Abstract

We present a real-time differential phase-front detector sensitive to better than 3 mrad rms, which corresponds to a precision of approximately 500  pm. This detector performs a spatially resolving measurement of the phase front of a heterodyne interferometer, with heterodyne frequencies up to approximately 10 kHz. This instrument was developed as part of the research for the Laser Interferometer Space Antenna Technology Package interferometer and will assist in the manufacture of its flight model. Because of the advantages this instrument offers, it also has general applications in optical metrology.

© 2007 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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  13. V. Wand, J. Bogenstahl, O. Braxmaier, K. Danzmann, A. García, F. Guzmán, G. Heinzel, J. Hough, O. Jennrich, C. Killow, D. Robertson, Z. Sodnik, F. Steier, and H. Ward, "Noise sources in the LTP heterodyne interferometer," Class. Quantum Grav. 23, 159-167 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2006 (1)

V. Wand, J. Bogenstahl, O. Braxmaier, K. Danzmann, A. García, F. Guzmán, G. Heinzel, J. Hough, O. Jennrich, C. Killow, D. Robertson, Z. Sodnik, F. Steier, and H. Ward, "Noise sources in the LTP heterodyne interferometer," Class. Quantum Grav. 23, 159-167 (2006).
[CrossRef]

2005 (4)

J. Millerd, N. Brock, J. Hayes, B. Kimbrough, M. Novak, M. North-Morris, and J. C. Wyant, "Modern approaches in phase measuring metrology," Proc. SPIE 5856, 14-22 (2005).
[CrossRef]

D. Robertson, C. Killow, H. Ward, J. Hough, G. Heinzel, A. García, V. Wand, U. Johann, and C. Braxmaier, "LTP interferometer-noise sources and performance," Class. Quantum Grav. 22, 155-163 (2005).
[CrossRef]

Y. Li, Z. Zhu, and X. Li, "Elimination of reference phase errors in phase-shifting interferometry," Meas. Sci. Technol. 16, 1335-1340 (2005).
[CrossRef]

G. Heinzel, C. Braxmaier, M. Caldwell, K. Danzmann, F. Draaisma, A. García, J. Hough, O. Jennrich, U. Johann, C. Killow, K. Middleton, M. te Plate, D. Robertson, A. Rüdiger, R. Schilling, F. Steier, V. Wand, and H. Ward, "Successful testing of the LISA Technology Package (LTP) interferometer engineering model," Class. Quantum Grav. 22, 149-154 (2005).
[CrossRef]

2004 (1)

G. Heinzel, V. Wand, A. Garcia, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, "The LTP interferometer and phasemeter," Class. Quantum Grav. 21, 581-587 (2004).
[CrossRef]

2003 (1)

G. Heinzel, C. Braxmaier, R. Schilling, A. Rüdiger, D. Robertson, M. te Plate, V. Wand, K. Arai, U. Johann, and K. Danzmann, "Interferometry for the LISA technology package (LTP) aboard SMART-2," Class. Quantum Grav. 20, 153-161 (2003).
[CrossRef]

2002 (1)

H. Zhao and G. Zhang, "Nonlinear error by orientation and elliptic polarization in a two-beam interferometer," Opt. Eng. 41, 3204-3208 (2002).
[CrossRef]

2001 (1)

S. Kaiser, T. Maier, A. Grossmann, and C. Zimmermann, "Fizeau interferometer for phase-shift interferometry in ultrahigh vacuum," Rev. Sci. Instrum. 72, 3726-3727 (2001).
[CrossRef]

2000 (1)

Y. Surrel, "Fringe analysis," Top. Appl. Phys. 77, 55-102 (2000).
[CrossRef]

1997 (2)

1994 (1)

1991 (1)

1990 (1)

1978 (1)

Appl. Opt. (1)

Class. Quantum Grav. (5)

G. Heinzel, C. Braxmaier, R. Schilling, A. Rüdiger, D. Robertson, M. te Plate, V. Wand, K. Arai, U. Johann, and K. Danzmann, "Interferometry for the LISA technology package (LTP) aboard SMART-2," Class. Quantum Grav. 20, 153-161 (2003).
[CrossRef]

V. Wand, J. Bogenstahl, O. Braxmaier, K. Danzmann, A. García, F. Guzmán, G. Heinzel, J. Hough, O. Jennrich, C. Killow, D. Robertson, Z. Sodnik, F. Steier, and H. Ward, "Noise sources in the LTP heterodyne interferometer," Class. Quantum Grav. 23, 159-167 (2006).
[CrossRef]

G. Heinzel, V. Wand, A. Garcia, O. Jennrich, C. Braxmaier, D. Robertson, K. Middleton, D. Hoyland, A. Rüdiger, R. Schilling, U. Johann, and K. Danzmann, "The LTP interferometer and phasemeter," Class. Quantum Grav. 21, 581-587 (2004).
[CrossRef]

D. Robertson, C. Killow, H. Ward, J. Hough, G. Heinzel, A. García, V. Wand, U. Johann, and C. Braxmaier, "LTP interferometer-noise sources and performance," Class. Quantum Grav. 22, 155-163 (2005).
[CrossRef]

G. Heinzel, C. Braxmaier, M. Caldwell, K. Danzmann, F. Draaisma, A. García, J. Hough, O. Jennrich, U. Johann, C. Killow, K. Middleton, M. te Plate, D. Robertson, A. Rüdiger, R. Schilling, F. Steier, V. Wand, and H. Ward, "Successful testing of the LISA Technology Package (LTP) interferometer engineering model," Class. Quantum Grav. 22, 149-154 (2005).
[CrossRef]

