Sun backward gazing method for measuring optomechanical errors of solar concentrators: experimental results

F. Hénault; C. Caliot; C. Caliot; M. Coquand; P.-H. Defieux; E. Guillot

doi:10.1364/AO.399595

Applied Optics
Vol. 59,
Issue 31,
pp. 9861-9877
(2020)
•https://doi.org/10.1364/AO.399595

Sun backward gazing method for measuring optomechanical errors of solar concentrators: experimental results

F. Hénault, C. Caliot, M. Coquand, P.-H. Defieux, and E. Guillot

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F. Hénault, C. Caliot, M. Coquand, P.-H. Defieux, and E. Guillot, "Sun backward gazing method for measuring optomechanical errors of solar concentrators: experimental results," Appl. Opt. 59, 9861-9877 (2020)

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Abstract

This paper presents the first experimental results obtained with the four cameras backward gazing method for measuring the optomechanical errors of solar concentrating surfaces in operation. It consists in combining the images simultaneously acquired by four cameras placed near the solar receiver in order to reconstruct the slope errors of the mirrors digitally. New algorithms adapted to real acquired images are described. The experiment has been conducted on a sun-tracking heliostat of the experimental solar tower THEMIS with canting error measurement accuracy estimated as 0.2 mrad. The main experimental error sources are analyzed, and possible ways of mitigation are proposed, giving reasonable hope of reaching an ultimate measurement accuracy of 0.1 mrad.

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A. Initial State
		$Y$ slopes			$Z$ slopes
Module Number	Spatial Coverage	Mean (mrad)	PTV (mrad)	RMS (mrad)	Mean (mrad)	PTV (mrad)	RMS (mrad)
1	0.000	1.066	0.041	0.020	–1.076	0.028	0.014
2	0.110	0.581	2.785	0.471	0.013	2.568	0.644
3	0.380	–0.118	2.667	0.378	–0.154	2.629	0.410
4	0.261	–0.086	2.813	0.460	0.244	3.079	0.610
5	0.304	0.157	2.965	0.526	–0.231	2.603	0.586
6	0.062	–0.060	2.417	0.498	0.272	2.364	0.516
7	0.237	–0.079	2.840	0.456	–0.051	3.087	0.531
8	0.201	–0.532	1.520	0.122	–0.021	2.335	0.209
9	0.498	–0.126	1.829	0.217	0.474	1.618	0.392
Average		0.089	2.209	0.350	–0.059	2.257	0.435
B. Added Defects
		$Y$ slopes			$Y$ slopes
Module Number	Spatial Coverage	Mean (mrad)	PTV (mrad)	RMS (mrad)	Mean (mrad)	PTV (mrad)	RMS (mrad)
1	0.000	–0.166	0.112	0.046	1.141	0.083	0.034
2	0.041	0.802	1.692	0.308	0.521	1.966	0.370
3	0.195	–0.246	2.089	0.394	–0.604	1.434	0.252
4	0.309	0.019	2.326	0.395	0.288	2.540	0.586
5	0.306	0.252	2.689	0.548	–0.124	2.647	0.541
6	0.062	–0.023	2.299	0.558	0.293	2.403	0.475
7	0.236	–0.046	2.638	0.573	–0.044	2.639	0.573
8	0.143	–0.723	1.237	0.163	–0.166	1.738	0.252
9	0.547	–0.050	1.723	0.211	0.551	1.768	0.320
Average		–0.020	1.867	0.355	0.206	1.913	0.378
C. Difference
		$Y$ slopes			$Z$ slopes
Module Number	Spatial Coverage	Mean (mrad)	PTV (mrad)	RMS (mrad)	Mean (mrad)	PTV (mrad)	RMS (mrad)
1	0.000
2	0.017	–0.085	1.884	0.404	–1.571	1.396	0.210
3	0.181	–0.044	2.501	0.203	0.796	1.874	0.163
4	0.253	–0.040	2.148	0.328	0.069	1.555	0.166
5	0.283	–0.086	1.849	0.151	–0.042	1.339	0.146
6	0.057	–0.041	2.337	0.199	0.063	1.191	0.128
7	0.200	0.000	1.981	0.210	0.127	1.707	0.144
8	0.138	0.218	1.566	0.098	0.183	1.624	0.120
9	0.470	–0.116	1.726	0.198	–0.045	1.151	0.155
Average		–0.024	1.999	0.224	–0.053	1.480	0.154

A. Initial State
	Shape Errors
Module Number	Coverage	Mean (mm)	PTV (mm)	RMS (mm)
1	0.000
2	0.110	0.011	0.482	0.116
3	0.380	–0.112	0.661	0.117
4	0.261	–0.239	0.819	0.190
5	0.304	–0.133	0.816	0.199
6	0.062	–0.040	0.409	0.074
7	0.237	–0.072	0.563	0.106
8	0.201	–0.063	0.506	0.096
9	0.498	0.025	0.729	0.204
Average		–0.078	0.623	0.138
B. Added Defects
	Shape Errors
Module Number	Coverage	Mean (mm)	PTV (mm)	RMS (mm)
1	0.000
2	0.041	0.059	0.363	0.067
3	0.195	–0.079	0.883	0.168
4	0.309	–0.151	0.774	0.183
5	0.306	–0.099	0.655	0.150
6	0.062	–0.023	0.496	0.082
7	0.236	–0.136	0.705	0.130
8	0.143	–0.069	0.597	0.127
9	0.547	–0.027	0.987	0.263
Average		–0.066	0.683	0.146
C. Difference
	Shape Errors
Module Number	Coverage	Mean (mm)	PTV (mm)	RMS (mm)
1	0.000
2	0.017	0.081	0.658	0.157
3	0.181	0.095	0.819	0.189
4	0.253	0.079	0.325	0.034
5	0.283	0.028	0.327	0.068
6	0.057	0.020	0.121	0.016
7	0.200	–0.058	0.279	0.059
8	0.138	0.010	0.281	0.054
9	0.470	–0.069	0.409	0.078
Average		0.023	0.403	0.082

