Abstract

A new scheme to improve the spectral resolution of grating-based spectrometers for diffuse light is proposed and demonstrated. It exploits an anamorphic transformation that reduces the beam divergence in the direction of the grating grooves while increasing the divergence in the orthogonal direction to improve the spectral resolution without any loss of light. Up to 12-fold improvement in the spectral resolution was obtained.

© 1999 Optical Society of America

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References

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  1. R. Winston and W. T. Weldford, High Collection Nonimaging Optics (Academic, New York, 1989).
  2. N. Davidson and A. A. Friesem, Opt. Commun. 99, 162 (1993).
    [CrossRef]
  3. A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 697; factors of the order of unity may vary in various definitions of Mx, My, and M2.
  4. For the largest angle used in our experiment, the paraxial approximation yields an error of <1%. In any case we can readily generalize the expression in the text to deal accurately with arbitrary large angles.
  5. We also rotated the prism array at 45° to the optical axis to separate the reflected wave from the incident wave. This rotation results in simple folding of the optical axis, as shown in Fig. 1.
  6. This is true when the retroreflector width W is much smaller than D2x. Otherwise, D3x?D2x+W/2.
  7. The improvement in the rms width of the resolution was only tenfold, as required by Eq. (1).
  8. B. Winston and H. Hinterberg, Sol. Energy 17, 255 (1975).
    [CrossRef]
  9. E. Hasman, S. Keren, N. Davidson, and A. A. Friesem, Opt. Lett. 24, 439 (1999).
    [CrossRef]
  10. Th. Graf and J. E. Balmer, Opt. Lett. 18, 1317 (1993).
    [CrossRef]
  11. J. R. Leger and W. C. Goltsos, IEEE J. Quantum Electron. 28, 1088 (1992).
    [CrossRef]
  12. N. Davidson and A. A. Friesem, Appl. Phys. Lett. 62, 334 (1993).
    [CrossRef]
  13. S. Yamaguchi, T. Kobayashi, Y. Saito, and K. Chiba, Opt. Lett. 20, 898 (1995).
    [CrossRef] [PubMed]
  14. B. Ehlers, K. Du, M. Baumann, H.-G. Treusch, P. Loosen, and R. Poprawe, Proc. SPIE 3097, 639 (1997).
    [CrossRef]
  15. W. A. Clarkson and D. C. Hanna, Opt. Lett. 21, 375 (1996).
    [CrossRef] [PubMed]

1999 (1)

1997 (1)

B. Ehlers, K. Du, M. Baumann, H.-G. Treusch, P. Loosen, and R. Poprawe, Proc. SPIE 3097, 639 (1997).
[CrossRef]

1996 (1)

1995 (1)

1993 (3)

Th. Graf and J. E. Balmer, Opt. Lett. 18, 1317 (1993).
[CrossRef]

N. Davidson and A. A. Friesem, Opt. Commun. 99, 162 (1993).
[CrossRef]

N. Davidson and A. A. Friesem, Appl. Phys. Lett. 62, 334 (1993).
[CrossRef]

1992 (1)

J. R. Leger and W. C. Goltsos, IEEE J. Quantum Electron. 28, 1088 (1992).
[CrossRef]

1975 (1)

B. Winston and H. Hinterberg, Sol. Energy 17, 255 (1975).
[CrossRef]

Balmer, J. E.

Baumann, M.

B. Ehlers, K. Du, M. Baumann, H.-G. Treusch, P. Loosen, and R. Poprawe, Proc. SPIE 3097, 639 (1997).
[CrossRef]

Chiba, K.

Clarkson, W. A.

Davidson, N.

E. Hasman, S. Keren, N. Davidson, and A. A. Friesem, Opt. Lett. 24, 439 (1999).
[CrossRef]

N. Davidson and A. A. Friesem, Opt. Commun. 99, 162 (1993).
[CrossRef]

N. Davidson and A. A. Friesem, Appl. Phys. Lett. 62, 334 (1993).
[CrossRef]

Du, K.

B. Ehlers, K. Du, M. Baumann, H.-G. Treusch, P. Loosen, and R. Poprawe, Proc. SPIE 3097, 639 (1997).
[CrossRef]

Ehlers, B.

B. Ehlers, K. Du, M. Baumann, H.-G. Treusch, P. Loosen, and R. Poprawe, Proc. SPIE 3097, 639 (1997).
[CrossRef]

Friesem, A. A.

E. Hasman, S. Keren, N. Davidson, and A. A. Friesem, Opt. Lett. 24, 439 (1999).
[CrossRef]

N. Davidson and A. A. Friesem, Opt. Commun. 99, 162 (1993).
[CrossRef]

N. Davidson and A. A. Friesem, Appl. Phys. Lett. 62, 334 (1993).
[CrossRef]

Goltsos, W. C.

