A heterodyne interferometer constructed in an integrated optics and its metrological evaluation of a picometre-order periodic error

Abstract It is known that the periodic error of heterodyne interferometers limits the accuracy of measurement to nanometre order. It is mainly derived from frequency mixing in the interferometer optics and this can be resolved using the configuration with two spatially separated beams. However, there remains a periodic error associated with parasitic reflections. Recently, we have developed a differential single-path heterodyne interferometer with two spatially separated beams, which was constructed within a single small quasi-cubic optical unit to minimize the parasitic reflections. In this work, the residual periodic error of this interferometer was evaluated with two evaluation methods, ‘the amplitude method’ and ‘the subtraction method’, and their results were compared. By applying uncertainty estimation procedures to the results, these two methods were shown to be highly consistent, confirming the reliability of our evaluation results. The error in λ/2 period of this interferometer was 7.6 pm.

[1]  J. Flügge,et al.  Nonlinearity of a double-path interferometer qualified with a non-constant moving speed. , 2016, Optics letters.

[2]  Satoshi Gonda,et al.  Periodic error evaluation system for linear encoders using a homodyne laser interferometer with 10 picometer uncertainty , 2018 .

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

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

[5]  Ichiko Misumi,et al.  Removing nonlinearity of a homodyne interferometer by adjusting the gains of its quadrature detector systems. , 2004, Applied optics.

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

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

[8]  M. Tanaka,et al.  Linear interpolation of periodic error in a heterodyne laser interferometer at subnanometer levels (dimension measurement) , 1989 .

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

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

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

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

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

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

[15]  Marco Pisani,et al.  Comparison of the performance of the next generation of optical interferometers , 2012 .

[16]  Peng Chen,et al.  Balanced plane-mirror heterodyne interferometer with subnanometer periodic nonlinearity. , 2014, Applied optics.

[17]  J. Stümpel,et al.  Combined optical and X–ray interferometry for high–precision dimensional metrology , 2000, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[18]  P. Ciddor.  Refractive index of air: new equations for the visible and near infrared. , 1996, Applied optics.