A. Initial State
		$Y$ slopes			$Z$ slopes
Module Number	Spatial Coverage	Mean (mrad)	PTV (mrad)	RMS (mrad)	Mean (mrad)	PTV (mrad)	RMS (mrad)
1	0.000	1.066	0.041	0.020	–1.076	0.028	0.014
2	0.110	0.581	2.785	0.471	0.013	2.568	0.644
3	0.380	–0.118	2.667	0.378	–0.154	2.629	0.410
4	0.261	–0.086	2.813	0.460	0.244	3.079	0.610
5	0.304	0.157	2.965	0.526	–0.231	2.603	0.586
6	0.062	–0.060	2.417	0.498	0.272	2.364	0.516
7	0.237	–0.079	2.840	0.456	–0.051	3.087	0.531
8	0.201	–0.532	1.520	0.122	–0.021	2.335	0.209
9	0.498	–0.126	1.829	0.217	0.474	1.618	0.392
Average		0.089	2.209	0.350	–0.059	2.257	0.435
B. Added Defects
		$Y$ slopes			$Y$ slopes
Module Number	Spatial Coverage	Mean (mrad)	PTV (mrad)	RMS (mrad)	Mean (mrad)	PTV (mrad)	RMS (mrad)
1	0.000	–0.166	0.112	0.046	1.141	0.083	0.034
2	0.041	0.802	1.692	0.308	0.521	1.966	0.370
3	0.195	–0.246	2.089	0.394	–0.604	1.434	0.252
4	0.309	0.019	2.326	0.395	0.288	2.540	0.586
5	0.306	0.252	2.689	0.548	–0.124	2.647	0.541
6	0.062	–0.023	2.299	0.558	0.293	2.403	0.475
7	0.236	–0.046	2.638	0.573	–0.044	2.639	0.573
8	0.143	–0.723	1.237	0.163	–0.166	1.738	0.252
9	0.547	–0.050	1.723	0.211	0.551	1.768	0.320
Average		–0.020	1.867	0.355	0.206	1.913	0.378
C. Difference
		$Y$ slopes			$Z$ slopes
Module Number	Spatial Coverage	Mean (mrad)	PTV (mrad)	RMS (mrad)	Mean (mrad)	PTV (mrad)	RMS (mrad)
1	0.000
2	0.017	–0.085	1.884	0.404	–1.571	1.396	0.210
3	0.181	–0.044	2.501	0.203	0.796	1.874	0.163
4	0.253	–0.040	2.148	0.328	0.069	1.555	0.166
5	0.283	–0.086	1.849	0.151	–0.042	1.339	0.146
6	0.057	–0.041	2.337	0.199	0.063	1.191	0.128
7	0.200	0.000	1.981	0.210	0.127	1.707	0.144
8	0.138	0.218	1.566	0.098	0.183	1.624	0.120
9	0.470	–0.116	1.726	0.198	–0.045	1.151	0.155
Average		–0.024	1.999	0.224	–0.053	1.480	0.154

A. Initial State
	Shape Errors
Module Number	Coverage	Mean (mm)	PTV (mm)	RMS (mm)
1	0.000
2	0.110	0.011	0.482	0.116
3	0.380	–0.112	0.661	0.117
4	0.261	–0.239	0.819	0.190
5	0.304	–0.133	0.816	0.199
6	0.062	–0.040	0.409	0.074
7	0.237	–0.072	0.563	0.106
8	0.201	–0.063	0.506	0.096
9	0.498	0.025	0.729	0.204
Average		–0.078	0.623	0.138
B. Added Defects
	Shape Errors
Module Number	Coverage	Mean (mm)	PTV (mm)	RMS (mm)
1	0.000
2	0.041	0.059	0.363	0.067
3	0.195	–0.079	0.883	0.168
4	0.309	–0.151	0.774	0.183
5	0.306	–0.099	0.655	0.150
6	0.062	–0.023	0.496	0.082
7	0.236	–0.136	0.705	0.130
8	0.143	–0.069	0.597	0.127
9	0.547	–0.027	0.987	0.263
Average		–0.066	0.683	0.146
C. Difference
	Shape Errors
Module Number	Coverage	Mean (mm)	PTV (mm)	RMS (mm)
1	0.000
2	0.017	0.081	0.658	0.157
3	0.181	0.095	0.819	0.189
4	0.253	0.079	0.325	0.034
5	0.283	0.028	0.327	0.068
6	0.057	0.020	0.121	0.016
7	0.200	–0.058	0.279	0.059
8	0.138	0.010	0.281	0.054
9	0.470	–0.069	0.409	0.078
Average		0.023	0.403	0.082

Abstract

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Figures (16)

Tables (2)

Equations (25)

Applied Optics