Abstract

In a well-manufactured deformable mirror (DM), the temperature-induced distortion (TID) has been reported exist on the surface shape of the DM, when the working environment temperature is not equal to that of the manufacturing environment. The DM could not effectively correct this actuator-corresponding TID and the correction ability of the DM would be limited. In this paper, the the TID’s essential mechanism is analyzed systematically based on the thermal stress characteristics. An efficient method based on an auxiliary temperature compensation module (TCM) and a hybrid closed-loop control algorithm are presented accordingly. A finite element model is built to evaluate the TID characteristics and the compensation capability of the TCM. In the simulation, by using the TCM, the the DM’s improved surface shape does not contain the dynamic high-frequency distortion caused by the actuators tilt. In the experiment, which uses a designed TCM and a hybrid closed-loop control algorithm, a DM’s TID is effectively depressed and a well-compensated DM surface shape is finally achieved.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (1)

2017 (3)

2016 (1)

Q. Bian, L. Huang, X. K. Ma, Q. Xue, and M. L. Gong, “Effect of the particular temperature field on a National Ignition Facility deformable mirror,” Opt. Commun. 374, 119–126 (2016).
[Crossref]

2015 (1)

2013 (1)

2012 (1)

C. Bruchmann, M. Appelfelder, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermo-mechanical properties of a deformable mirror with screenprinted actuator,” Proc. SPIE 8253, 82530D (2012).
[Crossref]

2011 (3)

2010 (3)

2008 (1)

2007 (1)

M. W. Ao, P. Yang, Z. P. Yang, E. D. Li, C. H. Rao, and W. H. Jiang, “A method of aberration measurement and correction for entire beam path of ICF beam path,” Proc. SPIE 6823, 68230I (2007).
[Crossref]

2006 (2)

2004 (3)

2000 (2)

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[Crossref]

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[Crossref]

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C. R. Wolfe and J. K. Lawson, “Measurement and analysis of wavefront structure from large-aperture ICF optics,” Office of Scientific & Technical Information Technical Reports 2633, 361–385 (1995).

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[Crossref] [PubMed]

1993 (1)

Abdeli, K.

Angel, R. P.

Ao, M. W.

M. W. Ao, P. Yang, Z. P. Yang, E. D. Li, C. H. Rao, and W. H. Jiang, “A method of aberration measurement and correction for entire beam path of ICF beam path,” Proc. SPIE 6823, 68230I (2007).
[Crossref]

Appelfelder, M.

C. Bruchmann, M. Appelfelder, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermo-mechanical properties of a deformable mirror with screenprinted actuator,” Proc. SPIE 8253, 82530D (2012).
[Crossref]

Beckert, E.

C. Bruchmann, M. Appelfelder, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermo-mechanical properties of a deformable mirror with screenprinted actuator,” Proc. SPIE 8253, 82530D (2012).
[Crossref]

Beletic, J. W.

Bennett, J. M.

Bian, Q.

Q. Bian, L. Huang, X. K. Ma, Q. Xue, and M. L. Gong, “Effect of the particular temperature field on a National Ignition Facility deformable mirror,” Opt. Commun. 374, 119–126 (2016).
[Crossref]

Bonora, S.

Bradley, C. H.

Bruchmann, C.

C. Bruchmann, M. Appelfelder, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermo-mechanical properties of a deformable mirror with screenprinted actuator,” Proc. SPIE 8253, 82530D (2012).
[Crossref]

Burge, J. H.

Cai, B. W.

R. Z. Zhang, B. W. Cai, C. L. Yang, Q. Xu, and Y. Y. Gu, “Calculation of the power spectral density of the Wavefront,” Proc. SPIE 4231, 295–300 (2000).
[Crossref]

Cao, Z.

Chen, J.

Choi, H.

L. Huang, C. L. Zhou, W. C. Zhao, H. Choi, L. Graves, and D. Kim, “Close-loop performance of a high precision deflectometry controlled deformable mirror (DCDM) unit for wavefront correction in adaptive optics system,” Opt. Commun. 393, 83–88 (2017).
[Crossref]

Chu, J.

Conan, R.

Crowe, D. G.

Dong, L.

Dziechciarczyk, L.

