Abstract

We measure short distances with a spectromètre interférentiel à sélection par l’amplitude de la modulation (SISAM) (interferential spectrometer by selection of amplitude modulation) interferometer that correlates optical fields. We present the method and the resolution of the system. A test with a Michelson interferometer shows SISAM’s ability to detect phase change in one arm of the Michelson interferometer.

© 1997 Optical Society of America

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References

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  1. E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).
  2. J. P. Pérez, Optique, Géométrique Ondulatoire et Polarisation, 4th ed. (Masson, Paris, 1993).
  3. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).
  4. G. Bruhat, A. Kastler, Cours de Physique Générale: Optique, 6th ed. (Masson, Paris, 1992).
  5. G. Brun, I. Verrier, M. Ramos, J. P. Goure, P. Ottavi, A. M. Lambert, “Measurement of mode time of flight in multimode fibers by an interferometric method using polychromatic light: theoretical approach and experimental results,” Appl. Opt. 35, 1129–1134 (1996).
    [CrossRef] [PubMed]
  6. G. Brun, I. Verrier, A. Barthélémy, C. Froehly, J. P. Goure, “Measurements of mode propagation time in multimode fibers using a real-time interferometric amplitude correlator,” J. Opt. Commun. 13, 134–139 (1992).
  7. P. Connes, “Principe et réalisation d’un nouveau type de spectromètre interférentiel,” Rev. Opt. Théor. Instrum. 38, 157–201 (1959).
  8. P. Connes, “Principe et réalisation d’un nouveau type de spectromètre interférentiel (suite et fin),” Rev. Opt. Théor. Instrum. 39, 402–436 (1960).

1996

1992

G. Brun, I. Verrier, A. Barthélémy, C. Froehly, J. P. Goure, “Measurements of mode propagation time in multimode fibers using a real-time interferometric amplitude correlator,” J. Opt. Commun. 13, 134–139 (1992).

1960

P. Connes, “Principe et réalisation d’un nouveau type de spectromètre interférentiel (suite et fin),” Rev. Opt. Théor. Instrum. 39, 402–436 (1960).

1959

P. Connes, “Principe et réalisation d’un nouveau type de spectromètre interférentiel,” Rev. Opt. Théor. Instrum. 38, 157–201 (1959).

Barthélémy, A.

G. Brun, I. Verrier, A. Barthélémy, C. Froehly, J. P. Goure, “Measurements of mode propagation time in multimode fibers using a real-time interferometric amplitude correlator,” J. Opt. Commun. 13, 134–139 (1992).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

Bruhat, G.

G. Bruhat, A. Kastler, Cours de Physique Générale: Optique, 6th ed. (Masson, Paris, 1992).

Brun, G.

G. Brun, I. Verrier, M. Ramos, J. P. Goure, P. Ottavi, A. M. Lambert, “Measurement of mode time of flight in multimode fibers by an interferometric method using polychromatic light: theoretical approach and experimental results,” Appl. Opt. 35, 1129–1134 (1996).
[CrossRef] [PubMed]

G. Brun, I. Verrier, A. Barthélémy, C. Froehly, J. P. Goure, “Measurements of mode propagation time in multimode fibers using a real-time interferometric amplitude correlator,” J. Opt. Commun. 13, 134–139 (1992).

Connes, P.

P. Connes, “Principe et réalisation d’un nouveau type de spectromètre interférentiel (suite et fin),” Rev. Opt. Théor. Instrum. 39, 402–436 (1960).

P. Connes, “Principe et réalisation d’un nouveau type de spectromètre interférentiel,” Rev. Opt. Théor. Instrum. 38, 157–201 (1959).

Froehly, C.

G. Brun, I. Verrier, A. Barthélémy, C. Froehly, J. P. Goure, “Measurements of mode propagation time in multimode fibers using a real-time interferometric amplitude correlator,” J. Opt. Commun. 13, 134–139 (1992).

Goure, J. P.

G. Brun, I. Verrier, M. Ramos, J. P. Goure, P. Ottavi, A. M. Lambert, “Measurement of mode time of flight in multimode fibers by an interferometric method using polychromatic light: theoretical approach and experimental results,” Appl. Opt. 35, 1129–1134 (1996).
[CrossRef] [PubMed]

G. Brun, I. Verrier, A. Barthélémy, C. Froehly, J. P. Goure, “Measurements of mode propagation time in multimode fibers using a real-time interferometric amplitude correlator,” J. Opt. Commun. 13, 134–139 (1992).

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).

Kastler, A.

G. Bruhat, A. Kastler, Cours de Physique Générale: Optique, 6th ed. (Masson, Paris, 1992).

Lambert, A. M.

Ottavi, P.

Pérez, J. P.

J. P. Pérez, Optique, Géométrique Ondulatoire et Polarisation, 4th ed. (Masson, Paris, 1993).

Ramos, M.

Verrier, I.

G. Brun, I. Verrier, M. Ramos, J. P. Goure, P. Ottavi, A. M. Lambert, “Measurement of mode time of flight in multimode fibers by an interferometric method using polychromatic light: theoretical approach and experimental results,” Appl. Opt. 35, 1129–1134 (1996).
[CrossRef] [PubMed]

G. Brun, I. Verrier, A. Barthélémy, C. Froehly, J. P. Goure, “Measurements of mode propagation time in multimode fibers using a real-time interferometric amplitude correlator,” J. Opt. Commun. 13, 134–139 (1992).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

Appl. Opt.

J. Opt. Commun.

G. Brun, I. Verrier, A. Barthélémy, C. Froehly, J. P. Goure, “Measurements of mode propagation time in multimode fibers using a real-time interferometric amplitude correlator,” J. Opt. Commun. 13, 134–139 (1992).

