Abstract

Displacement interferometry is widely used for accurately characterizing nanometer and subnanometer displacements in many applications. In many modern systems, fiber delivery is desired to limit optical alignment and remove heat sources from the system, but fiber delivery can exacerbate common interferometric measurement problems, such as periodic nonlinearity, and account for fiber-induced drift. In this Letter, we describe a novel, general Joo-type interferometer that inherently has an optical reference after any fiber delivery that eliminates fiber-induced drift. This interferometer demonstrated no detectable periodic nonlinearity in both free-space and fiber-delivered variants.

© 2011 Optical Society of America

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2010

2009

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

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

2008

D. Ren, K. M. Lawton, and J. A. Miller, Meas. Sci. Technol. 19, 025303 (2008).
[CrossRef]

2005

C. Evans, M. Holmes, F. Demarest, D. Newton, and A. Stein, CIRP Ann. 54, 495 (2005).
[CrossRef]

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, Rev. Sci. Instrum. 76, 055110 (2005).
[CrossRef]

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

2002

2000

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

1999

1998

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

1995

J. M. De Freitas and M. A. Player, J. Mod. Opt. 42, 1875 (1995).
[CrossRef]

1994

J. Bryan, D. Carter, and S. Thompson, CIRP Ann. 43, 453 (1994).
[CrossRef]

1993

N. Bobroff, Meas. Sci. Technol. 4, 907 (1993).
[CrossRef]

1992

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

N. P. Cooper and W. S. Rhode, Hearing Res. 63, 163(1992).
[CrossRef]

1990

S. W. P. van Sterkenburg, T. Kwaaitaal, and W. M. M. M. van den Eijnden, Rev. Sci. Instrum. 61, 2318 (1990).
[CrossRef]

1985

1983

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

Beckwith, J.

H. S. Kim, T. Schmitz, and J. Beckwith, J. Opt. Res. 11, 213 (2010).

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

Biegen, J.

Bobroff, N.

N. Bobroff, Meas. Sci. Technol. 4, 907 (1993).
[CrossRef]

Braxmaier, C.

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

Bryan, J.

J. Bryan, D. Carter, and S. Thompson, CIRP Ann. 43, 453 (1994).
[CrossRef]

Buice, E. S.

Carter, D.

J. Bryan, D. Carter, and S. Thompson, CIRP Ann. 43, 453 (1994).
[CrossRef]

Clark, J.

Cooper, N. P.

N. P. Cooper and W. S. Rhode, Hearing Res. 63, 163(1992).
[CrossRef]

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 Freitas, J. M.

J. M. De Freitas and M. A. Player, J. Mod. Opt. 42, 1875 (1995).
[CrossRef]

de Groot, P.

de Lega, X. C.

Demarest, F.

C. Evans, M. Holmes, F. Demarest, D. Newton, and A. Stein, CIRP Ann. 54, 495 (2005).
[CrossRef]

Demarest, F. C.

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

Deslattes, R. D.

Deutsch, B.

A. Mitra, B. Deutsch, F. Ignatovich, C. Dykes, and L. Novotny, ACS Nano 4, 1305 (2010).
[CrossRef] [PubMed]

Dykes, C.

A. Mitra, B. Deutsch, F. Ignatovich, C. Dykes, and L. Novotny, ACS Nano 4, 1305 (2010).
[CrossRef] [PubMed]

Ellis, J. D.

Estler, W. T.

Evans, C.

C. Evans, M. Holmes, F. Demarest, D. Newton, and A. Stein, CIRP Ann. 54, 495 (2005).
[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]

Holmes, M.

C. Evans, M. Holmes, F. Demarest, D. Newton, and A. Stein, CIRP Ann. 54, 495 (2005).
[CrossRef]

Hou, W.

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

Hsu, C.-C.

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, Rev. Sci. Instrum. 76, 055110 (2005).
[CrossRef]

Hsu, T.-H.

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, Rev. Sci. Instrum. 76, 055110 (2005).
[CrossRef]

Ignatovich, F.

A. Mitra, B. Deutsch, F. Ignatovich, C. Dykes, and L. Novotny, ACS Nano 4, 1305 (2010).
[CrossRef] [PubMed]

Johann, U.

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

Joo, K.

Jywe, W.-Y.

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, Rev. Sci. Instrum. 76, 055110 (2005).
[CrossRef]

Kessler, E.

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

Kim, H. S.

H. S. Kim, T. Schmitz, and J. Beckwith, J. Opt. Res. 11, 213 (2010).

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]

Kwaaitaal, T.

S. W. P. van Sterkenburg, T. Kwaaitaal, and W. M. M. M. van den Eijnden, Rev. Sci. Instrum. 61, 2318 (1990).
[CrossRef]

Lawall, J.

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

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

Lawton, K. M.

D. Ren, K. M. Lawton, and J. A. Miller, Meas. Sci. Technol. 19, 025303 (2008).
[CrossRef]

Liu, C.-H.

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, Rev. Sci. Instrum. 76, 055110 (2005).
[CrossRef]

Miller, J. A.

D. Ren, K. M. Lawton, and J. A. Miller, Meas. Sci. Technol. 19, 025303 (2008).
[CrossRef]

Mitra, A.

A. Mitra, B. Deutsch, F. Ignatovich, C. Dykes, and L. Novotny, ACS Nano 4, 1305 (2010).
[CrossRef] [PubMed]

Newton, D.

