Abstract

We describe the elimination of the astigmatism of a Czerny–Turner imaging spectrometer, built using spherical optics and a plane grating, over a broad spectral region. Starting with the principle of divergent illumination of the grating, which removes astigmatism at one chosen wavelength, we obtain design equations for the distance from the grating to the focusing mirror and the detector angle that remove the astigmatism to first order in wavelength. Experimentally, we demonstrate near diffraction-limited performance from 740 to 860 nm and over a 5mm transverse spatial extent, while ray-tracing calculations show that barring finite-aperture and detector size limitations, this range extends from 640 to 900 nm and over 10mm transversely. Our technique requires no additional optics and uses standard off-the-shelf components.

© 2009 Optical Society of America

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References

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  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]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. 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]
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  6. 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]
  7. A. B. Shafer, “Correcting for astigmatism in the Czerny-Turner spectrometer and spectrograph,” Appl. Opt. 6, 159-160 (1967).
    [CrossRef] [PubMed]
  8. M. L. Dalton, Jr., “Astigmatism compensation in the Czerny-Turner spectrometer,” Appl. Opt. 5, 1121-1123 (1966).
    [CrossRef] [PubMed]
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    [CrossRef]
  10. M. McDowell, “Design of Czerny-Turner spectrographs using divergent grating illumination,” Opt. Acta 22, 473-475 (1975).
    [CrossRef]
  11. 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]
  12. M. Czerny and A. Turner, “Über den Astigmatismus bei Spiegelspektrometern,” Z. Phys. A 61, 792-797 (1930).
  13. A. B. Shafer, L. R. Megill, and L. Droppleman, “Optimization of the Czerny-Turner spectrometer,” J. Opt. Soc. Am. 54, 879-886 (1964).
    [CrossRef]
  14. J. Reader, “Optimizing Czerny-Turner spectrographs: a comparison between analytic theory and ray tracing,” J. Opt. Soc. Am. 59, 1189-1194 (1969).
    [CrossRef]
  15. J. Simon, M. Gil, and A. Fantino, “Czerny-Turner monochromator: astigmatism in the classical and in the crossed beam dispositions,” Appl. Opt. 25, 3715-3720 (1986).
    [CrossRef] [PubMed]
  16. R. Gäuther, “The ABCD-matrix for holographic gratings,” Appl. Opt. 11, 97-104 (1981).

2009 (1)

2006 (2)

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]

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]

2005 (1)

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]

1995 (1)

1986 (1)

1981 (1)

R. Gäuther, “The ABCD-matrix for holographic gratings,” Appl. Opt. 11, 97-104 (1981).

1975 (1)

M. McDowell, “Design of Czerny-Turner spectrographs using divergent grating illumination,” Opt. Acta 22, 473-475 (1975).
[CrossRef]

1970 (1)

B. Bates, M. McDowell, and A. C. Newton, “Correction of astigmatism in a Czerny-Turner spectrograph using a plane grating in divergent illumination,” J. Phys. E 3, 206-210(1970).
[CrossRef]

1969 (1)

1967 (1)

1966 (1)

1964 (1)

1962 (1)

1930 (1)

M. Czerny and A. Turner, “Über den Astigmatismus bei Spiegelspektrometern,” Z. Phys. A 61, 792-797 (1930).

Bates, B.

B. Bates, M. McDowell, and A. C. Newton, “Correction of astigmatism in a Czerny-Turner spectrograph using a plane grating in divergent illumination,” J. Phys. E 3, 206-210(1970).
[CrossRef]

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]

Czerny, M.

M. Czerny and A. Turner, “Über den Astigmatismus bei Spiegelspektrometern,” Z. Phys. A 61, 792-797 (1930).

Dalton, M. L.

Dorrer, C.

Droppleman, L.

Fantino, A.

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]

Gäuther, R.

R. Gäuther, “The ABCD-matrix for holographic gratings,” Appl. Opt. 11, 97-104 (1981).

Gil, M.

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]

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]

Kosik, E.

Lu, F.

McDowell, M.

M. McDowell, “Design of Czerny-Turner spectrographs using divergent grating illumination,” Opt. Acta 22, 473-475 (1975).
[CrossRef]

B. Bates, M. McDowell, and A. C. Newton, “Correction of astigmatism in a Czerny-Turner spectrograph using a plane grating in divergent illumination,” J. Phys. E 3, 206-210(1970).
[CrossRef]

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]

Megill, L. R.

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]

Newton, A. C.

B. Bates, M. McDowell, and A. C. Newton, “Correction of astigmatism in a Czerny-Turner spectrograph using a plane grating in divergent illumination,” J. Phys. E 3, 206-210(1970).
[CrossRef]

Radunsky, A.

Reader, J.

Rosendahl, G. R.

Shafer, A. B.

Simon, J.

Steinmeyer, G.

Stibenz, G.

Torr, D. G.

Torr, M. R.

Turner, A.

M. Czerny and A. Turner, “Über den Astigmatismus bei Spiegelspektrometern,” Z. Phys. A 61, 792-797 (1930).

Walmsley, I.

Wang, S.

Wyatt, A.

Xue, Q.

