Abstract

we present a novel technique of calibrating the interaction matrix for high-order adaptive optics systems, called the multichannel-Hadamard method. In this method, the deformable mirror actuators are firstly divided into a series of channels according to their coupling relationship, and then the voltage-oriented Hadamard method is applied to these channels. Taking the 595-element adaptive optics system as an example, the procedure is described in detail. The optimal channel dividing is discussed and tested by numerical simulation. The proposed method is also compared with the voltage-oriented Hadamard only method and the multichannel only method by experiments. Results show that the multichannel-Hadamard method can produce significant improvement on interaction matrix measurement.

© 2014 Optical Society of America

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2012

A. Riccardi, R. Briguglio, E. Pinna, G. Agapito, F. Quiros-Pacheco, S. Esposito, “Calibration strategy of the pyramid wavefront sensor module of ERIS with the VLT deformable secondary mirror,” Proc. SPIE 8447, 84475M (2012).
[CrossRef]

E. Pinna, F. Quiros-Pacheco, A. Riccardi, R. Briguglio, A. Puglisi, L. Busoni, C. Arcidiacono, J. Argomedo, M. Xompero, E. Marchetti, S. Esposito, “First on-sky calibration of a high order adaptive optics system,” Proc. SPIE 8447, 84472B (2012).
[CrossRef]

X. Zhang, C. Arcidiacono, A. R. Conrad, T. M. Herbst, W. Gaessler, T. Bertram, R. Ragazzoni, L. Schreiber, E. Diolaiti, M. Kuerster, P. Bizenberger, D. Meschke, H. W. Rix, C. Rao, L. Mohr, F. Briegel, F. Kittmann, J. Berwein, J. Trowitzsch, “Calibrating the interaction matrix for the LINC-NIRVANA high layer wavefront sensor,” Opt. Express 20(7), 8078–8092 (2012).
[PubMed]

2011

S. J. Thomas, L. Poyneer, R. De Rosa, B. Macintosh, D. Dillon, J. K. Wallace, D. Palmer, D. Gavel, B. Bauman, L. Saddlemyer, S. Goodsell, “Integration and test of the Gemini Planet Imager,” Proc. SPIE 8149, 814903 (2011).
[CrossRef]

2010

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

2009

2008

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

2006

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

S. Esposito, R. Tubbs, A. Puglisi, S. Oberti, A. Tozzi, M. Xompero, D. Zanotti, “High SNR measurement of interaction matrix on-sky and in lab,” Proc. SPIE 6272, 62721C (2006).
[CrossRef]

2004

F. Wildi, G. Brusa, “Determining the interaction matrix using starlight,” Proc. SPIE 5490, 164–173 (2004).
[CrossRef]

M. Kasper, E. Fedrigo, D. P. Looze, H. Bonnet, L. Ivanescu, S. Oberti, “Fast calibration of high-order adaptive optics systems,” J. Opt. Soc. Am. A 21(6), 1004–1008 (2004).
[CrossRef] [PubMed]

S. Oberti, H. Bonnet, E. Fedrigo, L. Ivanescu, M. Kasper, J. Paufique, “Calibration of a curvature sensor/bimorph mirror AO system: interaction matrix measurement on MACAO systems,” Proc. SPIE 5490, 139–150 (2004).
[CrossRef]

1990

H. W. Babcock, “Adaptive optics revisited,” Science 249(4966), 253–257 (1990).
[CrossRef] [PubMed]

C. Boyer, V. Michau, G. Rousset, “Adaptive optics: Interaction matrix measurements and real time control algorithms for the COME-ON project,” Proc. SPIE 1237, 406–421 (1990).
[CrossRef]

W. Jiang, H. Li, “Hartmann-Shack wavefront sensing and wavefront control algorithm,” Proc. SPIE 1271, 82–93 (1990).
[CrossRef]

Agapito, G.

A. Riccardi, R. Briguglio, E. Pinna, G. Agapito, F. Quiros-Pacheco, S. Esposito, “Calibration strategy of the pyramid wavefront sensor module of ERIS with the VLT deformable secondary mirror,” Proc. SPIE 8447, 84475M (2012).
[CrossRef]

Angione, J.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Arcidiacono, C.

Argomedo, J.

