Abstract

Shack–Hartmann wavefront sensing in general requires careful registration of the reimaged telescope primary mirror to the Shack–Hartmann mask or lenslet array. The registration requirements are particularly demanding for applications in which segmented mirrors are phased using a physical optics generalization of the Shack–Hartmann test. In such cases the registration tolerances are less than 0.1% of the diameter of the primary mirror. We present a pupil registration algorithm suitable for such high accuracy applications that is based on the one used successfully for phasing the segments of the Keck telescopes. The pupil is aligned in four degrees of freedom (translations, rotation, and magnification) by balancing the intensities of subimages formed by small subapertures that straddle the periphery of the mirror. We describe the algorithm in general terms and then in the specific context of two very different geometries: the 492 segment Thirty Meter Telescope, and the seven “segment” Giant Magellan Telescope. Through detailed simulations we explore the accuracy of the algorithm and its sensitivity to such effects as cross talk, noise/counting statistics, atmospheric scintillation, and segment reflectivity variations.

© 2013 Optical Society of America

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References

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  1. G. Chanan, M. Troy, F. Dekens, S. Michaels, J. Nelson, T. Mast, and D. Kirkman, “Phasing the mirror segments of the Keck telescopes: the broadband phasing algorithm,” Appl. Opt. 37, 140–155 (1998).
    [CrossRef]
  2. G. Chanan, C. Ohara, and M. Troy, “Phasing the mirror segments of the Keck telescopes II: the narrow-band phasing algorithm,” Appl. Opt. 39, 4706–4714 (2000).
    [CrossRef]
  3. S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
    [CrossRef]
  4. J. Nelson and G. H. Sanders, “The status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
    [CrossRef]
  5. M. Johns, P. J. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. M. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
    [CrossRef]
  6. R. Gilmozzi and J. Spyromilio, “The 42-m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
    [CrossRef]
  7. A. Vigan, K. Dohlen, and S. Mazzanti, “On-sky multiwavelength phasing of segmented telescopes with the Zernike phase contrast sensor,” Appl. Opt. 50, 2708–2718 (2011).
    [CrossRef]
  8. J. Miller, private communication (1987).
  9. A. Murta, General Polygon Clipper Library. http://www.cs.man.ac.uk/toby/alan/software/ .
  10. F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics (Elsevier, 1981), Vol. 19, pp. 281–376.

2012

M. Johns, P. J. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. M. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[CrossRef]

2011

2008

J. Nelson and G. H. Sanders, “The status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
[CrossRef]

R. Gilmozzi and J. Spyromilio, “The 42-m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

2006

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

2000

1998

Anguiano, G.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Arciniega, S.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Bouchez, A.

M. Johns, P. J. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. M. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[CrossRef]

Bringas, V.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Castro, J.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Cavaller, L.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Chanan, G.

Chapa, O.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Chavoya, A.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Cobos, F.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Cuevas, S.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Dekens, F.

Devaney, N.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Dohlen, K.

Dorantes, A.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Espejo, C.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Farah, A.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Farahani, A.

M. Johns, P. J. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. M. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[CrossRef]

Filgueira, J. M.

M. Johns, P. J. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. M. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[CrossRef]

Flores, R.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Garfias, F.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Gilmozzi, R.

R. Gilmozzi and J. Spyromilio, “The 42-m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

Godoy, J.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Gonzalez, J. L.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Hernandez, H.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Jacoby, G.

M. Johns, P. J. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. M. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[CrossRef]

Johns, M.

M. Johns, P. J. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. M. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[CrossRef]

Kirkman, D.

Lara, G.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Mast, T.

Mazzanti, S.

McCarthy, P. J.

M. Johns, P. J. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. M. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[CrossRef]

Michaels, S.

Miller, J.

J. Miller, private communication (1987).

Montoya, J. M.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Nava, R.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Nelson, J.

Ohara, C.

Raybould, K.

M. Johns, P. J. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. M. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[CrossRef]

Roddier, F.

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics (Elsevier, 1981), Vol. 19, pp. 281–376.

Sanchez, B.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Sanders, G. H.

J. Nelson and G. H. Sanders, “The status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
[CrossRef]

Shectman, S.

M. Johns, P. J. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. M. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[CrossRef]

Sheehan, M.

M. Johns, P. J. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. M. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[CrossRef]

Spyromilio, J.

R. Gilmozzi and J. Spyromilio, “The 42-m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

Tejada, C.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Toral, R.