Rev. Opt. Théor. Instrum.

P. Connes, “Principe et réalisation d’un nouveau type de spectromètre interférentiel,” Rev. Opt. Théor. Instrum. 38, 157–201 (1959).

P. Connes, “Principe et réalisation d’un nouveau type de spectromètre interférentiel (suite et fin),” Rev. Opt. Théor. Instrum. 39, 402–436 (1960).

Other

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).

J. P. Pérez, Optique, Géométrique Ondulatoire et Polarisation, 4th ed. (Masson, Paris, 1993).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

G. Bruhat, A. Kastler, Cours de Physique Générale: Optique, 6th ed. (Masson, Paris, 1992).

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Figures (8)

Fig. 1
Fig. 1

SISAM interferometer.

Fig. 2
Fig. 2

(a) Grating setup and (b) measurement setup.

Fig. 3
Fig. 3

SISAM test with a Michelson interferometer.

Fig. 4
Fig. 4

Experimental results.

Fig. 5
Fig. 5

Theoretical signal.

Fig. 6
Fig. 6

Calibration of SISAM.

Fig. 7
Fig. 7

Measurement by SISAM of the width of a phase object.

Fig. 8
Fig. 8

Experimental results for the phase object.

Equations (25)

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S˘x, y, ν=S˘Tx, y, νexpjΨTν+S˘Rx, y, νexpjΨRν,
ξ=ν0-Δν2ν0+Δν2 C˘SSx, y, νdν,
C˘SSx, y, ν=S˘x, y, νS˘*x, y, ν,=S˘Tx, y, ν S˘T*x, y, ν+S˘Rx, y, νS˘R*x, y, ν+2PRS˘Tx, y, νS˘R*x, y, ν×expjΨT-ΨR.
S˘R,TXR,T, ZR,T, ν=S˘0R,0TνexpjkxdXR,T+kzdZR,T,
ΨR,Tν=2πνcsinθ XR,T+cosθ ZR,T.
ΨR,Tν=ΨR,Tν0+dΨR,Tνdνν=ν0ν-ν0,
ΨR,Tν0=2πA0R,0T, dΨR,Tνdνν=ν0=2πA1R,1T.
ΨR,Tν2πA0R,0T+A1R,1Tν-ν0
A0R,0T=ν0csin θ0 XR,T+cos θ0 ZR,T, A1R,1T=1csin θ XR,T+cos θ0-N0cν0tan θ0ZR,T, sin θ0=sin θ-N0cν0, cos θ0=1-sin2 θ01/2,
X=XT cos θ0-ZT sin θ0Z=XT sin θ0+ZT cos θ0andX=-XR cos θ0+ZR sin θ0Z=XR sin θ0+ZR cos θ0.
ΔΨν=ΨTν-ΨRν=2πA0R-A0T+A1R-A1Tν-ν0=2π-2N0Xν0 cos θ0ν-ν0.
ΔΨν=2πQ˜+QνX,
Q˜=2N0cos θ0, Q=-2N0ν0 cos θ0.
S˘RX, Y, ν=α0ΓνsX, Yexpjϕ0, S˘TX, Y, ν=α1ΓνsX, Yexpjφ0+expjφ2,
φ0=2πνcl0, φ1=2πνcl1, φ2=2πνcl1+2δx.
C˘S˘S˘X, Y, ν=α02Γ2νs2X, Y+2α12Γ2νs2X, Y×1+PRexpjφ2-φ1+2α0α1Γ2νs2X, YPRexpjφ1-φ0+expjφ2-φ0expjΨT-ΨR.
Γν=Γ rectν, ν0, Δν=Γif ν0-Δν2νν0+Δν20if ν<ν0-Δν2 and ν>ν0+Δν2,
ξ=ν0-Δν2ν0+Δν2α02Γ2s2+2α12Γ2s2dν+2α12Γ2s2PRν0-Δν2ν0+Δν2expjΔφ12νdν+2α0α1Γ2s2PRν0-Δν2ν0+Δν2expjΔφ01νexpjΔΨνdν+2α0α1Γ2s2PRν0-Δν2ν0+Δν2expjΔφ02νexpjΔΨνdν.
ξ=ξ0+ξ1+ξ2+ξ3, with ξ0=98α02Γ2s2 Δν, ξ1=2α12Γ2s2 PRT.F.2δx/c-1rectν, ν0, Δν=18α02Γ2s2Δν sinc2πΔνcδxcos4πν0cδx, ξ2=2α0α1Γ2s2 PRexpj2π˜QX×T.F.QX-1rectν, ν0, Δνexpj2πνcl1-l0=12α02Γ2s2Δν sincπΔνcl1-l0-2N0cXν0 cos θ0×cos2πν0cl1-l0,
ξ3=2α0α1Γ2s2 PR[expj2π˜QX×T.F.QX-1rectν, ν0, Δνexpj2πνcl1-l0+2δx=12α02Γ2s2Δν sincπΔνcl1-l0+2δx-2N0cXν0 cos θ0×cos2πν0cl1-l0+2δx.
T.F.x-1fx=-+fxexpj2πXxdx
ξ=A2+1+sinc2πΔνcδxcos4πν0cδx4+sincπΔνcl1-l0-2N0cXν0 cos θ0cos2πν0cl1-l0+sincπΔνcl1-l0+2δx-2N0cXν0 cos θ0cos2πν0cl1-l0-2δx,
A=α02Γ2s2x, yΔν2.
l1-l0=2N0cXν0 cos θ0, l1-l0+2δx=2N0cXν0 cos θ0.
δxδx=ΔXΔX+γγ

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