Abstract

A temporal electronic speckle pattern interferometry (ESPI) system is proposed for in-plane rotation measurement. The relationship between the rotation angle and the phase change distribution is established and the rotation direction is indicated by the sign of the partial differential of the phase change distribution. Temporal phase modulation is applied in the proposed symmetric illumination ESPI system. The phase is recovered by the temporal intensity analysis method which uses the temporal evolution history of the light intensity. The system can perform dynamic measurements and provide results in off-line real-time. Preliminary experiments were carried out with a continuously rotating target to show the feasibility and the dynamic feature of the temporal ESPI system. At present, the mean absolute error of the experiment is 0.39 arcsec.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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2017 (1)

2016 (2)

2014 (1)

N. Werth, F. Salazar-Bloise, and A. Koch, “Influence of roughness in the phase-shifting speckle method: An experimental study with applications,” Rev. Sci. Instruments 85, 015114 (2014).
[Crossref]

2011 (1)

2004 (1)

2003 (1)

2002 (1)

K. Abedin, M. Wahadoszamen, and A. Haider, “Measurement of in-plane motions and rotations using a simple electronic speckle pattern interferometer,” Opt. & Laser Technol. 34, 293–298 (2002).
[Crossref]

2001 (1)

B. Ráczkevi, F. Gyímesi, and S. Mike, “One-wavelength in-plane rotation analysis in electronic speckle pattern interferometry,” Opt. Lasers Eng. 35, 33–40 (2001).
[Crossref]

1999 (2)

A.-K. Nassim, L. Joannes, and A. Cornet, “In-plane rotation analysis by two-wavelength electronic speckle interferometry,” Appl. Opt. 38, 2467–2470 (1999).
[Crossref]

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[Crossref]

1996 (1)

L.-S. Wang and S. Krishnaswamy, “Shape measurement using additive-subtractive phase shifting speckle interferometry,” Meas. Sci. Technol. 7, 1748–1754 (1996).
[Crossref]

1991 (2)

1982 (1)

Abedin, K.

K. Abedin, M. Wahadoszamen, and A. Haider, “Measurement of in-plane motions and rotations using a simple electronic speckle pattern interferometer,” Opt. & Laser Technol. 34, 293–298 (2002).
[Crossref]

Aebischer, H. A.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[Crossref]

Aulbach, L.

Chatterjee, S.

Cornet, A.

Davis, C. C.

C. C. Davis, Lasers and electro-optics: fundamentals and engineering (Cambridge University, 2014).

de Groot, P.

Estrada, J. C.

Fournier, J.-M.

P. Jacquot and J.-M. Fournier, Interferometry in speckle light: Theory and applications (Springer Science & Business Media, 2012).

Gyímesi, F.

B. Ráczkevi, F. Gyímesi, and S. Mike, “One-wavelength in-plane rotation analysis in electronic speckle pattern interferometry,” Opt. Lasers Eng. 35, 33–40 (2001).
[Crossref]

Haider, A.

K. Abedin, M. Wahadoszamen, and A. Haider, “Measurement of in-plane motions and rotations using a simple electronic speckle pattern interferometer,” Opt. & Laser Technol. 34, 293–298 (2002).
[Crossref]

Häusler, G.

A. Koch, M. Ruprecht, O. Toedter, and G. Häusler, “Optische messtechnik an technischen oberflächen,” Expert. Renningen-Malmsheim, Ger. (1998).

Ina, H.

Jacquot, P.

P. Jacquot and J.-M. Fournier, Interferometry in speckle light: Theory and applications (Springer Science & Business Media, 2012).

Jakobi, M.

Joannes, L.

Kadono, H.

Kobayashi, S.

Koch, A.

N. Werth, F. Salazar-Bloise, and A. Koch, “Influence of roughness in the phase-shifting speckle method: An experimental study with applications,” Rev. Sci. Instruments 85, 015114 (2014).
[Crossref]

A. Koch, M. Ruprecht, O. Toedter, and G. Häusler, “Optische messtechnik an technischen oberflächen,” Expert. Renningen-Malmsheim, Ger. (1998).

Koch, A. W.

Krishnaswamy, S.

L.-S. Wang and S. Krishnaswamy, “Shape measurement using additive-subtractive phase shifting speckle interferometry,” Meas. Sci. Technol. 7, 1748–1754 (1996).
[Crossref]

Kumar, Y. P.

Lu, M.

Madjarova, V. D.

Martínez, A.

Mike, S.

B. Ráczkevi, F. Gyímesi, and S. Mike, “One-wavelength in-plane rotation analysis in electronic speckle pattern interferometry,” Opt. Lasers Eng. 35, 33–40 (2001).
[Crossref]

Nassim, A.-K.

Negi, S. S.

Nye, J. F.

