Tip-Tilt Error Detection for Segments via Phase Transfer Function

Fig. 3. Distributions of PTF side-lobes with different cophase errors. (a) Piston error is 0.2λ,tip-tilt error is 0; (b) Piston error is 0.2λ,tip error is 0.1475(0.1λ), tilt error is 0; (c) Piston error is 0, tip error is 1.1602(0.8λ), tilt error is 0

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Fig. 4. Simulation results of small tip-tilt error. (a) Relationship between settled tip-tilt and measured tip-tilt; (b) measured error of tip-tilt

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Fig. 5. Simulation results of large tip-tilt error. (a) Comparison between settled tip-tilt and measured tip-tilt; (b) measured error of tip-tilt error

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Fig. 6. Experimental platform of cophase imaging with segmented mirrors

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Fig. 7. Diagram of redesigned diaphragm configuration

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Fig. 8. PSF of three segment system

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Fig. 9. PTF distribution and side-lobe. (a) PTF distribution; (b) wavefront of side-lobe b

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Table 1. tip-tilt errors of segments 2 and 3 measured by centroid detection method

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Table 1. tip-tilt errors of segments 2 and 3 measured by centroid detection method

Experiment No.	Tip error of segment 2	Tilt error of segment 2	Tip error of segment 3	Tilt error of segment 3
1	0.1901	0.2036	0.1557	0.1822
2	0.1722	0.2445	0.1862	0.1701
3	0.4631	0.3910	0.4462	0.3791
4	0.6936	0.7534	0.7048	0.7470
5	1.0240	1.0696	0.9946	1.0503
6	1.2021	1.2559	1.1984	1.2553
7	1.4402	1.5232	1.4174	1.5101
8	1.5813	1.6816	1.5899	1.6895
9	1.8536	1.8101	1.7978	1.8547
10	1.9664	2.0376	1.9771	2.0396

Table 2. tip-tilt errors of segments 2 and 3 measured by tip-tilt detection method based on PTF

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Table 2. tip-tilt errors of segments 2 and 3 measured by tip-tilt detection method based on PTF

Experiment No.	Tip error of segment 2	Tilt error of segment 2	Tip error of segment 3	Tilt error of segment 3
1	0.1766	0.2179	0.1657	0.1662
2	0.1574	0.2684	0.1914	0.1609
3	0.4919	0.4116	0.4370	0.3688
4	0.7222	0.7615	0.6761	0.7344
5	1.0005	1.0635	0.9726	1.0290
6	1.1924	1.2401	1.1765	1.2447
7	1.4183	1.5001	1.4112	1.4936
8	1.5710	1.6631	1.5731	1.6643
9	1.8434	1.7869	1.8112	1.8664
10	1.9553	2.0172	2.0001	2.0516

Table 3. Error between measured results of two methods

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Table 3. Error between measured results of two methods

Experiment No.	Tip error of segment 2	Tilt error of segment 2	Tip error of segment 3	Tilt error of segment 3
1	0.0135	－0.0143	－0.0010	0.0160
2	0.0148	－0.0239	－0.0052	0.0092
3	－0.0288	－0.0206	0.0092	0.0103
4	－0.0286	－0.0081	0.0287	0.0126
5	0.0235	0.0061	0.0022	0.0213
6	0.0097	0.0158	0.0219	0.0106
7	0.0219	0.0231	0.0062	0.0165
8	0.0103	0.0185	0.0168	0.0252
9	0.0102	0.0232	－0.0134	－0.0117
10	0.0110	0.0204	－0.0230	－0.0120

Table 4. Measured error (RMS) of tip under different signal-to-noise ratio of CCD

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Table 4. Measured error (RMS) of tip under different signal-to-noise ratio of CCD

Signal-to-noise ratio of CCD /dB	RMS of tip error /λ	RMS of tip error /（ $''$ ）
10	0.3343	0.4848
15	0.1489	0.2159
20	0.1228	0.1781
25	0.1051	0.1524
30	0.0034	0.0049
35	3.33×10^-4	4.82×10^-4
40	2.06×10^-4	2.98×10^-4
45	4.26×10^-5	6.17×10^-5
50	1.06×10^-5	1.53×10^-5
55	2.89×10^-6	4.19×10^-6

Table 5. Measured RMS of tip error under different segment′s figure RMS error
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Table 5. Measured RMS of tip error under different segment′s figure RMS error
RMS of figure error /λ RMS of tip error /λ
RMS of tip
error /（ $''$ ）
0.01 0.0064 0.0092
0.02 0.0127 0.0184
0.03 0.0191 0.0277
0.04 0.0255 0.0370
0.05 0.0319 0.0463
0.06 0.0383 0.0554
0.07 0.0447 0.0648

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Lu Zhang, Weirui Zhao, Yuejin Zhao, Juan Liu. Tip-Tilt Error Detection for Segments via Phase Transfer Function[J]. Acta Optica Sinica, 2024, 44(4): 0407001

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Paper Information

Category: Fourier optics and signal processing

Received: Sep. 21, 2023

Accepted: Dec. 13, 2023

Published Online: Feb. 29, 2024

The Author Email: Zhao Weirui (zwrei@bit.edu.cn)

DOI:10.3788/AOS231592

CSTR:32393.14.AOS231592

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. tip-tilt errors of segments 2 and 3 measured by centroid detection method

Table 1. tip-tilt errors of segments 2 and 3 measured by centroid detection method

Table 2. tip-tilt errors of segments 2 and 3 measured by tip-tilt detection method based on PTF

Table 2. tip-tilt errors of segments 2 and 3 measured by tip-tilt detection method based on PTF

Table 3. Error between measured results of two methods

Table 3. Error between measured results of two methods

Table 4. Measured error (RMS) of tip under different signal-to-noise ratio of CCD

Table 4. Measured error (RMS) of tip under different signal-to-noise ratio of CCD

Table 5. Measured RMS of tip error under different segment′s figure RMS error

Table 5. Measured RMS of tip error under different segment′s figure RMS error