Abstract

The point-spread function and emissivity are calculated for a mirror made from regular hexagonal segments of just a few different sizes. A mirror of this type has many similar segments, which is an advantage for manufacturing, and for an ∼f/1 mirror with ≥1000 segments and ≥4 sizes of regular hexagons the increase in intersegment gap area is negligible. This result raises the possibility of making a mirror from very large numbers of identical small segments that are warped to the required figure.

© 2003 Optical Society of America

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References

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  1. J. R. Kuhn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concepts for a large-aperture high dynamic range telescope,” Astron. Soc. Pac. 113, 1486–1510 (2001).
    [CrossRef]
  2. J. E. Nelson, T. S. Mast, S. M. Faber, eds., “The Design of the Keck Observatory and Telescope,” Keck Observatory Report 90 (Keck Observatory, Kamuela, Hawaii, 1985).
  3. T. S. Mast, J. E. Nelson, “The fabrication of large optical surfaces using a combination of polishing and mirror bending,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 670–681 (1990).
    [CrossRef]
  4. R. N. Wilson, Reflecting Telescope Optics I (Springer-Verlag, Berlin, Germany, 1996), Chap. 2, p. 27.
  5. J. E. Nelson, T. S. Mast, eds., “Conceptual design for a thirty-meter telescope,” California Extremely Large Telescope Report 34 (University of California, Santa Cruz, 2002).
  6. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986), Chap. 6, p. 245.
  7. N. Woolf, J. R. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36, 507–537 (1998).
    [CrossRef]

2001 (1)

J. R. Kuhn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concepts for a large-aperture high dynamic range telescope,” Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

1998 (1)

N. Woolf, J. R. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36, 507–537 (1998).
[CrossRef]

Angel, J. R.

N. Woolf, J. R. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36, 507–537 (1998).
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986), Chap. 6, p. 245.

Coulter, R.

J. R. Kuhn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concepts for a large-aperture high dynamic range telescope,” Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

Kuhn, J. R.

J. R. Kuhn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concepts for a large-aperture high dynamic range telescope,” Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

Mast, T. S.

T. S. Mast, J. E. Nelson, “The fabrication of large optical surfaces using a combination of polishing and mirror bending,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 670–681 (1990).
[CrossRef]

Moretto, G.

J. R. Kuhn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concepts for a large-aperture high dynamic range telescope,” Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

Nelson, J. E.

T. S. Mast, J. E. Nelson, “The fabrication of large optical surfaces using a combination of polishing and mirror bending,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 670–681 (1990).
[CrossRef]

Racine, R.

J. R. Kuhn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concepts for a large-aperture high dynamic range telescope,” Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

Roddier, F.

J. R. Kuhn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concepts for a large-aperture high dynamic range telescope,” Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

Wilson, R. N.

R. N. Wilson, Reflecting Telescope Optics I (Springer-Verlag, Berlin, Germany, 1996), Chap. 2, p. 27.

Woolf, N.

N. Woolf, J. R. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36, 507–537 (1998).
[CrossRef]

Annu. Rev. Astron. Astrophys. (1)

N. Woolf, J. R. Angel, “Astronomical searches for Earth-like planets and signs of life,” Annu. Rev. Astron. Astrophys. 36, 507–537 (1998).
[CrossRef]

Astron. Soc. Pac. (1)

J. R. Kuhn, G. Moretto, R. Racine, F. Roddier, R. Coulter, “Concepts for a large-aperture high dynamic range telescope,” Astron. Soc. Pac. 113, 1486–1510 (2001).
[CrossRef]

Other (5)

J. E. Nelson, T. S. Mast, S. M. Faber, eds., “The Design of the Keck Observatory and Telescope,” Keck Observatory Report 90 (Keck Observatory, Kamuela, Hawaii, 1985).

T. S. Mast, J. E. Nelson, “The fabrication of large optical surfaces using a combination of polishing and mirror bending,” in Advanced Technology Optical Telescopes IV, L. D. Barr, ed., Proc. SPIE1236, 670–681 (1990).
[CrossRef]

R. N. Wilson, Reflecting Telescope Optics I (Springer-Verlag, Berlin, Germany, 1996), Chap. 2, p. 27.

J. E. Nelson, T. S. Mast, eds., “Conceptual design for a thirty-meter telescope,” California Extremely Large Telescope Report 34 (University of California, Santa Cruz, 2002).

