Abstract

The use of optical fibers presents several advantages with respect to free-space optical transport regarding source-frequency delivery to individual heterodyne interferometers. Unfortunately, fiber delivery to individual coaxial heterodyne interferometers leads to an increase of (periodic) nonlinearity in the measurement, because transporting coaxial frequencies through one optical fiber leads to frequency mixing. Coaxial beams thus require delivery via free-space transportation methods. In contrast, the heterodyne interferometer concept discussed in this Letter is based on separated source frequencies, which allow for fiber delivery without additional nonlinearity. This investigation analyzes the influence of external disturbances acting on the two fibers during delivery, causing asymmetry in phase between the two fibers (first-order effect), and irradiance fluctuations (second-order effect). Experiments using electro-optic phase modulation and acousto-optic irradiance modulation confirmed that the interferometer-concept can measure with sub-nanometer uncertainty using fiber delivered source frequencies, enabling fully fiber-coupled heterodyne displacement interferometers.

© 2014 Optical Society of America

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2014 (1)

2012 (1)

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

2011 (1)

2009 (2)

K.-N. Joo, J. D. Ellis, J. W. Spronck, P. J. M. van Kan, and R. H. M. Schmidt, Opt. Lett. 34, 386 (2009).
[CrossRef]

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, Class. Quantum Grav. 26, 085008 (2009).
[CrossRef]

2005 (1)

B. A. W. H. Knarren, S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 29, 229 (2005).
[CrossRef]

2003 (1)

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

2002 (2)

2000 (1)

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

1999 (1)

1998 (2)

C. Wu and R. D. Deslattes, Appl. Opt. 37, 6696 (1998).
[CrossRef]

F. C. Demarest, Meas. Sci. Technol. 9, 1024C (1998).
[CrossRef]

1994 (1)

J. Schneir, T. McWaid, J. Alexander, and B. Wilfley, J. Vac. Sci. Technol. B 12, 3561 (1994).
[CrossRef]

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. Sci. Technol. 23, 577 (1980).
[CrossRef]

Alexander, J.

J. Schneir, T. McWaid, J. Alexander, and B. Wilfley, J. Vac. Sci. Technol. B 12, 3561 (1994).
[CrossRef]

Andreas, B.

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

Beckwith, J.

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

Biegen, J.

Braxmaier, C.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, Class. Quantum Grav. 26, 085008 (2009).
[CrossRef]

Clark, J.

Colonna de Lega, X.

Cosijns, S. J. A. G.

B. A. W. H. Knarren, S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 29, 229 (2005).
[CrossRef]

de Groot, P.

Demarest, F. C.

F. C. Demarest, Meas. Sci. Technol. 9, 1024C (1998).
[CrossRef]

Deslattes, R. D.

Ellis, J. D.

Fedotova, G.

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

Flügge, J.

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

Gohlke, M.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, Class. Quantum Grav. 26, 085008 (2009).
[CrossRef]

Grigg, D.

Haitjema, H.

B. A. W. H. Knarren, S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 29, 229 (2005).
[CrossRef]

Hou, W.

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

Johann, U.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, Class. Quantum Grav. 26, 085008 (2009).
[CrossRef]

Joo, K.-N.

Kessler, E.

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

Knarren, B. A. W. H.

B. A. W. H. Knarren, S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 29, 229 (2005).
[CrossRef]

Köchert, P.

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

Köning, R.

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

Kuetgens, U.

C. Weichert, P. Köchert, R. Köning, J. Flügge, 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]

C.-M. Wu, J. Lawall, and R. D. Deslattes, Appl. Opt. 38, 4089 (1999).
[CrossRef]

McWaid, T.

J. Schneir, T. McWaid, J. Alexander, and B. Wilfley, J. Vac. Sci. Technol. B 12, 3561 (1994).
[CrossRef]

Meskers, A. J. H.

Munnig Schmidt, R. H.

Nakayama, K.

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

Peters, A.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, Class. Quantum Grav. 26, 085008 (2009).
[CrossRef]

Quenelle, R.

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

Schellekens, P. H. J.

B. A. W. H. Knarren, S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 29, 229 (2005).
[CrossRef]

Schmidt, R. H. M.

Schmitz, T.

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

Schneir, J.

J. Schneir, T. McWaid, J. Alexander, and B. Wilfley, J. Vac. Sci. Technol. B 12, 3561 (1994).
[CrossRef]

Schuldt, T.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, Class. Quantum Grav. 26, 085008 (2009).
[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]

van Kan, P. J. M.