G. Vdovin, O. Soloviev, M. Loktev, S. Savenko, and L. Dziechciarczyk, “Optimal correction and feedforward control of low-order aberrations with piezoelectric and membrane deformable mirrors,” Proc. SPIE 8165, 81650W (2011).
[Crossref]

Eberhardt, R.

C. Bruchmann, M. Appelfelder, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermo-mechanical properties of a deformable mirror with screenprinted actuator,” Proc. SPIE 8253, 82530D (2012).
[Crossref]

Elson, J. M.

Fan, J. B.

Feng, Z.

Fixler, J.

Fuchs, J.

Gong, M.

Gong, M. L.

Q. Bian, L. Huang, X. K. Ma, Q. Xue, and M. L. Gong, “Effect of the particular temperature field on a National Ignition Facility deformable mirror,” Opt. Commun. 374, 119–126 (2016).
[Crossref]

Graves, L.

L. Huang, C. L. Zhou, W. C. Zhao, H. Choi, L. Graves, and D. Kim, “Close-loop performance of a high precision deflectometry controlled deformable mirror (DCDM) unit for wavefront correction in adaptive optics system,” Opt. Commun. 393, 83–88 (2017).
[Crossref]

Gu, Y. Y.

R. Z. Zhang, B. W. Cai, C. L. Yang, Q. Xu, and Y. Y. Gu, “Calculation of the power spectral density of the Wavefront,” Proc. SPIE 4231, 295–300 (2000).
[Crossref]

Guesalaga, A.

Guzmán, D.

Haefner, C.

Hampton, P. J.

He, T.

Henesian, M. A.

M. L. Spaeth, K. R. Manes, C. C. Widmayer, W. H. Williams, P. K. Whitman, M. A. Henesian, I. F. Stowers, and J. Honig, “National Ignition Facility wavefront requirements and optical architecture,” Opt. Eng. 43(12), 2854–2865 (2004).
[Crossref]

Honig, J.

M. L. Spaeth, K. R. Manes, C. C. Widmayer, W. H. Williams, P. K. Whitman, M. A. Henesian, I. F. Stowers, and J. Honig, “National Ignition Facility wavefront requirements and optical architecture,” Opt. Eng. 43(12), 2854–2865 (2004).
[Crossref]

Hu, L.

Huang, L.

Jian, Y.

Jiang, W.

Jiang, W. H.

M. W. Ao, P. Yang, Z. P. Yang, E. D. Li, C. H. Rao, and W. H. Jiang, “A method of aberration measurement and correction for entire beam path of ICF beam path,” Proc. SPIE 6823, 68230I (2007).
[Crossref]

Jin, G.

Juez, F. J. D. C.

Kang, E.-C.

Kim, D.

L. Huang, C. L. Zhou, W. C. Zhao, H. Choi, L. Graves, and D. Kim, “Close-loop performance of a high precision deflectometry controlled deformable mirror (DCDM) unit for wavefront correction in adaptive optics system,” Opt. Commun. 393, 83–88 (2017).
[Crossref]

Lasheras, F. S.

Lawson, J. K.

C. R. Wolfe and J. K. Lawson, “Measurement and analysis of wavefront structure from large-aperture ICF optics,” Office of Scientific & Technical Information Technical Reports 2633, 361–385 (1995).

Lee, J. H.

Lee, Y.-C.

Lei, X.

Li, B.

Li, D.

Li, E. D.

M. W. Ao, P. Yang, Z. P. Yang, E. D. Li, C. H. Rao, and W. H. Jiang, “A method of aberration measurement and correction for entire beam path of ICF beam path,” Proc. SPIE 6823, 68230I (2007).
[Crossref]

Li, T.

Li, X.

Li, Y.

Liang, C.

Liang, X.

Liu, L.

Liu, W.

Liu, Y.

Loktev, M.

G. Vdovin, O. Soloviev, M. Loktev, S. Savenko, and L. Dziechciarczyk, “Optimal correction and feedforward control of low-order aberrations with piezoelectric and membrane deformable mirrors,” Proc. SPIE 8165, 81650W (2011).
[Crossref]

Ma, J.

Ma, X. K.

