Abstract

We report an optical design for a low-cost optics, broadband, astigmatism-corrected practical spectrometer. An off-the-shelf cylindrical lens is used to remove astigmatism over the full bandwidth. Results show that better than 0.1 nm spectral resolution and more than 50% throughput were achieved over a bandwidth of 400 nm centered at 800 nm.

©2010 Optical Society of America

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References

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  1. A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995).
    [Crossref]
  2. J. P. Rolland, P. Meemon, S. Murali, K. P. Thompson, and K. S. Lee, “Gabor-based fusion technique for Optical Coherence Microscopy,” Opt. Express 18(4), 3632–3642 (2010).
    [Crossref] [PubMed]
  3. S. Murali, P. Meemon, K. S. Lee, W. P. Kuhn, K. P. Thompson, and J. P. Rolland, “Assessment of a liquid lens enabled in vivo optical coherence microscope,” Appl. Opt. 49(16), D145–D156 (2010).
    [Crossref] [PubMed]
  4. A. S. Wyatt, I. A. 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(12), 1914–1916 (2006).
    [Crossref] [PubMed]
  5. M. Czerny and A. F. Turner, “On the Astigmatism of Mirror Spectrometers,” Z. Phys. 61(11-12), 792–797 (1930).
    [Crossref]
  6. A. B. Shafer, L. R. Megill, and L. Droppleman, “Optimization of the Czerny-Turner spectrometer,” J. Opt. Soc. Am. 54(7), 879–887 (1964).
    [Crossref]
  7. Q. Xue, S. Wang, and F. Lu, “Aberration-corrected Czerny-Turner imaging spectrometer with a wide spectral region,” Appl. Opt. 48(1), 11–16 (2009).
    [Crossref]
  8. G. R. Rosendahl, “Contributions to the optics of mirror systems and gratings with oblique incidence. III. Some applications,” J. Opt. Soc. Am. 52(4), 412–415 (1962).
    [Crossref]
  9. 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]
  10. A. B. Shafer, “Correcting for astigmatism in the czerny-turner spectrometer and spectrograph,” Appl. Opt. 6(1), 159–160 (1967).
    [Crossref] [PubMed]
  11. M. L. Dalton., “Astigmatism compensation in the Czerny-turner spectrometer,” Appl. Opt. 5(7), 1121–1123 (1966).
    [Crossref] [PubMed]
  12. 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(3), 206–210 (1970).
    [Crossref]
  13. M. McDowell, “Design of Czerny–Turner spectrographs using divergent grating illumination,” Opt. Acta (Lond.) 22, 473–475 (1975).
  14. D. R. Austin, T. Witting, and I. A. Walmsley, “Broadband astigmatism-free Czerny-Turner imaging spectrometer using spherical mirrors,” Appl. Opt. 48(19), 3846–3853 (2009).
    [Crossref] [PubMed]
  15. M. Born, and E. Wolf, Principles of Optics, (Cambridge University Press, 2002), Chap. 8.6.

2010 (2)

2009 (2)

2006 (2)

A. S. Wyatt, I. A. 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(12), 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]

1995 (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995).
[Crossref]

1975 (1)

M. McDowell, “Design of Czerny–Turner spectrographs using divergent grating illumination,” Opt. Acta (Lond.) 22, 473–475 (1975).

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(3), 206–210 (1970).
[Crossref]

1967 (1)

1966 (1)

1964 (1)

1962 (1)

1930 (1)

M. Czerny and A. F. Turner, “On the Astigmatism of Mirror Spectrometers,” Z. Phys. 61(11-12), 792–797 (1930).
[Crossref]

Austin, D. R.

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(3), 206–210 (1970).
[Crossref]

Czerny, M.

M. Czerny and A. F. Turner, “On the Astigmatism of Mirror Spectrometers,” Z. Phys. 61(11-12), 792–797 (1930).
[Crossref]

Dalton, M. L.

Droppleman, L.

El-Zaiat, S. Y.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995).
[Crossref]

Fercher, A. F.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995).
[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]

Hitzenberger, C. K.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995).
[Crossref]

Kamp, G.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995).
[Crossref]

Kuhn, W. P.

Lee, K. S.

Lu, F.

McDowell, M.

M. McDowell, “Design of Czerny–Turner spectrographs using divergent grating illumination,” Opt. Acta (Lond.) 22, 473–475 (1975).

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(3), 206–210 (1970).
[Crossref]

Meemon, P.

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]

Murali, S.

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(3), 206–210 (1970).
[Crossref]

Rolland, J. P.

Rosendahl, G. R.

Shafer, A. B.

Steinmeyer, G.

Stibenz, G.

Thompson, K. P.

Turner, A. F.

M. Czerny and A. F. Turner, “On the Astigmatism of Mirror Spectrometers,” Z. Phys. 61(11-12), 792–797 (1930).
[Crossref]

Walmsley, I. A.

