Practical, corrected Kirkpatrick-Baez telescope for x-ray astronomy

Dana Longcope; Loren Acton; Charles Kankelborg

doi:10.1364/AO.58.004969

Applied Optics
Vol. 58,
Issue 18,
pp. 4969-4980
(2019)
•https://doi.org/10.1364/AO.58.004969

Practical, corrected Kirkpatrick-Baez telescope for x-ray astronomy

Dana Longcope, Loren Acton, and Charles Kankelborg

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Dana Longcope, Loren Acton, and Charles Kankelborg, "Practical, corrected Kirkpatrick-Baez telescope for x-ray astronomy," Appl. Opt. 58, 4969-4980 (2019)

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Abstract

Kirkpatrick-Baez (K-B) optics offer a means of imaging soft x-rays with modest resolution and a multi-arc-minute field of view at a cost far below the conventional Wolter design. Such a low-cost system could be useful for dedicated, long-time-line observation of astronomical x-ray sources from orbit. A K-B telescope consists of crossed arrays of parabolic mirrors at grazing incidence. The classic K-B telescope is subject to significant aberration arising from the interplay between the focusing of the fore and aft mirror arrays. We demonstrate here a corrected K-B prescription with aberrations reduced by an order of magnitude. We show, furthermore, that it is possible to construct such a system by constraining flat “slats” of commercially available glass in precision-milled grooves. The slats deform into shapes that adequately approximate the optimal figures, thereby yielding focusing better than the best version of the classic K-B telescope. The result is a new approach that greatly simplifies the task of achieving both useful resolution and high effective area for x-ray astronomy applications.

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Fore: $Z_{1} = 160.0000 cm$
	$Y_{1} = 10.3897 cm$				$Y_{1} = 2.0480 cm$
$j$	$X_{1}^{(j)}$	$10^{3} \times b_{1}$	$10^{6} \times b_{2}$	$10^{8} \times b_{3}$	$X_{1}^{(j)}$	$10^{3} \times b_{1}$	$10^{6} \times b_{2}$	$10^{8} \times b_{3}$
$j$	[cm]	—	[ ${cm}^{- 1}$ ]	[ ${cm}^{- 2}$ ]	[cm]	—	[ ${cm}^{- 1}$ ]	[ ${cm}^{- 2}$ ]
1	10.33260	32.1866	49.7115	18.3878	10.33260	32.2678	49.9593	18.5483
2	9.64525	30.0493	46.4298	17.1338	9.64523	30.1252	46.6471	17.3194
3	9.00345	28.0530	43.3500	15.9984	9.00344	28.1239	43.5604	16.1543
4	8.40425	26.1888	40.4566	14.9933	8.40424	26.2550	40.6608	15.1034
5	7.84483	24.4477	37.7694	14.0013	7.84482	24.5094	37.9647	14.0966
6	7.32257	22.8218	35.2748	13.0219	7.32256	22.8795	35.4421	13.1619
7	6.83501	21.3037	32.9304	12.1597	6.83500	21.3576	33.0866	12.2919
8	6.37987	19.8863	30.7339	11.3751	6.37986	19.9366	30.8830	11.4833
9	5.95500	18.5628	28.6974	10.5991	5.95499	18.6098	28.8354	10.7001
10	5.55838	17.3274	26.7824	9.9127	5.55837	17.3711	26.9227	9.9686
11	5.18816	16.1739	24.9951	9.2685	5.18815	16.2148	25.1240	9.3277
12	4.84257	15.0970	23.3343	8.6458	4.84256	15.1352	23.4474	8.7242
13	4.51998	14.0917	21.7893	8.0435	4.51997	14.1274	21.8890	8.1420
14	4.21887	13.1533	20.3398	7.5034	4.21886	13.1866	20.4347	7.5903
15	3.93780	12.2773	18.9832	7.0111	3.93780	12.3083	19.0768	7.0780
16	3.67546	11.4596	17.7151	6.5591	3.67545	11.4885	17.8018	6.6203
17	3.43058	10.6962	16.5366	6.1173	3.43057	10.7233	16.6204	6.1638
18	3.20201	9.9837	15.4378	5.7023	3.20200	10.0090	15.5108	5.7634
19	2.98866	9.3187	14.4045	5.3389	2.98866	9.3422	14.4824	5.3653
20	2.78952	8.6979	13.4469	4.9749	2.78952	8.7199	13.5108	5.0311

