Abstract

This is a proposal and description of a new spectrometer based on the Schwarzschild optical system. The proposed design contains two Schwarzschild optical systems. Light diverging from the spectrometer entrance slit is collimated by the first one; the collimated light beam hits a planar diffraction grating and the light dispersed from the grating is focused by the second system, which is concentric with the first. A very simple procedure obtains designs that are anastigmatic for the center of the slit and for a particular wavelength. A specific example shows the performance of this type of spectrometer.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. E. S. Voropai, I. M. Gulis, and A. G. Kupreev, “Astigmatism correction for a large-aperture dispersive spectrometer,” J. Appl. Spectrosc. 75, 150–155 (2008).
    [CrossRef]
  2. L. Xu, K. Chen, Q. He, and G. Jin, “Design of freeform mirrors in Czerny–Turner spectrometers to suppress astigmatism,” Appl. Opt. 48, 2871–2879 (2009).
    [CrossRef] [PubMed]
  3. Q. Xue, S. Wang, and F. Lu, “Aberration-corrected Czerny–Turner imaging spectrometer with a wide spectral region,” Appl. Opt. 48, 11–16 (2009).
    [CrossRef]
  4. D. R. Austin, T. Witting, and I. A. Walmsley, “Broadband astigmatism-free Czerny–Turner imaging spectrometer using spherical mirrors,” Appl. Opt. 48, 3846–3853 (2009).
    [CrossRef] [PubMed]
  5. C. Chrystal, K. H. Burrell, and N. A. Pablant, “Straightforward correction for the astigmatism of a Czerny–Turner spectrometer,” Rev. Sci. Instrum. 81, 023503 (2010).
    [CrossRef] [PubMed]
  6. K.-S. Lee, K. P. Thompson, and J. P. Rolland, “Broadband astigmatism-corrected Czerny–Turner spectrometer,” Opt. Express 18, 23378–23384 (2010).
    [CrossRef] [PubMed]
  7. G. R. Rosendahl, “Contributions to the optics of mirror systems and gratings with oblique incidence. III. Some applications,” J. Opt. Soc. Am. 52, 412–415 (1962).
    [CrossRef]
  8. T. H. Kim, H. J. Kong, T. H. Kim, and J. S. Shin, “Design and fabrication of a 900–1700 nm hyper-spectral imaging spectrometer,” Opt. Commun. 283, 355–361 (2010).
    [CrossRef]
  9. I. A. Artioukov and K. M. Krymski, “Schwarzschild objective for soft x-rays,” Opt. Eng. 39, 2163–2170 (2000).
    [CrossRef]
  10. A. Budano, F. Flora, and L. Mezi, “Analytical design method for a modified Schwarzschild optics,” Appl. Opt. 45, 4254–4262 (2006).
    [CrossRef] [PubMed]
  11. W. B. Wetherell and M. P. Rimmer, “General analysis of aplanatic Cassegrain, Gregorian, and Schwarzschild telescopes,” Appl. Opt. 11, 2817–2832 (1972).
    [CrossRef] [PubMed]

2010 (3)

C. Chrystal, K. H. Burrell, and N. A. Pablant, “Straightforward correction for the astigmatism of a Czerny–Turner spectrometer,” Rev. Sci. Instrum. 81, 023503 (2010).
[CrossRef] [PubMed]

T. H. Kim, H. J. Kong, T. H. Kim, and J. S. Shin, “Design and fabrication of a 900–1700 nm hyper-spectral imaging spectrometer,” Opt. Commun. 283, 355–361 (2010).
[CrossRef]

K.-S. Lee, K. P. Thompson, and J. P. Rolland, “Broadband astigmatism-corrected Czerny–Turner spectrometer,” Opt. Express 18, 23378–23384 (2010).
[CrossRef] [PubMed]

2009 (3)

2008 (1)

E. S. Voropai, I. M. Gulis, and A. G. Kupreev, “Astigmatism correction for a large-aperture dispersive spectrometer,” J. Appl. Spectrosc. 75, 150–155 (2008).
[CrossRef]

2006 (1)

2000 (1)

I. A. Artioukov and K. M. Krymski, “Schwarzschild objective for soft x-rays,” Opt. Eng. 39, 2163–2170 (2000).
[CrossRef]

1972 (1)

1962 (1)

Artioukov, I. A.