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1986), Chap. 6, p. 245.

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Figures (6)

Fig. 1
Fig. 1

Folding a plane onto an axially symmetric curved surface.

Fig. 2
Fig. 2

Gap width predicted by Eq. (11) and results from a computer simulation (points) for a 30-m f/0.75 mirror tiled with 1-m diameter regular hexagons.

Fig. 3
Fig. 3

Emissivity as a function of focal ratio [Eq. (19)] for mirrors with four (solid curves) and eight (dashed curves) batches of regular hexagonal segments with d/ k = 1/90 (light curves) and d/ k = 1/900 (bold curves). The nominal gap width is s/ d = 0.004.

Fig. 4
Fig. 4

Maximum segment diameter as a function of focal ratio [Eq. (20)] for a 35% increase in emissivity due to tiling with four (solid curves) and eight (dashed curves) batches of regular hexagons with s/ d = 0.004 (light curves) and s/ d = 0.002 (bold curves).

Fig. 5
Fig. 5

(a) PSF for a 30-m f/0.75 mirror tiled with four batches of 1-m diameter regular hexagons with 4-mm nominal gaps. The plot is taken through the sidelobes closest to the PSF core, and the wavelength is 1 μm. (b) PSF for a 30-m mirror with segments that are projected in the aperture plane as 1-m diameter regular hexagons with 4-mm gaps.

Fig. 6
Fig. 6

PSF for a 30-m f/0.75 mirror tiled with four batches of 0.1-m diameter regular hexagons with 0.4-mm nominal gaps. The wavelength is 1 μm.

Tables (1)

Tables Icon

Table 1 Segment Diameter and Gap Width for a 30-m f/0.75 Mirror with 1-m Segments

Equations (26)

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vr=ρvrr.
lrvr=vr.
lρ=n=0 a2n+1ρ2n+1,
vr=r-12 a3r3+189a32-2a5r5+.
zρ=n=1 b2nρ2n,
lρ=0ρ1+zt21/2dt=ρ+23 b22ρ3+254b2b4-b24ρ5+,
vr=r-13 b22r3+153b24-2b2b4r5+.
vrr-112k2 r3+380k4 r5,
vr1-14k2 r2+316k4 r4.
hr=dvr+d4d1-14k2r+d42+316k4r+d44,
Δhr=havr-hr=dvr-vr+d4d2r8k2.
Δhr1πR20Rd2r8k2 2πrdr=23 ΔhR,
δrd4k2ri+12-r2,
δr=1πR2i=0n-10R δr2πrdrd8k2R2i=0n-1ri+12-ri22,
hrid1-in1/2Rd8k2-iR24nk2+3i2R416n2k4.
hri=1ni=1n hri d1-n+12n1/2Rd8k2-n+12nR24k2+n+12n+16n23R416k4,
hav=1πR20R dvr2πrdrd1-R28k2+R416k4,
Δhbatch=hav-hri+2s3n+12n1/2Rd28k2+R2d8nk2-3R4d32nk4+2s3.
εn+12n1/2116fdk+164nf2-34096nf4+4sd3,
dk2nn+11/264fsη-1d3-14fn1-364f2,
Hx=ij=12,23,31 SAij-1x,
ϕu=ij=12,23,31FTSAij-1x= detAijψAijtu,
ϕu=ij=12,23,31detAijFAijtu · e1FAijtu · e2= detAijFAije1 · uFAije2 · u= detAijFxi · uFxj · u.
ϕu=hρ2231+zρ21/2 exp-iu · ρ×ij=12,23,31 Fxi · uFxj · u =hρ2231+zρ21/2×exp-iu · ρx1 · ux2 · ux3 · u×i=13xi · ucosxi · u.
A=acbd,
FTfA-1x, y=-- fA-1x, y×exp-iuxexp-ivydxdy =-- fx, yexp-iuax+cyexp-ivbx+dydxdy =-- fx, yexp-ixua+vbexp-iyuc+vd×|JA|dxdy =detAFAtu, v,

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