Weichert, C.

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

Weise, D.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, Class. Quantum Grav. 26, 085008 (2009).
[CrossRef]

Wilfley, B.

J. Schneir, T. McWaid, J. Alexander, and B. Wilfley, J. Vac. Sci. Technol. B 12, 3561 (1994).
[CrossRef]

Wilkening, G.

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

Wu, C.

Wu, C.-M.

Yacoot, A.

C. Weichert, P. Köchert, R. Köning, J. Flügge, 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. (3)

Class. Quantum Grav. (1)

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, Class. Quantum Grav. 26, 085008 (2009).
[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]

J. Vac. Sci. Technol. B (1)

J. Schneir, T. McWaid, J. Alexander, and B. Wilfley, J. Vac. Sci. Technol. B 12, 3561 (1994).
[CrossRef]

Meas. Sci. Technol. (3)

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

F. C. Demarest, Meas. Sci. Technol. 9, 1024C (1998).
[CrossRef]

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

Opt. Commun. (1)

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

Opt. Lett. (3)

Precis. Eng. (2)

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

B. A. W. H. Knarren, S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, Precis. Eng. 29, 229 (2005).
[CrossRef]

Rev. Sci. Instrum. (1)

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

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Figures (3)

Fig. 1.
Fig. 1.

(a) In a free-space system, a coaxial beam (purple) is delivered to interferometers (i) inside a host system to measure stage displacement, using mirrors (m), and a beam splitter (s). (b) A more practical commercial system layout as is found in current lithography machines uses optical-fiber delivery, in which the two source frequencies are coaxially combined by a remote optical combiner (roc), resulting in a free-space beam. (c) The most practical system consists of fully fiber-coupled interferometers, easing system integration. An asterisk denotes the generation of a reference signal. Note that transport of interference signals from interferometers is less stringent and has already proven itself using optical fibers and external readout (not shown).

Fig. 2.
Fig. 2.

(a) Schematic of the experimental setup where an eom introduces a relative phase difference φeom, between f1 and f2. The half wave plate (hwp) in front of the eom is used for adjusting the polarization alignment between f2 and the eom crystal. (b), (c) Optical pathways of respectively f1 and f2 through the interferometer (dotted lines denote beams in the lower plane whereas solid lines are beams in the upper plane, see also [15,16]). Note that the tested interferometer was not a monolithic structure as suggested. Legend: aomx, acousto-optic modulator; fx, frequency; bs, beam sampler; rb, rhomboid; PDx, photodetector; m, mirror; nbs neutral beam splitter, pbs, polarizing beam splitter; ccx, cube corner reflector; qwp, quarter wave plate; and m′, target mirror.

Fig. 3.
Fig. 3.

(a) The eom has a phase modulation depth of 95° nm (170 nm) at feom=5kHz, which is present in the output of the classical interferometer, 170nm (red), while it is absent in the output of the Delft interferometer (blue). (b) Close-up of the result of (a), showing a residual error of 0.03nm. (c) The residual is affected by polarization misalignment between f2 and the eom crystal, which causes both an additional interference signal and a modulation of the irradiance. (d) Influence of irradiance modulation was analyzed by amplitude modulation of aom2 at 50% of the maximum irradiance (15μW interference signal strength at detectors PD3,4), with the eom switched off and the hwp at the position as was used for generating the results illustrated in (a).

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

J1=E1·[01]ei(ω1t+θ),
J2=E2·[01]ei(ω2t+φ),
IPD1J1·J2,
IPD1E1E2ei({ω2ω1}t+φθ).
φeom=Acos(ωeomt),
IPD2E1E2ei({ω2ω1}t+φ+φeomθ),
IPD3E1E2ei({ω2ω1}t+φ+φeom+φcc1θθcc3θm),
IPD4E1E2ei({ω2ω1}t+φ+φeom+φcc3+φmθθcc2).
IclassicalE1E2ei[({ω2ω1}t+φ+φeomθ)({ω2ω1}t+φθ)],
IclassicalE1E2ei(φeom).
IDelftE1E2ei[({ω2ω1}t+φ+φeom+φcc3+φmθθcc2)({ω2ω1}t+φ+φeom+φcc1θθcc3θm)],
IDelftE1E2ei(φcc3φcc1θcc2+θcc3+(φm+θm)).

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