Abstract

A new rapid scan phase modulator has been studied in a range of interferometric applications from the visible to the millimeter wave region. The modulator consists of two parallel mirrors mounted on a rotating platform. It causes little attenuation and is capable of large changes in optical path length at high speeds. The system is relatively insensitive to vibration and can yield a nearly flat transmission envelope.

© 1981 Optical Society of America

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References

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  1. R. S. Sternberg, J. F. James, J. Sci. Instrum. 41, 225 (1964).
    [CrossRef]
  2. D. V. Bartlett, R. G. L. Hewitt, L. C. Robinson, G. D. Tait, Infrared Phys. 17, 89 (1977).
    [CrossRef]
  3. P. Jacquinot, Rep. Prog. Phys. 23, 267 (1960).
    [CrossRef]
  4. W. H. Steel, Interferometry (Cambridge U. P., London, 1967).
  5. L. W. Kunz, D. Goorvitch, Appl. Opt. 13, 1077 (1974).
    [CrossRef] [PubMed]
  6. A. E. Costley, in Trends in Physics 1978, Proceedings, Fourth General Conf. of European Physical Soc., York (Inst. of Physics, London, 1978).
  7. D. H. Martin, E. Puplett, Infrared Phys. 10, 105 (1970).
    [CrossRef]
  8. N. R. Heckenberg, G. D. Tait, L. B. Whitbourn, J. Appl. Phys. 44, 4522 (1973).
    [CrossRef]
  9. P. A. Krug, I. S. Falconer, G. D. Tait, in preparation.
  10. W. A. Kricker, W. I. B. Smith, Phys. Lett. 14, 102 (1965).
  11. B. J. Meddens, R. J. Taylor, Association Euratom-FOM, Jutphaas, Rynhuizen Report 74-85 (1974).

1977 (1)

D. V. Bartlett, R. G. L. Hewitt, L. C. Robinson, G. D. Tait, Infrared Phys. 17, 89 (1977).
[CrossRef]

1974 (1)

1973 (1)

N. R. Heckenberg, G. D. Tait, L. B. Whitbourn, J. Appl. Phys. 44, 4522 (1973).
[CrossRef]

1970 (1)

D. H. Martin, E. Puplett, Infrared Phys. 10, 105 (1970).
[CrossRef]

1965 (1)

W. A. Kricker, W. I. B. Smith, Phys. Lett. 14, 102 (1965).

1964 (1)

R. S. Sternberg, J. F. James, J. Sci. Instrum. 41, 225 (1964).
[CrossRef]

1960 (1)

P. Jacquinot, Rep. Prog. Phys. 23, 267 (1960).
[CrossRef]

Bartlett, D. V.

D. V. Bartlett, R. G. L. Hewitt, L. C. Robinson, G. D. Tait, Infrared Phys. 17, 89 (1977).
[CrossRef]

Costley, A. E.

A. E. Costley, in Trends in Physics 1978, Proceedings, Fourth General Conf. of European Physical Soc., York (Inst. of Physics, London, 1978).

Falconer, I. S.

P. A. Krug, I. S. Falconer, G. D. Tait, in preparation.

Goorvitch, D.

Heckenberg, N. R.

N. R. Heckenberg, G. D. Tait, L. B. Whitbourn, J. Appl. Phys. 44, 4522 (1973).
[CrossRef]

Hewitt, R. G. L.

D. V. Bartlett, R. G. L. Hewitt, L. C. Robinson, G. D. Tait, Infrared Phys. 17, 89 (1977).
[CrossRef]

Jacquinot, P.

P. Jacquinot, Rep. Prog. Phys. 23, 267 (1960).
[CrossRef]

James, J. F.

R. S. Sternberg, J. F. James, J. Sci. Instrum. 41, 225 (1964).
[CrossRef]

Kricker, W. A.

W. A. Kricker, W. I. B. Smith, Phys. Lett. 14, 102 (1965).

Krug, P. A.

P. A. Krug, I. S. Falconer, G. D. Tait, in preparation.

Kunz, L. W.

Martin, D. H.

D. H. Martin, E. Puplett, Infrared Phys. 10, 105 (1970).
[CrossRef]

Meddens, B. J.

B. J. Meddens, R. J. Taylor, Association Euratom-FOM, Jutphaas, Rynhuizen Report 74-85 (1974).

Puplett, E.

