Abstract

A low-cost, broadband, astigmatism-corrected Czerny–Turner arrangement with a fixed plane grating is proposed. A wedge cylindrical lens is used to correct astigmatism over a broadband spectral range. The principle and method of astigmatism correction are described in detail. We compare the performance of this modified Czerny–Turner arrangement with that of the traditional Czerny–Turner arrangement by using a practical Czerny–Turner imaging spectrometer example.

© 2011 Optical Society of America

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References

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  16. ZEMAX is a trademark of Zemax Development Corporation, Bellevue, Washington 98004, USA.

2010 (4)

2009 (4)

2006 (2)

M. Goto and S. Morita, “Spatial distribution measurement of atomic radiation with an astigmatism-corrected Czerny–Turner-type spectrometer in the Large Helical Device,” Rev. Sci. Instrum. 77, 10F124 (2006).
[CrossRef]

A. Wyatt, I. Walmsley, G. Stibenz, and G. Steinmeyer, “Sub-10 fs pulse characterization using spatially encoded arrangement for spectral phase interferometry for direct electric field reconstruction,” Opt. Lett. 31, 1914–1916 (2006).
[CrossRef] [PubMed]

2000 (1)

R. D. McPeters, S. J. Janz, E. Hilsenrath, T. L. Brown, D. E. Flittner, and D. F. Heath, “The retrieval of  O3 profiles from limb scatter measurements: results from the Shuttle ozone limb sounding experiment,” Geophys. Res. Lett. 27, 2597–2600 (2000).
[CrossRef]

1967 (1)

1966 (2)

1962 (1)

Austin, D. R.

Brown, T. L.

R. D. McPeters, S. J. Janz, E. Hilsenrath, T. L. Brown, D. E. Flittner, and D. F. Heath, “The retrieval of  O3 profiles from limb scatter measurements: results from the Shuttle ozone limb sounding experiment,” Geophys. Res. Lett. 27, 2597–2600 (2000).
[CrossRef]

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]

Dalton, M. L.

Flittner, D. E.

R. D. McPeters, S. J. Janz, E. Hilsenrath, T. L. Brown, D. E. Flittner, and D. F. Heath, “The retrieval of  O3 profiles from limb scatter measurements: results from the Shuttle ozone limb sounding experiment,” Geophys. Res. Lett. 27, 2597–2600 (2000).
[CrossRef]

Goto, M.

M. Goto and S. Morita, “Spatial distribution measurement of atomic radiation with an astigmatism-corrected Czerny–Turner-type spectrometer in the Large Helical Device,” Rev. Sci. Instrum. 77, 10F124 (2006).
[CrossRef]

He, Q.

Heath, D. F.

R. D. McPeters, S. J. Janz, E. Hilsenrath, T. L. Brown, D. E. Flittner, and D. F. Heath, “The retrieval of  O3 profiles from limb scatter measurements: results from the Shuttle ozone limb sounding experiment,” Geophys. Res. Lett. 27, 2597–2600 (2000).
[CrossRef]

Hilsenrath, E.

R. D. McPeters, S. J. Janz, E. Hilsenrath, T. L. Brown, D. E. Flittner, and D. F. Heath, “The retrieval of  O3 profiles from limb scatter measurements: results from the Shuttle ozone limb sounding experiment,” Geophys. Res. Lett. 27, 2597–2600 (2000).
[CrossRef]

Janz, S. J.

R. D. McPeters, S. J. Janz, E. Hilsenrath, T. L. Brown, D. E. Flittner, and D. F. Heath, “The retrieval of  O3 profiles from limb scatter measurements: results from the Shuttle ozone limb sounding experiment,” Geophys. Res. Lett. 27, 2597–2600 (2000).
[CrossRef]

Jin, G.

Kuhn, W. P.

Lee, K. S.

Li, F.

Lu, F.

McPeters, R. D.

R. D. McPeters, S. J. Janz, E. Hilsenrath, T. L. Brown, D. E. Flittner, and D. F. Heath, “The retrieval of  O3 profiles from limb scatter measurements: results from the Shuttle ozone limb sounding experiment,” Geophys. Res. Lett. 27, 2597–2600 (2000).
[CrossRef]

Meemon, P.

Morita, S.

M. Goto and S. Morita, “Spatial distribution measurement of atomic radiation with an astigmatism-corrected Czerny–Turner-type spectrometer in the Large Helical Device,” Rev. Sci. Instrum. 77, 10F124 (2006).
[CrossRef]

Murali, S.

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]

Rolland, J. P.

