Approach based on χ<sup>2</sup> to phasing segmented-mirror telescopes
using multiple wavelengths: data reduction, wavelength selection, capture
range

Gary Chanan; Matthias Schoeck; Mitchell Troy

doi:10.1364/AO.447439

Applied Optics
Vol. 61,
Issue 4,
pp. 935-944
(2022)
•https://doi.org/10.1364/AO.447439

Approach based on χ² to phasing segmented-mirror telescopes using multiple wavelengths: data reduction, wavelength selection, capture range

Gary Chanan, Matthias Schoeck, and Mitchell Troy

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Gary Chanan, Matthias Schoeck, and Mitchell Troy, "Approach based on χ² to phasing segmented-mirror telescopes using multiple wavelengths: data reduction, wavelength selection, capture range," Appl. Opt. 61, 935-944 (2022)

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Abstract

The design of extremely large segmented-mirror telescopes (ELTs) calls for their segments to be phased, and a number of different interferometric techniques have been proposed in the literature for this purpose. To achieve the required large capture ranges for ELTs (typically a few microns), most of these techniques use measurements at multiple wavelengths, similar to what is done in standard distance-measuring laser interferometry. In this paper, we present a ${\chi ^2}$-based framework not tied to a specific phasing technique to obtain intersegment edge heights from multiwavelength data. We show how this scheme can be used to select an optimal set of wavelengths that maximizes the capture range while achieving the very low error rates required for ELT phasing. We take into account the wavelength uncertainty associated with the finite-width interference filters used in on-sky phasing. Finally, we present data from the Keck 2 telescope that illustrate the method for three-wavelength phasing.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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$χ_{0}^{2}$ ( $n m^{2}$ )	$λ_{2}$ (nm)	$C_{0}$ (nm)	$C_{min}$ (nm)	Large Jumps	Small Jumps
6000	—	—	—	—	—
5000	670–680	669–674	665–670	0–0.02	0.21–0.38
4000	665–690	667–679	662–675	0–0.06	0.15–0.83
3000	655–695	662–682	657–677	0–0.59	0.09–1.01
2000	655–690	662–679	657–675	0–0.73	0.07–0.91
1000	655–685	662–677	657–672	0–0.50	0.07–0.64

$λ_{2}$ (nm)	$λ_{3}$ (nm)	$C_{0}$ $(µ m)$	$C_{min}$ $(µ m)$	Large Jumps	Small Jumps
690	630	1.562	1.551	0.010	0.010
700	630	1.570	1.559	0.010	0.010
700	640	1.578	1.567	0.030	0.020
710	650	1.782	1.769	0.030	0.020
720	660	1.799	1.787	0.020	0.070
780	630	1.565	1.554	0.000	0.020
780	640	1.766	1.563	0.010	0.020
790	630	1.571	1.561	0.000	0.010
790	640	1.580	1.569	0.000	0.030
790	650	1.782	1.590	0.000	0.040
800	610	1.996	1.792	0.020	0.000
800	620	2.007	1.568	0.000	0.010
800	630	1.578	1.568	0.000	0.000
800	640	1.781	1.576	0.000	0.010
800	650	1.790	1.590	0.000	0.060
800	660	1.799	1.787	0.000	0.060
810	620	2.015	2.002	0.050	0.010
810	630	2.026	1.588	0.030	0.000
810	640	2.232	1.588	0.010	0.020
810	660	1.807	1.795	0.000	0.100

$λ_{2}$ (nm)	$λ_{3}$ (nm)	$λ_{4}$ (nm)	$C_{0}$ $(µ m)$	$C_{min}$ $(µ m)$	Large Jumps	Small Jumps
825	800	610	5.790	5.147	0.010	0.000
825	800	640	5.584	5.167	0.000	0.010
825	800	655	5.576	5.375	0.000	0.030
830	805	655	6.231	5.375	0.000	0.030
835	815	620	7.122	6.288	0.040	0.000
860	795	615	5.367	5.119	0.010	0.000
860	800	610	5.798	5.148	0.070	0.000
860	800	620	5.585	5.151	0.010	0.000
860	800	655	5.582	5.362	0.000	0.020
860	800	665	5.804	5.362	0.000	0.020
860	800	675	5.582	5.362	0.000	0.040
865	735	690	8.451	5.157	0.010	0.060
865	740	695	14.056	5.158	0.000	0.080
865	745	680	8.005	5.157	0.000	0.030
865	800	675	7.584	5.168	0.010	0.060
865	805	615	8.452	5.593	0.060	0.000
865	805	640	6.247	5.387	0.010	0.000
865	805	645	8.234	5.378	0.010	0.000
865	805	650	8.450	5.389	0.010	0.000
865	805	655	14.910	5.378	0.000	0.020
865	805	660	8.240	5.389	0.000	0.030
865	805	665	14.480	5.378	0.000	0.010
865	810	620	6.683	5.827	0.050	0.000
865	810	630	6.471	6.034	0.020	0.000
865	810	665	6.478	6.034	0.000	0.030

$χ_{0}^{2}$ ( $n m^{2}$ )	$λ_{2}$ (nm)	$C_{0}$ (nm)	$C_{min}$ (nm)	Large Jumps	Small Jumps
6000	—	—	—	—	—
5000	670–680	669–674	665–670	0–0.02	0.21–0.38
4000	665–690	667–679	662–675	0–0.06	0.15–0.83
3000	655–695	662–682	657–677	0–0.59	0.09–1.01
2000	655–690	662–679	657–675	0–0.73	0.07–0.91
1000	655–685	662–677	657–672	0–0.50	0.07–0.64

$λ_{2}$ (nm)	$λ_{3}$ (nm)	$C_{0}$ $(µ m)$	$C_{min}$ $(µ m)$	Large Jumps	Small Jumps
690	630	1.562	1.551	0.010	0.010
700	630	1.570	1.559	0.010	0.010
700	640	1.578	1.567	0.030	0.020
710	650	1.782	1.769	0.030	0.020
720	660	1.799	1.787	0.020	0.070
780	630	1.565	1.554	0.000	0.020
780	640	1.766	1.563	0.010	0.020
790	630	1.571	1.561	0.000	0.010
790	640	1.580	1.569	0.000	0.030
790	650	1.782	1.590	0.000	0.040
800	610	1.996	1.792	0.020	0.000
800	620	2.007	1.568	0.000	0.010
800	630	1.578	1.568	0.000	0.000
800	640	1.781	1.576	0.000	0.010
800	650	1.790	1.590	0.000	0.060
800	660	1.799	1.787	0.000	0.060
810	620	2.015	2.002	0.050	0.010
810	630	2.026	1.588	0.030	0.000
810	640	2.232	1.588	0.010	0.020
810	660	1.807	1.795	0.000	0.100

Abstract

Data availability

Cited By

Figures (6)

Tables (3)

Equations (13)

Applied Optics