I. A. Artioukov and K. M. Krymski, “Schwarzschild objective for soft x-rays,” Opt. Eng. 39, 2163–2170 (2000).
[CrossRef]

Austin, D. R.

Budano, A.

Burrell, K. H.

C. Chrystal, K. H. Burrell, and N. A. Pablant, “Straightforward correction for the astigmatism of a Czerny–Turner spectrometer,” Rev. Sci. Instrum. 81, 023503 (2010).
[CrossRef] [PubMed]

Chen, K.

Chrystal, C.

C. Chrystal, K. H. Burrell, and N. A. Pablant, “Straightforward correction for the astigmatism of a Czerny–Turner spectrometer,” Rev. Sci. Instrum. 81, 023503 (2010).
[CrossRef] [PubMed]

Flora, F.

Gulis, I. M.

E. S. Voropai, I. M. Gulis, and A. G. Kupreev, “Astigmatism correction for a large-aperture dispersive spectrometer,” J. Appl. Spectrosc. 75, 150–155 (2008).
[CrossRef]

He, Q.

Jin, G.

Kim, T. H.

T. H. Kim, H. J. Kong, T. H. Kim, and J. S. Shin, “Design and fabrication of a 900–1700 nm hyper-spectral imaging spectrometer,” Opt. Commun. 283, 355–361 (2010).
[CrossRef]

T. H. Kim, H. J. Kong, T. H. Kim, and J. S. Shin, “Design and fabrication of a 900–1700 nm hyper-spectral imaging spectrometer,” Opt. Commun. 283, 355–361 (2010).
[CrossRef]

Kong, H. J.

T. H. Kim, H. J. Kong, T. H. Kim, and J. S. Shin, “Design and fabrication of a 900–1700 nm hyper-spectral imaging spectrometer,” Opt. Commun. 283, 355–361 (2010).
[CrossRef]

Krymski, K. M.

I. A. Artioukov and K. M. Krymski, “Schwarzschild objective for soft x-rays,” Opt. Eng. 39, 2163–2170 (2000).
[CrossRef]

Kupreev, A. G.

E. S. Voropai, I. M. Gulis, and A. G. Kupreev, “Astigmatism correction for a large-aperture dispersive spectrometer,” J. Appl. Spectrosc. 75, 150–155 (2008).
[CrossRef]

Lee, K.-S.

Lu, F.

Mezi, L.

Pablant, N. A.

C. Chrystal, K. H. Burrell, and N. A. Pablant, “Straightforward correction for the astigmatism of a Czerny–Turner spectrometer,” Rev. Sci. Instrum. 81, 023503 (2010).
[CrossRef] [PubMed]

Rimmer, M. P.

Rolland, J. P.

Rosendahl, R.

Shin, J. S.

T. H. Kim, H. J. Kong, T. H. Kim, and J. S. Shin, “Design and fabrication of a 900–1700 nm hyper-spectral imaging spectrometer,” Opt. Commun. 283, 355–361 (2010).
[CrossRef]

Thompson, K. P.

Voropai, E. S.

E. S. Voropai, I. M. Gulis, and A. G. Kupreev, “Astigmatism correction for a large-aperture dispersive spectrometer,” J. Appl. Spectrosc. 75, 150–155 (2008).
[CrossRef]

Walmsley, I. A.

Wang, S.

Wetherell, W. B.

Witting, T.

Xu, L.

Xue, Q.