E. Pinna, F. Quiros-Pacheco, A. Riccardi, R. Briguglio, A. Puglisi, L. Busoni, C. Arcidiacono, J. Argomedo, M. Xompero, E. Marchetti, S. Esposito, “First on-sky calibration of a high order adaptive optics system,” Proc. SPIE 8447, 84472B (2012).
[CrossRef]

Arsenault, R.

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

Babcock, H. W.

H. W. Babcock, “Adaptive optics revisited,” Science 249(4966), 253–257 (1990).
[CrossRef] [PubMed]

Baranec, C.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Baudoz, P.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Bauman, B.

S. J. Thomas, L. Poyneer, R. De Rosa, B. Macintosh, D. Dillon, J. K. Wallace, D. Palmer, D. Gavel, B. Bauman, L. Saddlemyer, S. Goodsell, “Integration and test of the Gemini Planet Imager,” Proc. SPIE 8149, 814903 (2011).
[CrossRef]

Bertram, T.

Berwein, J.

Beuzit, J.-L.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Bizenberger, P.

Bonnet, H.

M. Kasper, E. Fedrigo, D. P. Looze, H. Bonnet, L. Ivanescu, S. Oberti, “Fast calibration of high-order adaptive optics systems,” J. Opt. Soc. Am. A 21(6), 1004–1008 (2004).
[CrossRef] [PubMed]

S. Oberti, H. Bonnet, E. Fedrigo, L. Ivanescu, M. Kasper, J. Paufique, “Calibration of a curvature sensor/bimorph mirror AO system: interaction matrix measurement on MACAO systems,” Proc. SPIE 5490, 139–150 (2004).
[CrossRef]

Bouchez, A.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Boyer, C.

C. Boyer, V. Michau, G. Rousset, “Adaptive optics: Interaction matrix measurements and real time control algorithms for the COME-ON project,” Proc. SPIE 1237, 406–421 (1990).
[CrossRef]

Briegel, F.

Briguglio, R.

A. Riccardi, R. Briguglio, E. Pinna, G. Agapito, F. Quiros-Pacheco, S. Esposito, “Calibration strategy of the pyramid wavefront sensor module of ERIS with the VLT deformable secondary mirror,” Proc. SPIE 8447, 84475M (2012).
[CrossRef]

E. Pinna, F. Quiros-Pacheco, A. Riccardi, R. Briguglio, A. Puglisi, L. Busoni, C. Arcidiacono, J. Argomedo, M. Xompero, E. Marchetti, S. Esposito, “First on-sky calibration of a high order adaptive optics system,” Proc. SPIE 8447, 84472B (2012).
[CrossRef]

Britton, M.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Brusa, G.

F. Wildi, G. Brusa, “Determining the interaction matrix using starlight,” Proc. SPIE 5490, 164–173 (2004).
[CrossRef]

Buey, T.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Bui, K.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Burns, S. A.

Burruss, R.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Busoni, L.

E. Pinna, F. Quiros-Pacheco, A. Riccardi, R. Briguglio, A. Puglisi, L. Busoni, C. Arcidiacono, J. Argomedo, M. Xompero, E. Marchetti, S. Esposito, “First on-sky calibration of a high order adaptive optics system,” Proc. SPIE 8447, 84472B (2012).
[CrossRef]

Charton, J.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Conrad, A. R.

Costille, A.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Cromer, J.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

De Rosa, R.

S. J. Thomas, L. Poyneer, R. De Rosa, B. Macintosh, D. Dillon, J. K. Wallace, D. Palmer, D. Gavel, B. Bauman, L. Saddlemyer, S. Goodsell, “Integration and test of the Gemini Planet Imager,” Proc. SPIE 8149, 814903 (2011).
[CrossRef]

Dekany, R.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Dillon, D.

S. J. Thomas, L. Poyneer, R. De Rosa, B. Macintosh, D. Dillon, J. K. Wallace, D. Palmer, D. Gavel, B. Bauman, L. Saddlemyer, S. Goodsell, “Integration and test of the Gemini Planet Imager,” Proc. SPIE 8149, 814903 (2011).
[CrossRef]

Diolaiti, E.

Dohlen, K.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Esposito, S.

