Abstract

We present a method which estimates the normalized point-source sensitivity (PSSN) of a segmented telescope when only information from a single segment surface is known. The estimation principle is based on a statistical approach with an assumption that all segment surfaces have the same power spectral density (PSD) as the given segment surface. As presented in this paper, the PSSN based on this statistical approach represents a worst-case scenario among statistical random realizations of telescopes when all segment surfaces have the same PSD. Therefore, this method, which we call the vendor table, is expected to be useful for individual segment specification such as the segment polishing specification. The specification based on the vendor table can be directly related to a science metric such as PSSN and provides the mirror vendors significant flexibility by specifying a single overall PSSN value for them to meet. We build a vendor table for the Thirty Meter Telescope (TMT) and test it using multiple mirror samples from various mirror vendors to prove its practical utility. Accordingly, TMT has a plan to adopt this vendor table for its M1 segment final mirror polishing requirement.

© 2013 Optical Society of America

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References

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  1. G. Z. Angeli, S. Roberts, and K. Vogiatzis, “Systems engineering for the preliminary design of the Thirty Meter Telescope,” Proc. SPIE 7017, 701704 (2008).
    [CrossRef]
  2. C. Nissly, B. Seo, M. Troy, G. Angeli, J. Angione, I. Crossfield, B. Ellerbroek, L. Gilles, N. Sigrist, and L. Wang, “High-resolution optical modeling of the Thirty Meter Telescope for systematic performance trades,” Proc. SPIE 7017, 70170U (2008).
    [CrossRef]
  3. G. Angeli, “Seeing limited PSS budget D16v2,” TMT Project Communication TMT.SEN.DRD.07.026.REL16 (2012).
  4. H. Bonnet, M. Esselborn, M. Muller, B. Sedghi, and F. Koch, “E-ELT active optics system modeling and performance evaluation,” Proc. SPIE 8336, 83360P (2011).
    [CrossRef]
  5. I. R. King, “Accuracy of measurement of star images on a pixel array,” Publ. Astron. Soc. Pac. 95, 163–168 (1983).
    [CrossRef]
  6. B.-J. Seo, C. Nissly, G. Angeli, B. Ellerbroek, J. Nelson, N. Sigrist, and M. Troy, “Analysis of normalized point source sensitivity as performance metric for large telescopes,” Appl. Opt. 48, 5997–6007 (2009).
    [CrossRef]
  7. B.-J. Seo, C. Nissly, M. Troy, G. Angeli, R. Bernier, L. Stepp, and E. Williams, “TMT M1 segment polishing specification analysis (draft),” TMT Project Communication TMT.SEN.TEC.11.018.DRF01 (2011).
  8. B.-J. Seo, C. Nissly, M. Troy, G. Angeli, V. Ford, L. Stepp, and E. Williams, “Approximation of normalized point source sensitivity using power spectral density and slopes of wavefront aberration” Appl. Opt. 17, 3910–3922 (2013).
  9. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976).
    [CrossRef]
  10. Thirty Meter Telescope, “Specification for finished 1.44-meter primary mirror segments,” TMT Project Communication TMT.OPT.SPE.07.002.CCR03 (2008), http://www.tmt.org/sites/default/files/TMT-OPT-SPE-07-002-CCR03-Specification-for-Finished-Primary-Mirror-Segments-Final.pdf .
  11. B. Seo, C. Nissly, G. Angeli, D. MacMynowski, N. Sigrist, M. Troy, and E. Williams, “Investigation of primary mirror segment’s residual errors for the Thirty Meter Telescope,” Proc. SPIE 7427, 74270F (2009).
    [CrossRef]
  12. B.-J. Seo, C. Nissly, M. Troy, and G. Angeli, “TMT figuring error modeling,” TMT Project Communication TMT.SEN.TEC.10.025.DRF01 (2010).

2013

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, V. Ford, L. Stepp, and E. Williams, “Approximation of normalized point source sensitivity using power spectral density and slopes of wavefront aberration” Appl. Opt. 17, 3910–3922 (2013).

