Abstract

Periodic nonlinearity (PNL) in displacement interferometers is a systematic error source that limits measurement accuracy. The PNL of coaxial heterodyne interferometers is highly influenced by the polarization state and orientation of the source frequencies. In this Letter, we investigate this error source and discuss two interferometer designs, designed at TU Delft, that showed very low levels of PNL when subjected to any polarization state and/or polarization orientation. In the experiments, quarter-wave plates (qwps) and half-wave plates (hwps) were used to manipulate the polarization state and polarization orientation, respectively. Results from a commercial coaxial system showed first-order PNL exceeding 10 nm (together with higher order PNL) when the system ceased operation at around ±15°hwp rotation or ±20°qwp rotation. The two “Delft interferometers,” however, continued operation beyond these maxima and obtained first-order PNLs in the order of several picometers, without showing higher order PNLs. The major advantage of these interferometers, beside their high linearity, is that they can be fully fiber coupled and thus allow for a modular system buildup.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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  21. Agilent Technologies interferometer E1826G (optical resolution of 4), Zeeman laser source 5517D, and phase measurement board N1225A.
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    [CrossRef]
  23. T. L. Schmitz, D. Chu, and L. Houck, Meas. Sci. Technol. 17, 3195 (2006).
    [CrossRef]
  24. C. Schluchter, V. Ganguly, D. Chu, and T. L. Schmitz, Precis. Eng. 35, 241 (2011).
    [CrossRef]
  25. Capacitive probe 2805MSE A9089 and electronic readout using MicroSense, LLC, model 4810.
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    [CrossRef]

2013 (1)

2012 (1)

C. Weichert, P. Kochert, R. Koning, J. Flugge, B. Andreas, U. Kuetgens, and A. Yacoot, Meas. Sci. Technol. 23, 094005 (2012).
[CrossRef]

2011 (2)

C. Schluchter, V. Ganguly, D. Chu, and T. L. Schmitz, Precis. Eng. 35, 241 (2011).
[CrossRef]

J. D. Ellis, A. J. H. Meskers, J. W. Spronck, and R. H. M. Schmidt, Opt. Lett. 36, 3584 (2011).
[CrossRef]

2010 (3)

K.-N. Joo, J. D. Ellis, E. S. Buice, J. W. Spronck, and R. H. M. Schmidt, Opt. Express 18, 1159 (2010).
[CrossRef]

G. M. Harry, Class. Quantum Grav. 27, 084006 (2010).
[CrossRef]

C. Wagner and N. Harned, Nat. Photonics 4, 24 (2010).
[CrossRef]

2009 (1)

2006 (2)

W. Hou, Precis. Eng. 30, 337 (2006).
[CrossRef]

T. L. Schmitz, D. Chu, and L. Houck, Meas. Sci. Technol. 17, 3195 (2006).
[CrossRef]

2003 (1)

C.-M. Wu, Opt. Commun. 215, 17 (2003).
[CrossRef]

2002 (3)

T. Schmitz and J. Beckwith, J. Mod. Opt. 49, 2105 (2002).
[CrossRef]

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 26, 448 (2002).
[CrossRef]

Th. Udem, R. Holzwarth, and T. W. Hansch, Nature 416, 233 (2002).
[CrossRef]

2000 (2)

J. Lawall and E. Kessler, Rev. Sci. Instrum. 71, 2669 (2000).
[CrossRef]

V. G. Badami and S. R. Paterson, Precis. Eng. 24, 41 (2000).
[CrossRef]

1999 (1)

1998 (1)

1992 (1)

W. Hou and G. Wilkening, Precis. Eng. 14, 91 (1992).
[CrossRef]

1989 (1)

M. Tanaka, T. Yamagami, and K. Nakayama, IEEE Trans. Instrum. Meas. 38, 552 (1989).
[CrossRef]

1987 (1)

C. Sutton, J. Phys. E 20, 1290 (1987).
[CrossRef]

1983 (1)

R. Quenelle, Hewlett Packard J. 34, 10 (1983).

1980 (1)

G. Fedotova, Meas. Tech. 23, 577 (1980).
[CrossRef]

Andreas, B.

C. Weichert, P. Kochert, R. Koning, J. Flugge, B. Andreas, U. Kuetgens, and A. Yacoot, Meas. Sci. Technol. 23, 094005 (2012).
[CrossRef]

Badami, V. G.

V. G. Badami and S. R. Paterson, Precis. Eng. 24, 41 (2000).
[CrossRef]

Beckwith, J.

T. Schmitz and J. Beckwith, J. Mod. Opt. 49, 2105 (2002).
[CrossRef]

Buice, E. S.

Chu, D.

C. Schluchter, V. Ganguly, D. Chu, and T. L. Schmitz, Precis. Eng. 35, 241 (2011).
[CrossRef]

T. L. Schmitz, D. Chu, and L. Houck, Meas. Sci. Technol. 17, 3195 (2006).
[CrossRef]

Cosijns, S. J. A. G.