Q. Bian, L. Huang, X. K. Ma, Q. Xue, and M. L. Gong, “Effect of the particular temperature field on a National Ignition Facility deformable mirror,” Opt. Commun. 374, 119–126 (2016).
[Crossref]

Makidon, R.

R. Winsor, A. Sivaramakrishnan, and R. Makidon, “Low cost membrane type deformable mirror with high density actuator spacing,” Proc. SPIE 4007, 563–572 (2000).
[Crossref]

Manes, K. R.

M. L. Spaeth, K. R. Manes, C. C. Widmayer, W. H. Williams, P. K. Whitman, M. A. Henesian, I. F. Stowers, and J. Honig, “National Ignition Facility wavefront requirements and optical architecture,” Opt. Eng. 43(12), 2854–2865 (2004).
[Crossref]

McHugh, S. L.

Morse, K. A.

Mu, Q.

Myers, R.

Ning, Y.

Niu, S.

Parks, R. E.

Pépin, H.

Pugh, E. N.

Qiu, Y.

Rao, C. H.

M. W. Ao, P. Yang, Z. P. Yang, E. D. Li, C. H. Rao, and W. H. Jiang, “A method of aberration measurement and correction for entire beam path of ICF beam path,” Proc. SPIE 6823, 68230I (2007).
[Crossref]

Sarunic, M. V.

Savenko, S.

G. Vdovin, O. Soloviev, M. Loktev, S. Savenko, and L. Dziechciarczyk, “Optimal correction and feedforward control of low-order aberrations with piezoelectric and membrane deformable mirrors,” Proc. SPIE 8165, 81650W (2011).
[Crossref]

Shamir, J.

Shen, J.

Sivaramakrishnan, A.

R. Winsor, A. Sivaramakrishnan, and R. Makidon, “Low cost membrane type deformable mirror with high density actuator spacing,” Proc. SPIE 4007, 563–572 (2000).
[Crossref]

Soloviev, O.

G. Vdovin, O. Soloviev, M. Loktev, S. Savenko, and L. Dziechciarczyk, “Optimal correction and feedforward control of low-order aberrations with piezoelectric and membrane deformable mirrors,” Proc. SPIE 8165, 81650W (2011).
[Crossref]

Spaeth, M. L.

M. L. Spaeth, K. R. Manes, C. C. Widmayer, W. H. Williams, P. K. Whitman, M. A. Henesian, I. F. Stowers, and J. Honig, “National Ignition Facility wavefront requirements and optical architecture,” Opt. Eng. 43(12), 2854–2865 (2004).
[Crossref]

Stowers, I. F.

M. L. Spaeth, K. R. Manes, C. C. Widmayer, W. H. Williams, P. K. Whitman, M. A. Henesian, I. F. Stowers, and J. Honig, “National Ignition Facility wavefront requirements and optical architecture,” Opt. Eng. 43(12), 2854–2865 (2004).
[Crossref]

Su, P.

Sun, C.

Sun, L.

Sun, L. C.

Tang, X.

Tünnermann, A.

C. Bruchmann, M. Appelfelder, E. Beckert, R. Eberhardt, and A. Tünnermann, “Thermo-mechanical properties of a deformable mirror with screenprinted actuator,” Proc. SPIE 8253, 82530D (2012).
[Crossref]

Vdovin, G.

G. Vdovin, O. Soloviev, M. Loktev, S. Savenko, and L. Dziechciarczyk, “Optimal correction and feedforward control of low-order aberrations with piezoelectric and membrane deformable mirrors,” Proc. SPIE 8165, 81650W (2011).
[Crossref]

Wallace, B. P.

Wang, C.

Wang, L.

Wattellier, B.

Whitman, P. K.

M. L. Spaeth, K. R. Manes, C. C. Widmayer, W. H. Williams, P. K. Whitman, M. A. Henesian, I. F. Stowers, and J. Honig, “National Ignition Facility wavefront requirements and optical architecture,” Opt. Eng. 43(12), 2854–2865 (2004).
[Crossref]

Widmayer, C. C.

M. L. Spaeth, K. R. Manes, C. C. Widmayer, W. H. Williams, P. K. Whitman, M. A. Henesian, I. F. Stowers, and J. Honig, “National Ignition Facility wavefront requirements and optical architecture,” Opt. Eng. 43(12), 2854–2865 (2004).
[Crossref]

Williams, W. H.