2011

H. Bonnet, M. Esselborn, M. Muller, B. Sedghi, and F. Koch, “E-ELT active optics system modeling and performance evaluation,” Proc. SPIE 8336, 83360P (2011).
[CrossRef]

2009

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

B. Seo, C. Nissly, G. Angeli, D. MacMynowski, N. Sigrist, M. Troy, and E. Williams, “Investigation of primary mirror segment’s residual errors for the Thirty Meter Telescope,” Proc. SPIE 7427, 74270F (2009).
[CrossRef]

2008

G. Z. Angeli, S. Roberts, and K. Vogiatzis, “Systems engineering for the preliminary design of the Thirty Meter Telescope,” Proc. SPIE 7017, 701704 (2008).
[CrossRef]

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

1983

I. R. King, “Accuracy of measurement of star images on a pixel array,” Publ. Astron. Soc. Pac. 95, 163–168 (1983).
[CrossRef]

1976

Angeli, G.

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, V. Ford, L. Stepp, and E. Williams, “Approximation of normalized point source sensitivity using power spectral density and slopes of wavefront aberration” Appl. Opt. 17, 3910–3922 (2013).

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

B. Seo, C. Nissly, G. Angeli, D. MacMynowski, N. Sigrist, M. Troy, and E. Williams, “Investigation of primary mirror segment’s residual errors for the Thirty Meter Telescope,” Proc. SPIE 7427, 74270F (2009).
[CrossRef]

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

G. Angeli, “Seeing limited PSS budget D16v2,” TMT Project Communication TMT.SEN.DRD.07.026.REL16 (2012).

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, R. Bernier, L. Stepp, and E. Williams, “TMT M1 segment polishing specification analysis (draft),” TMT Project Communication TMT.SEN.TEC.11.018.DRF01 (2011).

B.-J. Seo, C. Nissly, M. Troy, and G. Angeli, “TMT figuring error modeling,” TMT Project Communication TMT.SEN.TEC.10.025.DRF01 (2010).

Angeli, G. Z.

G. Z. Angeli, S. Roberts, and K. Vogiatzis, “Systems engineering for the preliminary design of the Thirty Meter Telescope,” Proc. SPIE 7017, 701704 (2008).
[CrossRef]

Angione, J.

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

Bernier, R.

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, R. Bernier, L. Stepp, and E. Williams, “TMT M1 segment polishing specification analysis (draft),” TMT Project Communication TMT.SEN.TEC.11.018.DRF01 (2011).

Bonnet, H.

H. Bonnet, M. Esselborn, M. Muller, B. Sedghi, and F. Koch, “E-ELT active optics system modeling and performance evaluation,” Proc. SPIE 8336, 83360P (2011).
[CrossRef]

Crossfield, I.

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

Ellerbroek, B.

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

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

Esselborn, M.

H. Bonnet, M. Esselborn, M. Muller, B. Sedghi, and F. Koch, “E-ELT active optics system modeling and performance evaluation,” Proc. SPIE 8336, 83360P (2011).
[CrossRef]

Ford, V.

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, V. Ford, L. Stepp, and E. Williams, “Approximation of normalized point source sensitivity using power spectral density and slopes of wavefront aberration” Appl. Opt. 17, 3910–3922 (2013).

Gilles, L.

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

King, I. R.

I. R. King, “Accuracy of measurement of star images on a pixel array,” Publ. Astron. Soc. Pac. 95, 163–168 (1983).
[CrossRef]

Koch, F.

H. Bonnet, M. Esselborn, M. Muller, B. Sedghi, and F. Koch, “E-ELT active optics system modeling and performance evaluation,” Proc. SPIE 8336, 83360P (2011).
[CrossRef]

MacMynowski, D.

B. Seo, C. Nissly, G. Angeli, D. MacMynowski, N. Sigrist, M. Troy, and E. Williams, “Investigation of primary mirror segment’s residual errors for the Thirty Meter Telescope,” Proc. SPIE 7427, 74270F (2009).
[CrossRef]

Muller, M.

H. Bonnet, M. Esselborn, M. Muller, B. Sedghi, and F. Koch, “E-ELT active optics system modeling and performance evaluation,” Proc. SPIE 8336, 83360P (2011).
[CrossRef]

Nelson, J.

