Non-linearity in length measurement using heterodyne laser Michelson interferometry

Sutton, C M

doi:10.1088/0022-3735/20/10/034

Cited by 96 publications

(45 citation statements)

References 6 publications

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“…COS0B (26) By insertion of Eqs. (22), (24), (25), and (26) This term is two orders of magnitude smaller than the intended uncertainty (a few parts in 10") in the lattice spacing comparison and is therefore neglected in the following.…”

Section: )mentioning

confidence: 99%

Precision comparison of the lattice parameters of silicon monocrystals

Kessler¹,

Henins²,

Deslattes³

et al. 1994

J. RES. NATL. INST. STAN.

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The lattice spacing comparator estabMshcd MC the National InMitute of Standards and Technology to measure the lattice spacing differences between nearly perfect crystals i^ described in detail, t^tticc spacing differences are inferred from the measured differcrrces in Br3g;g Hngics for different crystals. The comparator is a vna crystal spectrometer uficd in the nearly nondispersive geometry. It has two s-ray sources, two detectors, and a ilevicc which permits rcmiUe interchange of the second crystal sample. .\ sensitive heterodyne interferometer which it calibrated with an optical polygon is used to measure the Bragg an^es. The crystals are manufactured with nearly equal rhicknesscs so that the recorded profiles exhibit pcndclhisung oscillatinifs which permit more precise division of the x-ray profiles. The difference in lattice spacing between silicon •umpks used at Physikalisch-TcchnischcBundcsansiait (PTB) and NIST has been measured with a relittive uncertainty of 1 x I0~*. This measurement Ls consisitcnt with absolute lattice spacing measurements made at PTB and NIST, Components of uncertainty associated with systematic effects due to misaligt^ments arc derived and estimated. Key word.s: Bragg angle; lattice spacing; silicon; x-ray difTraction; x-ray specAccepl«d: October 25. 1993

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Section: )mentioning

confidence: 99%

Precision comparison of the lattice parameters of silicon monocrystals

Kessler¹,

Henins²,

Deslattes³

et al. 1994

J. RES. NATL. INST. STAN.

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“…This reduction approach is based on the quality of the coaxial beam's source frequency orthogonality together with the quality of the linear polarizations. If these are of high quality, it is also essential that highquality polarized optics are applied for beam splitting, combined with alignment [5][6][7][8][9].A less expensive approach is to digitally compensate for the PNL through analytical modeling [5,[9][10][11]. The advantage of this method is that it typically ensures PNL below 1 nm for small system imperfections, without changing the interferometer configuration.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

“…When operating at this level, a heterodyne interferometer system is hampered by many error sources. The main error sources are the frequency stability of the laser source, noncommon optical pathway variations due to variations in the refractive indices of optical transport media, system alignment (i.e., cosine error, Abbé error), optical wavefront quality combined with beam walkoff [4], and periodic nonlinearity (PNL) in the measured phase [5][6][7][8][9][10]. Operating in vacuum will improve the obtained measurement error.…”

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confidence: 99%

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Heterodyne displacement interferometer, insensitive for input polarization

Meskers¹,

Spronck²,

Schmidt³

2014

Opt. Lett.

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Periodic nonlinearity (PNL) in displacement interferometers is a systematic error source that limits measurement accuracy. The PNL of coaxial heterodyne interferometers is highly influenced by the polarization state and orientation of the source frequencies. In this Letter, we investigate this error source and discuss two interferometer designs, designed at TU Delft, that showed very low levels of PNL when subjected to any polarization state and/or polarization orientation. In the experiments, quarter-wave plates (qwps) and half-wave plates (hwps) were used to manipulate the polarization state and polarization orientation, respectively. Results from a commercial coaxial system showed first-order PNL exceeding 10 nm (together with higher order PNL) when the system ceased operation at around 15°hwp rotation or 20°qwp rotation. The two "Delft interferometers," however, continued operation beyond these maxima and obtained first-order PNLs in the order of several picometers, without showing higher order PNLs. The major advantage of these interferometers, beside their high linearity, is that they can be fully fiber coupled and thus allow for a modular system buildup. Laser interferometry is an often applied measurement method in several fields of research, since it allows for noncontact measurements. It is especially preferred in the field of metrology, because of its direct traceability to the length standard [1]. Interferometry is also used in lithography machines in the semiconductor industry, gravitational wave detection [2], coordinate measuring machines, and as a calibration tool for other measurement devices, such as capacitive sensors, inductive sensors, and optical encoders. Many types of displacement interferometer systems can be distinguished; this publication deals with heterodyne displacement interferometry using a stabilized He-Ne laser (λ 632.8 nm) combined with two acoustooptic modulators for generating two (fixed-offset) source frequencies.Industrial manufacturing processes currently operate with measurement errors at the subnanometer level and will require even smaller errors in the near future [3]. When operating at this level, a heterodyne interferometer system is hampered by many error sources. The main error sources are the frequency stability of the laser source, noncommon optical pathway variations due to variations in the refractive indices of optical transport media, system alignment (i.e., cosine error, Abbé error), optical wavefront quality combined with beam walkoff [4], and periodic nonlinearity (PNL) in the measured phase [5][6][7][8][9][10]. Operating in vacuum will improve the obtained measurement error. However, PNL in the measurand remains a substantial error source.PNL manifests itself primarily in traditional heterodyne systems with coaxial beams. Such beams contain two linearly polarized frequencies that are orthogonally oriented. These frequencies may mix (due to "frequency leakage"), resulting in periodic errors that are superimposed on the obtained displacement data. This type ...

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“…However, some error sources remain, one of which is periodic nonlinearity (PNL). This error source is attributed by ghost reflections, by imperfections in polarization alignment, and by the polarization quality of both the source frequencies and polarizing optics [5][6][7][8][9].…”

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Validation of separated source frequency delivery for a fiber-coupled heterodyne displacement interferometer

2014

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The use of optical fibers presents several advantages with respect to free-space optical transport regarding sourcefrequency 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 interferometerconcept can measure with sub-nanometer uncertainty using fiber delivered source frequencies, enabling fully fiber-coupled heterodyne displacement interferometers.

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Non-linearity in length measurement using heterodyne laser Michelson interferometry

Cited by 96 publications

References 6 publications

Precision comparison of the lattice parameters of silicon monocrystals

Precision comparison of the lattice parameters of silicon monocrystals

Heterodyne displacement interferometer, insensitive for input polarization

Validation of separated source frequency delivery for a fiber-coupled heterodyne displacement interferometer

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