D. H. Martin, E. Puplett, Infrared Phys. 10, 105 (1970).
[CrossRef]

Robinson, L. C.

D. V. Bartlett, R. G. L. Hewitt, L. C. Robinson, G. D. Tait, Infrared Phys. 17, 89 (1977).
[CrossRef]

Smith, W. I. B.

W. A. Kricker, W. I. B. Smith, Phys. Lett. 14, 102 (1965).

Steel, W. H.

W. H. Steel, Interferometry (Cambridge U. P., London, 1967).

Sternberg, R. S.

R. S. Sternberg, J. F. James, J. Sci. Instrum. 41, 225 (1964).
[CrossRef]

Tait, G. D.

D. V. Bartlett, R. G. L. Hewitt, L. C. Robinson, G. D. Tait, Infrared Phys. 17, 89 (1977).
[CrossRef]

N. R. Heckenberg, G. D. Tait, L. B. Whitbourn, J. Appl. Phys. 44, 4522 (1973).
[CrossRef]

P. A. Krug, I. S. Falconer, G. D. Tait, in preparation.

Taylor, R. J.

B. J. Meddens, R. J. Taylor, Association Euratom-FOM, Jutphaas, Rynhuizen Report 74-85 (1974).

Whitbourn, L. B.

N. R. Heckenberg, G. D. Tait, L. B. Whitbourn, J. Appl. Phys. 44, 4522 (1973).
[CrossRef]

Appl. Opt. (1)

Infrared Phys. (2)

D. V. Bartlett, R. G. L. Hewitt, L. C. Robinson, G. D. Tait, Infrared Phys. 17, 89 (1977).
[CrossRef]

D. H. Martin, E. Puplett, Infrared Phys. 10, 105 (1970).
[CrossRef]

J. Appl. Phys. (1)

N. R. Heckenberg, G. D. Tait, L. B. Whitbourn, J. Appl. Phys. 44, 4522 (1973).
[CrossRef]

J. Sci. Instrum. (1)

R. S. Sternberg, J. F. James, J. Sci. Instrum. 41, 225 (1964).
[CrossRef]

Phys. Lett. (1)

W. A. Kricker, W. I. B. Smith, Phys. Lett. 14, 102 (1965).

Rep. Prog. Phys. (1)

P. Jacquinot, Rep. Prog. Phys. 23, 267 (1960).
[CrossRef]

Other (4)

W. H. Steel, Interferometry (Cambridge U. P., London, 1967).

A. E. Costley, in Trends in Physics 1978, Proceedings, Fourth General Conf. of European Physical Soc., York (Inst. of Physics, London, 1978).

B. J. Meddens, R. J. Taylor, Association Euratom-FOM, Jutphaas, Rynhuizen Report 74-85 (1974).

P. A. Krug, I. S. Falconer, G. D. Tait, in preparation.

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Figures (10)

Fig. 1
Fig. 1

Simple Michelson interferometer in which a rotating mirror modulator forms the scanning element. Ray paths XY and YZ are added to the optical path by the passage of the radiation through the rotating mirror modulator.

Fig. 2
Fig. 2

Rotating mirror modulator is arranged so that a narrow beam of radiation incident at π/4 on A passes through the center O of the mirror assembly. Quantities defined in the figure are L1, the distance from C (or C′) to the outer edge of the mirror plate; L2, half of the plate separation; L3, distance from C′ (or C) to the inner edge of the mirror plate; L4, distance from C to the point of reflection of the ray on mirror A; L5, distance from C′ to the point of reflection of the ray on mirror B.

Fig. 3
Fig. 3

Parallel plates of the rotating mirror modulator. Source is rotated about the center of the RMM to illustrate the movement of reflection points along the mirrors as the angle of incidence is varied. Ray A is incident at the lower cutoff angle θL and undergoes double passing; ray B is the required case; ray C is incident at the upper cutoff angle θU.

Fig. 4
Fig. 4

Transmission envelope of the mid-IR modulator for a beam of 12.5-mm diam. Modulator parameters are L1 = 50.8 mm, L2 = 12.77 mm, L3 = 0.0 mm.

