Abstract

The conventional experimental setup used to measure anomalous dispersion by the hook method has been modified by replacing the spectrograph by a single grating in combination with a camera. The grating is used for diffraction angles close to π/2 rad, and the focal distance for projection of the hook spectrum is 4 m. The high dispersion thus obtained (typically 200 mm/nm) considerably facilitates the use of the hook method for diagnostic purposes. Further, it is demonstrated that, for such large diffraction angles, a focusing element after diffraction at the grating can be avoided without losing too much sharpness in the hook spectrum.

© 1983 Optical Society of America

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References

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  1. D. S. Rozhdestvenskii, Ann. Phys. 39, 307 (1912).
  2. N. P. Penkin, J. Quant. Spectrosc. Radiat. Transfer 4, 41 (1964).
    [CrossRef]
  3. W. C. Marlow, Appl. Opt. 6, 1715 (1967).
    [CrossRef] [PubMed]
  4. M. C. E. Huber, “Interferometric Gas Diagnostics by the Hook Method,” in Modern Optical Methods in Gas Dynamic Research, D. S. Dosanjh, Ed. (Plenum, New York, 1971), pp. 85–112.
    [CrossRef]
  5. L. Zehnder, Z. Instrumentenkd 11, 275 (1891).
  6. L. Mach. Z. Instrumentenkd. 12, 89 (1892).
  7. P. van de Weijer, R. M. M. Cremers, J. Appl. Phys. 53, 1401 (1982).
    [CrossRef]
  8. P. van de Weijer, R. M. M. Cremers, J. Appl. Phys. 54, 2835 (1983).
    [CrossRef]

1983 (1)

P. van de Weijer, R. M. M. Cremers, J. Appl. Phys. 54, 2835 (1983).
[CrossRef]

1982 (1)

P. van de Weijer, R. M. M. Cremers, J. Appl. Phys. 53, 1401 (1982).
[CrossRef]

1967 (1)

1964 (1)

N. P. Penkin, J. Quant. Spectrosc. Radiat. Transfer 4, 41 (1964).
[CrossRef]

1912 (1)

D. S. Rozhdestvenskii, Ann. Phys. 39, 307 (1912).

1892 (1)

L. Mach. Z. Instrumentenkd. 12, 89 (1892).

1891 (1)

L. Zehnder, Z. Instrumentenkd 11, 275 (1891).

Cremers, R. M. M.

P. van de Weijer, R. M. M. Cremers, J. Appl. Phys. 54, 2835 (1983).
[CrossRef]

P. van de Weijer, R. M. M. Cremers, J. Appl. Phys. 53, 1401 (1982).
[CrossRef]

Huber, M. C. E.

M. C. E. Huber, “Interferometric Gas Diagnostics by the Hook Method,” in Modern Optical Methods in Gas Dynamic Research, D. S. Dosanjh, Ed. (Plenum, New York, 1971), pp. 85–112.
[CrossRef]

Mach, L.

L. Mach. Z. Instrumentenkd. 12, 89 (1892).

Marlow, W. C.

Penkin, N. P.

N. P. Penkin, J. Quant. Spectrosc. Radiat. Transfer 4, 41 (1964).
[CrossRef]

Rozhdestvenskii, D. S.

D. S. Rozhdestvenskii, Ann. Phys. 39, 307 (1912).

van de Weijer, P.

P. van de Weijer, R. M. M. Cremers, J. Appl. Phys. 54, 2835 (1983).
[CrossRef]

P. van de Weijer, R. M. M. Cremers, J. Appl. Phys. 53, 1401 (1982).
[CrossRef]

Zehnder, L.

L. Zehnder, Z. Instrumentenkd 11, 275 (1891).

Ann. Phys. (1)

D. S. Rozhdestvenskii, Ann. Phys. 39, 307 (1912).

Appl. Opt. (1)

J. Appl. Phys. (2)

P. van de Weijer, R. M. M. Cremers, J. Appl. Phys. 53, 1401 (1982).
[CrossRef]

P. van de Weijer, R. M. M. Cremers, J. Appl. Phys. 54, 2835 (1983).
[CrossRef]

J. Quant. Spectrosc. Radiat. Transfer (1)

N. P. Penkin, J. Quant. Spectrosc. Radiat. Transfer 4, 41 (1964).
[CrossRef]

Z. Instrumentenkd (1)

L. Zehnder, Z. Instrumentenkd 11, 275 (1891).

Z. Instrumentenkd. (1)

L. Mach. Z. Instrumentenkd. 12, 89 (1892).

Other (1)

M. C. E. Huber, “Interferometric Gas Diagnostics by the Hook Method,” in Modern Optical Methods in Gas Dynamic Research, D. S. Dosanjh, Ed. (Plenum, New York, 1971), pp. 85–112.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Example of a hook spectrum, showing hooks around the 546.1-nm mercury transition. Note the vertical fringes explained later on in the text which are used as a calibration of the wavelength scale. In this example the distance between two vertical fringes is 3 × 10−2 nm.

Fig. 2
Fig. 2

Schematic diagram of the experimental setup used for measuring the anomalous dispersion by the hook method: G = gas tube, V = vacuum tube, L = positive lens, M = flat mirror, BS = 50/50 beam splitter.

Fig. 3
Fig. 3

Use of the grating with slightly converging incident beam. As a consequence, the diffracted beam is convergent, too, but the focus on the screen is not sharp: it has a width w1.

Equations (10)

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

N = π k Δ 2 / r 0 l f λ 0 3
d x / d λ = nkF / 10 6 cos β mm / nm ,
d β = W cos β / 2 F cos α ,
w 1 = W 2 sin 2 β / 8 F cos 2 α .
sin α + sin β = n λ ,
Δ β = n Δ λ / cos β .
Δ F / F = 2 n Δ λ tan β / cos β .
w 2 = 2 n Δ λ W tan β / cos α .
d α = cos β d β / cos α .
Δ λ = λ 2 / 2 L .

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