Aft: $Z_{2} = 138.0000 cm$
	$X_{2} = 2.6098 cm$				$X_{2} = 10.9515 cm$
$i$	$Y_{2}^{(i)}$	$10^{3} \times b_{1}$	$10^{6} \times b_{2}$	$10^{8} \times b_{3}$	$Y_{2}^{(i)}$	$10^{3} \times b_{1}$	$10^{6} \times b_{2}$	$10^{8} \times b_{3}$
$i$	[cm]	—	[ ${cm}^{- 1}$ ]	[ ${cm}^{- 2}$ ]	[cm]	—	[ ${cm}^{- 1}$ ]	[ ${cm}^{- 2}$ ]
1	10.39000	37.5927	67.2924	29.8534	10.39000	37.5927	67.2924	29.8534
2	9.57942	34.6673	62.0723	27.5291	9.57942	34.6673	62.0723	27.5291
3	8.83183	31.9677	57.2466	25.3951	8.83183	31.9677	57.2466	25.3951
4	8.14237	29.4765	52.7960	23.4224	8.14237	29.4765	52.7960	23.4224
5	7.50657	27.1785	48.6769	21.6319	7.50657	27.1785	48.6769	21.6319
6	6.92029	25.0584	44.8963	19.9143	6.92029	25.0584	44.8963	19.9143
7	6.37969	23.1032	41.3945	18.3662	6.37969	23.1032	41.3945	18.3662
8	5.88125	21.2998	38.1656	16.9384	5.88125	21.2998	38.1656	16.9384
9	5.42169	19.6368	35.1888	15.6180	5.42169	19.6368	35.1888	15.6180
10	4.99799	18.1032	32.4423	14.4036	4.99799	18.1032	32.4423	14.4036
11	4.60736	16.6891	29.9117	13.2738	4.60736	16.6891	29.9117	13.2738
12	4.24723	15.3853	27.5750	12.2394	4.24723	15.3853	27.5750	12.2394
13	3.91523	14.1832	25.4243	11.2747	3.91523	14.1832	25.4243	11.2747
14	3.60916	13.0748	23.4333	10.4074	3.60916	13.0748	23.4333	10.4074
15	3.32701	12.0529	21.6081	9.5806	3.32701	12.0529	21.6081	9.5806
16	3.06690	11.1109	19.9173	8.8347	3.06690	11.1109	19.9173	8.8347
17	2.82712	10.2424	18.3589	8.1526	2.82712	10.2424	18.3589	8.1526
18	2.60608	9.4417	16.9255	7.5094	2.60608	9.4417	16.9255	7.5094
19	2.40231	8.7036	15.6026	6.9231	2.40231	8.7036	15.6026	6.9231
20	2.21448	8.0231	14.3846	6.3779	2.21448	8.0231	14.3846	6.3779

