Abstract

We describe a complexity reduction approach intended to solve the tomographic alignment problem for the Thirty Meter Telescope by means of its alignment and phasing system (APS) with little loss of information. This approach is computationally efficient enough to perform detailed Monte-Carlo simulations of the APS on a standard PC. We present sample simulations to model error propagation through the system and to build a preliminary APS alignment error budget.

© 2012 Optical Society of America

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References

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  1. J. Nelson and G. H. Sanders, “TMT status report,” Proc. SPIE 6267, 626728 (2006).
  2. R. Gilmozzi and J. Spyromilio, “The 42 m European ELT: status,” Proc. SPIE 7012, 701219 (2008).
    [CrossRef]
  3. G. A. Chanan, M. Troy, F. G. 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]
  4. G. A. Chanan, C. Ohara, and M. Troy, “Phasing the mirror segments of the Keck telescopes: the narrowband phasing algorithm,” Appl. Opt. 39, 4706–4714 (2000).
    [CrossRef]
  5. G. H. Golub and C. F. Van Loan, Matrix Computations (The Johns Hopkins University, 1996).
  6. P. Piatrou and G. Chanan, “Tomographic alignment algorithm for an extremely large three-mirror telescope: invisible modes,” Appl. Opt. 49, 6395–6401 (2010).
    [CrossRef]
  7. P. L. Schechter and R. S. Levinson, “Generic misalignment aberration patterns in wide-field telescopes,” http://arxiv.org/abs/1009.0708v1 .
  8. B.-J. Seo, C. Nissly, G. Angeli, B. Ellerbroek, J. Nelson, N. Sigrist, and M. Troy, “Analysis of normalized point spread source sensitivity as performance metric for large telescopes,” Appl. Opt. 48, 5997–6007 (2009).
    [CrossRef]
  9. B.-J. Seo, C. Nissly, and M. Troy, “Normalized point source sensitivity for off-axis optical performance evaluation of the Thirty Meter Telescope,” Proc. SPIE 7738, 77380G (2010).
  10. M. C. Roggemann and B. M. Welsh, Imaging Through Turbulence (CRC, 1996).
  11. “Specification for finished primary mirror segments,” TMT project documentation. TMT.OPT.SPE.07.002.CCR03.
  12. “Design requirements document for the M2 system,” TMT project documentation. TMT.OPT.DRD.07.004.CCR28.
  13. “Design requirements document for the M3 system,” TMT project documentation. TMT.OPT.DRD.07.006.CCR28.
  14. TMT construction proposal, http://www.tmt.org/sites/default/files/TMT-Construction-Proposal-Public.pdf .
  15. C. Nissly, B.-J. Seo, M. Troy, G. Angeli, J. Angione, I. Crossfield, B. Ellerbroek, L. Gilles, and N. Sigrist, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Proc. SPIE 7017, 70170U (2008).
    [CrossRef]

2010

B.-J. Seo, C. Nissly, and M. Troy, “Normalized point source sensitivity for off-axis optical performance evaluation of the Thirty Meter Telescope,” Proc. SPIE 7738, 77380G (2010).

P. Piatrou and G. Chanan, “Tomographic alignment algorithm for an extremely large three-mirror telescope: invisible modes,” Appl. Opt. 49, 6395–6401 (2010).
[CrossRef]

2009

2008

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

C. Nissly, B.-J. Seo, M. Troy, G. Angeli, J. Angione, I. Crossfield, B. Ellerbroek, L. Gilles, and N. Sigrist, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Proc. SPIE 7017, 70170U (2008).
[CrossRef]

2006

J. Nelson and G. H. Sanders, “TMT status report,” Proc. SPIE 6267, 626728 (2006).

2000

1998

Angeli, G.

B.-J. Seo, C. Nissly, G. Angeli, B. Ellerbroek, J. Nelson, N. Sigrist, and M. Troy, “Analysis of normalized point spread source sensitivity as performance metric for large telescopes,” Appl. Opt. 48, 5997–6007 (2009).
[CrossRef]

C. Nissly, B.-J. Seo, M. Troy, G. Angeli, J. Angione, I. Crossfield, B. Ellerbroek, L. Gilles, and N. Sigrist, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Proc. SPIE 7017, 70170U (2008).
[CrossRef]

Angione, J.

C. Nissly, B.-J. Seo, M. Troy, G. Angeli, J. Angione, I. Crossfield, B. Ellerbroek, L. Gilles, and N. Sigrist, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Proc. SPIE 7017, 70170U (2008).
[CrossRef]

Chanan, G.

Chanan, G. A.

Crossfield, I.

