Abstract

We present the optical principle of a white-pupil collimator made up of two mirrors with unequal focal lengths. Analytic formulas for third-order aberrations are derived and compared with the results of ray-tracing experiments. It is shown that the image quality is good if the second mirror has a suitable conic coefficient and the F ratio is not too small. Furthermore, third-order coma and astigmatism can be zeroed simultaneously if the angles are also appropriately selected. When implemented in high-resolution echelle spectrographs, this design permits smaller cross dispersers and cameras, with considerable savings in cost.

© 2000 Optical Society of America

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References

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  1. A. Baranne, “Equipment Spectrographique du Foyer Coude du Telescope de 3.60 metres,” in ESO/CERN Conference on Auxiliary Instrumentation for Large Telescopes, eds. S. Laustsen, A. Reiz, eds., European Southern Observatory-CERN, Geneve, 1972), pp. 227–239.
  2. H. Dekker, S. D’Odorico, “UVES, the UV-Visual echelle spectrograph for the VLT,” Messenger 70, 13–16 (1992).
  3. R. G. Tull, P. J. McQueen, C. Sneden, D. L. Lambert, “The high-resolution cross-dispersed echelle white-pupil spectrometer of the McDonald Observatory 2.7-m telescope,” Publ. Astron. Soc. Pac. 107, 251–264 (1995).
    [CrossRef]
  4. D. W. Schroeder, Astronomical Optics (Academic, San Diego, Calif., 1987).

1995 (1)

R. G. Tull, P. J. McQueen, C. Sneden, D. L. Lambert, “The high-resolution cross-dispersed echelle white-pupil spectrometer of the McDonald Observatory 2.7-m telescope,” Publ. Astron. Soc. Pac. 107, 251–264 (1995).
[CrossRef]

1992 (1)

H. Dekker, S. D’Odorico, “UVES, the UV-Visual echelle spectrograph for the VLT,” Messenger 70, 13–16 (1992).

Baranne, A.

A. Baranne, “Equipment Spectrographique du Foyer Coude du Telescope de 3.60 metres,” in ESO/CERN Conference on Auxiliary Instrumentation for Large Telescopes, eds. S. Laustsen, A. Reiz, eds., European Southern Observatory-CERN, Geneve, 1972), pp. 227–239.

D’Odorico, S.

H. Dekker, S. D’Odorico, “UVES, the UV-Visual echelle spectrograph for the VLT,” Messenger 70, 13–16 (1992).

Dekker, H.

H. Dekker, S. D’Odorico, “UVES, the UV-Visual echelle spectrograph for the VLT,” Messenger 70, 13–16 (1992).

Lambert, D. L.

R. G. Tull, P. J. McQueen, C. Sneden, D. L. Lambert, “The high-resolution cross-dispersed echelle white-pupil spectrometer of the McDonald Observatory 2.7-m telescope,” Publ. Astron. Soc. Pac. 107, 251–264 (1995).
[CrossRef]

McQueen, P. J.

R. G. Tull, P. J. McQueen, C. Sneden, D. L. Lambert, “The high-resolution cross-dispersed echelle white-pupil spectrometer of the McDonald Observatory 2.7-m telescope,” Publ. Astron. Soc. Pac. 107, 251–264 (1995).
[CrossRef]

Schroeder, D. W.

D. W. Schroeder, Astronomical Optics (Academic, San Diego, Calif., 1987).

Sneden, C.

R. G. Tull, P. J. McQueen, C. Sneden, D. L. Lambert, “The high-resolution cross-dispersed echelle white-pupil spectrometer of the McDonald Observatory 2.7-m telescope,” Publ. Astron. Soc. Pac. 107, 251–264 (1995).
[CrossRef]

Tull, R. G.

R. G. Tull, P. J. McQueen, C. Sneden, D. L. Lambert, “The high-resolution cross-dispersed echelle white-pupil spectrometer of the McDonald Observatory 2.7-m telescope,” Publ. Astron. Soc. Pac. 107, 251–264 (1995).
[CrossRef]

Messenger (1)

H. Dekker, S. D’Odorico, “UVES, the UV-Visual echelle spectrograph for the VLT,” Messenger 70, 13–16 (1992).

Publ. Astron. Soc. Pac. (1)

R. G. Tull, P. J. McQueen, C. Sneden, D. L. Lambert, “The high-resolution cross-dispersed echelle white-pupil spectrometer of the McDonald Observatory 2.7-m telescope,” Publ. Astron. Soc. Pac. 107, 251–264 (1995).
[CrossRef]

Other (2)

D. W. Schroeder, Astronomical Optics (Academic, San Diego, Calif., 1987).

A. Baranne, “Equipment Spectrographique du Foyer Coude du Telescope de 3.60 metres,” in ESO/CERN Conference on Auxiliary Instrumentation for Large Telescopes, eds. S. Laustsen, A. Reiz, eds., European Southern Observatory-CERN, Geneve, 1972), pp. 227–239.

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Figures (3)

Fig. 1
Fig. 1

Typical optical scheme of an echelle cross-dispersed spectrograph with a Baranne white-pupil collimator: S, slit; C, collimator; E, echelle; TC, transfer collimator; CD, cross disperser; CA, camera; o a , collimator off-axis angle; γ, off-plane angle. The echelle and cross disperser are on the two pupil images. A flat (unlabeled element) has been introduced to fold the optical path.

Fig. 2
Fig. 2

Runs of the transfer collimator conic coefficient K with the ratio between collimator focal lengths 1 - t = f c /f c1 for the asymmetric white-pupil collimator in the example. The thick solid line represents solutions in which TAS is twice equal to TSC. Thick short and long dashed lines are solutions with zero astigmatism and coma, respectively. The thin solid lines are the loci of equal 80% encircled energy (in micrometers) from ray-tracing simulations.

Fig. 3
Fig. 3

Comparison between a diameter of 80% encircled energy EE80 provided by the ray-tracing simulations with the predictions from Eq. (15) (where we assumed that EE80 is 0.8 times TSC) as a function of the ratio between collimator focal lengths 1 - t = f c /f c1 for the asymmetric white-pupil collimator in the example. The thick solid line is the result from ray-tracing simulations, whereas the thin line is the prediction from Eq. (15).

Tables (1)

Tables Icon

Table 1 Equivalence of Schroeder’s Parameters for Aberrations with Mirrors Used with Decentered Pupils and the Parameters of the White-Pupil Design

Equations (18)

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B1 =-oaγ/fc1-y2/y12,
B2=-γ/2fc21+x2/x13
kp=3fc.
d=fct tan γ.
a=8zt1+4z-4z2,
a=4zt2z-1,
z=γoa=±32,
a=K+1=±23±3-1 t.
B3=±23±3-1132t2fc3,
TSA=±23±3-1tfcam64F3.
a=czt,
c=416oaF-18oaF1+4z-z2+1-2z.
TDI=oa3c8 fcamzt,
TSC=-2TAS=oac2z-1-432F2 fcamzt,
TSA=-c64F3 fcamzt.
t-1000fcamF1026oa0.1oaγΔ17,
t=1-fcfc1,  a=K+1,  z=γoa.
B0=aoa38,B1=-aoa28fct-11+4z-z2-8zt/a,B2=aoa8fc2t-121-2z+4zt/a,B3=a32fc3t-13,TDI=afcamoa38,TAS=-afcamoa28F1+4z-z2-8zt/a,TSC=- afcamoa32F21-2z+4zt/a,TSA=-afcam64F3,kp=1fc3-t,kt=1fc3-t+3a1-t16z2.

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