Abstract

The effect of finite aperture of a Fabry Perot interferometer on the fringe intensity distribution in the interferometer pattern is investigated. An equation is derived for a square etalon which illustrates clearly the decrease in fringe intensity for increasing angles of incidence. The computations show that this effect becomes significant only for high reflecting powers and comparatively large plate separations.

© 1949 Optical Society of America

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References

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  1. S. Tolansky, High Resolution Spectroscopy (Pitman Publishing Corporation, New York, 1947), Chapter VII, p. 98.
  2. See reference 1, Chapter IX, p. 161.
  3. In Fig. 1 and elsewhere, whereas δ is the phase difference between strictly consecutive reflections, references to successively reflected beams, and to the nth and pth reflected beams apply, not to strictly consecutive reflections, but to consecutive beams reflected at the first plate and transmitted through the second to the camera.

Tolansky, S.

S. Tolansky, High Resolution Spectroscopy (Pitman Publishing Corporation, New York, 1947), Chapter VII, p. 98.

Other (3)

S. Tolansky, High Resolution Spectroscopy (Pitman Publishing Corporation, New York, 1947), Chapter VII, p. 98.

See reference 1, Chapter IX, p. 161.

In Fig. 1 and elsewhere, whereas δ is the phase difference between strictly consecutive reflections, references to successively reflected beams, and to the nth and pth reflected beams apply, not to strictly consecutive reflections, but to consecutive beams reflected at the first plate and transmitted through the second to the camera.

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Figures (5)

Fig. 1
Fig. 1

Amplitudes of transmitted beam and multiply reflected beams. The first reflected beam is shifted by 2. The phase difference 3δ, between successive beams is 0, π, 2π, etc.

Fig. 2
Fig. 2

Schematic diagram of a spectrograph crossed with the Fabry Perot etalon, showing the effect of the aperture of the camera on the number of beams brought to interference in the focal plane F.

Fig. 3
Fig. 3

Decrease of maximum fringe intensity for various reflectivities, and a plate separation of 1 cm, as the angle of incidence is increased.

Fig. 4
Fig. 4

Decrease of maximum fringe intensity for various reflectivities, and a plate separation of 10 cm, as the angle of incidence is increased.

Fig. 5
Fig. 5

In a given Fabry Perot interference pattern, maxima occur at approximately 0°, 0.52°, 0.73° 0.90°, 1.04°, 1.16°. The reflecting power is 90 percent, the plate separation 1 cm, and A = 6 cm. The graph shows how the intensity of the maxima decreases with decreasing order number.

Equations (16)

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I = 1 / ( 1 + a 2 sin 2 δ ) ,
I p = d 2 [ ( 1 - r p ) 2 + 4 r p sin 2 p δ / ( 1 - r ) 2 + 4 r sin 2 δ ] ,
E p = d e i δ ( 1 + r e 2 i δ + + r p - 1 e 2 ( p - 1 ) i δ ) .
[ A 2 - A ( 2 t θ ) ] / A 2 = ( 1 - 2 t θ / A ) .
c 1 = ( 1 - 2 t θ / A ) 1 2 .
c n = ( 1 - n / p ) 1 2 ,
c n = ( 1 - n / 2 p ) ,             n = 1 ,             2 ,             ( p - 1 ) .
E p = d e i δ ( 1 + c 1 r e 2 i δ + + c p - 1 r p - 1 e 2 ( p - 1 ) i δ ) .
E p = ( d e i δ / 1 - r e 2 i δ ) { ( 1 - r p e 2 p i δ ) - ( r e 2 p i δ / 2 p ) × [ ( 1 - r p - 1 ) / ( 1 - r e 2 i δ ) - r p - 1 ( p - 1 ) ] } .
E max = ( d / 1 - r ) { ( 1 - r p ) - ( r / 2 p ) × [ ( 1 - r p - 1 ) / ( 1 - r ) - ( p - 1 ) r p - 1 ] } .
E max = ( d / 1 - r ) { ( 1 - r p ) × [ 1 - ( r / 2 p ( 1 - r ) ) ] + r p / 2 } .
I max = ( d / 1 - r ) 2 { ( 1 - r p ) × [ 1 - ( r / 2 p ( 1 - r ) ) ] + r p / 2 } 2 .
lim p I max = 1 ,
lim r 1 I max = 0.
lim r 1 ( 1 - r p ) / ( 1 - r ) ,
lim r 1 p r p - 1 = p ,