C. Nissly, B.-J. Seo, M. Troy, G. Angeli, J. Angione, I. Crossfield, B. Ellerbroek, L. Gilles, and N. Sigrist, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Proc. SPIE 7017, 70170U (2008).
[CrossRef]

Dekens, F. G.

Ellerbroek, B.

B.-J. Seo, C. Nissly, G. Angeli, B. Ellerbroek, J. Nelson, N. Sigrist, and M. Troy, “Analysis of normalized point spread source sensitivity as performance metric for large telescopes,” Appl. Opt. 48, 5997–6007 (2009).
[CrossRef]

C. Nissly, B.-J. Seo, M. Troy, G. Angeli, J. Angione, I. Crossfield, B. Ellerbroek, L. Gilles, and N. Sigrist, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Proc. SPIE 7017, 70170U (2008).
[CrossRef]

Gilles, L.

C. Nissly, B.-J. Seo, M. Troy, G. Angeli, J. Angione, I. Crossfield, B. Ellerbroek, L. Gilles, and N. Sigrist, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Proc. SPIE 7017, 70170U (2008).
[CrossRef]

Gilmozzi, R.

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

Golub, G. H.

G. H. Golub and C. F. Van Loan, Matrix Computations (The Johns Hopkins University, 1996).

Kirkman, D.

Mast, T.

Michaels, S.

Nelson, J.

Nissly, C.

B.-J. Seo, C. Nissly, and M. Troy, “Normalized point source sensitivity for off-axis optical performance evaluation of the Thirty Meter Telescope,” Proc. SPIE 7738, 77380G (2010).

B.-J. Seo, C. Nissly, G. Angeli, B. Ellerbroek, J. Nelson, N. Sigrist, and M. Troy, “Analysis of normalized point spread source sensitivity as performance metric for large telescopes,” Appl. Opt. 48, 5997–6007 (2009).
[CrossRef]

C. Nissly, B.-J. Seo, M. Troy, G. Angeli, J. Angione, I. Crossfield, B. Ellerbroek, L. Gilles, and N. Sigrist, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Proc. SPIE 7017, 70170U (2008).
[CrossRef]

Ohara, C.

Piatrou, P.

Roggemann, M. C.

M. C. Roggemann and B. M. Welsh, Imaging Through Turbulence (CRC, 1996).

Sanders, G. H.

J. Nelson and G. H. Sanders, “TMT status report,” Proc. SPIE 6267, 626728 (2006).

Seo, B.-J.

B.-J. Seo, C. Nissly, and M. Troy, “Normalized point source sensitivity for off-axis optical performance evaluation of the Thirty Meter Telescope,” Proc. SPIE 7738, 77380G (2010).

B.-J. Seo, C. Nissly, G. Angeli, B. Ellerbroek, J. Nelson, N. Sigrist, and M. Troy, “Analysis of normalized point spread source sensitivity as performance metric for large telescopes,” Appl. Opt. 48, 5997–6007 (2009).
[CrossRef]

C. Nissly, B.-J. Seo, M. Troy, G. Angeli, J. Angione, I. Crossfield, B. Ellerbroek, L. Gilles, and N. Sigrist, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Proc. SPIE 7017, 70170U (2008).
[CrossRef]

Sigrist, N.

B.-J. Seo, C. Nissly, G. Angeli, B. Ellerbroek, J. Nelson, N. Sigrist, and M. Troy, “Analysis of normalized point spread source sensitivity as performance metric for large telescopes,” Appl. Opt. 48, 5997–6007 (2009).
[CrossRef]

C. Nissly, B.-J. Seo, M. Troy, G. Angeli, J. Angione, I. Crossfield, B. Ellerbroek, L. Gilles, and N. Sigrist, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Proc. SPIE 7017, 70170U (2008).
[CrossRef]

Spyromilio, J.

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

Troy, M.

B.-J. Seo, C. Nissly, and M. Troy, “Normalized point source sensitivity for off-axis optical performance evaluation of the Thirty Meter Telescope,” Proc. SPIE 7738, 77380G (2010).

B.-J. Seo, C. Nissly, G. Angeli, B. Ellerbroek, J. Nelson, N. Sigrist, and M. Troy, “Analysis of normalized point spread source sensitivity as performance metric for large telescopes,” Appl. Opt. 48, 5997–6007 (2009).
[CrossRef]

C. Nissly, B.-J. Seo, M. Troy, G. Angeli, J. Angione, I. Crossfield, B. Ellerbroek, L. Gilles, and N. Sigrist, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Proc. SPIE 7017, 70170U (2008).
[CrossRef]

G. A. Chanan, C. Ohara, and M. Troy, “Phasing the mirror segments of the Keck telescopes: the narrowband phasing algorithm,” Appl. Opt. 39, 4706–4714 (2000).
[CrossRef]

G. A. Chanan, M. Troy, F. G. 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]

Van Loan, C. F.