Appl. Opt. (5)

J. Appl. Spectrosc. (1)

E. S. Voropai, I. M. Gulis, and A. G. Kupreev, “Astigmatism correction for a large-aperture dispersive spectrometer,” J. Appl. Spectrosc. 75, 150–155 (2008).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

T. H. Kim, H. J. Kong, T. H. Kim, and J. S. Shin, “Design and fabrication of a 900–1700 nm hyper-spectral imaging spectrometer,” Opt. Commun. 283, 355–361 (2010).
[CrossRef]

Opt. Eng. (1)

I. A. Artioukov and K. M. Krymski, “Schwarzschild objective for soft x-rays,” Opt. Eng. 39, 2163–2170 (2000).
[CrossRef]

Opt. Express (1)

Rev. Sci. Instrum. (1)

C. Chrystal, K. H. Burrell, and N. A. Pablant, “Straightforward correction for the astigmatism of a Czerny–Turner spectrometer,” Rev. Sci. Instrum. 81, 023503 (2010).
[CrossRef] [PubMed]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

(a) Schwarzschild optical system comprising two spherical mirrors; (b) proposed Schwarzschild spectrometer. The collimator and the focuser are anastigmatic Schwarzschild optical systems. O, object point; I, image; M 1 M 5 , mirrors; G, diffraction grating.

Fig. 2
Fig. 2

Schwarzschild optical system with off-axis illumination. M p , primary convex mirror; M s , secondary concave mirror; A S , aperture stop.

Fig. 3
Fig. 3

Longitudinal astigmatism versus impact parameter in a Schwarzschild optical system. Both magnitudes are normalized with respect to the convex mirror radius. (a)  R s / R p = 3 ; (b)  R s / R p = 1.2 ; (c)  R s / R p = 2 .

Fig. 4
Fig. 4

(a) Radii ratio and (b) normalized focal distance ( z f / R p ) as a function of the normalized impact parameter ( h / R p ) in anastigmatic Schwarzschild optical systems.

Fig. 5
Fig. 5

Scheme of a Schwarzschild spectrometer.

Fig. 6
Fig. 6

Locus of sagittal (solid curve) and meridional (dashed curve) images corresponding to the spectrometer of Section 5. The band between the vertical dotted lines corresponds to the spectral band between 565 and 835 nm .

Fig. 7
Fig. 7

(a) Spot diagram of the on-axis point and for the design wavelength. The circle represents to the diffraction limit. (b) Sagittal (solid curve) and meridional (dashed curve) image curves for a 10 mm long slit (only the upper half is shown).

Fig. 8
Fig. 8

RMS spot radius versus object height at the design wavelength for on-axis optimization (solid curve) and off-axis optimization (dashed curve).

Fig. 9
Fig. 9

RMS spot radius versus wavelength for on-axis (solid curve), 0.7 (dashed curve), and full field (dotted–dashed curve) object height.

Tables (2)

Tables Icon

Table 1 Optical Parameters of the Schwarzschild Spectrometer

Tables Icon

Table 2 Spectral Coverage and RMS Spot Radius for Different Gratings

Equations (12)

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

h = R p sin θ p = R s sin θ s = z f sin ω ,
ω = 2 ( θ p θ s ) .
x cos ω + z sin ω = h ,
d ω d h ( x sin ω + z cos ω ) = 1.
d ω d h = 2 h ( tan θ p tan θ s ) .
x m = h [ cos ω sin ω 2 ( tan θ p tan θ s ) ] , z m = h [ sin ω + cos ω 2 ( tan θ p tan θ s ) ] .
Δ r = h [ 1 2 ( tan θ p tan θ s ) 1 tan ω ] .
tan ω = 2 ( tan θ p tan θ s ) .
tan θ p = tan ( 2 β ) 4 [ 1 + 5 4 tan 2 β ] ,
tan θ s = tan ( 2 β ) 4 [ 1 + 5 4 tan 2 β ] .
sin ( α + δ ) + sin ( α δ ) = m g λ ,
tan β = tan θ 2 2 5 + 4 tan 2 θ 2 1 1 + tan 2 θ 2 .

Metrics