E. Pinna, F. Quiros-Pacheco, A. Riccardi, R. Briguglio, A. Puglisi, L. Busoni, C. Arcidiacono, J. Argomedo, M. Xompero, E. Marchetti, S. Esposito, “First on-sky calibration of a high order adaptive optics system,” Proc. SPIE 8447, 84472B (2012).
[CrossRef]

A. Riccardi, R. Briguglio, E. Pinna, G. Agapito, F. Quiros-Pacheco, S. Esposito, “Calibration strategy of the pyramid wavefront sensor module of ERIS with the VLT deformable secondary mirror,” Proc. SPIE 8447, 84475M (2012).
[CrossRef]

S. Esposito, R. Tubbs, A. Puglisi, S. Oberti, A. Tozzi, M. Xompero, D. Zanotti, “High SNR measurement of interaction matrix on-sky and in lab,” Proc. SPIE 6272, 62721C (2006).
[CrossRef]

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

Fedrigo, E.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

M. Kasper, E. Fedrigo, D. P. Looze, H. Bonnet, L. Ivanescu, S. Oberti, “Fast calibration of high-order adaptive optics systems,” J. Opt. Soc. Am. A 21(6), 1004–1008 (2004).
[CrossRef] [PubMed]

S. Oberti, H. Bonnet, E. Fedrigo, L. Ivanescu, M. Kasper, J. Paufique, “Calibration of a curvature sensor/bimorph mirror AO system: interaction matrix measurement on MACAO systems,” Proc. SPIE 5490, 139–150 (2004).
[CrossRef]

Fusco, T.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Gaessler, W.

Gavel, D.

S. J. Thomas, L. Poyneer, R. De Rosa, B. Macintosh, D. Dillon, J. K. Wallace, D. Palmer, D. Gavel, B. Bauman, L. Saddlemyer, S. Goodsell, “Integration and test of the Gemini Planet Imager,” Proc. SPIE 8149, 814903 (2011).
[CrossRef]

Goodsell, S.

S. J. Thomas, L. Poyneer, R. De Rosa, B. Macintosh, D. Dillon, J. K. Wallace, D. Palmer, D. Gavel, B. Bauman, L. Saddlemyer, S. Goodsell, “Integration and test of the Gemini Planet Imager,” Proc. SPIE 8149, 814903 (2011).
[CrossRef]

Guiwits, S.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Henning, J.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Herbst, T. M.

Hickey, J.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Hubin, N.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Ivanescu, L.

S. Oberti, H. Bonnet, E. Fedrigo, L. Ivanescu, M. Kasper, J. Paufique, “Calibration of a curvature sensor/bimorph mirror AO system: interaction matrix measurement on MACAO systems,” Proc. SPIE 5490, 139–150 (2004).
[CrossRef]

M. Kasper, E. Fedrigo, D. P. Looze, H. Bonnet, L. Ivanescu, S. Oberti, “Fast calibration of high-order adaptive optics systems,” J. Opt. Soc. Am. A 21(6), 1004–1008 (2004).
[CrossRef] [PubMed]

Jiang, W.

W. Jiang, H. Li, “Hartmann-Shack wavefront sensing and wavefront control algorithm,” Proc. SPIE 1271, 82–93 (1990).
[CrossRef]

Kasper, M.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

S. Oberti, H. Bonnet, E. Fedrigo, L. Ivanescu, M. Kasper, J. Paufique, “Calibration of a curvature sensor/bimorph mirror AO system: interaction matrix measurement on MACAO systems,” Proc. SPIE 5490, 139–150 (2004).
[CrossRef]

M. Kasper, E. Fedrigo, D. P. Looze, H. Bonnet, L. Ivanescu, S. Oberti, “Fast calibration of high-order adaptive optics systems,” J. Opt. Soc. Am. A 21(6), 1004–1008 (2004).
[CrossRef] [PubMed]

Kittmann, F.

Kolb, J.

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

Kuerster, M.

Li, H.

W. Jiang, H. Li, “Hartmann-Shack wavefront sensing and wavefront control algorithm,” Proc. SPIE 1271, 82–93 (1990).
[CrossRef]

Looze, D. P.

Macintosh, B.

