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Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Propagation of Uncertainty from Systematic Error01:10

Propagation of Uncertainty from Systematic Error

The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next sampling...
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...

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Related Experiment Video

Updated: May 28, 2026

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

A Nonlinear Error Compensation Method for Heterodyne Interferometry Based on Self-Supervised Physics-Informed Neural

Yao Wang1, Hongyu Sun1, Jiakun Li1

  • 1Key Lab of Luminescence and Optical Information, School of Physical Science and Engineering, Beijing Jiaotong University, Beijing 100044, China.

Sensors (Basel, Switzerland)
|May 27, 2026
PubMed
Summary
This summary is machine-generated.

A novel self-supervised Physics-Informed Neural Network (PINN) method precisely calibrates laser heterodyne interferometric sensors. This approach significantly reduces nonlinear errors, enhancing precision metrology sensor performance even in low signal-to-noise ratios (SNR).

Keywords:
PINNheterodyne interferometric sensingindustrial sensorsintelligent signal processingnonlinear errorprecision metrology sensorsself-supervised learning

Related Experiment Videos

Last Updated: May 28, 2026

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques
09:01

Gain-compensation Methodology for a Sinusoidal Scan of a Galvanometer Mirror in Proportional-Integral-Differential Control Using Pre-emphasis Techniques

Published on: April 4, 2017

Area of Science:

  • Precision Metrology
  • Optical Sensing Systems
  • Artificial Intelligence in Engineering

Background:

  • Laser heterodyne interferometric systems have high theoretical resolution but are limited by nonlinear errors from optical imperfections.
  • Existing compensation methods are complex, hardware-dependent, and perform poorly under low signal-to-noise ratios (SNR).

Purpose of the Study:

  • To develop a novel precision calibration method for laser heterodyne interferometric sensing systems.
  • To address limitations of conventional methods by utilizing a self-supervised Physics-Informed Neural Network (PINN).

Main Methods:

  • A self-supervised PINN guided by frequency-domain priors was employed for robust nonlinear error compensation.
  • Measurement residuals with periodic physical features were extracted using high-precision displacement references.
  • Frequency-domain priors were integrated into a physically constrained network, using theoretical frequency characteristics for pseudo-label generation and the error equation as a differentiable physical layer for hard constraints.

Main Results:

  • The root-mean-square (RMS) nonlinear error was reduced from 1.90 nm to 0.23 nm.
  • A significant nonlinear error compensation rate of up to 88.13% was achieved.
  • The method demonstrated effective identification of nonlinear physical properties even in high background noise.

Conclusions:

  • The proposed PINN-based method offers a reliable framework for intelligent calibration and self-characterization of heterodyne interferometric industrial sensors.
  • This approach enhances the practical precision of interferometric sensing systems, particularly in demanding metrology applications.
  • The method overcomes limitations of conventional techniques, offering improved performance and robustness.