Current ways and means for reduction or elimination of periodic nonlinearity in heterodyne interferometer

This paper reviews ways and means used for reduction or elimination of periodic nonlinearity in heterodyne interferometers. The periodic nonlinearity resulting from polarization mixing or frequency mixing in heterodyne interferometers was modeled into one expression, which included the initial polarization state of the laser source, the rotational alignment of the beam splitter along with different transmission coefficients for polarization states and the rotational misalignment of a receiving polarizer. Three compensation techniques, measuring two orthogonal output signals, Lissajous Compensation and Chu-Ray Algorithm, are described and discussed for reduction of periodic nonlinearity. These algorithms needed at least one fringe of motion or a constant velocity sweep to properly correct the motion. And five types of two spatially separated beam interferometer configurations are described and discussed for elimination of periodic nonlinearity to a picometer level. It is concluded that the main disadvantage of these configurations was their complex architecture with unbalanced long beam paths.

[1]  Ki-Nam Joo,et al.  High resolution heterodyne interferometer without detectable periodic nonlinearity. , 2010, Optics express.

[2]  Hyun-Seung Choi,et al.  A simple method for the compensation of the nonlinearity in the heterodyne interferometer , 2002 .

[3]  M A Player,et al.  Phase-step insensitive algorithms for phase-shifting interferometry , 1994 .

[4]  Gwo-Sheng Peng,et al.  Correction of nonlinearity in one-frequency optical interferometry , 1996 .

[5]  Tony L. Schmitz,et al.  First-order periodic error correction: validation for constant and non-constant velocities with variable error magnitudes , 2006 .

[6]  Wenmei Hou,et al.  A simple technique for eliminating the nonlinearity of a heterodyne interferometer , 2009 .

[7]  V. Badami,et al.  A frequency domain method for the measurement of nonlinearity in heterodyne interferometry , 2000 .

[8]  H Han Haitjema,et al.  Modeling and verifying non-linearities in heterodyne displacement interferometry , 2002 .

[9]  Michael A. Player,et al.  Phase step measurement and variable step algorithms in phase-shifting interferometry , 1992 .

[10]  Ki-Nam Joo,et al.  Simple heterodyne laser interferometer with subnanometer periodic errors. , 2009, Optics letters.

[11]  Byong Chon Park,et al.  A simple phase-encoding electronics for reducing the nonlinearity error of a heterodyne interferometer , 2008 .

[12]  Wenmei Hou.  Optical parts and the nonlinearity in heterodyne interferometers , 2006 .

[13]  Marco Pisani,et al.  A homodyne Michelson interferometer with sub-picometer resolution , 2009 .

[14]  Tony L. Schmitz,et al.  Acousto-optic displacement-measuring interferometer: a new heterodyne interferometer with Ångstrom-level periodic error , 2002 .

[15]  irst and second order periodic error measurement for on-constant velocity motions ony , 2009 .

[16]  Wenmei Hou,et al.  Investigation and compensation of the nonlinearity of heterodyne interferometers , 1992 .

[17]  P L Heydemann,et al.  Determination and correction of quadrature fringe measurement errors in interferometers. , 1981, Applied optics.

[18]  J. Lawall,et al.  Michelson Interferometry With 10 PM Accuracy , 2000 .

[19]  Jonathan D Ellis,et al.  Fiber-coupled displacement interferometry without periodic nonlinearity. , 2011, Optics letters.

[20]  Kyuwon Jeong,et al.  The dynamic compensation of nonlinearity in a homodyne laser interferometer , 2001 .

[21]  Alan E. Rosenbluth,et al.  Optical sources of non-linearity in heterodyne interferometers , 1990 .

[22]  R. Deslattes,et al.  Analytical modeling of the periodic nonlinearity in heterodyne interferometry. , 1998, Applied optics.

[23]  Martin Gohlke,et al.  Picometer and nanoradian optical heterodyne interferometry for translation and tilt metrology of the LISA gravitational reference sensor , 2009 .

[24]  Lowell P. Howard,et al.  A simple technique for observing periodic nonlinearities in Michelson interferometers , 1998 .

[25]  Serge Dubovitsky,et al.  Polarization compensation: a passive approach to a reducing heterodyne interferometer nonlinearity. , 2002, Optics letters.

[26]  Chien-ming Wu.  Periodic nonlinearity resulting from ghost reflections in heterodyne interferometry , 2003 .

[27]  H Han Haitjema,et al.  Improving a commercially available heterodyne laser interferometer to sub-nm uncertainty , 2003, SPIE Optics + Photonics.

[28]  Martin Gohlke,et al.  A high precision heterodyne interferometer for relative and absolute displacement measurement , 2009, 2009 International Symposium on Optomechatronic Technologies.

[29]  Birk Andreas,et al.  A heterodyne interferometer with periodic nonlinearities smaller than ±10 pm , 2012 .

[30]  J. Lawall,et al.  Heterodyne interferometer with subatomic periodic nonlinearity. , 1999, Applied optics.

[31]  Chien‐Ming Wu,et al.  Nonlinearity in measurements of length by optical interferometry , 1996 .

[32]  Martin Gohlke,et al.  Compact laser interferometer for translation and tilt measurement as optical readout for the LISA inertial sensor , 2007, International Symposium on Optomechatronic Technologies.