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

Troy, M.

Vigan, A.

Appl. Opt.

Proc. SPIE

S. Cuevas, B. Sanchez, V. Bringas, C. Espejo, R. Flores, O. Chapa, G. Lara, A. Chavoya, G. Anguiano, S. Arciniega, A. Dorantes, J. L. Gonzalez, J. M. Montoya, R. Toral, H. Hernandez, R. Nava, N. Devaney, J. Castro, L. Cavaller, A. Farah, J. Godoy, F. Cobos, C. Tejada, and F. Garfias, “The commissioning instrument for the Gran Telescopio Canarias: made in Mexico,” Proc. SPIE 6046, 604628 (2006).
[CrossRef]

J. Nelson and G. H. Sanders, “The status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008).
[CrossRef]

M. Johns, P. J. McCarthy, K. Raybould, A. Bouchez, A. Farahani, J. M. Filgueira, G. Jacoby, S. Shectman, and M. Sheehan, “Giant Magellan Telescope: overview,” Proc. SPIE 8444, 84441H (2012).
[CrossRef]

R. Gilmozzi and J. Spyromilio, “The 42-m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
[CrossRef]

Other

J. Miller, private communication (1987).

A. Murta, General Polygon Clipper Library. http://www.cs.man.ac.uk/toby/alan/software/ .

F. Roddier, “The effects of atmospheric turbulence in optical astronomy,” in Progress in Optics (Elsevier, 1981), Vol. 19, pp. 281–376.

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Figures (4)

Fig. 1.
Fig. 1.

Top: Fragment of the TMT pupil segmentation pattern with peripheral subaperture patterns (small hexagons) of the APS SH WFS superimposed. The subapertures that lie completely inside the segments are references for those on the segment periphery. Bottom: Analogous peripheral subaperture pattern of the GMT LTAO SH WFS superimposed on the GMT segmented pupil. A total of 648 peripheral/reference subaperture pairs are chosen for TMT and 120 for GMT.

Fig. 2.
Fig. 2.

Family of input/output curves for all GMT LTAO WFS peripheral subapertures used in the pupil stabilization algorithm as functions of the pupil shift in the x-direction (top, y-direction is nearly identical), rotation (middle), and magnification (bottom).

Fig. 3.
Fig. 3.

Exposure-averaged [Eq. (13), top] and subaperture “plus” exposure-averaged [Eq. (11), bottom] covariance function maps (in units of squared relative scintillation intensity) for the standard GMT seven-layer turbulence model. Exposure time is 0.1 s, wavelength 0.589 μm, and the apertures are the 0.43×0.43m square subapertures of GMT LTAO WFS. Elongations correspond to the wind directions in each turbulence layer. The subaperture averaging results in a five-fold reduction in the scintillation variance.

Fig. 4.
Fig. 4.

Fragments of the GMT LTAO WFS image (left, exposure time 0.05 s) and TMT APS WFS image (right, exposure time 10 s) showing the intensity distributions of the peripheral spots with diffraction- (TMT case) and LGS-induced elongation (GMT case). Intensity scale is in photons/second.

Tables (1)

Tables Icon

Table 1. Standard GMT Seven-Layer Turbulence Model Parametersa

Equations (18)

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

δc=PδI,
δIi=(IiI)/I,i=1,,N,
δIi=Ii/Iiref|SiP0|/|Siref|,
Pij1|Siref|(|SiPj||SiP0|),
P^δc=δI^,
W(f)=0.039k2f11/30dhCn2(h)sin2(πλhf2),
S(r)=1|S|{1,rS,0,otherwise.
Wse(f)=|S˜(f)|2W(f),
Cse(r1,r2)=1T2T/2T/2dtdrS1(r1r)×T/2T/2dtdrS2(r2r)C(r,t;r,t),
C(r,t;r,t)=I(r,t)I(r,t)
Cl(r,t;r,t)=Cl(|rr+vl(tt)|),
Cse(r1,r2)=drR(r+r2r1)l=1LCle(r,vl),
R(r)=drS1(r)S2(r+r),
Cle(r,vl)=1T2TTdτ(1|τ/T|)Cl(|r+vlτ|).
δIi(1)=|SiP0||Siref|(1+IplSiP1+IplSiref1),
δIi(2)=|SiP0|/|Siref|+Ibgi1+Ibgi|SiP0||Siref|,
IS=1|S|SI(x,y)dxdy,
Ii=1Nil,mBiIlm

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