J. F. Nye, Physical properties of crystals: their representation by tensors and matrices (Oxford University, 1985).

Puga, H. J.

Quiroga, J. A.

Ráczkevi, B.

B. Ráczkevi, F. Gyímesi, and S. Mike, “One-wavelength in-plane rotation analysis in electronic speckle pattern interferometry,” Opt. Lasers Eng. 35, 33–40 (2001).
[Crossref]

Rayas, J. A.

Rodríguez-Vera, R.

Ruprecht, M.

A. Koch, M. Ruprecht, O. Toedter, and G. Häusler, “Optische messtechnik an technischen oberflächen,” Expert. Renningen-Malmsheim, Ger. (1998).

Salazar-Bloise, F.

N. Werth, F. Salazar-Bloise, and A. Koch, “Influence of roughness in the phase-shifting speckle method: An experimental study with applications,” Rev. Sci. Instruments 85, 015114 (2014).
[Crossref]

Santoyo, F. M.

Servin, M.

Shellabear, M. C.

Takeda, M.

Toedter, O.

A. Koch, M. Ruprecht, O. Toedter, and G. Häusler, “Optische messtechnik an technischen oberflächen,” Expert. Renningen-Malmsheim, Ger. (1998).

Toyooka, S.

Tyrer, J. R.

Wahadoszamen, M.

K. Abedin, M. Wahadoszamen, and A. Haider, “Measurement of in-plane motions and rotations using a simple electronic speckle pattern interferometer,” Opt. & Laser Technol. 34, 293–298 (2002).
[Crossref]

Waldner, S.

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[Crossref]

Wang, L.-S.

L.-S. Wang and S. Krishnaswamy, “Shape measurement using additive-subtractive phase shifting speckle interferometry,” Meas. Sci. Technol. 7, 1748–1754 (1996).
[Crossref]

Wang, S.

Werth, N.

N. Werth, F. Salazar-Bloise, and A. Koch, “Influence of roughness in the phase-shifting speckle method: An experimental study with applications,” Rev. Sci. Instruments 85, 015114 (2014).
[Crossref]

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Meas. Sci. Technol. (1)

L.-S. Wang and S. Krishnaswamy, “Shape measurement using additive-subtractive phase shifting speckle interferometry,” Meas. Sci. Technol. 7, 1748–1754 (1996).
[Crossref]

Opt. & Laser Technol. (1)

K. Abedin, M. Wahadoszamen, and A. Haider, “Measurement of in-plane motions and rotations using a simple electronic speckle pattern interferometer,” Opt. & Laser Technol. 34, 293–298 (2002).
[Crossref]

Opt. Commun. (1)

H. A. Aebischer and S. Waldner, “A simple and effective method for filtering speckle-interferometric phase fringe patterns,” Opt. Commun. 162, 205–210 (1999).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (1)

B. Ráczkevi, F. Gyímesi, and S. Mike, “One-wavelength in-plane rotation analysis in electronic speckle pattern interferometry,” Opt. Lasers Eng. 35, 33–40 (2001).
[Crossref]

Opt. Lett. (2)

Rev. Sci. Instruments (1)

N. Werth, F. Salazar-Bloise, and A. Koch, “Influence of roughness in the phase-shifting speckle method: An experimental study with applications,” Rev. Sci. Instruments 85, 015114 (2014).
[Crossref]

Other (4)

A. Koch, M. Ruprecht, O. Toedter, and G. Häusler, “Optische messtechnik an technischen oberflächen,” Expert. Renningen-Malmsheim, Ger. (1998).

J. F. Nye, Physical properties of crystals: their representation by tensors and matrices (Oxford University, 1985).

C. C. Davis, Lasers and electro-optics: fundamentals and engineering (Cambridge University, 2014).

P. Jacquot and J.-M. Fournier, Interferometry in speckle light: Theory and applications (Springer Science & Business Media, 2012).

Supplementary Material (1)

NameDescription
» Visualization 1       This video provides the real-time results of the in-plane rotation measurement. The playback frame rate is 30 fps. At the top left is the real-time recovered phase map, at the top right is a demonstration of the in-plane rotation (not drawn to scale)

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Figures (7)