Rosendahl, G. R.

Shafer, A. B.

Steinmeyer, G.

Stibenz, G.

Thompson, K. P.

Walmsley, I.

Walmsley, I. A.

Wang, S.

Witting, T.

Wyatt, A.

Xu, L.

Xue, Q.

Appl. Opt. (7)

Chin. Opt. Lett. (1)

Geophys. Res. Lett. (1)

R. D. McPeters, S. J. Janz, E. Hilsenrath, T. L. Brown, D. E. Flittner, and D. F. Heath, “The retrieval of  O3 profiles from limb scatter measurements: results from the Shuttle ozone limb sounding experiment,” Geophys. Res. Lett. 27, 2597–2600 (2000).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Express (2)

Opt. Lett. (1)

Rev. Sci. Instrum. (2)

M. Goto and S. Morita, “Spatial distribution measurement of atomic radiation with an astigmatism-corrected Czerny–Turner-type spectrometer in the Large Helical Device,” Rev. Sci. Instrum. 77, 10F124 (2006).
[CrossRef]

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]

Other (1)

ZEMAX is a trademark of Zemax Development Corporation, Bellevue, Washington 98004, USA.

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Figures (8)

Fig. 1
Fig. 1

Astigmatism correction by a wedge cylindrical lens in (a) tangential view and (b) sagittal view before the detector. The solid rays denote the rays not using a wedge cylindrical lens, and the dashed rays denote the rays using a wedge cylindrical lens.

Fig. 2
Fig. 2

Astigmatism correction by a wedge cylindrical lens for broadband spectral simultaneity in the tangential view of the chief ray tracing for the different wavelengths; i is the angle incident to the grating and H is the distance between the chief ray of the central wavelength with the chief ray of other wavelengths in the tangential view.

Fig. 3
Fig. 3

Program block diagram for calculating the initial structural parameters.

Fig. 4
Fig. 4

Layout of the modified Czerny–Turner imaging spectrometer.

Fig. 5
Fig. 5

Spot diagrams of different fields of view for (a) a traditional Czerny–Turner spectrometer and (b) the modified Czerny–Turner imaging spectrometer.

Fig. 6
Fig. 6

RMS spot radius versus wavelength for (a) the modified Czerny–Turner imaging spectrometer and (b) a traditional Czerny–Turner spectrometer.

Fig. 7
Fig. 7

MTF of the modified Czerny–Turner imaging spectrometer at the central and marginal wavelengths.

Fig. 8
Fig. 8

RMS spot radius versus wavelength for three different methods: the method reported here (blue triangles), a method using divergent illumination (black squares), and a method using a tilting cylindrical lens (red circles).

Tables (2)

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Table 1 Imaging Spectrometer Basic Parameters

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Table 2 Imaging Spectrometer Designed Parameters

Equations (18)

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1 l s 1 l = 2 cos ( α / 2 ) r ,
1 l t 1 l = 2 r cos ( α / 2 ) .
f s = r / 2 cos ( α / 2 ) ,
f t = ( r / 2 ) cos ( α / 2 ) .
δ f = ( r 1 / 2 ) [ sin ( α 1 / 2 ) tan ( α 1 / 2 ) ] + ( r 2 / 2 ) [ sin ( α 2 / 2 ) tan ( α 2 / 2 ) ] ,
l w t l w t = [ ( n 1 ) / n ] · t ,
1 / l w s 1 / l w t = 1 / f w s ,
δ f = l w t l w t + l w s l w s ,
δ f = [ ( n 1 ) / n ] t + l w s 2 / ( f w s + l w s ) .
d ( δ f ) d ( α 2 / 2 ) · d ( α 2 / 2 ) d θ · d θ d λ = t n 2 · d n d λ + n 1 n · d t d λ 2 f w s l w s + l w s 2 ( f w s + l w s ) 2 · d l w s d H · d H d λ .
d t d λ = d t d H · d H d λ .
d t d H | H = 0 = tan γ ,
d H d λ | λ = λ c = r 2 2 d cos θ ,
d l w s d H | H = 0 = tan ( β γ ) ,
L g f = r 2 cos ( α 2 / 2 ) ,
d ( α 2 / 2 ) d θ = 0 ,
t n 2 ( d n d λ ) λ = λ c + ( n 1 n ) tan γ 2 f w s l w s + l w s 2 ( f w s + l w s ) 2 tan ( β γ ) = 0 ,
sin ( α 1 / 2 ) sin ( α 2 / 2 ) = ( r 1 r 2 ) 2 ( cos θ cos i ) 3 .

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