Abstract

Many error sources can affect the accuracy of displacement measuring interferometer systems. In heterodyne interferometry two laser source frequencies constitute the finally detected wavefront. When the wavefronts of these source frequencies are non-ideal and one of them walks off the detector, the shape of the detected wavefront will vary. This leads to a change in measured phase at the detector resulting in increased measurement uncertainty. A new wavefront measurement tool described in this publication measures the relative phase difference between the two wavefronts of the two source frequencies of a coaxial heterodyne laser source as used in commercial heterodyne interferometer systems. The proposed measurement method uses standard commercial optics and operates with the same phase measurement equipment that is normally used for heterodyne displacement interferometry. In the presented method a bare tip of a multimode fiber represents the receiving detection aperture and is used for locally sampling the wavefront during a line scan. The difference in phase between the beating frequency of the scanning fiber and a reference beating frequency that results from integration over the entire beam, is used for the reconstruction of the wavefront. The method shows to have a phase resolution in the order of ~25 pm or ~λ/25000 for λ 632.8 nm, and a spatial resolution of ~60 µm at a repeatability better than 1 nm over one week.

© 2013 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol.4(9), 907–926 (1993).
    [CrossRef]
  2. F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol.9(7), 1024 (1998).
    [CrossRef]
  3. A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
    [CrossRef] [PubMed]
  4. K. Danzmann and L. I. S. A. team, “LISA: laser interferometer space antenna for gravitational wave measurements,” Class. Quantum Gravity13(11A), A247–A250 (1996).
    [CrossRef]
  5. T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gravity26(8), 085008 (2009).
    [CrossRef]
  6. H.-J. Butt, B. Cappella, and M. Kappl, “Force measurements with the atomic force microscope: Technique, interpretation and applications,” Surf. Sci. Rep.59(1-6), 1–152 (2005).
    [CrossRef]
  7. J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the Orbital Angular Momentum of a Single Photon,” Phys. Rev. Lett.88(25), 257901 (2002).
    [CrossRef] [PubMed]
  8. P. de Groot, J. Biegen, J. Clark, X. C. de Lega, and D. Grigg, “Optical interferometry for measurement of the geometric dimensions of industrial parts,” Appl. Opt.41(19), 3853–3860 (2002).
    [CrossRef] [PubMed]
  9. S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng.26(4), 448–455 (2002).
    [CrossRef]
  10. W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng.14(2), 91–98 (1992).
    [CrossRef]
  11. J. M. De Freitas and M. A. Player, “Polarization effects in heterodyne interferometry,” J. Mod. Opt.42(9), 1875–1899 (1995).
    [CrossRef]
  12. K. N. Joo, J. D. Ellis, E. S. Buice, J. W. Spronck, and R. H. Schmidt, “High resolution heterodyne interferometer without detectable periodic nonlinearity,” Opt. Express18(2), 1159–1165 (2010).
    [CrossRef] [PubMed]
  13. J. D. Ellis, A. J. H. Meskers, J. W. Spronck, and R. H. Munnig Schmidt, “Fiber-coupled displacement interferometry without periodic nonlinearity,” Opt. Lett.36(18), 3584–3586 (2011).
    [CrossRef] [PubMed]
  14. G. Mana, “Diffraction Effects in Optical Interferometers Illuminated by Laser Sources,” Metrologia26(2), 87–93 (1989).
    [CrossRef]
  15. K. Dorenwendt and G. Bönsch, “Über den EinfluB der Beugung auf die interferentielle Längenmessung,” Metrologia12(2), 57–60 (1976).
    [CrossRef]
  16. A. Chernyshov, U. Sterr, F. Riehle, J. Helmcke, and J. Pfund, “Calibration of a Shack-Hartmann sensor for absolute measurements of wavefronts,” Appl. Opt.44(30), 6419–6425 (2005).
    [CrossRef] [PubMed]
  17. A. F. Brooks, T. L. Kelly, P. J. Veitch, and J. Munch, “Ultra-sensitive wavefront measurement using a Hartmann sensor,” Opt. Express15(16), 10370–10375 (2007).
    [CrossRef] [PubMed]
  18. H. Medecki, E. Tejnil, K. A. Goldberg, and J. Bokor, “Phase-shifting point diffraction interferometer,” Opt. Lett.21(19), 1526–1528 (1996).
    [CrossRef] [PubMed]
  19. G. R. Brady, M. Guizar-Sicairos, and J. R. Fienup, “Optical wavefront measurement using phase retrieval with transverse translation diversity,” Opt. Express17(2), 624–639 (2009).
    [CrossRef] [PubMed]