G. H. Golub and C. F. Van Loan, Matrix Computations (The Johns Hopkins University, 1996).

Welsh, B. M.

M. C. Roggemann and B. M. Welsh, Imaging Through Turbulence (CRC, 1996).

Appl. Opt.

Proc. SPIE

B.-J. Seo, C. Nissly, and M. Troy, “Normalized point source sensitivity for off-axis optical performance evaluation of the Thirty Meter Telescope,” Proc. SPIE 7738, 77380G (2010).

J. Nelson and G. H. Sanders, “TMT status report,” Proc. SPIE 6267, 626728 (2006).

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

C. Nissly, B.-J. Seo, M. Troy, G. Angeli, J. Angione, I. Crossfield, B. Ellerbroek, L. Gilles, and N. Sigrist, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Proc. SPIE 7017, 70170U (2008).
[CrossRef]

Other

P. L. Schechter and R. S. Levinson, “Generic misalignment aberration patterns in wide-field telescopes,” http://arxiv.org/abs/1009.0708v1 .

G. H. Golub and C. F. Van Loan, Matrix Computations (The Johns Hopkins University, 1996).

M. C. Roggemann and B. M. Welsh, Imaging Through Turbulence (CRC, 1996).

“Specification for finished primary mirror segments,” TMT project documentation. TMT.OPT.SPE.07.002.CCR03.

“Design requirements document for the M2 system,” TMT project documentation. TMT.OPT.DRD.07.004.CCR28.

“Design requirements document for the M3 system,” TMT project documentation. TMT.OPT.DRD.07.006.CCR28.

TMT construction proposal, http://www.tmt.org/sites/default/files/TMT-Construction-Proposal-Public.pdf .

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Figures (3)

Fig. 1.
Fig. 1.

(a) Shack-Hartmann WFS lenslet grid superimposed onto the TMT primary mirror segment map (fragment). Large hexagons are the M1 segments, small hexagons are the WFS lenslets. The lenslet groups inside each segment correspond to column blocks in the O-matrix. The lenslets on the border between the adjacent segments are excluded from the WFS measurements. (b) The “3-ring configuration” of the WFS block corresponding to one segment. Internal (light gray) lenslets are used for wavefront sensing; external (dark gray) lenslets are used for interferometric segment phasing.

Fig. 2.
Fig. 2.

Logarithmic plots of absolute values for typical M2 (a) and M3 (b) observability blocks computed via Eq. (5) as projections of M2/M3 rigid body and Zernike polynomial deformations onto M1 segment tip/tilt and 33 Zernike polynomial deformation basis. The rows above ninth (M1 segment trefoil) can be set to zero.

Fig. 3.
Fig. 3.

(a) Singular spectrum of the tRTC observability block. (b) Close-up showing the most singular part of the spectrum consisting of 15 “invisible” modes. All singular values of the hRTC block are equal to 1 by construction.

Tables (7)

Tables Icon

Table 1. Expected TMT Optical Element Rigid Body Post-Installation Errorsa

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Table 2. Expected TMT Optical Element Surface Warp Post-Installation Errorsa

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Table 3. Best Achievable System Performance Metrics Computed for the Standard Perturbations Listed in Tables a in Case of Noiseless WFS Measurements and the Turbulence Noise

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Table 4. Results of Monte-Carlo Simulation of the Residual Errors due to the Turbulence Noisea

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Table 5. Results of Monte-Carlo Simulation of the Aliasing Residual Errorsa

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Table 6. Results of Monte-Carlo Simulation for the Full RTC Errors in Case of Noiseless WFS Measurements and the Turbulence Noisea

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Table 7. Results of Monte-Carlo Simulation for the Errors of the Alignment Sequence Involving RTC Followed by M1 Segment Controller and the M1 Phasera

Equations (9)

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

Os=a,
OTOa=OTs.
POa=Ps
P=diag(Pi)i=1N.
P=diag(Mij,1j)i=1,,w,j=1,,s,
Z(x,y)=n=0dnZn(x,y),Zn(x,y)=m=0nanmxnmym.
Zn(xx0k,yy0k)=1knm=0nanm(xx0)nm(yy0)m,
ROa=Rs,R=IQQT,
PSSN=|OTFr+e(f)|2df|OTFr(f)|2df=OTFr+e/OTFr,

Metrics