M. L. Spaeth, K. R. Manes, C. C. Widmayer, W. H. Williams, P. K. Whitman, M. A. Henesian, I. F. Stowers, and J. Honig, “National Ignition Facility wavefront requirements and optical architecture,” Opt. Eng. 43(12), 2854–2865 (2004).
[Crossref]

Winsor, R.

R. Winsor, A. Sivaramakrishnan, and R. Makidon, “Low cost membrane type deformable mirror with high density actuator spacing,” Proc. SPIE 4007, 563–572 (2000).
[Crossref]

Wolfe, C. R.

C. R. Wolfe and J. K. Lawson, “Measurement and analysis of wavefront structure from large-aperture ICF optics,” Office of Scientific & Technical Information Technical Reports 2633, 361–385 (1995).

Xu, B.

Xu, Q.

R. Z. Zhang, B. W. Cai, C. L. Yang, Q. Xu, and Y. Y. Gu, “Calculation of the power spectral density of the Wavefront,” Proc. SPIE 4231, 295–300 (2000).
[Crossref]

Xuan, L.

Xue, Q.

Q. Bian, L. Huang, X. K. Ma, Q. Xue, and M. L. Gong, “Effect of the particular temperature field on a National Ignition Facility deformable mirror,” Opt. Commun. 374, 119–126 (2016).
[Crossref]

Q. Xue, L. Huang, P. Yan, M. Gong, Z. Feng, Y. Qiu, T. Li, and G. Jin, “Research on the particular temperature-induced surface shape of a National Ignition Facility deformable mirror,” Appl. Opt. 52(2), 280–287 (2013).
[Crossref] [PubMed]

Yan, H.

Yan, M.

Yan, P.

Yang, C. L.

R. Z. Zhang, B. W. Cai, C. L. Yang, Q. Xu, and Y. Y. Gu, “Calculation of the power spectral density of the Wavefront,” Proc. SPIE 4231, 295–300 (2000).
[Crossref]

Yang, P.

Yang, Z. P.

M. W. Ao, P. Yang, Z. P. Yang, E. D. Li, C. H. Rao, and W. H. Jiang, “A method of aberration measurement and correction for entire beam path of ICF beam path,” Proc. SPIE 6823, 68230I (2007).
[Crossref]

Zam, A.

Zawadzki, R. J.

Zhang, P.

Zhang, R. Z.

R. Z. Zhang, B. W. Cai, C. L. Yang, Q. Xu, and Y. Y. Gu, “Calculation of the power spectral density of the Wavefront,” Proc. SPIE 4231, 295–300 (2000).
[Crossref]

Zhang, Y.

Zhao, W. C.

L. Huang, C. L. Zhou, W. C. Zhao, H. Choi, L. Graves, and D. Kim, “Close-loop performance of a high precision deflectometry controlled deformable mirror (DCDM) unit for wavefront correction in adaptive optics system,” Opt. Commun. 393, 83–88 (2017).
[Crossref]

Zheng, Y.

Zheng, Y. M.

Zhou, C. L.

L. Huang, C. L. Zhou, W. C. Zhao, H. Choi, L. Graves, and D. Kim, “Close-loop performance of a high precision deflectometry controlled deformable mirror (DCDM) unit for wavefront correction in adaptive optics system,” Opt. Commun. 393, 83–88 (2017).
[Crossref]

Zhu, Z.

Zou, J. P.

Appl. Opt. (7)

J. Opt. Soc. Korea (1)

Office of Scientific & Technical Information Technical Reports (1)

C. R. Wolfe and J. K. Lawson, “Measurement and analysis of wavefront structure from large-aperture ICF optics,” Office of Scientific & Technical Information Technical Reports 2633, 361–385 (1995).