Fig. 1
Fig. 1 System configuration. The precise and controllable in-plane rotation of the target is provided by a micromechanical rotation stage. The lithium niobate crystal is driven by an external power supply. Note that the power supply are omitted for clarity. LN: lithium niobate crystal; Q: quarter-wave plate; L: lens; AP: aperture; PBS: polarizing beam splitter; M: mirror; P: polarizer; k : wave vector.
Fig. 2
Fig. 2 Mathematical model of the in-plane rotation counterclockwise. P(x1, y1) is an arbitary point on the target surface. Points P and Q share the same abscissa. O, center of rotation; Ω, rotation angle; ∆lx, lateral displacement along the sensitive direction.
Fig. 3
Fig. 3 The phase modulator consists of a powered-up lithium niobate crystal (LiNbO3, LN) and a stationary quarter-wave plate. The four rectangular surfaces are covered with electrodes, respectively. ω is the angular frequency of the driving electric field and t denotes the time parameter. Greek letters in each dash line square represent corresponding angles which are marked by short arc. The azimuth (β) of the u v-axis is time-varying. The double-arrow red lines stand for polarizations (input, Vy, and Vx) and F is the fast axis of the quarter-wave plate. The coordinate transformations and detailed interpretations regarding to all parameters can be found in Section 2.2.
Fig. 4
Fig. 4 (a) illustrates the normalized intensity evolution history. (b), (c), and (d) shows three captured frames, where the 80th horizontal slices are marked with red line. For all of the captured 544 frames, the 80th horizontal slices are extracted and stacked together in time sequences to generate (a).
Fig. 5
Fig. 5 The Fourier spectrum of the temporal intensity evolution history of the pixel located at (100,150) of each frame. DC component is the spectrum of the background intensity. 34 Hz is the temporal frequency which is introduced by the phase modulator.
Fig. 6
Fig. 6 The recovered phase maps. From (a) to (i), the corresponding frame index runs from 250 to 1050 with a step length of 100. The equivalent time interval is 100 (f rames )/272 (f ps ).
Fig. 7
Fig. 7 Dynamic measurement results of a continuously rotating target. (a) shows the measured results and the theoretical values. (b) shows the absolute errors of the measurement.

Equations (20)

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k ( u , v , w ) = ( k 21 k 1 ) ( k 22 k 1 ) = 4 π λ sin θ u ,
Δ φ ( x , y ) = k ( u , v , w ) Δ l ( x , y ) = k ( u , v , w ) ( Δ l x u + Δ l y v + Δ l z w ) = 4 π λ sin θ Δ l x ( x , y ) ,
Δ l x P = x 2 x 1 = x 1 cos Ω y 1 sin Ω x 1 Δ l x Q = x 4 x 1 = x 1 cos Ω y 3 sin Ω x 1 ,
Δ l x ( x , y ) y = Δ l x   P Δ l x Q y 1 y 3 = sin Ω .
Ω = arcsin [ λ 4 π sin θ Δ φ ( x , y ) y ] ,
[ E x E y E z ] = E 0 [ cos ω t sin ω t 0   ] ,
[ x y ] T [ 1 / n o 2 λ 22 E y γ 22 E x γ 22 E x 1 / n o 2 λ 22 E y ] [ x y ] = 1 .
[ u v ] = [ cos β sin β sin β cos β ] [ x y ] = ( β ) [ x y ] ,
[ u v ] T = [ 1 n o 2 γ 22 E x sin 2 β γ 22 E y cos 2 β γ 22 E x cos 2 β + γ 22 E y sin 2 β γ 22 E x cos 2 β + γ 22 E y sin 2 β 1 n o 2 + γ 22 E x sin 2 β + γ 22 E y cos 2 β ] [ u v ] = 1 .
β = π 4 ω t 2 , if γ 22 E x cos 2 β + γ 22 E y sin 2 β = 0 ,
Δ φ = 2 π L | n u n v | λ = 2 2 π L n o λ 1 sin ξ sin 2 ξ ,
ξ = arccos ( n o 2 γ 22 E 0 ) .
V c r y s t a l = ( β ) [ e j π 2 0 0 e j π 2 ] phase delay π ( β ) cos α sin α e j ω 0 t input laser ,
[ V x V y ] = ( η π 4 ) [ 1 + j cos 2 η j sin 2 η j sin 2 η 1 j cos 2 η ] QWP , oriented at η V c r y s t a l ,
V i m g = ( ψ ) [ cos 2 ψ sin ψ cos ψ sin ψ cos ψ sin 2 ψ ] polarizer , oriented at ψ [ V x V y ] ,
I = V i m g V i m g = 1 sin ( 2 ψ ) cos ( 2 ω t + 2 η + 2 α ) ,
I ( x , y , t ) = I 0 ( x , y ) + I v cos [ 2 ω t + Δ φ ( x , y , t ) + φ 0 ] = I 0 + I v 2 exp { j [ 2 ω t + Δ φ ( x , y , t ) + φ 0 ] } + I v 2 exp { j [ 2 ω t + Δ φ ( x , y , t ) + φ 0 ] } ,
G ( f t ) = A ( f t ) + C ( f t f 0 ) + C * ( f t + f 0 ) ,
Δ φ ( x 1 , y 1 , t ) = arctan Im [ c ( x 1 , y 1 , t ) ] Re [ c ( x 1 , y 1 , t ) ] 2 ω t ,
f e = 1 2 π Δ φ ( x , y , t ) t < f 0 ,

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