2011 (1)

2010 (1)

2009 (2)

G. R. Brady, M. Guizar-Sicairos, and J. R. Fienup, “Optical wavefront measurement using phase retrieval with transverse translation diversity,” Opt. Express17(2), 624–639 (2009).
[CrossRef] [PubMed]

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gravity26(8), 085008 (2009).
[CrossRef]

2007 (1)

2005 (2)

A. Chernyshov, U. Sterr, F. Riehle, J. Helmcke, and J. Pfund, “Calibration of a Shack-Hartmann sensor for absolute measurements of wavefronts,” Appl. Opt.44(30), 6419–6425 (2005).
[CrossRef] [PubMed]

H.-J. Butt, B. Cappella, and M. Kappl, “Force measurements with the atomic force microscope: Technique, interpretation and applications,” Surf. Sci. Rep.59(1-6), 1–152 (2005).
[CrossRef]

2002 (3)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the Orbital Angular Momentum of a Single Photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

P. de Groot, J. Biegen, J. Clark, X. C. de Lega, and D. Grigg, “Optical interferometry for measurement of the geometric dimensions of industrial parts,” Appl. Opt.41(19), 3853–3860 (2002).
[CrossRef] [PubMed]

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng.26(4), 448–455 (2002).
[CrossRef]

1998 (1)

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol.9(7), 1024 (1998).
[CrossRef]

1996 (2)

K. Danzmann and L. I. S. A. team, “LISA: laser interferometer space antenna for gravitational wave measurements,” Class. Quantum Gravity13(11A), A247–A250 (1996).
[CrossRef]

H. Medecki, E. Tejnil, K. A. Goldberg, and J. Bokor, “Phase-shifting point diffraction interferometer,” Opt. Lett.21(19), 1526–1528 (1996).
[CrossRef] [PubMed]

1995 (1)

J. M. De Freitas and M. A. Player, “Polarization effects in heterodyne interferometry,” J. Mod. Opt.42(9), 1875–1899 (1995).
[CrossRef]

1993 (1)

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol.4(9), 907–926 (1993).
[CrossRef]

1992 (2)

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng.14(2), 91–98 (1992).
[CrossRef]

1989 (1)

G. Mana, “Diffraction Effects in Optical Interferometers Illuminated by Laser Sources,” Metrologia26(2), 87–93 (1989).
[CrossRef]

1976 (1)

K. Dorenwendt and G. Bönsch, “Über den EinfluB der Beugung auf die interferentielle Längenmessung,” Metrologia12(2), 57–60 (1976).
[CrossRef]

Abramovici, A.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Althouse, W. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Barnett, S. M.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the Orbital Angular Momentum of a Single Photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

Biegen, J.

Bobroff, N.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol.4(9), 907–926 (1993).
[CrossRef]

Bokor, J.

Bönsch, G.

K. Dorenwendt and G. Bönsch, “Über den EinfluB der Beugung auf die interferentielle Längenmessung,” Metrologia12(2), 57–60 (1976).
[CrossRef]

Brady, G. R.

Braxmaier, C.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gravity26(8), 085008 (2009).
[CrossRef]

Brooks, A. F.

Buice, E. S.

Butt, H.-J.

H.-J. Butt, B. Cappella, and M. Kappl, “Force measurements with the atomic force microscope: Technique, interpretation and applications,” Surf. Sci. Rep.59(1-6), 1–152 (2005).
[CrossRef]

Cappella, B.

H.-J. Butt, B. Cappella, and M. Kappl, “Force measurements with the atomic force microscope: Technique, interpretation and applications,” Surf. Sci. Rep.59(1-6), 1–152 (2005).
[CrossRef]

Chernyshov, A.

Clark, J.

Cosijns, S. J. A. G.

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng.26(4), 448–455 (2002).
[CrossRef]

Courtial, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the Orbital Angular Momentum of a Single Photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

Danzmann, K.

K. Danzmann and L. I. S. A. team, “LISA: laser interferometer space antenna for gravitational wave measurements,” Class. Quantum Gravity13(11A), A247–A250 (1996).
[CrossRef]

De Freitas, J. M.

J. M. De Freitas and M. A. Player, “Polarization effects in heterodyne interferometry,” J. Mod. Opt.42(9), 1875–1899 (1995).
[CrossRef]

de Groot, P.

de Lega, X. C.

Demarest, F. C.

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol.9(7), 1024 (1998).
[CrossRef]

Dorenwendt, K.