C. Evans, M. Holmes, F. Demarest, D. Newton, and A. Stein, CIRP Ann. 54, 495 (2005).
[CrossRef]

Novotny, L.

A. Mitra, B. Deutsch, F. Ignatovich, C. Dykes, and L. Novotny, ACS Nano 4, 1305 (2010).
[CrossRef] [PubMed]

Peters, A.

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

Player, M. A.

J. M. De Freitas and M. A. Player, J. Mod. Opt. 42, 1875 (1995).
[CrossRef]

Quenelle, R. C.

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

Ren, D.

D. Ren, K. M. Lawton, and J. A. Miller, Meas. Sci. Technol. 19, 025303 (2008).
[CrossRef]

Rhode, W. S.

N. P. Cooper and W. S. Rhode, Hearing Res. 63, 163(1992).
[CrossRef]

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. Munnig

Schmitz, T.

H. S. Kim, T. Schmitz, and J. Beckwith, J. Opt. Res. 11, 213 (2010).

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

Stein, A.

C. Evans, M. Holmes, F. Demarest, D. Newton, and A. Stein, CIRP Ann. 54, 495 (2005).
[CrossRef]

Thompson, S.

J. Bryan, D. Carter, and S. Thompson, CIRP Ann. 43, 453 (1994).
[CrossRef]

van den Eijnden, W. M. M. M.

S. W. P. van Sterkenburg, T. Kwaaitaal, and W. M. M. M. van den Eijnden, Rev. Sci. Instrum. 61, 2318 (1990).
[CrossRef]

van Kan, P. J. M.

van Sterkenburg, S. W. P.

S. W. P. van Sterkenburg, T. Kwaaitaal, and W. M. M. M. van den Eijnden, Rev. Sci. Instrum. 61, 2318 (1990).
[CrossRef]

Weise, D.

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

Wilkening, G.

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

Wu, C.

ACS Nano

A. Mitra, B. Deutsch, F. Ignatovich, C. Dykes, and L. Novotny, ACS Nano 4, 1305 (2010).
[CrossRef] [PubMed]

Appl. Opt.

CIRP Ann.

J. Bryan, D. Carter, and S. Thompson, CIRP Ann. 43, 453 (1994).
[CrossRef]

C. Evans, M. Holmes, F. Demarest, D. Newton, and A. Stein, CIRP Ann. 54, 495 (2005).
[CrossRef]

Class. Quantum Grav.

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

Hearing Res.

N. P. Cooper and W. S. Rhode, Hearing Res. 63, 163(1992).
[CrossRef]

Hewlett-Packard J.

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

J. Mod. Opt.

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

J. M. De Freitas and M. A. Player, J. Mod. Opt. 42, 1875 (1995).
[CrossRef]

J. Opt. Res.

H. S. Kim, T. Schmitz, and J. Beckwith, J. Opt. Res. 11, 213 (2010).

Meas. Sci. Technol.

N. Bobroff, Meas. Sci. Technol. 4, 907 (1993).
[CrossRef]

D. Ren, K. M. Lawton, and J. A. Miller, Meas. Sci. Technol. 19, 025303 (2008).
[CrossRef]

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

Opt. Express

Opt. Lett.

Precis. Eng.

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

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

Rev. Sci. Instrum.

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

C.-H. Liu, W.-Y. Jywe, C.-C. Hsu, and T.-H. Hsu, Rev. Sci. Instrum. 76, 055110 (2005).
[CrossRef]

S. W. P. van Sterkenburg, T. Kwaaitaal, and W. M. M. M. van den Eijnden, Rev. Sci. Instrum. 61, 2318 (1990).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Schematic of the general Joo-type interferometer with the same measurement target footprint as a traditional plane mirror interferometer. The two spatially separated input beams have a slight optical frequency difference and varying phases due to fiber-induced Doppler shifts. No beam overlaps occur until the final interfering surface.

Fig. 2
Fig. 2

Two AOMs driven at slightly different frequencies frequency modulate an optical beam from a stabilized source. Prior to fiber coupling into PM fibers, parts of each beam are split and combined to generate an optical reference.

Fig. 3
Fig. 3

Linear displacement of 10 μm comparing the free space (FS) and fiber-coupled (PM) general Joo-type interferometer. Using a reference prior to the fiber delivery causes micrometer-level errors from fiber thermal expansion, while using a reference postfiber eliminates fiber-induced errors. The FS and PM measurements are offset for clarity, and the peak dwell time differs by 1 s .

Fig. 4
Fig. 4

Comparison of displacement errors after detrending for four linear displacements in the (a) frequency and (b) spatial frequency domains. A large error source is at 34 Hz in (a), which is attributed to the laboratory environment and also apparent in other measurement systems. In the spatial frequency domain, no peaks are observed at the first and second fringe orders, demonstrating no detectable periodic nonlinearity for both the free-space- and fiber-delivered measurements.

Equations (6)

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

I o cos ( 2 π f 1 t ) cos ( 2 π f 2 t ) ,
I r cos ( 2 π f 2 t + θ 2 + θ r ) cos ( 2 π f 1 t + θ 1 + δ 1 ) ,
I m cos ( 2 π f 1 t + θ 1 + θ m ) cos ( 2 π f 2 t + θ 2 + δ 2 ) ,
I o cos ( 2 π f s t ) ,
I r cos ( 2 π f s t + θ 1 θ 2 θ r + δ 1 ) ,
I m cos ( 2 π f s t + θ 1 θ 2 + θ m δ 2 ) ,

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