Abstract

The Alignment and Phasing System (APS) of the Thirty Meter Telescope (TMT) is an instrument that will be responsible for aligning the primary, secondary, and tertiary mirrors of TMT. The telescope and APS are modeled with a ray tracing simulation program. Various sets of initial conditions and alignment procedures are simulated, and results are compared to the image quality specifications for the telescope. A key factor in alignment quality is the rotation of the flat tertiary mirror (M3), which rotates to serve the science instruments. The procedures that use only APS measurements yield unacceptably large image diameters, while procedures that use measurements from APS and another WFS at a different location result in telescope alignments that produce acceptable image diameters at the 90% confidence level. These two-sensor procedures can separate M3 errors from errors on other mirrors better than APS-only procedures. However, APS-only procedures should be adequate for the restricted configurations of instruments available at first light. In general, APS-only procedures should also be capable of maintaining the alignment produced initially by the more complex two-sensor procedures.

© 2010 Optical Society of America

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References

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  1. “Thirty Meter Telescope construction proposal,” Report TMT.PMO.MGT.07.009 (Thirty Meter Telescope, 2007), http://www.tmt.org/news/TMT-Construction%20 Proposal-Public.pdf.
  2. J. Nelson and G. H. Sanders, “The status of the Thirty Meter Telescope project,” Proc. SPIE 7012, 70121A (2008),
    [CrossRef]
  3. M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
    [CrossRef]
  4. G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, and B. A. Schaefer, ”W. M. Keck Telescope phasing camera system,” Proc. SPIE 2198, 1139–1150 (1994).
    [CrossRef]
  5. 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]
  6. G. Chanan, C. Ohara, and M. Troy, “Phasing the mirror segments of the Keck Telescopes. II. The narrowband phasing algorithm,” Appl. Opt. 39, 4706–4714 (2000).
    [CrossRef]
  7. C. Shelton, T. Mast, G. Chanan, J. Nelson, J. LewisC. Roberts, M. Troy, M. J. Sirota, B.-J Seo, and D. R. MacDonald, “Advances in edge sensors for the Thirty Meter Telescope primary mirror,” Proc. SPIE 7012, 701210 (2008).
    [CrossRef]
  8. G. Chanan, “Limitations on the control of hexagonal mirror segment figures by means of edge measurements,” Appl. Opt. 48, 6281–6289 (2009).
    [CrossRef] [PubMed]
  9. G. Chanan, M. Troy, and I. Crossfield, “Predicted measurement accuracy of the TMT alignment and phasing system,” Report TMT.CTR.PRE.07.007.REL01 (Thirty Meter Telescope, 2007).
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    [CrossRef]
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  12. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  13. D. C. Zimmerman, “Feasibility studies for the alignment of the Thirty Meter Telescope,” Ph.D. thesis, (University of California, Irvine, 2009).
  14. C. Nissly, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Report TMT.SEN.JOU.08.009.DRF01 (Thirty Meter Telescope, 2008).
  15. J. Nelson, “Time variable misalignments of m1, m2, m3,” Report TMT.PSC.TEC.09.005.DRF01 (Thirty Meter Telescope, 2009).
  16. “Observatory requirements document,” Report TMT.SEN.DRD.05.001.CCR21 (Thirty Meter Telescope, 2009) (latest revision at http://www.tmt.org/sites/default/files/ORD-CCR22.pdf).
  17. J. B. Shellan and D. C. Zimmerman, “Computation and comparison of slope discrepancy for Hartmann sensors and shearing interferometers,” Report TR-1519R (The Optical Sciences Company, 2004).

2009 (1)

2008 (3)

C. Shelton, T. Mast, G. Chanan, J. Nelson, J. LewisC. Roberts, M. Troy, M. J. Sirota, B.-J Seo, and D. R. MacDonald, “Advances in edge sensors for the Thirty Meter Telescope primary mirror,” Proc. SPIE 7012, 701210 (2008).
[CrossRef]

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

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

2000 (1)

1998 (1)

1994 (1)

G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, and B. A. Schaefer, ”W. M. Keck Telescope phasing camera system,” Proc. SPIE 2198, 1139–1150 (1994).
[CrossRef]

1976 (1)

1966 (1)

Bartos, R.

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

Bothwell, G.

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

Chanan, G.

G. Chanan, “Limitations on the control of hexagonal mirror segment figures by means of edge measurements,” Appl. Opt. 48, 6281–6289 (2009).
[CrossRef] [PubMed]

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

C. Shelton, T. Mast, G. Chanan, J. Nelson, J. LewisC. Roberts, M. Troy, M. J. Sirota, B.-J Seo, and D. R. MacDonald, “Advances in edge sensors for the Thirty Meter Telescope primary mirror,” Proc. SPIE 7012, 701210 (2008).
[CrossRef]

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

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]

G. Chanan, M. Troy, and I. Crossfield, “Predicted measurement accuracy of the TMT alignment and phasing system,” Report TMT.CTR.PRE.07.007.REL01 (Thirty Meter Telescope, 2007).