K. Dorenwendt and G. Bönsch, “Über den EinfluB der Beugung auf die interferentielle Längenmessung,” Metrologia12(2), 57–60 (1976).
[CrossRef]

Drever, R. W. P.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Ellis, J. D.

Fienup, J. R.

Franke-Arnold, S.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the Orbital Angular Momentum of a Single Photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

Gohlke, M.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gravity26(8), 085008 (2009).
[CrossRef]

Goldberg, K. A.

Grigg, D.

Guizar-Sicairos, M.

Gürsel, Y.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Haitjema, H.

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng.26(4), 448–455 (2002).
[CrossRef]

Helmcke, J.

Hou, W.

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng.14(2), 91–98 (1992).
[CrossRef]

Johann, U.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gravity26(8), 085008 (2009).
[CrossRef]

Joo, K. N.

Kappl, M.

H.-J. Butt, B. Cappella, and M. Kappl, “Force measurements with the atomic force microscope: Technique, interpretation and applications,” Surf. Sci. Rep.59(1-6), 1–152 (2005).
[CrossRef]

Kawamura, S.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Kelly, T. L.

Leach, J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the Orbital Angular Momentum of a Single Photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

Mana, G.

G. Mana, “Diffraction Effects in Optical Interferometers Illuminated by Laser Sources,” Metrologia26(2), 87–93 (1989).
[CrossRef]

Medecki, H.

Meskers, A. J. H.

Munch, J.

Munnig Schmidt, R. H.

Padgett, M. J.

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the Orbital Angular Momentum of a Single Photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

Peters, A.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gravity26(8), 085008 (2009).
[CrossRef]

Pfund, J.

Player, M. A.

J. M. De Freitas and M. A. Player, “Polarization effects in heterodyne interferometry,” J. Mod. Opt.42(9), 1875–1899 (1995).
[CrossRef]

Raab, F. J.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Riehle, F.

Schellekens, P. H. J.

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng.26(4), 448–455 (2002).
[CrossRef]

Schmidt, R. H.

Schuldt, T.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gravity26(8), 085008 (2009).
[CrossRef]

Shoemaker, D.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Sievers, L.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Spero, R. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Spronck, J. W.

Sterr, U.

team, L. I. S. A.

K. Danzmann and L. I. S. A. team, “LISA: laser interferometer space antenna for gravitational wave measurements,” Class. Quantum Gravity13(11A), A247–A250 (1996).
[CrossRef]

Tejnil, E.

Thorne, K. S.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Veitch, P. J.

Vogt, R. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Weise, D.

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gravity26(8), 085008 (2009).
[CrossRef]

Weiss, R.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Whitcomb, S. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Wilkening, G.

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng.14(2), 91–98 (1992).
[CrossRef]

Zucker, M. E.

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Appl. Opt. (2)

Class. Quantum Gravity (2)

K. Danzmann and L. I. S. A. team, “LISA: laser interferometer space antenna for gravitational wave measurements,” Class. Quantum Gravity13(11A), A247–A250 (1996).
[CrossRef]

T. Schuldt, M. Gohlke, D. Weise, U. Johann, A. Peters, and C. Braxmaier, “Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor,” Class. Quantum Gravity26(8), 085008 (2009).
[CrossRef]

J. Mod. Opt. (1)

J. M. De Freitas and M. A. Player, “Polarization effects in heterodyne interferometry,” J. Mod. Opt.42(9), 1875–1899 (1995).
[CrossRef]

Meas. Sci. Technol. (2)

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol.4(9), 907–926 (1993).
[CrossRef]

F. C. Demarest, “High-resolution, high-speed, low data age uncertainty, heterodyne displacement measuring interferometer electronics,” Meas. Sci. Technol.9(7), 1024 (1998).
[CrossRef]

Metrologia (2)

G. Mana, “Diffraction Effects in Optical Interferometers Illuminated by Laser Sources,” Metrologia26(2), 87–93 (1989).
[CrossRef]

K. Dorenwendt and G. Bönsch, “Über den EinfluB der Beugung auf die interferentielle Längenmessung,” Metrologia12(2), 57–60 (1976).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

J. Leach, M. J. Padgett, S. M. Barnett, S. Franke-Arnold, and J. Courtial, “Measuring the Orbital Angular Momentum of a Single Photon,” Phys. Rev. Lett.88(25), 257901 (2002).
[CrossRef] [PubMed]

Precis. Eng. (2)