Appl. Opt. (6)

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. (3)

J. Phys. E (1)

B. Bates, M. McDowell, and A. C. Newton, “Correction of astigmatism in a Czerny-Turner spectrograph using a plane grating in divergent illumination,” J. Phys. E 3, 206-210(1970).
[CrossRef]

Opt. Acta (1)

M. McDowell, “Design of Czerny-Turner spectrographs using divergent grating illumination,” Opt. Acta 22, 473-475 (1975).
[CrossRef]

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

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]

Z. Phys. A (1)

M. Czerny and A. Turner, “Über den Astigmatismus bei Spiegelspektrometern,” Z. Phys. A 61, 792-797 (1930).

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Figures (7)

Fig. 1
Fig. 1

Classical Czerny–Turner spectrometer design: entrance slit S, slit to collimating mirror length L SC , spherical collimating mirror C with angle of incidence in tangential plane θ C and radius R C , collimating mirror to grating distance L CG , grating G with angles of incidence α and diffraction β, grating to focusing mirror distance L GF , spherical focusing mirror F with angle of incidence in tangential plane θ F and radius R F , focusing mirror to detector distance L FD , and detector D angled θ D to beam.

Fig. 2
Fig. 2

Change of the size and divergence of an imaging bundle upon reflection from a grating. As drawn here, the diffracted angle exceeds the incident angle, so the transverse reflected beam size w is smaller than the incident beam size w. The reflected beam is also more divergent due to the nonlinearity of the grating equation. These two effects combine to bring the apparent image O closer to the grating than the object O.

Fig. 3
Fig. 3

Ray diagram of the spectrometer in the tangential plane: virtual image S of the entrance slit S formed by collimating mirror C, virtual image S of the same after displacement by the grating G, and other symbols are as defined previously. The diagram has been drawn with L SC less than the tangential focal length of C; otherwise, S and S would be to the right, rather than the left, of the system. A similar diagram can be drawn for the sagittal plane, in which the grating acts as a plane mirror.

Fig. 4
Fig. 4

Diagram of the output half of the spectrometer, showing the central ray (unprimed symbols) and a ray with a slightly different wavelength (primed symbols) whose displacement on the detector is d. O is the center of curvature of the focusing mirror, and the coordinate system used in the text is shown.

Fig. 5
Fig. 5

(1,2) element of ray transfer matrix describing propagation from the entrance slit to the detector versus wavelength in the tangential plane (blue, solid) and the sagittal plane (red, dashed), for (a) our first-order astigmatism corrected design and (b) standard divergent illumination. The value required for diffraction-limited imaging is shown for comparison (black, dotted).

Fig. 6
Fig. 6

RMS spot radius ( μm ) versus wavelength and source position on the entrance slit, for (a) our first-order astigmatism corrected design, contour interval 2 μm , and (b) standard divergent illumination, contour interval 10 μm .

Fig. 7
Fig. 7

Composite image of mercury–argon lamp filtered using a 10 μm diameter pinhole in place of the entrance slit. The pinhole was vertically displaced in 0.5 mm increments, and its dispersed image is plotted for each position and for various emission line wavelengths. The left and bottom axes show the detector coordinates, the top axis shows the nominal wavelength of the emission line for each column, and the right axis shows the relative pinhole position for each row. Only selected emission lines are displayed. Both the horizontal and vertical axes are broken to allow the spots, each only a few pixels in diameter, to be adequately viewed across the 1280 × 1024 pixel range.

Tables (2)

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Table 1 Imaging Spectrometer Basic Parameters

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Table 2 Imaging Spectrometer Designed Parameters

Equations (25)

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υ t , s 1 = f t , s 1 + u 1
sin β = sin α + Γ λ ,
υ t = cos 2 β cos 2 α u .
S S = R C R F L SC 2 L SC ( R C cos θ F + R F cos θ C ) R C R F ,
S T = R C R F L SC 2 L SC ( R C sec θ F + R F cos 2 α cos 2 β sec θ C ) R C R F cos 2 α cos 2 β .
L SC = 1 2 R C R F ( cos 2 α cos 2 β 1 ) R C ( sec θ F cos θ F ) + R F ( cos 2 α cos 2 β sec θ C cos θ C ) .
d S S d β = d S T d β = d L FD d β ,
d S S d β = S S θ F d θ F d β ,
d S T d β = S T β + S T θ F d θ F d β .
X A = L GF ( cos β , sin β ) ,
X A = L GF ( cos β , sin β ) ,
O A = R F ( cos [ β θ F ] , sin [ β θ F ] ) ,
O A = R F ( cos [ β θ F ] , sin [ β θ F ] ) .
L GF cos β L GF cos β R F cos ( β θ F ) + R F cos ( β θ F ) = 0 ,
L GF sin β L GF sin β + R F sin ( β θ F ) R F sin ( β θ F ) = 0.
d θ F d β = 1 L GF R F cos θ F ,
d L GF d β = L GF tan θ F .
A B = L FD ( cos [ β 2 θ F ] , sin [ β 2 θ F ] ) ,
A B = L FD ( cos [ β 2 θ F ] , sin [ β 2 θ F ] ) ,
B B = d ( sin [ β 2 θ F + θ D ] , cos [ β 2 θ F + θ D ] ) .
d L FD d β = tan θ D ( L GF + L FD 2 L GF L FD R F cos θ F ) L GF tan θ F ,
d d d β = sec θ D ( L GF + L FD 2 L GF L FD R F cos θ F ) .
S S θ F = 2 S S L SC R C sin θ F 2 L SC ( R C cos θ F + R F cos θ C ) R C R F ,
S T β = 2 S T R F ( 2 L SC sec θ C R C ) cos 2 α tan β sec β 2 L SC ( R C sec θ F + R F cos 2 α cos 2 β sec θ V ) R C R V cos 2 α cos 2 β ,
S T θ F = 2 S T L SC R C sec θ F tan F 2 L SC ( R S sec θ F + R F cos 2 α cos 2 β sec θ C ) R C R F cos 2 α cos 2 β .

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