G. Chanan and M. Troy, “Modal aliasing in wavefront reconstruction for telescope mirror segment warping harnesses,” Report TMT.CTR.TEC.08.051.REL01 (Thirty Meter Telescope, 2008).

Chanan, G. A.

G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, and B. A. Schaefer, ”W. M. Keck Telescope phasing camera system,” Proc. SPIE 2198, 1139–1150 (1994).
[CrossRef]

Crossfield, I.

G. Chanan, M. Troy, and I. Crossfield, “Predicted measurement accuracy of the TMT alignment and phasing system,” Report TMT.CTR.PRE.07.007.REL01 (Thirty Meter Telescope, 2007).

Dekens, F.

Fried, D. L.

Giveon, A.

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

Hein, R.

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

Kirkman, D.

Lewis, J.

C. Shelton, T. Mast, G. Chanan, J. Nelson, J. LewisC. Roberts, M. Troy, M. J. Sirota, B.-J Seo, and D. R. MacDonald, “Advances in edge sensors for the Thirty Meter Telescope primary mirror,” Proc. SPIE 7012, 701210 (2008).
[CrossRef]

MacDonald, D. R.

C. Shelton, T. Mast, G. Chanan, J. Nelson, J. LewisC. Roberts, M. Troy, M. J. Sirota, B.-J Seo, and D. R. MacDonald, “Advances in edge sensors for the Thirty Meter Telescope primary mirror,” Proc. SPIE 7012, 701210 (2008).
[CrossRef]

Mast, T.

C. Shelton, T. Mast, G. Chanan, J. Nelson, J. LewisC. Roberts, M. Troy, M. J. Sirota, B.-J Seo, and D. R. MacDonald, “Advances in edge sensors for the Thirty Meter Telescope primary mirror,” Proc. SPIE 7012, 701210 (2008).
[CrossRef]

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]

Mast, T. S.

G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, and B. A. Schaefer, ”W. M. Keck Telescope phasing camera system,” Proc. SPIE 2198, 1139–1150 (1994).
[CrossRef]

Michaels, S.

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

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]

Nelson, J.

C. Shelton, T. Mast, G. Chanan, J. Nelson, J. LewisC. Roberts, M. Troy, M. J. Sirota, B.-J Seo, and D. R. MacDonald, “Advances in edge sensors for the Thirty Meter Telescope primary mirror,” Proc. SPIE 7012, 701210 (2008).
[CrossRef]

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

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]

J. Nelson, “Time variable misalignments of m1, m2, m3,” Report TMT.PSC.TEC.09.005.DRF01 (Thirty Meter Telescope, 2009).

Nelson, J. E.

G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, and B. A. Schaefer, ”W. M. Keck Telescope phasing camera system,” Proc. SPIE 2198, 1139–1150 (1994).
[CrossRef]

Nissly, C.

C. Nissly, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Report TMT.SEN.JOU.08.009.DRF01 (Thirty Meter Telescope, 2008).

Noll, R. J.

Ohara, C.

Radin, M.

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

Roberts, C.

C. Shelton, T. Mast, G. Chanan, J. Nelson, J. LewisC. Roberts, M. Troy, M. J. Sirota, B.-J Seo, and D. R. MacDonald, “Advances in edge sensors for the Thirty Meter Telescope primary mirror,” Proc. SPIE 7012, 701210 (2008).
[CrossRef]

Roberts, J.

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

Rodgers, J. M.

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

Sanders, G. H.

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

Schaefer, B. A.

G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, and B. A. Schaefer, ”W. M. Keck Telescope phasing camera system,” Proc. SPIE 2198, 1139–1150 (1994).
[CrossRef]

Scherr, L. M.

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

Seo, B.-J

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

C. Shelton, T. Mast, G. Chanan, J. Nelson, J. LewisC. Roberts, M. Troy, M. J. Sirota, B.-J Seo, and D. R. MacDonald, “Advances in edge sensors for the Thirty Meter Telescope primary mirror,” Proc. SPIE 7012, 701210 (2008).
[CrossRef]

Shellan, J. B.

J. B. Shellan and D. C. Zimmerman, “Computation and comparison of slope discrepancy for Hartmann sensors and shearing interferometers,” Report TR-1519R (The Optical Sciences Company, 2004).

Shelton, C.

C. Shelton, T. Mast, G. Chanan, J. Nelson, J. LewisC. Roberts, M. Troy, M. J. Sirota, B.-J Seo, and D. R. MacDonald, “Advances in edge sensors for the Thirty Meter Telescope primary mirror,” Proc. SPIE 7012, 701210 (2008).
[CrossRef]

Sirota, M. J.