Nissly, C.

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, V. Ford, L. Stepp, and E. Williams, “Approximation of normalized point source sensitivity using power spectral density and slopes of wavefront aberration” Appl. Opt. 17, 3910–3922 (2013).

B. Seo, C. Nissly, G. Angeli, D. MacMynowski, N. Sigrist, M. Troy, and E. Williams, “Investigation of primary mirror segment’s residual errors for the Thirty Meter Telescope,” Proc. SPIE 7427, 74270F (2009).
[CrossRef]

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

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

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, R. Bernier, L. Stepp, and E. Williams, “TMT M1 segment polishing specification analysis (draft),” TMT Project Communication TMT.SEN.TEC.11.018.DRF01 (2011).

B.-J. Seo, C. Nissly, M. Troy, and G. Angeli, “TMT figuring error modeling,” TMT Project Communication TMT.SEN.TEC.10.025.DRF01 (2010).

Noll, R. J.

Roberts, S.

G. Z. Angeli, S. Roberts, and K. Vogiatzis, “Systems engineering for the preliminary design of the Thirty Meter Telescope,” Proc. SPIE 7017, 701704 (2008).
[CrossRef]

Sedghi, B.

H. Bonnet, M. Esselborn, M. Muller, B. Sedghi, and F. Koch, “E-ELT active optics system modeling and performance evaluation,” Proc. SPIE 8336, 83360P (2011).
[CrossRef]

Seo, B.

B. Seo, C. Nissly, G. Angeli, D. MacMynowski, N. Sigrist, M. Troy, and E. Williams, “Investigation of primary mirror segment’s residual errors for the Thirty Meter Telescope,” Proc. SPIE 7427, 74270F (2009).
[CrossRef]

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

Seo, B.-J.

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, V. Ford, L. Stepp, and E. Williams, “Approximation of normalized point source sensitivity using power spectral density and slopes of wavefront aberration” Appl. Opt. 17, 3910–3922 (2013).

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

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, R. Bernier, L. Stepp, and E. Williams, “TMT M1 segment polishing specification analysis (draft),” TMT Project Communication TMT.SEN.TEC.11.018.DRF01 (2011).

B.-J. Seo, C. Nissly, M. Troy, and G. Angeli, “TMT figuring error modeling,” TMT Project Communication TMT.SEN.TEC.10.025.DRF01 (2010).

Sigrist, N.

B. Seo, C. Nissly, G. Angeli, D. MacMynowski, N. Sigrist, M. Troy, and E. Williams, “Investigation of primary mirror segment’s residual errors for the Thirty Meter Telescope,” Proc. SPIE 7427, 74270F (2009).
[CrossRef]

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

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

Stepp, L.

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, V. Ford, L. Stepp, and E. Williams, “Approximation of normalized point source sensitivity using power spectral density and slopes of wavefront aberration” Appl. Opt. 17, 3910–3922 (2013).

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, R. Bernier, L. Stepp, and E. Williams, “TMT M1 segment polishing specification analysis (draft),” TMT Project Communication TMT.SEN.TEC.11.018.DRF01 (2011).

Troy, M.

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, V. Ford, L. Stepp, and E. Williams, “Approximation of normalized point source sensitivity using power spectral density and slopes of wavefront aberration” Appl. Opt. 17, 3910–3922 (2013).

B. Seo, C. Nissly, G. Angeli, D. MacMynowski, N. Sigrist, M. Troy, and E. Williams, “Investigation of primary mirror segment’s residual errors for the Thirty Meter Telescope,” Proc. SPIE 7427, 74270F (2009).
[CrossRef]

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

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

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, R. Bernier, L. Stepp, and E. Williams, “TMT M1 segment polishing specification analysis (draft),” TMT Project Communication TMT.SEN.TEC.11.018.DRF01 (2011).

B.-J. Seo, C. Nissly, M. Troy, and G. Angeli, “TMT figuring error modeling,” TMT Project Communication TMT.SEN.TEC.10.025.DRF01 (2010).

