Alignment strategy for an optomechanical image derotator using a laser Doppler vibrometer

Bettina Altmann; Tim Betker; Christian Pape; Eduard Reithmeier

doi:10.1364/AO.58.006555

Applied Optics
Vol. 58,
Issue 24,
pp. 6555-6568
(2019)
•https://doi.org/10.1364/AO.58.006555

Alignment strategy for an optomechanical image derotator using a laser Doppler vibrometer

Bettina Altmann, Tim Betker, Christian Pape, and Eduard Reithmeier

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Bettina Altmann, Tim Betker, Christian Pape, and Eduard Reithmeier, "Alignment strategy for an optomechanical image derotator using a laser Doppler vibrometer," Appl. Opt. 58, 6555-6568 (2019)

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Abstract

When monitoring the condition of technical components, it is of particular interest to obtain information of the current condition of the component during operation. The main objectives are safety and machine efficiency. A special extension in this area is the derotator, since the derotator can be used to extend measuring methods designed for static components to rotating systems. In this paper, we present a new, to the best of our knowledge, approach to align a derotator using a laser Doppler vibrometer (LDV). When aligning the derotator, the optical axis must be coaxial with the rotating object to be measured. Current conventional approaches only ensure that the optical axis and the rotational axis intersect at the center of the measuring object. In our approach, a LDV is used to determine the angular deviation between the two axes, which cannot be determined by common methods. Our approach is easy to implement because the LDV is often already used in combination with the derotator as a measuring device. Experiments are carried out to show that this approach is feasible. In addition, several investigations are being performed to analyze how different parameters affect the result, creating reproducible conditions and deriving an alignment approach. By combining the approach developed in this work for determining a rotational deviation with common image-based approaches for determining a translational deviation of the axes, the derotator can be calibrated entirely. In this way, the quality of the measurement with the derotator can be further increased, as calibration errors can be reduced.

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Pos.	$x$ in mm	$y$ in mm	$z$ in mm	$α$ in °	$β$ in °	$γ$ in °
1	11.14	1.48	−24.74	−0.01	0.00	−1.45
2	3.64	1.52	−24.90	−0.03	0.00	−0.79
3	−2.87	1.48	−24.79	−0.01	0.00	−0.20
4	−10.01	1.37	−24.53	0.01	0.00	0.44
5	−16.91	1.18	−24.78	−0.01	0.00	1.05
6	−23.96	0.91	−24.99	−0.03	0.00	1.69
7	−31.06	0.56	−24.78	−0.01	0.00	2.32
8	−37.85	0.14	−24.78	−0.02	0.00	2.93
9	−44.89	−0.35	−24.80	−0.01	0.00	3.55
10	−51.87	−0.93	−24.80	−0.01	0.00	4.18
11	−58.83	−1.58	−24.83	−0.01	0.00	4.80

$ω_{o}$ in Hz	$ω_{d}$ in Hz	$ω_{{\hat{A}}_{\max}}$ in Hz	${\hat{A}}_{\max}$ in V	$σ_{{\hat{A}}_{\max}}$ in V	Pos.
0	1.667	6.653	$3.6 \cdot 10^{- 3}$	$2.2 \cdot 10^{- 4}$	7
0	2.834	11.353	$3.9 \cdot 10^{- 3}$	$4.8 \cdot 10^{- 4}$	7
0	5.167	20.691	$4.7 \cdot 10^{- 3}$	$1.6 \cdot 10^{- 4}$	7
0	6.667	26.672	$5.9 \cdot 10^{- 3}$	$4.5 \cdot 10^{- 4}$	7
0	6.667	6.653	$4.5 \cdot 10^{- 3}$	$9.2 \cdot 10^{- 4}$	1
0	6.667	6.653	$3.0 \cdot 10^{- 3}$	$6.1 \cdot 10^{- 4}$	3
0	6.667	13.306	$4.0 \cdot 10^{- 3}$	$9.1 \cdot 10^{- 4}$	5
0	6.667	26.672	$5.9 \cdot 10^{- 3}$	$4.5 \cdot 10^{- 4}$	7
0	6.667	26.672	$7.1 \cdot 10^{- 3}$	$7.3 \cdot 10^{- 4}$	9
0	6.667	26.672	$12.5 \cdot 10^{- 3}$	$8.9 \cdot 10^{- 4}$	11