Opt. Commun. (2)

L. Huang, C. L. Zhou, W. C. Zhao, H. Choi, L. Graves, and D. Kim, “Close-loop performance of a high precision deflectometry controlled deformable mirror (DCDM) unit for wavefront correction in adaptive optics system,” Opt. Commun. 393, 83–88 (2017).
[Crossref]

Q. Bian, L. Huang, X. K. Ma, Q. Xue, and M. L. Gong, “Effect of the particular temperature field on a National Ignition Facility deformable mirror,” Opt. Commun. 374, 119–126 (2016).
[Crossref]

Opt. Eng. (1)

M. L. Spaeth, K. R. Manes, C. C. Widmayer, W. H. Williams, P. K. Whitman, M. A. Henesian, I. F. Stowers, and J. Honig, “National Ignition Facility wavefront requirements and optical architecture,” Opt. Eng. 43(12), 2854–2865 (2004).
[Crossref]

Opt. Express (8)

P. Yang, Y. Ning, X. Lei, B. Xu, X. Li, L. Dong, H. Yan, W. Liu, W. Jiang, L. Liu, C. Wang, X. Liang, and X. Tang, “Enhancement of the beam quality of non-uniform output slab laser amplifier with a 39-actuator rectangular piezoelectric deformable mirror,” Opt. Express 18(7), 7121–7130 (2010).
[Crossref] [PubMed]

L. Hu, L. Xuan, Y. Liu, Z. Cao, D. Li, and Q. Mu, “Phase-only liquid crystal spatial light modulator for wavefront correction with high precision,” Opt. Express 12(26), 6403–6409 (2004).
[Crossref] [PubMed]

B. P. Wallace, P. J. Hampton, C. H. Bradley, and R. Conan, “Evaluation of a MEMS deformable mirror for an adaptive optics test bench,” Opt. Express 14(22), 10132–10138 (2006).
[Crossref] [PubMed]

D. Guzmán, F. J. D. C. Juez, R. Myers, A. Guesalaga, and F. S. Lasheras, “Modeling a MEMS deformable mirror using non-parametric estimation techniques,” Opt. Express 18(20), 21356–21369 (2010).
[Crossref] [PubMed]

S. Bonora, Y. Jian, P. Zhang, A. Zam, E. N. Pugh, R. J. Zawadzki, and M. V. Sarunic, “Wavefront correction and high-resolution in vivo OCT imaging with an objective integrated multi-actuator adaptive lens,” Opt. Express 23(17), 21931–21941 (2015).
[Crossref] [PubMed]

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Opt. Lett. (1)

Proc. SPIE (5)

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Figures (13)