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 26, 448 (2002).
[CrossRef]

Deslattes, R. D.

Ellis, J. D.

Fedotova, G.

G. Fedotova, Meas. Tech. 23, 577 (1980).
[CrossRef]

Flugge, J.

C. Weichert, P. Kochert, R. Koning, J. Flugge, B. Andreas, U. Kuetgens, and A. Yacoot, Meas. Sci. Technol. 23, 094005 (2012).
[CrossRef]

Ganguly, V.

C. Schluchter, V. Ganguly, D. Chu, and T. L. Schmitz, Precis. Eng. 35, 241 (2011).
[CrossRef]

Haitjema, H.

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 26, 448 (2002).
[CrossRef]

Hansch, T. W.

Th. Udem, R. Holzwarth, and T. W. Hansch, Nature 416, 233 (2002).
[CrossRef]

Harned, N.

C. Wagner and N. Harned, Nat. Photonics 4, 24 (2010).
[CrossRef]

Harry, G. M.

G. M. Harry, Class. Quantum Grav. 27, 084006 (2010).
[CrossRef]

Holzwarth, R.

Th. Udem, R. Holzwarth, and T. W. Hansch, Nature 416, 233 (2002).
[CrossRef]

Hou, W.

W. Hou, Precis. Eng. 30, 337 (2006).
[CrossRef]

W. Hou and G. Wilkening, Precis. Eng. 14, 91 (1992).
[CrossRef]

Houck, L.

T. L. Schmitz, D. Chu, and L. Houck, Meas. Sci. Technol. 17, 3195 (2006).
[CrossRef]

Joo, K.-N.

Kessler, E.

J. Lawall and E. Kessler, Rev. Sci. Instrum. 71, 2669 (2000).
[CrossRef]

Kochert, P.

C. Weichert, P. Kochert, R. Koning, J. Flugge, B. Andreas, U. Kuetgens, and A. Yacoot, Meas. Sci. Technol. 23, 094005 (2012).
[CrossRef]

Koning, R.

C. Weichert, P. Kochert, R. Koning, J. Flugge, B. Andreas, U. Kuetgens, and A. Yacoot, Meas. Sci. Technol. 23, 094005 (2012).
[CrossRef]

Kuetgens, U.

C. Weichert, P. Kochert, R. Koning, J. Flugge, B. Andreas, U. Kuetgens, and A. Yacoot, Meas. Sci. Technol. 23, 094005 (2012).
[CrossRef]

Lawall, J.

J. Lawall and E. Kessler, Rev. Sci. Instrum. 71, 2669 (2000).
[CrossRef]

Meskers, A. J. H.

Nakayama, K.

M. Tanaka, T. Yamagami, and K. Nakayama, IEEE Trans. Instrum. Meas. 38, 552 (1989).
[CrossRef]

Paterson, S. R.

V. G. Badami and S. R. Paterson, Precis. Eng. 24, 41 (2000).
[CrossRef]

Quenelle, R.

R. Quenelle, Hewlett Packard J. 34, 10 (1983).

Schellekens, P. H. J.

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 26, 448 (2002).
[CrossRef]

Schluchter, C.

C. Schluchter, V. Ganguly, D. Chu, and T. L. Schmitz, Precis. Eng. 35, 241 (2011).
[CrossRef]

Schmidt, R. H. M.

Schmitz, T.

T. Schmitz and J. Beckwith, J. Mod. Opt. 49, 2105 (2002).
[CrossRef]

Schmitz, T. L.

C. Schluchter, V. Ganguly, D. Chu, and T. L. Schmitz, Precis. Eng. 35, 241 (2011).
[CrossRef]

T. L. Schmitz, D. Chu, and L. Houck, Meas. Sci. Technol. 17, 3195 (2006).
[CrossRef]

Spronck, J. W.

Sutton, C.

C. Sutton, J. Phys. E 20, 1290 (1987).
[CrossRef]

Tanaka, M.

M. Tanaka, T. Yamagami, and K. Nakayama, IEEE Trans. Instrum. Meas. 38, 552 (1989).
[CrossRef]

Udem, Th.

Th. Udem, R. Holzwarth, and T. W. Hansch, Nature 416, 233 (2002).
[CrossRef]

van Kan, P. J. M.

Voigt, D.

Wagner, C.

C. Wagner and N. Harned, Nat. Photonics 4, 24 (2010).
[CrossRef]

Weichert, C.

C. Weichert, P. Kochert, R. Koning, J. Flugge, B. Andreas, U. Kuetgens, and A. Yacoot, Meas. Sci. Technol. 23, 094005 (2012).
[CrossRef]

Wilkening, G.

W. Hou and G. Wilkening, Precis. Eng. 14, 91 (1992).
[CrossRef]

Wu, C.

Wu, C.-M.

Yacoot, A.

C. Weichert, P. Kochert, R. Koning, J. Flugge, B. Andreas, U. Kuetgens, and A. Yacoot, Meas. Sci. Technol. 23, 094005 (2012).
[CrossRef]

Yamagami, T.