S. J. A. G. Cosijns, H. Haitjema, and P. H. J. Schellekens, “Modeling and verifying non-linearities in heterodyne displacement interferometry,” Precis. Eng.26(4), 448–455 (2002).
[CrossRef]

W. Hou and G. Wilkening, “Investigation and compensation of the nonlinearity of heterodyne interferometers,” Precis. Eng.14(2), 91–98 (1992).
[CrossRef]

Science (1)

A. Abramovici, W. E. Althouse, R. W. P. Drever, Y. Gürsel, S. Kawamura, F. J. Raab, D. Shoemaker, L. Sievers, R. E. Spero, K. S. Thorne, R. E. Vogt, R. Weiss, S. E. Whitcomb, and M. E. Zucker, “LIGO: The Laser Interferometer Gravitational-Wave Observatory,” Science256(5055), 325–333 (1992).
[CrossRef] [PubMed]

Surf. Sci. Rep. (1)

H.-J. Butt, B. Cappella, and M. Kappl, “Force measurements with the atomic force microscope: Technique, interpretation and applications,” Surf. Sci. Rep.59(1-6), 1–152 (2005).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1

System alignment and beam walkoff: a) ideal aligned single DOF heterodyne interferometer where reference and measurement beams ~fully overlap. Beam walkoff depends on target tilt α, target displacement ∆z and distance l between the target mirror and photodetector. Blue denotes the reference frequency f1 and red the measurement frequency f2, b) ideal aligned system, c) initial misalignment due to target tilt α and distance l, d) displacement dependent walkoff due to target displacement ∆z in combination with α and l.

Fig. 2
Fig. 2

Two measurements with non-ideal wavefronts: one without walkoff and with walkoff. The vertical axis shows the incoming wavefronts of the source frequencies that interfere and create the wavefront of the beat frequency were they overlap. Our heterodyne phase measurement signal retrieves a relative wavefront that consists of the wavefront differences between the wavefronts of f1 and f2. The horizontal axis represents the diameter of the photodetector that integrates the phase of the incoming relative wavefront over its surface area. Beam walkoff results in a different phase integration compared to the situation without walkoff, the phase difference Δθ is falsely interpreted as target displacement.

Fig. 3
Fig. 3

Schematic overview of the measurement setup. An optionally inserted interferometer assembly is indicated. Such configuration should allow investigation of wavefront distortions as caused by the additional optical system After exiting the heterodyne system the coaxial heterodyne beam passes a polarizer at 45° creating the interference signal, an 8% pellicle beam sampler (pbs) samples and integrates the interference signal over the entire beam to serve as a reference signal. An Ø62.5 μm multimode fiber measures locally the beating signal which is compared to the reference beating signal, resulting in phase changes ∆θ over the cross section of the beam when the wavefront is non-ideal i.e. deformed.

Fig. 4
Fig. 4

The wavefront measurement system illustrated in Fig. 3, build in the lab. The left image shows the coaxial heterodyne beam coming in from the lower left passing a polarizer at 45°, then propagating through the 8% pbs (creating a reference signal) and finally reaching the multimode fiber on the automated stage. The right image shows more clearly the manual vertical y-displacement stage with the automated stage on top of it.

Fig. 5
Fig. 5

Allan deviation plot showing an optimum at a sample integration period of 90ms, i.e. averaging over ~500 data samples, at this location the noise presence is the lowest and a resolution of ~25pm (i.e. ~λ/25000) is obtained. From this graph we can also conclude that sub-nm resolution is still obtained when measuring at higher sampling rates.

Fig. 6
Fig. 6

Two line-scans showing the relative wavefront differences between f1 and f2, measured with a 62.5 µm multimode fiber scanning through the centers of the two laser beams.

Fig. 7
Fig. 7

The top two figures show the wavefronts from Fig. 5 but now measured using a lens with an Ø11 mm integration area. The grey areas denote the locations of the Ø6 mm coaxial beams. The two bottom figures are zoomed in on the 6 mm center parts of the two upper figures and show what is measured when using a large aperture instead of an optical fiber.

Fig. 8
Fig. 8

3D wavefront reconstructions build from multiple line-scans as shown in Fig. 5. The top images show front views, the bottom two images show isometric projections (see Figs. 3 and 4 for the orientation). Measurements at the top and bottom of the beam of laser 1 showed to contain much noise and have been left away for clarity. Laser 2 shows unexplainable behavior at ~5 mm y-axis height that is not caused by the measurement method, multiple line scans at the same y-location showed the same outcome; therefore the laser source must be the cause.

Metrics