J. R. Leger and W. C. Goltsos, IEEE J. Quantum Electron. 28, 1088 (1992).
[CrossRef]

Graf, Th.

Hanna, D. C.

Hasman, E.

Hinterberg, H.

B. Winston and H. Hinterberg, Sol. Energy 17, 255 (1975).
[CrossRef]

Keren, S.

Kobayashi, T.

Leger, J. R.

J. R. Leger and W. C. Goltsos, IEEE J. Quantum Electron. 28, 1088 (1992).
[CrossRef]

Loosen, P.

B. Ehlers, K. Du, M. Baumann, H.-G. Treusch, P. Loosen, and R. Poprawe, Proc. SPIE 3097, 639 (1997).
[CrossRef]

Poprawe, R.

B. Ehlers, K. Du, M. Baumann, H.-G. Treusch, P. Loosen, and R. Poprawe, Proc. SPIE 3097, 639 (1997).
[CrossRef]

Saito, Y.

Siegman, A. E.

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 697; factors of the order of unity may vary in various definitions of Mx, My, and M2.

Treusch, H.-G.

B. Ehlers, K. Du, M. Baumann, H.-G. Treusch, P. Loosen, and R. Poprawe, Proc. SPIE 3097, 639 (1997).
[CrossRef]

Weldford, W. T.

R. Winston and W. T. Weldford, High Collection Nonimaging Optics (Academic, New York, 1989).

Winston, B.

B. Winston and H. Hinterberg, Sol. Energy 17, 255 (1975).
[CrossRef]

Winston, R.

R. Winston and W. T. Weldford, High Collection Nonimaging Optics (Academic, New York, 1989).

Yamaguchi, S.

Appl. Phys. Lett. (1)

N. Davidson and A. A. Friesem, Appl. Phys. Lett. 62, 334 (1993).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. R. Leger and W. C. Goltsos, IEEE J. Quantum Electron. 28, 1088 (1992).
[CrossRef]

Opt. Commun. (1)

N. Davidson and A. A. Friesem, Opt. Commun. 99, 162 (1993).
[CrossRef]

Opt. Lett. (4)

Proc. SPIE (1)

B. Ehlers, K. Du, M. Baumann, H.-G. Treusch, P. Loosen, and R. Poprawe, Proc. SPIE 3097, 639 (1997).
[CrossRef]

Sol. Energy (1)

B. Winston and H. Hinterberg, Sol. Energy 17, 255 (1975).
[CrossRef]

Other (6)

R. Winston and W. T. Weldford, High Collection Nonimaging Optics (Academic, New York, 1989).

A. E. Siegman, Lasers (University Science, Mill Valley, Calif., 1986), p. 697; factors of the order of unity may vary in various definitions of Mx, My, and M2.

For the largest angle used in our experiment, the paraxial approximation yields an error of <1%. In any case we can readily generalize the expression in the text to deal accurately with arbitrary large angles.

We also rotated the prism array at 45° to the optical axis to separate the reflected wave from the incident wave. This rotation results in simple folding of the optical axis, as shown in Fig. 1.

This is true when the retroreflector width W is much smaller than D2x. Otherwise, D3x?D2x+W/2.

The improvement in the rms width of the resolution was only tenfold, as required by Eq. (1).

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Figures (4)

Fig. 1
Fig. 1

Experimental optical arrangement for our high-resolution spectrometer: 1–4, building blocks; D, diffuser; A0, A1, apertures; L0L4, lenses. The arrows mark the ray paths through the optical system in the xz plane.

Fig. 2
Fig. 2

Illustrations of spatial and angular light distributions at several planes along the optical axis of the anamorphic concentrator (block 2 of Fig. 1). The width and height of the rectangle represent the dimensions of the beam in the x and y directions, respectively, and the lengths of the double-shafted arrows represent the diffuse angles in each direction: (a) at the input, (b) at the back focal plane of L1 before retroreflection (the one-dimensional Porro prism array is also shown for orientation), (c) after retroreflection, (d) at the back focal plane of L2.

Fig. 3
Fig. 3

Measured light-intensity distributions at the output of the anamorphic concentrator (dashed curve) and at the back focal plain of L1 (solid curve).

Fig. 4
Fig. 4

Measured spectral impulse response of the homemade spectrometer with (solid curve) the anamorphic concentrator and (dashed curve) without it. The FWHM resolution is 2.8 and 36 nm with and without the concentrator, respectively.

Equations (1)

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dλ=Mx2/Nqλ,

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