Harmonic calibration of quadrature phase interferometry

Baptiste, Ferrero,; Bellon, Ludovic

doi:10.1209/0295-5075/ac8761

EPL

2022

DOI: 10.1209/0295-5075/ac8761

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Harmonic calibration of quadrature phase interferometry

Ferrero, Baptiste

Ludovic Bellon

Abstract: The two output signals of quadrature phase interferometers allow to benefit both from the high sensitivity of interferometry (working inside a fringe) and from an extended input range (counting fringes). Their calibration to reach a linear output is traditionally performed using Heydemann's correction, which involves fitting one output versus the other by an ellipse. Here we present two alternative methods based on the linear response of the measurement to a sinusoidal input in time, which enables a direct cal… Show more

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2024

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Cited by 3 publications

References 17 publications

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Correction of non-linearities in quadrature phase differential interferometry

Velasco,

Cramail,

Giraud

et al. 2024

Meas. Sci. Technol.

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Quadrature phase differential interferometry is a technique of choice for measuring arbitrary large displacements with record resolution. The so-called Heydemann corrections are generally employed to take account of the unavoidable imperfections due to the optics or the electronics, and a linearisation of the signals is usually performed when the displacement to be determined is the superposition of a quasi-static component and a small harmonic component. Here we show that this standard analysis can lead to non-linearities of two types. The first type of non-linearities is due to optical and electronic imperfections that were not reported in the past and not included in the Heydemann corrections. These imperfections appear as amplitude difference and phase shift between each pair of intensity signals, and produce periodic non-linearities of nanometer amplitude when the intensity signals are combined to obtain contrats, i.e., quantities that are insensitive to intensity fluctuations of the light source. The second type of non-linearities is due to large amplitudes of harmonic oscillation, which become significant when the oscillations are typically larger than 20 nm for a red-emitting laser source, and can lead to an underestimation of the measured amplitude of ∼ 20 %. In order to correct these non-linearities, new procedures of calibration and analysis are presented, implemented and successfully tested over a wide range of quasi-static velocities, frequencies and amplitudes of harmonic oscillation. The proposed corrections reduce non-linearities below the noise level, making them smaller than 100 pm and 10 pm for the quasi-static and harmonic displacement, respectively.

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Correction of non-linearities in quadrature phase differential interferometry

Velasco,

Cramail,

Giraud

et al. 2024

Meas. Sci. Technol.

View full text Add to dashboard Cite

show abstract

High precision 3 × 3 coupler demodulation algorithm with an additional phase shift judgment module

Pan,

Ge,

Zhang

et al. 2024

Appl. Opt.

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Ellipse fitting algorithms (EFAs) have been widely used in 3×3 coupler demodulation systems to reduce the requirement for symmetry of the 3×3 couplers. Based on the relative stability of the splitting ratio and phase difference after the establishment of the 3×3 coupler demodulation system, we solve the problem that EFA fails to work when the stimulating signal is small. Depending on the existence of a symmetry point about the origin, an additional phase shift judgment module is used to determine whether the Lissajous figure is larger than π rad. If the elliptical arc exceeds π rad, the EFA is executed. Otherwise, the previous parameters are used to correct the ellipse. Parameters are updated in real time to ensure high precision. The experimental results show that the total harmonic distortion (THD) of the ameliorated algorithm is improved by 1.28% compared to the EFA without the judgment module with a stimulus amplitude of 30 mV. The proposed scheme can effectively improve the dynamic range of the 3×3 coupler demodulation to reach 125.64 dB @ 1 kHz and 1% THD. The algorithm ensures the effective operation of the EFA under small phase shift conditions and improves the accuracy of phase demodulation.

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A Novel Demodulation Algorithm for Micro-Displacement Measurement Based on FMCW Sinusoidal Modulation

Xu,

Wang,

et al. 2024

Photonics

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Frequency-modulated continuous wave (FMCW) interferometry, an emerging laser interferometry technology, can be applied in the field of fibre-optic sensing to achieve high-precision micro-displacement measurements. To address nonlinearity issues in laser frequency modulation and localisation deviations of feature points in traditional algorithms, this paper proposes a demodulation algorithm suitable for sinusoidal frequency modulation schemes, incorporating the principle of orthogonal phase-locked amplification. The algorithm includes signal preprocessing, phase-locked amplification, error correction, and phase calculation. Experimental results show that the system achieves a measurement error standard deviation of 3.23 nanometres for static targets. The displacement measurement error at 100 μm is 0.057% F.S., and the linearity between the measured values and the actual displacement values is 0.99997. Compared with conventional methods, the approach introduced in this paper eliminates the need for separate nonlinear corrections of the current-to-optical frequency relationship and minimises the issue of feature point localization deviations, showing significant potential for practical applications.

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Harmonic calibration of quadrature phase interferometry

Cited by 3 publications

References 17 publications

Correction of non-linearities in quadrature phase differential interferometry

Correction of non-linearities in quadrature phase differential interferometry

High precision 3 × 3 coupler demodulation algorithm with an additional phase shift judgment module

A Novel Demodulation Algorithm for Micro-Displacement Measurement Based on FMCW Sinusoidal Modulation

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