Wang, S.

Witting, T.

Wyatt, A. S.

Xue, Q.

Appl. Opt. (5)

J. Opt. Soc. Am. (2)

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(3), 206–210 (1970).
[Crossref]

Opt. Acta (Lond.) (1)

M. McDowell, “Design of Czerny–Turner spectrographs using divergent grating illumination,” Opt. Acta (Lond.) 22, 473–475 (1975).

Opt. Commun. (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995).
[Crossref]

Opt. Express (1)

Opt. Lett. (1)

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. (1)

M. Czerny and A. F. Turner, “On the Astigmatism of Mirror Spectrometers,” Z. Phys. 61(11-12), 792–797 (1930).
[Crossref]

Other (1)

M. Born, and E. Wolf, Principles of Optics, (Cambridge University Press, 2002), Chap. 8.6.

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Figures (4)

Fig. 1
Fig. 1 Astigmatism correction by a cylindrical lens in (a) tangential view (b) sagittal view after the second mirror in a Czerny-Turner spectrometer.

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Fig. 2
Fig. 2 Broadband astigmatism correction by a tilted cylindrical lens in the tangential view of chief ray-tracing for the different wavelengths in the part of the spectrometer, i is the incident angle to the grating.

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Fig. 3
Fig. 3 (a) Optimized layout of the broadband astigmatism-corrected Czerny-Turner spectrometer (b) The pixel function in a red dotted line and the LSF in a blue solid line (c) the convolution over the pixel (d) the 80% dip in the separation of the two convolutions.

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Fig. 4
Fig. 4 (a) spectral resolutions over the full bandwidth and (b) power efficiencies collected by the pixel array with 10 µm width for three different methods, the new method reported here (blue), a method based on a divergent wavefront [14] (red), and a method that replaces the spherical mirrors of a traditional Czerny-Turner with toroidal mirrors [7] (green).

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Tables (2)

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Table 2 Fixed parameters

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Table 1 Initial and optimized parameters

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Equations (16)

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Δ z = ( R 1 / 2 ) ⋅ ( sin α 1 tan α 1 ) + ( R 2 / 2 ) ⋅ ( sin α 2 tan α 2 )   ,
s c s − s ' c s = s c s − [ f c s s c s / ( f c s + s c s ) ]  ,
s ' c t − s c t = [ ( n − 1 ) / n ] ⋅ t 0  ,
Δ z = s c s − s ' c s + s ' c t − s c t  ,
s c s 2 − [ Δ z − ( ( n − 1 ) / n )   t 0 ] ⋅ s c s − f c s [ Δ z − ( ( n − 1 ) / n )   t 0 ] = 0 ,          s c s & f c s > 0.
s c s = [ P + P 2 + 4 P f c s ] / 2  ,
L c = f s − s c s − t 0  ,
d s c s / d Δ z = ( 1 / 2 ) + [ ( P + 2 f c s ) / ( 2 P 2 + 4 P f c s ) ]   .
tan ξ ≡ ( d s c s / d H ) | H = 0 = ( d s c s / d Δ z ) | Δ z = Δ ¯ z ⋅ ( d Δ z / d λ ) | λ = λ ¯ ⋅ ( d λ / d H ) | H = 0  ,
( d s c s / d Δ z ) | Δ z = Δ ¯ z = ( 1 / 2 ) + [ ( P ¯ + 2 f c s ) / ( 2 P ¯ 2 + 4 P ¯ f c s ) ]  ,
Δ ¯ z = ( R 1 / 2 ) ⋅ ( sin α 1 tan α 1 ) + ( R 2 / 2 ) ⋅ ( sin α ¯ 2 tan α ¯ 2 )   .
( d Δ z / d λ ) | λ = λ ¯ = ( d Δ z / d α 2 ) | α 2 = α ¯ 2 ⋅ ( d α 2 / d θ ) | θ = θ ¯ ⋅ ( d θ / d λ ) λ = λ ¯ = [ ( R 2 / 2 ) ⋅ sin α ¯ 2 ⋅ ( 1 + sec 2 α ¯ 2 ) ] ⋅ [ 1 − ( L ¯ G F / R 2 cos α ¯ 2 ) ] ⋅ [ 1 / d cos θ ¯ ]  ,
( d λ / d H ) | H = 0 = 2 d cos θ ¯ / R 2   .
δ = ξ − [ tan − 1 ( ( d f s / d H ) | f s = f ¯ s ) + α ¯ 2 ]  ,
  Δ θ =   ( d θ / d λ ) | λ = λ ¯ ⋅ Δ λ = ( Δ λ / d ⋅ cos θ ¯ )   .
d = ( Δ λ / cos θ ¯ ) ⋅ ( f 2 / L )  ,

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