C. Shelton, T. Mast, G. Chanan, J. Nelson, J. LewisC. Roberts, M. Troy, M. J. Sirota, B.-J Seo, and D. R. MacDonald, “Advances in edge sensors for the Thirty Meter Telescope primary mirror,” Proc. SPIE 7012, 701210 (2008).
[CrossRef]

Troy, M.

C. Shelton, T. Mast, G. Chanan, J. Nelson, J. LewisC. Roberts, M. Troy, M. J. Sirota, B.-J Seo, and D. R. MacDonald, “Advances in edge sensors for the Thirty Meter Telescope primary mirror,” Proc. SPIE 7012, 701210 (2008).
[CrossRef]

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

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

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]

G. Chanan, M. Troy, and I. Crossfield, “Predicted measurement accuracy of the TMT alignment and phasing system,” Report TMT.CTR.PRE.07.007.REL01 (Thirty Meter Telescope, 2007).

G. Chanan and M. Troy, “Modal aliasing in wavefront reconstruction for telescope mirror segment warping harnesses,” Report TMT.CTR.TEC.08.051.REL01 (Thirty Meter Telescope, 2008).

Wizinowich, P. L.

G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, and B. A. Schaefer, ”W. M. Keck Telescope phasing camera system,” Proc. SPIE 2198, 1139–1150 (1994).
[CrossRef]

Zimmerman, D.

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

Zimmerman, D. C.

J. B. Shellan and D. C. Zimmerman, “Computation and comparison of slope discrepancy for Hartmann sensors and shearing interferometers,” Report TR-1519R (The Optical Sciences Company, 2004).

D. C. Zimmerman, “Feasibility studies for the alignment of the Thirty Meter Telescope,” Ph.D. thesis, (University of California, Irvine, 2009).

Appl. Opt. (3)

J. Opt. Soc. Am. (2)

Proc. SPIE (4)

C. Shelton, T. Mast, G. Chanan, J. Nelson, J. LewisC. Roberts, M. Troy, M. J. Sirota, B.-J Seo, and D. R. MacDonald, “Advances in edge sensors for the Thirty Meter Telescope primary mirror,” Proc. SPIE 7012, 701210 (2008).
[CrossRef]

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

M. Troy, G. Chanan, S. Michaels, R. Bartos, G. Bothwell, A. Giveon, R. Hein, M. Radin, J. Roberts, J. M. Rodgers, L. M. Scherr, B.-J Seo, and D. Zimmerman, “A conceptual design for the Thirty Meter Telescope alignment and phasing system,” Proc. SPIE 7012, 70120Y (2008).
[CrossRef]

G. A. Chanan, J. E. Nelson, T. S. Mast, P. L. Wizinowich, and B. A. Schaefer, ”W. M. Keck Telescope phasing camera system,” Proc. SPIE 2198, 1139–1150 (1994).
[CrossRef]

Other (8)

G. Chanan and M. Troy, “Modal aliasing in wavefront reconstruction for telescope mirror segment warping harnesses,” Report TMT.CTR.TEC.08.051.REL01 (Thirty Meter Telescope, 2008).

G. Chanan, M. Troy, and I. Crossfield, “Predicted measurement accuracy of the TMT alignment and phasing system,” Report TMT.CTR.PRE.07.007.REL01 (Thirty Meter Telescope, 2007).

D. C. Zimmerman, “Feasibility studies for the alignment of the Thirty Meter Telescope,” Ph.D. thesis, (University of California, Irvine, 2009).

C. Nissly, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Report TMT.SEN.JOU.08.009.DRF01 (Thirty Meter Telescope, 2008).

J. Nelson, “Time variable misalignments of m1, m2, m3,” Report TMT.PSC.TEC.09.005.DRF01 (Thirty Meter Telescope, 2009).

“Observatory requirements document,” Report TMT.SEN.DRD.05.001.CCR21 (Thirty Meter Telescope, 2009) (latest revision at http://www.tmt.org/sites/default/files/ORD-CCR22.pdf).

J. B. Shellan and D. C. Zimmerman, “Computation and comparison of slope discrepancy for Hartmann sensors and shearing interferometers,” Report TR-1519R (The Optical Sciences Company, 2004).

“Thirty Meter Telescope construction proposal,” Report TMT.PMO.MGT.07.009 (Thirty Meter Telescope, 2007), http://www.tmt.org/news/TMT-Construction%20 Proposal-Public.pdf.

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Figures (10)

Fig. 1
Fig. 1

Initial and final layouts of TMT instruments. These images represent the layout of instruments on the Nasmyth platforms (a) at first light and (b) when all instruments are installed. In the initial layout, APS and WFOS are on the elevation axis. In the final layout, APS is moved off of the elevation axis. Images taken from [1].