Fig. 5
Fig. 5

Rotating mirror interferometer: (1) millimeter wave rotating mirror modulator; (2) return mirror; (3) reference arm and mirror; (4) polarizing grid beam splitters; (5) condensing lens; (6) InSb cryogenic detector; (7) visible light modulator mounted on the top disk of the millimeter wave modulator; (8) He–Ne laser; (9) beam splitter for He–Ne interferometer; (10) stationary mirrors for He–Ne interferometer; (11) solid state detector.

Fig. 6
Fig. 6

Interferograrn (a), transformed to give a spectrum (b), obtained using the rotating mirror interferometer for monochromatic radiation of 2.42-mm wavelength.

Fig. 7
Fig. 7

Interferogram (a) and the corresponding spectrum (b) obtained with the rotating mirror interferometer during observations of electron cyclotron emission on the DITE tokamak. Spectrum shows emission at the first three harmonics of the electron cyclotron frequency in the tokamak.

Fig. 8
Fig. 8

Self-modulating CO2 laser interferometer. Radiation from the grating tuned cw CO2 laser passes through the modulator and is returned. to the laser output mirror. Attenuator and aperture control the proportion of the output radiation returned to the laser, while the beam splitter couples some output to a radiation detector and also provides additional attenuation.

Fig. 9
Fig. 9

Self-modulating CO2 laser interferometer fringe envelopes. Each envelope represents a burst of more than 6000 fringes. Quiescent level is the laser output when no radiation is fed back into the laser cavity. (a) Fringe envelope when return mirror is well aligned. The bumps in the envelope are mostly due to 100-Hz ripple in the CO2 laser power supply. (b) Poorly aligned return mirror. Transmitted amplitude varies by a factor of >3.5 over the envelope. Sharp bumps at either end of the envelope are believed to be due to diffraction effects.

Fig. 10
Fig. 10

Interferometry system for fast plasma electron density measurements. Configuration consists of two interferometers sharing a common reference arm (main reference arm). Secondary reference arm is actually the probing arm of a reference interferometer, whose output (reference fringe detector) is solely the result of the phase shift due to the RMM. Plasma fringe detector gives fringes whose phase is shifted with respect to those from the reference fringe detector by the presence of the plasma. Measured phase shift is proportional to the plasma’s electron density. Apertures (not shown) and slight misalignment ensure that no radiation from the probing arm reaches the reference fringe detector.

Equations (23)

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d = 8 L 2 cos θ ,
d ˙ = - 8 ω L 2 sin θ ,
θ U = cos - 1 [ 3 ( x 2 + 7 ) 1 / 2 - 2 x x 2 + 9 ] ,
θ L = cos - 1 [ 3 ( y 2 + 7 ) 1 / 2 + 2 y y 2 + 9 ] ,
θ L = cos - 1 [ 5 ( y 2 + 23 ) 1 / 2 - 2 y y 2 + 25 ] .
d = 8 L 2 cos θ cos α 1 ( t ) 8 L 2 cos θ [ 1 + α 1 2 ( t ) 2 ] .
A = 2 π 2 [ ( β R ) / λ ] 2 ,
d = 8 L 2 ( cos θ - cos θ 0 ) .
L = 4 L 2 sin θ
d = 8 L 2 ( cos θ - cos θ 0 ) ± 8 L 2 β ( sin θ - sin θ 0 ) ,
= d - d d = ± β ( sin θ - sin θ 0 ) cos θ - cos θ 0 = β cot ( θ + θ 0 2 ) ,
d i = ( L 2 / l 2 ) × 0.6328 μ m ,
l = 2 L 2 sin θ c .
L 4 = L 2 sin ( 2 θ c - θ ) cos θ + 2 cos ( 2 θ c - θ ) sin θ c - sin 2 θ c cos θ cos ( 2 θ c - θ ) ,
L 5 = L 2 × 2 cos ( 2 θ c - θ ) ( sin θ - sin θ c ) - sin ( 2 θ c - θ ) cos θ + sin 2 θ c cos θ cos ( 2 θ c - θ ) ,
L 4 ( θ c , θ , Δ ) = L 4 + Δ cos θ ,
L 5 ( θ c , θ , Δ ) = L 5 - Δ cos θ .
L 1 L 4 ;
L 1 L 5 ;
- L 3 L 4 .
L 3 2 L 5 + L 4 ;
- L 3 L 5 ;
L 3 2 L 4 + L 5 .

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