Fore: $Z_{1} = 160.0000 cm$
	$Y_{1} = 10.3897 cm$				$Y_{1} = 2.0480 cm$
$j$	$X_{1}^{(j)}$	$10^{3} \times b_{1}$	$10^{6} \times b_{2}$	$10^{8} \times b_{3}$	$X_{1}^{(j)}$	$10^{3} \times b_{1}$	$10^{6} \times b_{2}$	$10^{8} \times b_{3}$
$j$	[cm]	—	[ ${cm}^{- 1}$ ]	[ ${cm}^{- 2}$ ]	[cm]	—	[ ${cm}^{- 1}$ ]	[ ${cm}^{- 2}$ ]
1	10.33260	32.1866	49.7115	18.3878	10.33260	32.2678	49.9593	18.5483
2	9.64525	30.0493	46.4298	17.1338	9.64523	30.1252	46.6471	17.3194
3	9.00345	28.0530	43.3500	15.9984	9.00344	28.1239	43.5604	16.1543
4	8.40425	26.1888	40.4566	14.9933	8.40424	26.2550	40.6608	15.1034
5	7.84483	24.4477	37.7694	14.0013	7.84482	24.5094	37.9647	14.0966
6	7.32257	22.8218	35.2748	13.0219	7.32256	22.8795	35.4421	13.1619
7	6.83501	21.3037	32.9304	12.1597	6.83500	21.3576	33.0866	12.2919
8	6.37987	19.8863	30.7339	11.3751	6.37986	19.9366	30.8830	11.4833
9	5.95500	18.5628	28.6974	10.5991	5.95499	18.6098	28.8354	10.7001
10	5.55838	17.3274	26.7824	9.9127	5.55837	17.3711	26.9227	9.9686
11	5.18816	16.1739	24.9951	9.2685	5.18815	16.2148	25.1240	9.3277
12	4.84257	15.0970	23.3343	8.6458	4.84256	15.1352	23.4474	8.7242
13	4.51998	14.0917	21.7893	8.0435	4.51997	14.1274	21.8890	8.1420
14	4.21887	13.1533	20.3398	7.5034	4.21886	13.1866	20.4347	7.5903
15	3.93780	12.2773	18.9832	7.0111	3.93780	12.3083	19.0768	7.0780
16	3.67546	11.4596	17.7151	6.5591	3.67545	11.4885	17.8018	6.6203
17	3.43058	10.6962	16.5366	6.1173	3.43057	10.7233	16.6204	6.1638
18	3.20201	9.9837	15.4378	5.7023	3.20200	10.0090	15.5108	5.7634
19	2.98866	9.3187	14.4045	5.3389	2.98866	9.3422	14.4824	5.3653
20	2.78952	8.6979	13.4469	4.9749	2.78952	8.7199	13.5108	5.0311

Aft: $Z_{2} = 138.0000 cm$
	$X_{2} = 2.6098 cm$				$X_{2} = 10.9515 cm$
$i$	$Y_{2}^{(i)}$	$10^{3} \times b_{1}$	$10^{6} \times b_{2}$	$10^{8} \times b_{3}$	$Y_{2}^{(i)}$	$10^{3} \times b_{1}$	$10^{6} \times b_{2}$	$10^{8} \times b_{3}$
$i$	[cm]	—	[ ${cm}^{- 1}$ ]	[ ${cm}^{- 2}$ ]	[cm]	—	[ ${cm}^{- 1}$ ]	[ ${cm}^{- 2}$ ]
1	10.39000	37.5927	67.2924	29.8534	10.39000	37.5927	67.2924	29.8534
2	9.57942	34.6673	62.0723	27.5291	9.57942	34.6673	62.0723	27.5291
3	8.83183	31.9677	57.2466	25.3951	8.83183	31.9677	57.2466	25.3951
4	8.14237	29.4765	52.7960	23.4224	8.14237	29.4765	52.7960	23.4224
5	7.50657	27.1785	48.6769	21.6319	7.50657	27.1785	48.6769	21.6319
6	6.92029	25.0584	44.8963	19.9143	6.92029	25.0584	44.8963	19.9143
7	6.37969	23.1032	41.3945	18.3662	6.37969	23.1032	41.3945	18.3662
8	5.88125	21.2998	38.1656	16.9384	5.88125	21.2998	38.1656	16.9384
9	5.42169	19.6368	35.1888	15.6180	5.42169	19.6368	35.1888	15.6180
10	4.99799	18.1032	32.4423	14.4036	4.99799	18.1032	32.4423	14.4036
11	4.60736	16.6891	29.9117	13.2738	4.60736	16.6891	29.9117	13.2738
12	4.24723	15.3853	27.5750	12.2394	4.24723	15.3853	27.5750	12.2394
13	3.91523	14.1832	25.4243	11.2747	3.91523	14.1832	25.4243	11.2747
14	3.60916	13.0748	23.4333	10.4074	3.60916	13.0748	23.4333	10.4074
15	3.32701	12.0529	21.6081	9.5806	3.32701	12.0529	21.6081	9.5806
16	3.06690	11.1109	19.9173	8.8347	3.06690	11.1109	19.9173	8.8347
17	2.82712	10.2424	18.3589	8.1526	2.82712	10.2424	18.3589	8.1526
18	2.60608	9.4417	16.9255	7.5094	2.60608	9.4417	16.9255	7.5094
19	2.40231	8.7036	15.6026	6.9231	2.40231	8.7036	15.6026	6.9231
20	2.21448	8.0231	14.3846	6.3779	2.21448	8.0231	14.3846	6.3779

Abstract

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Figures (12)

Tables (2)

Equations (23)

Applied Optics