Vogiatzis, K.

G. Z. Angeli, S. Roberts, and K. Vogiatzis, “Systems engineering for the preliminary design of the Thirty Meter Telescope,” Proc. SPIE 7017, 701704 (2008).
[CrossRef]

Wang, L.

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

Williams, E.

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, V. Ford, L. Stepp, and E. Williams, “Approximation of normalized point source sensitivity using power spectral density and slopes of wavefront aberration” Appl. Opt. 17, 3910–3922 (2013).

B. Seo, C. Nissly, G. Angeli, D. MacMynowski, N. Sigrist, M. Troy, and E. Williams, “Investigation of primary mirror segment’s residual errors for the Thirty Meter Telescope,” Proc. SPIE 7427, 74270F (2009).
[CrossRef]

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, R. Bernier, L. Stepp, and E. Williams, “TMT M1 segment polishing specification analysis (draft),” TMT Project Communication TMT.SEN.TEC.11.018.DRF01 (2011).

Appl. Opt.

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

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, V. Ford, L. Stepp, and E. Williams, “Approximation of normalized point source sensitivity using power spectral density and slopes of wavefront aberration” Appl. Opt. 17, 3910–3922 (2013).

J. Opt. Soc. Am.

Proc. SPIE

G. Z. Angeli, S. Roberts, and K. Vogiatzis, “Systems engineering for the preliminary design of the Thirty Meter Telescope,” Proc. SPIE 7017, 701704 (2008).
[CrossRef]

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

H. Bonnet, M. Esselborn, M. Muller, B. Sedghi, and F. Koch, “E-ELT active optics system modeling and performance evaluation,” Proc. SPIE 8336, 83360P (2011).
[CrossRef]

B. Seo, C. Nissly, G. Angeli, D. MacMynowski, N. Sigrist, M. Troy, and E. Williams, “Investigation of primary mirror segment’s residual errors for the Thirty Meter Telescope,” Proc. SPIE 7427, 74270F (2009).
[CrossRef]

Publ. Astron. Soc. Pac.

I. R. King, “Accuracy of measurement of star images on a pixel array,” Publ. Astron. Soc. Pac. 95, 163–168 (1983).
[CrossRef]

Other

G. Angeli, “Seeing limited PSS budget D16v2,” TMT Project Communication TMT.SEN.DRD.07.026.REL16 (2012).

Thirty Meter Telescope, “Specification for finished 1.44-meter primary mirror segments,” TMT Project Communication TMT.OPT.SPE.07.002.CCR03 (2008), http://www.tmt.org/sites/default/files/TMT-OPT-SPE-07-002-CCR03-Specification-for-Finished-Primary-Mirror-Segments-Final.pdf .

B.-J. Seo, C. Nissly, M. Troy, G. Angeli, R. Bernier, L. Stepp, and E. Williams, “TMT M1 segment polishing specification analysis (draft),” TMT Project Communication TMT.SEN.TEC.11.018.DRF01 (2011).

B.-J. Seo, C. Nissly, M. Troy, and G. Angeli, “TMT figuring error modeling,” TMT Project Communication TMT.SEN.TEC.10.025.DRF01 (2010).

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Figures (11)

Fig. 1.
Fig. 1.

Two differently configured telescopes are compared conceptually. Left is for a telescope where segments are arranged homogeneously. Right is for a telescope where segments are arranged randomly. Both telescopes have a single segment type, whose anisotropic OPD aberration makes the PSF spread to a point away from its center core in only one direction. This imaginary conceptual situation is only for demonstrating the correctness of Eq. (5).

Fig. 2.
Fig. 2.

Two differently configured telescopes are compared as the 2D version of Fig. 1. (a) is for a telescope that arranges the segments homogeneously while (b) is for the same telescope but with segments arranged in a zig-zag pattern. The corresponding PSFs are shown in (c) and (d), respectively. Similarly as in the discussion for Fig. 1, the PSF is spread in more diverse directions in (d). Consequently, the corresponding PSSN is larger in (c) than that in (d). This conceptual situation is for demonstrating the correctness of Eq. (5).