S. J. Thomas, L. Poyneer, R. De Rosa, B. Macintosh, D. Dillon, J. K. Wallace, D. Palmer, D. Gavel, B. Bauman, L. Saddlemyer, S. Goodsell, “Integration and test of the Gemini Planet Imager,” Proc. SPIE 8149, 814903 (2011).
[CrossRef]

Marchetti, E.

E. Pinna, F. Quiros-Pacheco, A. Riccardi, R. Briguglio, A. Puglisi, L. Busoni, C. Arcidiacono, J. Argomedo, M. Xompero, E. Marchetti, S. Esposito, “First on-sky calibration of a high order adaptive optics system,” Proc. SPIE 8447, 84472B (2012).
[CrossRef]

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

Mckenna, D.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Meimon, S.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Meschke, D.

Michau, V.

C. Boyer, V. Michau, G. Rousset, “Adaptive optics: Interaction matrix measurements and real time control algorithms for the COME-ON project,” Proc. SPIE 1237, 406–421 (1990).
[CrossRef]

Mohr, L.

Moore, A.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Mouillet, D.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Muradore, R.

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

Oberti, S.

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

S. Esposito, R. Tubbs, A. Puglisi, S. Oberti, A. Tozzi, M. Xompero, D. Zanotti, “High SNR measurement of interaction matrix on-sky and in lab,” Proc. SPIE 6272, 62721C (2006).
[CrossRef]

M. Kasper, E. Fedrigo, D. P. Looze, H. Bonnet, L. Ivanescu, S. Oberti, “Fast calibration of high-order adaptive optics systems,” J. Opt. Soc. Am. A 21(6), 1004–1008 (2004).
[CrossRef] [PubMed]

S. Oberti, H. Bonnet, E. Fedrigo, L. Ivanescu, M. Kasper, J. Paufique, “Calibration of a curvature sensor/bimorph mirror AO system: interaction matrix measurement on MACAO systems,” Proc. SPIE 5490, 139–150 (2004).
[CrossRef]

Palmer, D.

S. J. Thomas, L. Poyneer, R. De Rosa, B. Macintosh, D. Dillon, J. K. Wallace, D. Palmer, D. Gavel, B. Bauman, L. Saddlemyer, S. Goodsell, “Integration and test of the Gemini Planet Imager,” Proc. SPIE 8149, 814903 (2011).
[CrossRef]

Paufique, J.

S. Oberti, H. Bonnet, E. Fedrigo, L. Ivanescu, M. Kasper, J. Paufique, “Calibration of a curvature sensor/bimorph mirror AO system: interaction matrix measurement on MACAO systems,” Proc. SPIE 5490, 139–150 (2004).
[CrossRef]

Petit, C.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Pinna, E.

A. Riccardi, R. Briguglio, E. Pinna, G. Agapito, F. Quiros-Pacheco, S. Esposito, “Calibration strategy of the pyramid wavefront sensor module of ERIS with the VLT deformable secondary mirror,” Proc. SPIE 8447, 84475M (2012).
[CrossRef]

E. Pinna, F. Quiros-Pacheco, A. Riccardi, R. Briguglio, A. Puglisi, L. Busoni, C. Arcidiacono, J. Argomedo, M. Xompero, E. Marchetti, S. Esposito, “First on-sky calibration of a high order adaptive optics system,” Proc. SPIE 8447, 84472B (2012).
[CrossRef]

Poyneer, L.

S. J. Thomas, L. Poyneer, R. De Rosa, B. Macintosh, D. Dillon, J. K. Wallace, D. Palmer, D. Gavel, B. Bauman, L. Saddlemyer, S. Goodsell, “Integration and test of the Gemini Planet Imager,” Proc. SPIE 8149, 814903 (2011).
[CrossRef]

Puglisi, A.

E. Pinna, F. Quiros-Pacheco, A. Riccardi, R. Briguglio, A. Puglisi, L. Busoni, C. Arcidiacono, J. Argomedo, M. Xompero, E. Marchetti, S. Esposito, “First on-sky calibration of a high order adaptive optics system,” Proc. SPIE 8447, 84472B (2012).
[CrossRef]

S. Esposito, R. Tubbs, A. Puglisi, S. Oberti, A. Tozzi, M. Xompero, D. Zanotti, “High SNR measurement of interaction matrix on-sky and in lab,” Proc. SPIE 6272, 62721C (2006).
[CrossRef]

Quiros-Pacheco, F.

