DampedHarmonicVibration

class hcipy.optics.DampedHarmonicVibration(mode, natural_frequency, damping_ratio, driving_psd, refractive_index=1.0, seed=None)[source]

Bases: DynamicSurfaceAberration

A damped harmonic oscillator vibration model driven by white noise.

This class models a damped harmonic oscillator with natural frequency and damping ratio, driven by white noise with a given power spectral density. The model uses a continuous-time state space representation with exact covariance evolution.

Parameters:

modeField: The spatial mode of the vibration. This mode is assumed to be normalized to an RMS of one.
natural_frequencyscalar: The natural frequency of the oscillator in Hz. Must be positive.
damping_ratioscalar: The damping ratio (dimensionless). Must be positive.
driving_psdscalar: The power spectral density of the driving acceleration noise in m^2 s^-4 per rad/s. This represents the strength of the external disturbance. Must be non-negative.
refractive_indexfloat or callable, optional: Refractive index of the medium. Can be a constant (float) or a callable that takes wavelength and returns refractive index. Default is 1.0.
seedint, optional: Random seed for reproducibility. Default is None.

Attributes Summary

`damping_ratio`	The damping ratio of the oscillator.
`displacement`	The current displacement of the oscillator in meters.
`driving_psd`	The power spectral density of the driving white noise.
`mode`	The spatial mode of the vibration.
`natural_frequency`	The natural resonant frequency in Hz.
`oscillation_frequency`	The frequency of the damped oscillation in Hz.
`quality_factor`	The quality factor of the oscillator.
`rms_displacement`	The stationary RMS displacement in meters.

Attributes Documentation

damping_ratio: The damping ratio of the oscillator.

displacement

The current displacement of the oscillator in meters.

Returns:

float: The displacement in meters.

driving_psd: The power spectral density of the driving white noise.

mode: The spatial mode of the vibration.

natural_frequency: The natural resonant frequency in Hz.

oscillation_frequency

The frequency of the damped oscillation in Hz.

For critically damped (damping_ratio = 1) and overdamped (damping_ratio > 1) systems, the oscillator does not oscillate and this returns NaN.

quality_factor: The quality factor of the oscillator.

rms_displacement

The stationary RMS displacement in meters.

For a damped harmonic oscillator driven by white noise with PSD S_0, the stationary RMS displacement is sqrt(S_0 / (4*zeta*omega_0^3)).

Returns:

float: The stationary RMS displacement in meters.