Abstract

Two methods are described to attain high resolution holographic spectroscopy. One is an interferometer construction to record the localized interference fringes on the photographic plate directly. The limitation due to the use of an imaging lens is removed. The other is the application of heterodyning techniques to holographic spectroscopy. By this method, a hologram with high resolving power is recorded on relatively low resolution photographic film.

© 1971 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. W. Stroke, A. T. Funkhouser, Phys. Lett. 16, 272 (1965).
    [CrossRef]
  2. K. Yoshihara, A. Kitade, Japan. J. appl. Phys. 6, 116 (1967).
    [CrossRef]

1967 (1)

K. Yoshihara, A. Kitade, Japan. J. appl. Phys. 6, 116 (1967).
[CrossRef]

1965 (1)

G. W. Stroke, A. T. Funkhouser, Phys. Lett. 16, 272 (1965).
[CrossRef]

Funkhouser, A. T.

G. W. Stroke, A. T. Funkhouser, Phys. Lett. 16, 272 (1965).
[CrossRef]

Kitade, A.

K. Yoshihara, A. Kitade, Japan. J. appl. Phys. 6, 116 (1967).
[CrossRef]

Stroke, G. W.

G. W. Stroke, A. T. Funkhouser, Phys. Lett. 16, 272 (1965).
[CrossRef]

Yoshihara, K.

K. Yoshihara, A. Kitade, Japan. J. appl. Phys. 6, 116 (1967).
[CrossRef]

Japan. J. appl. Phys. (1)

K. Yoshihara, A. Kitade, Japan. J. appl. Phys. 6, 116 (1967).
[CrossRef]

Phys. Lett. (1)

G. W. Stroke, A. T. Funkhouser, Phys. Lett. 16, 272 (1965).
[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 (7)

Fig. 1
Fig. 1

Schematic diagram of the holographic interferometer. Two beams divided by the beam splitter, B.S., intersect at the photographic plate, P. M1, M2, M3 are reflecting mirrors; C is the compensator plate.

Fig. 2
Fig. 2

Concept of adjustment of the holographic interferometer. Using the adjusting mirror, M4, the optical path difference between 002SP2 and 001P1, is set to equal nearly zero by moving the mirror, M3. Two interfering rays intersect on the plane of the mirror, M4 by rotating the mirrors, M1, M2. Real localized interference fringes are observed in the plane of mirror, M4 by removing the mirror, M4.

Fig. 3
Fig. 3

Optical system of heterodyned holographic spectroscopy. Interference fringes produced by the diffracted beams are recorded as the hologram.

Fig. 4
Fig. 4

Off-axis wavefronts. The optical path difference between two off-axis wavefronts, ∑1α, ∑2α is equal to PQ′ + PR′. S1, L1 and S2, L2 are the conjugate spectral sources and collimator lenses. α is the off-axis angle.

Fig. 5
Fig. 5

Reconstructed spectra of the hollgram directly recorded with a cold mercury arc. Wavelength is shown in Å.

Fig. 6
Fig. 6

Heterodyned hologram of a sodium spectral lamp. The heterodyned interference gratings corresponding to D1 and D2 lines are superimposed.

Fig. 7
Fig. 7

Reconstructed spectra of the heterodyned hologram shown in Fig. 6. Wavelength is shown in Å.

Equations (12)

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

2 σ 0 sin ( θ / 4 ) = m / d σ 0 { sin ( θ / 4 ) + sin [ ( θ / 4 ) - ( δ / 2 ) ] } = m / d
I ( x ) = σ 0 σ I ( σ ) { 1 + cos [ 2 π · 2 σ sin ( δ / 2 ) · x ] } d σ .
I ( x ) = σ 0 σ I ( σ ) { 1 + cos [ 2 π · 4 ( σ - σ 0 ) tan ( θ / 4 ) x ] } d σ .
F = sinc [ 8 ( σ - σ 0 ) tan ( θ / 4 ) - w ] X ,
R = σ / ( Δ σ ) σ 0 / ( Δ σ ) = ( 4 X ) / ( d cos θ / 4 ) = 2 m N ,
0 < 4 ( σ min - σ 0 ) tan ( θ / 4 ) < 4 ( σ max - σ 0 ) tan ( θ / 4 ) < R 0 ,
Δ α = P Q + P R = 2 x sin ( θ / 2 ) cos α ,
d I ( x ) = 0 σ I ( σ ) d σ ( 1 + cos { 2 π · 2 σ sin ( θ / 2 ) [ 1 - ( α 2 / 2 ) ] x } ) d Ω .
I ( x ) = Ω 0 σ I ( σ ) d σ { 1 + sinc [ 2 σ ( sin θ / 2 ) Ω x 2 π ] × cos [ 2 π 2 σ sin θ 2 ( 1 - Ω 4 π ) x ] } .
2 σ [ sin ( θ / 2 ) ] Ω x = 2 π .
Ω m ( 2 π ) / [ 2 σ ( sin θ / 2 ) X ] .
Ω m ( 4 π ) / R

Metrics