E. Pinna, F. Quiros-Pacheco, A. Riccardi, R. Briguglio, A. Puglisi, L. Busoni, C. Arcidiacono, J. Argomedo, M. Xompero, E. Marchetti, S. Esposito, “First on-sky calibration of a high order adaptive optics system,” Proc. SPIE 8447, 84472B (2012).
[CrossRef]

A. Riccardi, R. Briguglio, E. Pinna, G. Agapito, F. Quiros-Pacheco, S. Esposito, “Calibration strategy of the pyramid wavefront sensor module of ERIS with the VLT deformable secondary mirror,” Proc. SPIE 8447, 84475M (2012).
[CrossRef]

Quirós-Pacheco, F.

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

Rabou, P.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Ragazzoni, R.

Rao, C.

Riccardi, A.

A. Riccardi, R. Briguglio, E. Pinna, G. Agapito, F. Quiros-Pacheco, S. Esposito, “Calibration strategy of the pyramid wavefront sensor module of ERIS with the VLT deformable secondary mirror,” Proc. SPIE 8447, 84475M (2012).
[CrossRef]

E. Pinna, F. Quiros-Pacheco, A. Riccardi, R. Briguglio, A. Puglisi, L. Busoni, C. Arcidiacono, J. Argomedo, M. Xompero, E. Marchetti, S. Esposito, “First on-sky calibration of a high order adaptive optics system,” Proc. SPIE 8447, 84472B (2012).
[CrossRef]

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

Rix, H. W.

Roberts, J.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Rousset, G.

C. Boyer, V. Michau, G. Rousset, “Adaptive optics: Interaction matrix measurements and real time control algorithms for the COME-ON project,” Proc. SPIE 1237, 406–421 (1990).
[CrossRef]

Saddlemyer, L.

S. J. Thomas, L. Poyneer, R. De Rosa, B. Macintosh, D. Dillon, J. K. Wallace, D. Palmer, D. Gavel, B. Bauman, L. Saddlemyer, S. Goodsell, “Integration and test of the Gemini Planet Imager,” Proc. SPIE 8149, 814903 (2011).
[CrossRef]

Sauvage, J.-F.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Schreiber, L.

Sevin, A.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Soenke, C.

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

Stroebele, S.

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

Suarez Valles, M.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

Thomas, S. J.

S. J. Thomas, L. Poyneer, R. De Rosa, B. Macintosh, D. Dillon, J. K. Wallace, D. Palmer, D. Gavel, B. Bauman, L. Saddlemyer, S. Goodsell, “Integration and test of the Gemini Planet Imager,” Proc. SPIE 8149, 814903 (2011).
[CrossRef]

Tozzi, A.

S. Esposito, R. Tubbs, A. Puglisi, S. Oberti, A. Tozzi, M. Xompero, D. Zanotti, “High SNR measurement of interaction matrix on-sky and in lab,” Proc. SPIE 6272, 62721C (2006).
[CrossRef]

Trinh, T.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Trowitzsch, J.

Troy, M.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Truong, T.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Tubbs, R.

S. Esposito, R. Tubbs, A. Puglisi, S. Oberti, A. Tozzi, M. Xompero, D. Zanotti, “High SNR measurement of interaction matrix on-sky and in lab,” Proc. SPIE 6272, 62721C (2006).
[CrossRef]

Velur, V.

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

Wallace, J. K.

S. J. Thomas, L. Poyneer, R. De Rosa, B. Macintosh, D. Dillon, J. K. Wallace, D. Palmer, D. Gavel, B. Bauman, L. Saddlemyer, S. Goodsell, “Integration and test of the Gemini Planet Imager,” Proc. SPIE 8149, 814903 (2011).
[CrossRef]

Wildi, F.

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

F. Wildi, G. Brusa, “Determining the interaction matrix using starlight,” Proc. SPIE 5490, 164–173 (2004).
[CrossRef]

Xompero, M.