Fig. 3.
Fig. 3.

rmsSRF ratio by WH correction for each Zernike mode. The green and red curves are for 10 or 21 SVD mode correction. TMT WH for M1 segment has 21 influence functions, and thus 21 SVD modes total.

Fig. 4.
Fig. 4.

Procedure to compute the alpha prime α coefficients. The segment focus mode is used as an example.

Fig. 5.
Fig. 5.

PSD computed from surface measurements of real mirrors from various vendors listed in Table 2. The black dashed line and the blue dashed line in both plots are the reference PSDs, representing the PSD interpretation of the current TMT structure function specification [12] and a von Karman PSD with parameters of A=1.5nm2m2, fo=2cycles/m, and γ=3. We split the data set into two groups to make plots easier to read.

Fig. 6.
Fig. 6.

Procedure to compute αvk, the alpha value based on the von Karman PSD.

Fig. 7.
Fig. 7.

Alpha values computed from Fig. 6 as a function of fo and γ of the von Karman PSD. Since the amplitude parameter A has negligible dependency, we merge its dependency as the dots on the plot.

Fig. 8.
Fig. 8.

Numerical validation setup using real sample mirrors for αHO evaluated in Table 3. We numerically synthesize 492 segments for TMT M1 set using the computed PSD of the real sample mirrors shown in Fig. 5. Then, we remove the LOZ for all segments and compute rmsSRF and PSSN. This computed PSSN is compared to the approximated PSSN, that is, 1αHO·rmsSRF2. In order to verify that the number of included LOZs is enough, we perform the WH correction on segments and evaluate the PSSN afterward.

Fig. 9.
Fig. 9.

(a) Actual PSSN for mirror samples after LOZ removal. For the samples whose PSSNs are larger than 0.96, their approximated PSSNs using αvk are also marked with the same colored “×.” (b) PSSN difference (Actual PSSN—Approximated PSSN) for sample mirrors that generate PSSN higher than 0.96. (c) PSSN difference for mirror samples after LOZ removal and after WH correction as described in the bottom part of Fig. 8.

Fig. 10.
Fig. 10.

Differently configured telescopes are compared conceptually. (a) Replicated I: we replicate the MUTs and install them homogeneously in one direction for all 492 segments. We remove the piston, tip, and tilt and apply the 10 SVD WH correction to all segments. (b) Replicated II: similarly as with the “Replicated I” case, we replicate the MUT. However, we orient the segments randomly by rotating segments, that is, by 60 deg, 120 deg, and so forth. We also randomly flip the segment surfaces numerically by changing the sign. (c) PSD-based method: we numerically synthesize the 492 segments using the PSD computed from the MUT. All segments have the same (or same within the numerical precision) PSD as the MUT, but the phase information of the MUT is lost or random from segment to segment. This procedure is depicted in Fig. 8 as indicated by “For Section 5.”

Fig. 11.
Fig. 11.

Validation of vendor table: the computed or estimated PSSN values are shown for various methods described in Section 5. Their numerical values are also listed in Table 4.

Tables (4)

Tables Icon

Table 1. Example Vendor Table Developed for TMT M1 Segmentsa

Tables Icon

Table 2. Real Mirror Samples Used in This Papera

Tables Icon

Table 3. Various Alpha Values Corresponding to the Residual High-Order Wavefront Errors After Removing Different Numbers of LOZ Shapes from the von Karman PSD with fo=2c/m and γ=3

Tables Icon

Table 4. Validation of Vendor Table: The Computed or Estimated PSSN and rmsWFE Values for Various Methods in Section 5 are Listed under Each Corresponding Columna

Equations (7)

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

{PSSNLO=i=415(1αi·Zi2)PSSNHO=1αHO·rmsSRFHO2PSSNSR=1αSR·rmsSRFSR2,
PSSN=PSSNLO×PSSNHO×PSSNSR.
PSSNH=(1δ)2+δ2.
PSSNR=(1δ)2+δ22.
PSSNHPSSNR.
αi=1PSSN^Zi2.
αvk=1PSSN^rmsSRFvk2,

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