Abstract

Compact spectrometers fabricated by placing a wedged etalon or a linear variable filter in front of a linear photodiode array typically do not exhibit the spectral resolution of a parallel filter of the same finesse. A theoretical analysis of the beam emerging from a wedged etalon is shown to predict a comalike aberration, explaining the loss in resolution. This analysis also predicts a focused beam waist whose axial position depends on the incidence angle, indicating that resolution can be improved by placing this waist on the detector. These results are experimentally confirmed in a multicavity linear variable filter to achieve 0.09nm spectral resolution at 1550nm.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. A. Rob, Opt. Lett. 11, 604 (1990).
    [CrossRef]
  2. K. Kinoshita, J. Phys. Soc. Jpn. 8, 219 (1953).
    [CrossRef]
  3. M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), Chap. 7, p. 351.
  4. H. Takahashi, Appl. Opt. 34, 667 (1995).
    [CrossRef]
  5. G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, 1997), p. 284.
  6. J. W. Goodman, Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  7. H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (McGraw-Hill, 1986).
    [CrossRef]

1995 (1)

1990 (1)

M. A. Rob, Opt. Lett. 11, 604 (1990).
[CrossRef]

1953 (1)

K. Kinoshita, J. Phys. Soc. Jpn. 8, 219 (1953).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, 1997), p. 284.

Born, M.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), Chap. 7, p. 351.

Goodman, J. W.

J. W. Goodman, Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

Kinoshita, K.

K. Kinoshita, J. Phys. Soc. Jpn. 8, 219 (1953).
[CrossRef]

Macleod, H. A.

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (McGraw-Hill, 1986).
[CrossRef]

Rob, M. A.

M. A. Rob, Opt. Lett. 11, 604 (1990).
[CrossRef]

Takahashi, H.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), Chap. 7, p. 351.

Appl. Opt. (1)

J. Phys. Soc. Jpn. (1)

K. Kinoshita, J. Phys. Soc. Jpn. 8, 219 (1953).
[CrossRef]

Opt. Lett. (1)

M. A. Rob, Opt. Lett. 11, 604 (1990).
[CrossRef]

Other (4)

M. Born and E. Wolf, Principles of Optics (Pergamon, 1975), Chap. 7, p. 351.

G. P. Agrawal, Fiber-Optic Communication Systems, 2nd ed. (Wiley, 1997), p. 284.

J. W. Goodman, Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

H. A. Macleod, Thin-Film Optical Filters, 2nd ed. (McGraw-Hill, 1986).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Theoretical model.

Fig. 2
Fig. 2

Numerical results of the intensity profile of the transmitted beam for a wedged etalon. The intensity was normalized by the incident intensity.

Fig. 3
Fig. 3

Experimental results of the intensity profile of the transmitted beam for a linear variable filter.

Equations (9)

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

a N = a in r 2 N t 2 = a 0 r 2 N ( 1 r 2 ) ,
Φ N = Φ 0 + 4 π n h λ j = 1 N cos ( θ t + 2 j α ) Φ 0 + 4 π n h λ j = 1 N [ 1 ( θ t + 2 j α ) 2 2 ] ,
Φ N = Φ 0 + 4 π n h λ [ N ( 1 θ t 2 2 ) N ( N + 1 ) α θ t N ( N + 1 ) ( 2 N + 1 ) α 2 3 ] .
Φ N = Φ 0 + 4 π n h λ [ N ( 1 θ t 2 2 ) N 2 α θ t 2 N 3 α 2 3 ] = Φ C + 2 π h α λ ( θ N θ N 3 6 n 2 ) ,
Φ N = Φ C + 2 π S ( θ N θ N 3 6 n 2 ) .
X = λ 2 π d Φ N d θ N + m λ 2 n α ,
X = λ S ( 1 θ N 2 2 n 2 ) + m λ 2 n α .
Z = λ 2 π d 2 Φ N d θ N 2 .
Z = λ S n 2 ( θ in + Δ θ ) .

Metrics