E. Pinna, F. Quiros-Pacheco, A. Riccardi, R. Briguglio, A. Puglisi, L. Busoni, C. Arcidiacono, J. Argomedo, M. Xompero, E. Marchetti, S. Esposito, “First on-sky calibration of a high order adaptive optics system,” Proc. SPIE 8447, 84472B (2012).
[CrossRef]

S. Esposito, R. Tubbs, A. Puglisi, S. Oberti, A. Tozzi, M. Xompero, D. Zanotti, “High SNR measurement of interaction matrix on-sky and in lab,” Proc. SPIE 6272, 62721C (2006).
[CrossRef]

Zanotti, D.

S. Esposito, R. Tubbs, A. Puglisi, S. Oberti, A. Tozzi, M. Xompero, D. Zanotti, “High SNR measurement of interaction matrix on-sky and in lab,” Proc. SPIE 6272, 62721C (2006).
[CrossRef]

Zhang, X.

Zou, W.

J. Opt. Soc. Am. A

Opt. Express

Proc. SPIE

F. Wildi, G. Brusa, “Determining the interaction matrix using starlight,” Proc. SPIE 5490, 164–173 (2004).
[CrossRef]

S. Esposito, R. Tubbs, A. Puglisi, S. Oberti, A. Tozzi, M. Xompero, D. Zanotti, “High SNR measurement of interaction matrix on-sky and in lab,” Proc. SPIE 6272, 62721C (2006).
[CrossRef]

E. Pinna, F. Quiros-Pacheco, A. Riccardi, R. Briguglio, A. Puglisi, L. Busoni, C. Arcidiacono, J. Argomedo, M. Xompero, E. Marchetti, S. Esposito, “First on-sky calibration of a high order adaptive optics system,” Proc. SPIE 8447, 84472B (2012).
[CrossRef]

S. Oberti, H. Bonnet, E. Fedrigo, L. Ivanescu, M. Kasper, J. Paufique, “Calibration of a curvature sensor/bimorph mirror AO system: interaction matrix measurement on MACAO systems,” Proc. SPIE 5490, 139–150 (2004).
[CrossRef]

A. Riccardi, R. Briguglio, E. Pinna, G. Agapito, F. Quiros-Pacheco, S. Esposito, “Calibration strategy of the pyramid wavefront sensor module of ERIS with the VLT deformable secondary mirror,” Proc. SPIE 8447, 84475M (2012).
[CrossRef]

C. Boyer, V. Michau, G. Rousset, “Adaptive optics: Interaction matrix measurements and real time control algorithms for the COME-ON project,” Proc. SPIE 1237, 406–421 (1990).
[CrossRef]

W. Jiang, H. Li, “Hartmann-Shack wavefront sensing and wavefront control algorithm,” Proc. SPIE 1271, 82–93 (1990).
[CrossRef]

A. Bouchez, R. Dekany, J. Angione, C. Baranec, M. Britton, K. Bui, R. Burruss, J. Cromer, S. Guiwits, J. Henning, J. Hickey, D. Mckenna, A. Moore, J. Roberts, T. Trinh, M. Troy, T. Truong, V. Velur, “The PALM-3000 high-order adaptive optics system for Palomar Observatory,” Proc. SPIE 7015, 70150Z (2008).
[CrossRef]

J.-F. Sauvage, T. Fusco, C. Petit, S. Meimon, E. Fedrigo, M. Suarez Valles, M. Kasper, N. Hubin, J.-L. Beuzit, J. Charton, A. Costille, P. Rabou, D. Mouillet, P. Baudoz, T. Buey, A. Sevin, F. Wildi, K. Dohlen, “SAXO, the eXtreme Adaptive Optics System of SPHERE. Overview and calibration procedure,” Proc. SPIE 7736, 77360F (2010).
[CrossRef]

S. J. Thomas, L. Poyneer, R. De Rosa, B. Macintosh, D. Dillon, J. K. Wallace, D. Palmer, D. Gavel, B. Bauman, L. Saddlemyer, S. Goodsell, “Integration and test of the Gemini Planet Imager,” Proc. SPIE 8149, 814903 (2011).
[CrossRef]

S. Oberti, F. Quirós-Pacheco, S. Esposito, R. Muradore, R. Arsenault, E. Fedrigo, M. Kasper, J. Kolb, E. Marchetti, A. Riccardi, C. Soenke, S. Stroebele, “Large DM AO systems: synthetic IM or calibration on sky?” Proc. SPIE 6272, 627220 (2006).
[CrossRef]

Science

H. W. Babcock, “Adaptive optics revisited,” Science 249(4966), 253–257 (1990).
[CrossRef] [PubMed]

Other

J. W. Hardy, Adaptive Optics for Astronomical Telescopes (Oxford University, 1998), Chap. 1.

S. Meimon, T. Fusco and C. Petit, “An optimized calibration strategy for high order adaptive optics systems: the Slope-Oriented Hadmard Actuation,” in 1st AO4ELT Conference (2010), paper 07009.