M. Tanaka, T. Yamagami, and K. Nakayama, IEEE Trans. Instrum. Meas. 38, 552 (1989).
[CrossRef]

Appl. Opt. (2)

Class. Quantum Grav. (1)

G. M. Harry, Class. Quantum Grav. 27, 084006 (2010).
[CrossRef]

Hewlett Packard J. (1)

R. Quenelle, Hewlett Packard J. 34, 10 (1983).

IEEE Trans. Instrum. Meas. (1)

M. Tanaka, T. Yamagami, and K. Nakayama, IEEE Trans. Instrum. Meas. 38, 552 (1989).
[CrossRef]

J. Mod. Opt. (1)

T. Schmitz and J. Beckwith, J. Mod. Opt. 49, 2105 (2002).
[CrossRef]

J. Phys. E (1)

C. Sutton, J. Phys. E 20, 1290 (1987).
[CrossRef]

Meas. Sci. Technol. (2)

C. Weichert, P. Kochert, R. Koning, J. Flugge, B. Andreas, U. Kuetgens, and A. Yacoot, Meas. Sci. Technol. 23, 094005 (2012).
[CrossRef]

T. L. Schmitz, D. Chu, and L. Houck, Meas. Sci. Technol. 17, 3195 (2006).
[CrossRef]

Meas. Tech. (1)

G. Fedotova, Meas. Tech. 23, 577 (1980).
[CrossRef]

Nat. Photonics (1)

C. Wagner and N. Harned, Nat. Photonics 4, 24 (2010).
[CrossRef]

Nature (1)

Th. Udem, R. Holzwarth, and T. W. Hansch, Nature 416, 233 (2002).
[CrossRef]

Opt. Commun. (1)

C.-M. Wu, Opt. Commun. 215, 17 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Precis. Eng. (5)

V. G. Badami and S. R. Paterson, Precis. Eng. 24, 41 (2000).
[CrossRef]

C. Schluchter, V. Ganguly, D. Chu, and T. L. Schmitz, Precis. Eng. 35, 241 (2011).
[CrossRef]

W. Hou, Precis. Eng. 30, 337 (2006).
[CrossRef]

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 26, 448 (2002).
[CrossRef]

W. Hou and G. Wilkening, Precis. Eng. 14, 91 (1992).
[CrossRef]

Rev. Sci. Instrum. (1)

J. Lawall and E. Kessler, Rev. Sci. Instrum. 71, 2669 (2000).
[CrossRef]

Other (3)

Spatial heterodyne frequency generation Delft system: Thorlabs stabilized He–Ne laser HRS015, ISOMET acousto-optic modulators OAM 1141-T40-2 and drivers 531C-L (39 and 41 MHz), and phase measurement readout according to Agilent Technologies phase measurement board N1225A.

Agilent Technologies interferometer E1826G (optical resolution of 4), Zeeman laser source 5517D, and phase measurement board N1225A.

Capacitive probe 2805MSE A9089 and electronic readout using MicroSense, LLC, model 4810.

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Figures (3)

Fig. 1.
Fig. 1.

Demonstration of digital PNL compensation in open air, using an Agilent interferometer system [21]. The results show the amplitudes of first-order PNL over “fringe order” [Eq. (1)], calculated by an FFT performed on displacement data of a mirror mounted on an Aerotech stage (ABL10100LT), displacing at a constant velocity of 0.5mm/s. Compensation is (a) OFF and (b) ON, demonstrating a PNL reduction factor of 75.

Fig. 2.
Fig. 2.

(a) Experimental setup overview; two interferometers measure target displacement simultaneously. A capacitive probe [25] is used for vibration analysis of the stage’s motion. On the left either the Delft-CC or Delft-PM interferometer is included (together with [20]), while on the right one finds a commercial (coaxial) interferometer system [21]. The optical pathways of the (b) Delft-CC and (c) Delft-PM interferometers are shown. fx, source frequency; PDx, photodetector; pol, polarizer; nbs, neutral beam splitter; pbs, polarized beam splitter; qwp, quarter wave plate; cc, corner cube mirror; CC, corner cube target mirror; PM, plane target mirror; wplx, waveplate. Note that the two Delft interferometers consist of separate optical components, whereas the commercial interferometer [21] is an optical monolith.

Fig. 3.
Fig. 3.

Measurement results showing PNL amplitudes of three interferometers. (a) Both source frequencies were rotated (coaxial beam) using a hwp; (c), (d) only f1 was rotated. (b) For both source frequencies, their linear polarization states were transformed from linearly polarized toward left and right circularly polarized; (e), (f) this was only done for f1 (i.e., f2 remained linear). (g), (h) The polarization state of f1 was manipulated again from linearly polarized to left- and right-circularly polarized, while f2 was kept continuously circularly polarized. Note that below noise level indicates that no PNL was observed.

Equations (1)

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fPNL=(k·N·vtarget)/λ,

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