J. Opt. Soc. Am. A (5)

Meas. Sci. Technol. (1)

Y. Li, Z. Zhu, and X. Li, "Elimination of reference phase errors in phase-shifting interferometry," Meas. Sci. Technol. 16, 1335-1340 (2005).
[CrossRef]

Opt. Eng. (1)

H. Zhao and G. Zhang, "Nonlinear error by orientation and elliptic polarization in a two-beam interferometer," Opt. Eng. 41, 3204-3208 (2002).
[CrossRef]

Proc. SPIE (1)

J. Millerd, N. Brock, J. Hayes, B. Kimbrough, M. Novak, M. North-Morris, and J. C. Wyant, "Modern approaches in phase measuring metrology," Proc. SPIE 5856, 14-22 (2005).
[CrossRef]

Rev. Sci. Instrum. (1)

S. Kaiser, T. Maier, A. Grossmann, and C. Zimmermann, "Fizeau interferometer for phase-shift interferometry in ultrahigh vacuum," Rev. Sci. Instrum. 72, 3726-3727 (2001).
[CrossRef]

Top. Appl. Phys. (1)

Y. Surrel, "Fringe analysis," Top. Appl. Phys. 77, 55-102 (2000).
[CrossRef]

Other (5)

A. E. Siegman, Lasers (University Science Books, 1986).

HASO II User Manual, Imagine Optic, Rue Charles de Gaulle 18, F-91400 Orsay, France.

F. Zhao, "Picometer laser metrology for the Space Interferometry Mission (SIM)," in Conference on Lasers and Electro-Optics (CLEO), Vol. 96 of Trends in Optics and Photonics Series (Optical Society of America, 2004), paper CTuo5.

XFPA-320*256 User Manual, XenICs n.v., Kapeldreef 75, B-3001 Leuven, Belgium, July 2003.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

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Figures (14)

Fig. 1
Fig. 1

(Color online) Experimental setup used for the phasemeter.

Fig. 2
Fig. 2

(Color online) Time diagram of the signals processed to trigger the CCD camera. Note that the sinusoid is measured by the SED and yields a 180° phase shift with respect to the interference pattern measured by the CCD camera.

Fig. 3
Fig. 3

(Color online) GUI programmed to display the measured data in real time.

Fig. 4
Fig. 4

(Color online) Spatial distribution of the phase.

Fig. 5
Fig. 5

(Color online) Spatial distribution of the contrast.

Fig. 6
Fig. 6

(Color online) Exposure of a dark fringe.

Fig. 7
Fig. 7

(Color online) Average intensity over four exposures.

Fig. 8
Fig. 8

(Color online) Maximum intensity over four exposures.

Fig. 9
Fig. 9

(Color online) Experimental setup with an additional lens in the path of one beam to intentionally change the curvature of its wavefront.

Fig. 10
Fig. 10

(Color online) (a) Phase front measured with a lens f = + 500   mm in one arm of the interferometer. The phase front is clearly wrapped, due to the high curvature of the wavefront being transmitted through the lens with respect to the other one. (b) Phase front obtained by postprocessing the data measured in (a) with a two-dimensional phase-unwrapping algorithm.

Fig. 11
Fig. 11

(Color online) (a) Phase front measured with a lens f = 500   mm in one arm of the interferometer. (b) Phase front obtained from postprocessing the data of (a) with a two-dimensional phase-unwrapping algorithm.

Fig. 12
Fig. 12

(Color online) (a) Phase front measured with a cylindrical lens f = + 80   mm in one arm of the interferometer. (b) Phase front obtained from postprocessing the data of (a) with a two-dimensional phase-unwrapping algorithm.

Fig. 13
Fig. 13

(Color online) Phase front measured at the engineering model of the optical bench for the LTP.

Fig. 14
Fig. 14

(Color online) Adjusted phasefront measured on a table-top Mach–Zehnder interferometer.

Tables (1)

Tables Icon

Table 1 Main Noise Sources of the Phase Measurement

Equations (17)

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E j ( r , t ) = E j p j   exp { i [ 2 π f j t + φ j + ψ j ( r ) ] } ,
I ( r , t ) = A ( r ) { 1 + C ( r ) cos [ 2 π f het t φ ( r ) ] } ,
φ ( r ) = [ φ 1 + ψ 1 ( r ) ] [ φ 2 + ψ 2 ( r ) ]
Δ L = λ 2 π ( φ 1 φ 2 ) ,
I k = I avg [ 1 + C   cos ( φ + k π 2 ) ] ,
φ γ = arctan [ I 3 ( γ ) I 1 ( γ ) I 0 ( γ ) I 2 ( γ ) ] .
a γ = I 0 ( γ ) I 2 ( γ ) ,
b γ = I 3 ( γ ) I 1 ( γ ) ,
d γ = I 0 ( γ ) + I 1 ( γ ) + I 2 ( γ ) + I 3 ( γ ) ,
C γ = 2 a γ 2 + b γ 2 d γ .
φ total = arctan ( γ b γ γ a γ ) .
C total = 2 ( γ a γ ) 2 + ( γ b γ ) 2 γ d γ .
I avg ( γ ) = d γ 4 .
τ df = 3 π / 2 φ total 2 π T het .
Δ t k = m T het + τ k ,
Δ φ rms = k ( φ I k ) 2 Δ I rms = 2 ( I 0 I 2 ) 2 + ( I 1 I 3 ) 2 Δ I rms .
Δ φ rms = 2 C Δ I rms I avg .

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