Fig. 2
Fig. 2

Comparison of the Huygens PSF calculation to wave-optics propagation. The OPD on M1 is plotted in (a); the rest of the telescope is perfectly aligned. Note that the PSF is much smaller than the ray tracing spot.

Fig. 3
Fig. 3

RMS mode amplitudes in turbulence, M2 control matrix. This figure plots the RMS number of units of each singular mode of the M2 control matrix reconstructed from turbulence. The last five singular modes have large values due to the small singular values. See the text for a detailed description of how these values are computed. The analytic results are discussed in Appendix A.

Fig. 4
Fig. 4

Maximum allowed spot diameter due to telescope errors. The specified spot diameter due to APS measurement error is the greater of 0.04 and 1.07 times the nominal spot diameter. Spot diameters are measured using a circle containing 80% enclosed energy. The specified spot diameter due to all errors modeled in this simulation is 0.195 on axis; 1.07 times the nominal spot diameter is added in quadrature off axis.

Fig. 5
Fig. 5

Image diameter CDFs for one alignment scheme. The curves plot the probability that the postalignment image diameter is less than a given diameter X at one focal station, for one alignment procedure (“2 WFS (7) off” in the list on page 16). The solid line corresponds to on-axis images, the dashed line corresponds to images 200 off axis, and the dotted line corresponds to images 400 off axis. The specifications for maximum allowable image diameter based on all modeled errors are 0.195 , 0.206 , and 0.321 for sources 0 , 200 , and 400 off axis, respectively. These particular CDFs meet all specifications at the 99th percentile level or above.

Fig. 6
Fig. 6

90th percentile image diameters for various alignment schemes. Plotted here are the 90th percentile postalignment image diameters for the various alignment schemes. The specifications for maximum allowable image diameter based on all modeled errors are 0.195 , 0.206 , and 0.321 for sources 0 , 200 , and 400 off axis, respectively. The legend corresponds to the different alignment schemes, and is explained in a list in the text. The solid lines correspond to on-axis sources, the dashed lines correspond to sources 200 off axis, and the dotted lines correspond to sources 400 off axis. The horizontal lines represent the image diameter specifications for all modeled errors, using the same line types as the results. Note that at the 90th percentile level, several alignment schemes do not meet the specifications. These include “1 WFS on” and “2 WFS (60) on” on the APS platform, and “1 WFS on” and “1 WFS off” on the other platform.

Fig. 7
Fig. 7

Image displacement CDFs for one alignment scheme. The curves plot the probability that the postalignment image displacement is less than a given displacement X at one focal station, for one alignment procedure (“2 WFS (7) off” in a list in the text). The solid line corresponds to on-axis images, the dashed line corresponds to images 200 off axis, and the dotted line corresponds to images 400 off axis. The specification for maximum allowable image displacement based on all telescope errors (modeled or not) is 0.06 over the entire field of view.

Fig. 8
Fig. 8

90th percentile image displacements for various alignment schemes. Same as Fig. 6, but for the 90th percentile image displacements instead of 90th percentile image diameters. Note that at the 90th percentile level, several alignment schemes do not meet the specification for images 400 off axis. These include “1 WFS on,” “1 WFS off,” “2 WFS (7) off,” and “2 WFS (60) on” on both platforms.

Fig. 9
Fig. 9

Example postalignment PSFs. In each subfigure, the two on-axis PSFs are plotted on the same color scale. The result of on-axis alignment is on the left, and the result of APS / 60 × 60 off-axis alignment is on the right. Each PSF is normalized by the total amount of energy it contains. The linear scale in (a) clearly shows that the off-axis alignment produces a sharper PSF. The log scale in (b) (the color scale is given as the log base 10 of the intensity) shows that low-intensity speckles exist far from the central peak. These speckles are an artifact of the PSF calculation, and are discussed in the text. The wavelength used to calculate these PSFs is 1 μm .

Fig. 10
Fig. 10

PSF enclosed energy versus enclosure di ameter. This figure is for the on-axis alignment example discussed in the text. The legend gives the number of rays used to calculate the PSF for each curve. The curves plot the fraction of enclosed energy at each diameter. While a significant fraction of the energy on the focal surface is far from the central peak, the diameter of the circle enclosing 80% of the energy is stable at this number of rays.

Tables (2)

Tables Icon

Table 1 Initial M1 Segment Errors a

Tables Icon

Table 2 Initial M2 and M3 Surface and Displacement Errors a

Equations (5)

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

Γ = U S V T ,
H = V S U T ,
H = S U T .
d ray = d PSF 2 + d HSF 2 ,
E = H C H T .

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