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Figures (10)

Fig. 1
Fig. 1

Multichannel mode of the 595-actuator DM. The circles denote the DM actuators and the numbers in the circles represent which channel the actuators belong to. The squares mean the subapertures.

Fig. 2
Fig. 2

Channel dividing matrix (C) of the 595-actuator DM. The x axis represents the channel number and the y axis denotes the actuator number. Elements that equal 1 are black and those equal 0 are white.

Fig. 3
Fig. 3

The effective influence matrix Seffect. The x axis represents the actuator number and the y axis denotes the slope number. Elements that equal 1 are black and those equal 0 are white.

Fig. 4
Fig. 4

The relationship between optimal EIR, coupling and the measurement SNR. The markers are the average of 10 times repeated results and the dashed lines are the fitted results.

Fig. 5
Fig. 5

Optical schematic of the 595-element AO system.

Fig. 6
Fig. 6

Calibration errors of the MO, HO and MH methods with calibration SNR from 5 to 15. These errors are calculated by Eq. (1). The dash lines are simulation results by using the three methods and the markers are the experimental results of the average calibration error of ten IMs.

Fig. 7
Fig. 7

Slope variances induced by the IM error after the “one-shot” close with calibration SNR from 5 to 15.

Fig. 8
Fig. 8

Phase variances induced by the IM error after the “one-shot” close with calibration SNR from 5 to 15. These variances were calculated by subtracting the phase variance caused by the fitting error (this variance equaled the phase residual variance when snr equaled 35 in our experiments) from the phase residual variances. The unit λ denotes wavelength.

Fig. 9
Fig. 9

Focal plane intensities of the imaging system by using MO, HO and MH methods for calibration.

Fig. 10
Fig. 10

PSD of the closed-loop residual phase error by using the IM calibrated with snr 10.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

J=trace[ ( D 0 D m ) T ( D 0 D m )]/trace( D 0 T D 0 ).
C(i,j)={ =1 whilethe i th actuatorbelongstothe j th channel =0 otherwise .
S effect (2p1,q) 2 n sub × n act = S e ffect (2p,q) 2 n sub × n act ={ 1;while the centerofthe p th subaperture is in the EIA of the q th actuator 0; otherwise ,
V MO = v MO I n MO ,
V MH = v MH H n MH ,
C MH =[ C 0 ],
G= D c V+N,
D cm =G V 1 .
D temp = D cm C MH T .
D MH = D temp × S effect .
Δ D MH = D MH D 0 1 v MH n MH N MH H n MH T C MH T × S effect ,
Δ D MO = D MO D 0 1 v MO N MO C T × S effect ,
Δ D HO = D HO D 0 = 1 v HO n HO N HO H n HO T ,
N MH T N MH =2 n sub σ n 2 I n MH ,
σ n 2 = [ noise(j,k)noise(j,k1) 2 ] 2 j,k
H n MH H n MH T = n MH I n MH ,
trace( C MH C MH T )= n act .
J MH 2( n D n 0 ) n act n sub σ n 2 n D n MH v MH 2 trace( D 0 T D 0 ) ,
J MO 2( n D n 0 ) n act n sub σ n 2 n D v MO 2 trace( D 0 T D 0 )
J HO 2 n act n sub σ n 2 n HO v HO 2 trace( D 0 T D 0 ) .
J MH : J MO : J HO n D n 0 n D n MH v MH 2 : n D n 0 n D v MO 2 : 1 n HO v HO 2 .
snr= vmax(| D 0 |) σ n n n MH
v MH : v MO : v HO =1: n MH / n MO : n MH / n HO
J MH : J MO : J HO =1: n MO : n D n D n 0
J MH : J MO : J HO =1:19:49.4
σ gIM 2 ( D + )= σ g 2 ( D + ) σ g 2 ( D 0 + ),

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