$ω_{o}$ in Hz	$ω_{d}$ in Hz	$ω_{{\hat{A}}_{\max}}$ in Hz	${\hat{A}}_{\max}$ in V	$σ_{{\hat{A}}_{\max}}$ in V	Pos.
2.167	0	2.197	$0.5 \cdot 10^{- 3}$	$0.6 \cdot 10^{- 4}$	7
4.333	0	4.333	$0.9 \cdot 10^{- 3}$	$0.5 \cdot 10^{- 4}$	7
8.667	0	8.667	$1.5 \cdot 10^{- 3}$	$0.6 \cdot 10^{- 4}$	7
13.333	0	13.306	$1.6 \cdot 10^{- 3}$	$5.7 \cdot 10^{- 4}$	7
13.333	0	13.306	$1.7 \cdot 10^{- 3}$	$5.3 \cdot 10^{- 4}$	1
13.333	0	26.672	$1.8 \cdot 10^{- 3}$	$7.2 \cdot 10^{- 4}$	3
13.333	0	13.306	$1.9 \cdot 10^{- 3}$	$7.8 \cdot 10^{- 4}$	5
13.333	0	13.306	$1.6 \cdot 10^{- 3}$	$5.7 \cdot 10^{- 4}$	7
13.333	0	13.306	$4.2 \cdot 10^{- 3}$	$5.2 \cdot 10^{- 4}$	9
13.333	0	13.306	$3.2 \cdot 10^{- 3}$	$7.2 \cdot 10^{- 4}$	11

$ω_{o}$ in Hz	$ω_{d}$ in Hz	$ω_{{\hat{A}}_{\max}}$ in Hz	${\hat{A}}_{\max}$ in V	$σ_{{\hat{A}}_{\max}}$ in V	Pos.
2	6.667	13.306	$5.6 \cdot 10^{- 2}$	$2.5 \cdot 10^{- 3}$	7
4	6.667	13.306	$10.9 \cdot 10^{- 2}$	$5.4 \cdot 10^{- 3}$	7
8	6.667	13.306	$21.5 \cdot 10^{- 2}$	$11.3 \cdot 10^{- 3}$	7
13.333	6.667	13.306	$36.2 \cdot 10^{- 2}$	$11.3 \cdot 10^{- 3}$	7
15.833	6.667	13.306	$41.8 \cdot 10^{- 2}$	$21.2 \cdot 10^{- 3}$	7
13.333	1.667	3.357	$32.3 \cdot 10^{- 2}$	$7.4 \cdot 10^{- 3}$	7
13.333	2.833	5.676	$36.6 \cdot 10^{- 2}$	$5.4 \cdot 10^{- 3}$	7
13.333	4.167	8.362	$36.8 \cdot 10^{- 2}$	$4.5 \cdot 10^{- 3}$	7
13.333	10	20.02	$36.9 \cdot 10^{- 2}$	$2.9 \cdot 10^{- 3}$	7
1.667	0.833	1.648	$4.7 \cdot 10^{- 2}$	$0.4 \cdot 10^{- 3}$	7
2.667	1.333	2.686	$7.0 \cdot 10^{- 2}$	$4.2 \cdot 10^{- 3}$	7
5.667	2.833	5.676	$13.6 \cdot 10^{- 2}$	$10.6 \cdot 10^{- 3}$	7
10.333	5.167	10.315	$28.1 \cdot 10^{- 2}$	$10.3 \cdot 10^{- 3}$	7
17.333	8.667	17.334	$44.0 \cdot 10^{- 2}$	$25.9 \cdot 10^{- 3}$	7

$ω_{o}$ in Hz	$ω_{d}$ in Hz	$ω_{{\hat{A}}_{\max}}$ in Hz	${\hat{A}}_{\max}$ in V	$σ_{{\hat{A}}_{\max}}$ in V	Pos.
13.333	6.667	13.306	$18.8 \cdot 10^{- 2}$	$3.3 \cdot 10^{- 3}$	1
13.333	6.667	13.306	$1.3 \cdot 10^{- 2}$	$0.3 \cdot 10^{- 3}$	3
13.333	6.667	13.306	$18.7 \cdot 10^{- 2}$	$5.6 \cdot 10^{- 3}$	5
13.333	6.667	13.306	$36.1 \cdot 10^{- 2}$	$22.7 \cdot 10^{- 3}$	7
13.333	6.667	13.306	$52.0 \cdot 10^{- 2}$	$39.5 \cdot 10^{- 3}$	9
13.333	6.667	13.306	$64.6 \cdot 10^{- 2}$	$59.7 \cdot 10^{- 3}$	11

Abstract

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Applied Optics