Abstract

Spatial distribution of optical phase and amplitude can be measured by using a single-mode optical-fiber interferometric system. Following the first proposal of the measuring principle by the present authors in 1978, a further development of the measuring system is now reported. The major achievement is the use of a novel spatial filter and a set of photodetectors by which the interference fringe position is located. Combining them with analog signal-processing circuitry and with a mechanical feedback system, fully automated recording of the optical phase and amplitude distribution is successfully achieved. The method is used to measure phase-front distribution near a Gaussian beam waist.

© 1981 Optical Society of America

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References

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  1. V. Vali, R. W. Shorthill, Appl. Opt. 15, 1099 (1976); Appl. Opt. 16, 290 (1977).
    [CrossRef] [PubMed]
  2. J. A. Bucaro, H. D. Dardy, E. F. Carome, Appl. Opt. 16, 1761 (1977).
    [CrossRef] [PubMed]
  3. T. G. Giallorenzi, J. A. Bucaro, in Technical Digest, Third International Conference IOOC (Optical Society of America, Washington, D.C., 1981), paper WI1.
  4. M. Iiyama, T. Kamiya, H. Yanai, Appl. Opt. 17, 1965 (1978).
    [CrossRef]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, London1965), Chap. 6.
  6. A. Yariv, Quantum Electronics (Wiley, New York, 1975), Chap. 3.

1978 (1)

1977 (1)

1976 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, London1965), Chap. 6.

Bucaro, J. A.

J. A. Bucaro, H. D. Dardy, E. F. Carome, Appl. Opt. 16, 1761 (1977).
[CrossRef] [PubMed]

T. G. Giallorenzi, J. A. Bucaro, in Technical Digest, Third International Conference IOOC (Optical Society of America, Washington, D.C., 1981), paper WI1.

Carome, E. F.

Dardy, H. D.

Giallorenzi, T. G.

T. G. Giallorenzi, J. A. Bucaro, in Technical Digest, Third International Conference IOOC (Optical Society of America, Washington, D.C., 1981), paper WI1.

Iiyama, M.

Kamiya, T.

Shorthill, R. W.

Vali, V.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, London1965), Chap. 6.

Yanai, H.

Yariv, A.

A. Yariv, Quantum Electronics (Wiley, New York, 1975), Chap. 3.

Appl. Opt. (3)

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, London1965), Chap. 6.

A. Yariv, Quantum Electronics (Wiley, New York, 1975), Chap. 3.

T. G. Giallorenzi, J. A. Bucaro, in Technical Digest, Third International Conference IOOC (Optical Society of America, Washington, D.C., 1981), paper WI1.

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Figures (12)

Fig. 1
Fig. 1

Principle of optical field mapping.

Fig. 2
Fig. 2

Elementary structure of a spatial filter. Displacement of the interference fringe from its equilibrium position is detected by the incident optical power difference between two same dimension slits.

Fig. 3
Fig. 3

Three slits widths constituting the spatial filter are shown relative to the spacing of the interference fringes Λ in the equilibrium condition.

Fig. 4
Fig. 4

Block diagram of the phase and intensity information extraction apparatus. The interference pattern is changed to an electrical signal and processed by use of an analog calculator.

Fig. 5
Fig. 5

Structure of a spatial filter: (a) Shape of one slit pattern. Upper and lower portions are used for phase detection. Middle portion is for the peak intensity of the fringe detection. (b) Spatial filter consisting of fifteen slit patterns. (c) Solar cells are used for photodetectors. They are attached on the spatial filter to detect the selected portion of the fringes.

Fig. 6
Fig. 6

Block diagram of the analog calculator to obtain the intensity (Ed) and attenuated phase (Ep) signals.

Fig. 7
Fig. 7

Experimental setup used for the evaluation of the semiautomated optical field mapping apparatus. Two Gaussian beams are made by use of a half-mirror and two microscope objectives. Two fibers are set together by a 60° V-groove to cause the interference pattern.

Fig. 8
Fig. 8

Optical probe is moved in the axial direction to change the intensity (Ed) and phase (Ep) signals. The maximum difference from the theoretical curve is <1% after correction of the noninterference light contribution.

Fig. 9
Fig. 9

Optical field distribution of a Gaussian beam is measured near its beam waist by the semiautomated apparatus. The fiber probe is moved in the axial direction 135 μm away from the beam waist.

Fig. 10
Fig. 10

Block diagram of automated field mapping apparatus. Electromechanical feedback loop consists of the addition of a dc motor to the spatial filter manipulator. The phase difference signal is current amplified and drives the motor to equilibrate the slit relative to the fringes. A gate circuit is used to suppress the dc motor overrun caused by the offset error of the calculator.

Fig. 11
Fig. 11

Reaction of the automated apparatus to compensate the axial displacement of the optical probe. The probe is displaced by the PZM, and the spatial filter position is measured by the potentiometer attached to the manipulator.

Fig. 12
Fig. 12

Measurement of inclined Gaussian beams by the automated apparatus. Inclined angles are (a) −4°00′ (b) +2°30′. Measured angles are (a) −3°50′ (b) +2°22′.

Equations (13)

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I p ( u , l , w ) = I d ( u , l , w ) + I r ( u , l , w ) + 2 I d ( u , l , w ) I r ( u , l , w ) cos ( 2 π u Λ + δ ) ,
Λ = λ l / d
Δ Q Q U - Q L ,
Q L U = - b b - a a I p ( u ± c , l , w ) d w d u = 4 a b ( I d + I r ) + 4 I d I r Λ a 2 π sin ( 2 π Λ b ) cos ( ± 2 π c Λ + δ ) .
Δ Q = 4 I d I r 2 a Λ π sin δ .
Q M K 4 a M b M ( I r + I d ) 2 .
I d = 1 2 { ( I d + I r ) - [ ( I d + I r ) 2 - ( 2 I d I r ) 2 ] 1 / 2 } ,
I d = 1 2 { Q U + Q L 8 a b - [ 2 ( Q U + Q L 8 a b ) 2 - ( Q M 2 a M b M ) 2 ] 1 / 2 } .
sin δ = [ ( Q U - Q L ) π a M b M 2 a Λ Q M ] .
I = 1 2 { I d + I r + I n - [ I d 2 + ( I r + I ) 2 + 2 I r I d - 4 I r I d ( sin 2 π α 2 π α cos δ ) 2 ] 1 / 2 } .
W ( Z ) 2 = W 0 2 ( 1 + Z 2 Z 0 2 ) ,
R ( Z ) = Z ( 1 + Z 0 2 Z 2 ) ,
W ( Z ) = [ W ( Z ) 2 + a 2 ] 1 / 2 ,

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