Fig. 1
Fig. 1 (a) Simplified schematic of the NIF-type deformable mirror structure. (b) The XOY coordinates and the distribution of the actuators.
Fig. 2
Fig. 2 (a) The XYZ coordinates and the total displacements of the actuator. (b) The XOY and X ' O ' Y ' coordinates and the shear displacement of the mirror. (c) The Y ' O ' Z ' section and the normal displacement of the mirror.
Fig. 3
Fig. 3 (a)The DM with the TCM. (b) Distribution of four TECs.
Fig. 4
Fig. 4 The temperature gradient maps and the displacement maps of the DM at Δ T e =5. The temperature gradient map (a) and the displacement map (b) without any distortion compensation. The temperature gradient map (c) and the displacement map (d) with the TCM working at the optimal compensation temperature.
Fig. 5
Fig. 5 The TIDs of the DM without temperature compensation. (a1) is the distorted WSS at  Δ T e =-5. (b1) is the distorted WSS at  Δ T e =5. (a2) and (b2) are the PSD curves of the distorted WSSs. (a3) and (b3) are the 3D maps of the distorted SSHFs. (a4) and (b4) are the 2D maps of (a3) and (b3), respectively. (a5) and (b5) are the 2D maps of the fitting residues of the distorted WSSs in (a1) and (b1) respectively, while (a6) and (b6) are the 3D maps of the fitting residues.
Fig. 6
Fig. 6 The surface shape distortion of the DM with (a) different temperature difference and (c)different thermal expansion coefficient difference at  Δ T e = 5. (b) and (d) are the self-compensation residues of (a) and (c).
Fig. 7
Fig. 7 The TIDs with the TCM working at the optimal compensation temperature. (a1) is the pre-compensated WSS at Δ T e = −5. (b1) is the pre-compensated WSS at Δ T e =5. (a2) and (b2) are the PSD curves of the compensated WSSs in (a1) and (b1). (a3) and (b3) are the 3D maps of the pre-compensated SSHFs. (a4) and (b4) are the 2D maps of (a3) and (b3), respectively. (a5) and (b5) are the 2D maps of the fitting residues of the WSS in (a1) and (b1) respectively, while (a6) and (b6) are the 3D maps.
Fig. 8
Fig. 8 The PV values of the TIDs with the TCM working at different temperatures. (a)–(d) show the influence of the set compensation temperature of the TCM at different T e . (e) shows the influence of the Δ T e on the optimal Δ T TCM , the Δ T eB and the PV of the WSS.
Fig. 9
Fig. 9 (a) is the experiment setup; (b) is the layout of the experiment setup containing the control circuits; (c) is the lab-manufactured DM with a TCM; (d) is the bottom of the water-cooling block.
Fig. 10
Fig. 10 The TIDs of the DM without the TCM working. (a1) is the distorted WSS at Δ T e =-5.7, PV value = 2.17μm. (b1) is the distorted WSS at Δ T e =5.7, PV value = 1.97μm. (a2) and (b2) are the PSD curves of the WSSs. (a3) is the SSHF after filtering the first 40-orders Zernike aberration of (a1), PV value = 0.71μm, with the actuators’ position marked by black circles. (b3) is the SSHF after filtering the first 40-orders Zernike aberration of (b1), PV value = 0.69μm. with the actuators’ position marked by black circles. (a4) and (b4) are the influence of Δ T e on the PV and RMS of the distorted WSSs.
Fig. 11
Fig. 11 The compensation residues of the TIDs without the TCM working. (a1) is the compensation residue at Δ T e = −5.7 , PV = 1.46μm, RMS = 0.27 μm. (b1) is the compensation residue at Δ T e =5.7, PV = 1.41μm, RMS = 0.29 μm. (a2) (PV = 1.02μm, RMS = 0.09 μm) and (b2) (PV = 0.75μm, RMS = 0.08 μm) are the SSHFs of the compensation residues after filtering the first 40-orders Zernike aberration. (a3) and (b3) are the PSD curves of the TIDs and the compensation residues without TCM working at Δ T e = −5.7 and Δ T e =5.7 , respectively.
Fig. 12
Fig. 12 The hybrid close-loop control algorithm.
Fig. 13
Fig. 13 (a1) and (b1) are the WSSs of the pre-compensation results of the TIDs after the first step (only the TCM working) at Δ T e =-5.7 (PV = 1.61 μm, RMS = 0.32 μm) and Δ T e = 5.7 (PV = 1.48 μm, RMS = 0.30 μm). (a2) and (b2) are the self-compensation results when the hybrid close-loop algorithm is accomplished at Δ T e = −5.7 (PV = 0.44 μm, RMS = 0.09 μm) and Δ T e = 5.7 (PV = 0.45 μm, RMS = 0.09 μm). (a3) and (b3) are the SSHF of the self-compensation residues after filtering the first 40-orders Zernike aberration at Δ T e = −5.7 (PV = 0.22μm, RMS = 0.03 μm) and Δ T e = 5.7 (PV = 0.22μm, RMS = 0.03 μm). (a4) and (b4) are the PSDs of the initial distorted WSSs and the compensation residues after the hybrid close-loop algorithm is accomplished at Δ T e = −5.7 and Δ T e = 5.7.

Tables (1)

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Table 1 Material parameters in the finite element simulation

Equations (13)

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δ iA = x iA ' x i =Δ T e ia α G
δ jA = y jA ' y j =Δ T e ja α G
δ iB = x iB ' x i =Δ T e ia α B
δ jB = y jB ' y j =Δ T e ja α B
Δ T e = T e T m
{ Δ h ijz =Δ h ij cos( θ i,j ) Δ h ijx =Δ h ij sin( θ i,j )sin( α i,j ) Δ h ijy =Δ h ij sin( θ i,j )cos( α i,j )
tan( α i,j )= δ iA δ jA = i j (j0)
tan( θ i,j )= δ Bi,j δ Ai,j h
δ Ai,j = δ iA 2 + δ jA 2
tan( θ i,j )= a i 2 + j 2 (Δ T eB α B Δ T eG α G ) h
Δ T eB = α G α B Δ T eG
Δ T eB = α G α B Δ T e
Δ T eB =f( T e , T TCM , T m )

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