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Laser Resonance

Laser Resonance refers to the phenomenon where laser light oscillates within a laser cavity, consisting of mirrors that reflect the light back and forth. This process allows the light waves to constructively interfere, amplifying specific wavelengths and producing a coherent, monochromatic light beam. The resonance is a fundamental part of how lasers generate a focused and intense light output.

Rayleigh Backscattering Noise

Rayleigh Backscattering Noise refers to the noise caused by Rayleigh scattering when light propagates through an optical fiber or other medium.

Rayleigh scattering occurs due to microscopic fluctuations in the refractive index of the medium, caused by density variations or impurities. When a light wave travels through the fiber, a portion of it gets scattered in different directions, including backward. This backward scattering interferes with the original signal, leading to noise, which can degrade the performance and signal quality in optical communication systems or fiber-optic sensors. Rayleigh backscattering noise is a significant factor to consider in designing high-precision optical systems, as it affects signal-to-noise ratio and overall transmission quality.

Ponderomotive Force

Ponderomotive Force is a nonlinear force experienced by charged particles in an oscillating electromagnetic field, such as a laser field. Unlike forces that result from constant fields, the ponderomotive force arises due to the variation in the intensity of the oscillating field.

The force tends to push charged particles, like electrons or ions, away from regions of higher intensity to lower intensity. It essentially acts as an averaging effect over the rapid oscillations of the electromagnetic wave. In laser-plasma interactions and high-intensity laser experiments, the ponderomotive force plays a crucial role in shaping particle trajectories and affecting energy transfer processes.

Misalignment Angle

The misalignment angle refers to the deviation between the actual sensing axis of the accelerometer and the intended or ideal axis in the sensor’s coordinate system. This angle represents how much the accelerometer’s sensitive axis is off from the expected alignment, even if it is perfectly mounted according to its designated orientation.

Installation Error Angle

The installation error angle refers to the deviation caused by inaccuracies in how the accelerometer is physically mounted on the structure or system it is meant to measure. This error represents the difference between the intended installation orientation and the actual orientation after mounting.

Zero-bias Instability Noise

Zero-bias Instability Noise is a type of noise that affects the stability of the zero-bias point in inertial sensors such as gyroscopes and accelerometers. It represents the drift or variation in the sensor’s output signal when there is no actual input or movement. This noise is an important parameter in characterizing the accuracy and performance of inertial measurement units (IMUs).

Inertia Product

The inertia product describes how mass is distributed in a rigid body concerning its axes of rotation. It represents the off-diagonal elements of the inertia tensor, which is a matrix that characterizes how the mass of a body resists rotational motion around different axes. The inertia product (product of inertia) describes the asymmetry of a rigid body with respect to a given set of coordinate axes.

Inertial Coupling

In a multi-axis inertial system, such as gyroscopes or IMUs (Inertial Measurement Units), movements along one axis can cause unintended interactions or effects on other axes. This phenomenon, known as inertial coupling, is a result of the mass distribution and the inertia properties of the system.

Dynamic Drift Error

Dynamic drift error occurs specifically when the system is in motion. Unlike static drift, which occurs when the device is stationary, dynamic drift is influenced by external factors such as acceleration, vibrations, changes in orientation, and other dynamic conditions. This error manifests as inaccurate readings that change with the motion of the sensor or system. Causes of Dynamic Drift Error

  1. Non-linear sensor behavior: During movement, sensors may exhibit non-linear responses, resulting in inaccurate measurements.
  2. External influences: Vibrations, shocks, or changes in velocity can introduce additional errors that are not present in static conditions.
  3. Temperature changes: Variations in temperature can alter the sensor’s response, especially under dynamic conditions.
  4. Mechanical imperfections: Slight imperfections or misalignments in the sensor’s design or mounting can become more pronounced during motion, contributing to dynamic drift.
inertia tensor

a mathematical representation used in physics and engineering to describe how an object’s mass is distributed relative to its rotational axes. The inertia tensor provides a comprehensive way to describe an object’s resistance to rotational acceleration in three-dimensional space. It’s an essential concept for analyzing the rotational motion of rigid bodies in various fields, including physics, engineering, and robotics.

principal axes of inertia

The principal axes of inertia are the unique axes around which an object can rotate without experiencing off-axis torques, and they provide the simplest representation of an object’s inertia properties. Identifying and using these axes are crucial for accurately analyzing and predicting rotational behavior in various applications.

gyroscopic precession

gyroscopic precession is the phenomenon where a rotating object’s axis of rotation moves in response to an applied torque, resulting in a predictable circular motion. This behavior is a fundamental principle in gyroscopes and plays a crucial role in many practical applications, particularly in navigation, stabilization, and dynamic systems. During gyroscopic precession, the axis of a rotating object traces out a cone-shaped path around a fixed point. This conical motion is a defining characteristic of gyroscopic precession. The base of the cone is a circle centered around the fixed pivot point (usually the point of contact with the ground or the gyroscope’s support).

Common Errors to Model During Calibration

  1. Bias (Offset)
  2. Scale Factor Error
  3. Misalignment
  4. Nonlinearity
  5. Cross-axis Sensitivity: In multi-axis IMUs, the motion along one axis can influence measurements on other axes. Calibrating for this cross-coupling ensures independent and accurate axis readings.

Inertial Sensor Errors

Stochastic Errors

  1. Quantization Noise(QN)
  2. Angular Random Walk，ARW
  3. Bias Instability，BI
  4. Rate Random Walk，RRW
  5. Angle Rate Ramp，RR

    Systematic Errors

    These errors that can be modeled, identified, and corrected through calibration

  6. bias
  7. scale factor
  8. misalignment

other

unit is gravity

MEMS IMUs are generally calibrated assuming a standard gravity of g≈9.80665 m/s^2, as defined by the International Committee for Weights and Measures. This value is used globally for consistency, even though local gravity varies.

Use a known local gravity value instead of assuming the standard g:

  • Gravity at poles: ∼9.832m/s^2
  • Gravity at equator: ∼9.780m/s^2

Convert to m/s^2:

Always convert IMU output:

Acceleration in m/s^2 = Measured g × Local g

Local g with the actual gravitational acceleration for your region.