO.38.004766

Optimization of graded multilayer designs for astronomical x-ray telescopes

Peter H. Mao, Fiona A. Harrison, David L. Windt, and Finn E. Christensen

Applied Optics
Vol. 38,
Issue 22,
pp. 4766-4775
(1999)
•https://doi.org/10.1364/AO.38.004766

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Peter H. Mao, Fiona A. Harrison, David L. Windt, and Finn E. Christensen, "Optimization of graded multilayer designs for astronomical x-ray telescopes," Appl. Opt. 38, 4766-4775 (1999)

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Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Telescopes (110.6770)
- Multilayers (230.4170)
- Astronomical optics (350.1260)
- X-ray mirrors (340.7470)

About this Article
History
- Original Manuscript: February 8, 1999
- Revised Manuscript: May 12, 1999
- Published: August 1, 1999

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Abstract

We developed a systematic method for optimizing the design of depth-graded multilayers for astronomical hard-x-ray and soft-γ-ray telescopes based on the instrument’s bandpass and the field of view. We apply these methods to the design of the conical-approximation Wolter I optics employed by the balloon-borne High Energy Focusing Telescope, using W/Si as the multilayer materials. In addition, we present optimized performance calculations of mirrors, using other material pairs that are capable of extending performance to photon energies above the W K-absorption edge (69.5 keV), including Pt/C, Ni/C, Cu/Si, and Mo/Si.

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Mirror Group	Angular Range (mrad)	Radial Range (cm)	Shells per Module	d _min (Å) (with θ_max = α_max)	d _min (Å) (adjusted)	Δd _min	d _max (Å)
1	1.67–1.86	4.00–4.46	6	47.6	33.3	-30%	297.6
2	1.86–2.08	4.46–4.99	6	42.7	29.9	-30%	266.6
3	2.08–2.32	4.99–5.57	7	38.2	28.7	-25%	238.9
4	2.32–2.59	5.57–6.22	7	34.2	27.4	-20%	214.0
5	2.59–2.89	6.22–6.94	7	30.7	26.1	-15%	191.8
6	2.89–3.22	6.94–7.73	7	27.5	24.7	-10%	171.8
7	3.22–3.60	7.73–8.64	7	24.6	24.6	0%	153.9
8	3.60–4.01	8.64–9.62	8	22.1	24.3	+10%	137.9
9	4.01–4.48	9.62–10.75	8	19.8	23.7	+20%	123.6
10	4.48–5.00	10.75–12.0	8	17.7	23.0	+30%	110.7

Mirror Group	Optimum Designa					Near-Optimum Designb
Mirror Group	Nc	cd	Γe	tf	FOM	N	c	Γ	t	FOM
1	250	0.200	0.35	1.06	0.532	150	0.225	0.40	0.66	0.525
2	350	0.205	0.35	1.33	0.609	200	0.230	0.40	0.79	0.600
3	350	0.210	0.35	1.28	0.796	250	0.220	0.40	0.93	0.790
4	400	0.205	0.35	1.39	0.865	250	0.225	0.40	0.90	0.852
5	450	0.200	0.35	1.48	0.905	300	0.220	0.40	1.01	0.893
6	500	0.195	0.35	1.54	0.913	350	0.215	0.40	1.11	0.899
7	450	0.195	0.35	1.38	0.865	350	0.200	0.40	1.08	0.852
8	450	0.190	0.35	1.36	0.867	350	0.205	0.35	1.08	0.858
9	450	0.185	0.35	1.31	0.725	350	0.200	0.35	1.04	0.710
10	450	0.180	0.35	1.27	0.588	350	0.195	0.35	1.00	0.574

Materials	ρ₁/ρ₂	µ₁ (cm^-1)b	µ₂ (cm^-1)c
Pt/C	9.77	566	0.435
W/Si	8.28	439	3.35
Mo/Si	4.38	287	3.35
Ni/C	4.05	92.0	0.435
Cu/Si	3.85	97.8	3.35

Mirror Group	Angular Range (mrad)	Radial Range (cm)	Shells per Module	d _min (Å) (with θ_max = α_max)	d _min (Å) (adjusted)	Δd _min	d _max (Å)
1	1.67–1.86	4.00–4.46	6	47.6	33.3	-30%	297.6
2	1.86–2.08	4.46–4.99	6	42.7	29.9	-30%	266.6
3	2.08–2.32	4.99–5.57	7	38.2	28.7	-25%	238.9
4	2.32–2.59	5.57–6.22	7	34.2	27.4	-20%	214.0
5	2.59–2.89	6.22–6.94	7	30.7	26.1	-15%	191.8
6	2.89–3.22	6.94–7.73	7	27.5	24.7	-10%	171.8
7	3.22–3.60	7.73–8.64	7	24.6	24.6	0%	153.9
8	3.60–4.01	8.64–9.62	8	22.1	24.3	+10%	137.9
9	4.01–4.48	9.62–10.75	8	19.8	23.7	+20%	123.6
10	4.48–5.00	10.75–12.0	8	17.7	23.0	+30%	110.7

Mirror Group	Optimum Designa					Near-Optimum Designb
Mirror Group	Nc	cd	Γe	tf	FOM	N	c	Γ	t	FOM
1	250	0.200	0.35	1.06	0.532	150	0.225	0.40	0.66	0.525
2	350	0.205	0.35	1.33	0.609	200	0.230	0.40	0.79	0.600
3	350	0.210	0.35	1.28	0.796	250	0.220	0.40	0.93	0.790
4	400	0.205	0.35	1.39	0.865	250	0.225	0.40	0.90	0.852
5	450	0.200	0.35	1.48	0.905	300	0.220	0.40	1.01	0.893
6	500	0.195	0.35	1.54	0.913	350	0.215	0.40	1.11	0.899
7	450	0.195	0.35	1.38	0.865	350	0.200	0.40	1.08	0.852
8	450	0.190	0.35	1.36	0.867	350	0.205	0.35	1.08	0.858
9	450	0.185	0.35	1.31	0.725	350	0.200	0.35	1.04	0.710
10	450	0.180	0.35	1.27	0.588	350	0.195	0.35	1.00	0.574

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