Calibration and Physical Units#
Techniques for applying frequency-dependent calibration transfer functions, verifying physical dimensional units, and guarding against inversion and grid errors.
Analysis Pathways#
Core tutorial: Apply frequency response \(C(f)\) [count / m] to complex spectra and spectral densities while enforcing Astropy physical unit contracts and defensive exception guards.
Case study: End-to-end swept/stepped sine excitation analysis, coherence tracking, and parametric actuator transfer function fitting.
Case study: Ingest and reuse pre-measured calibration transfer function products directly from LIGO Diagnostic Test Tool (DTT) XML files.
Case study: Broad automated sanity checks, dimensional integrity auditing, and consistency validation across GWexpy containers.
Role Separation and Scope#
Resource |
Primary Scope |
Typical Usage |
Key Focus |
|---|---|---|---|
Calibration Units Contract (Tutorial) |
In-memory series calibration |
Daily script analysis |
Unit safety, wrong-direction guards, grid mismatch errors |
Calibration Pipeline (Case Study) |
Experimental measurement |
Hardware commissioning |
Swept sine analysis, actuator calibration, TF modeling |
DTT XML Calibration (Case Study) |
File I/O & legacy interop |
Commissioning data reuse |
Parsing XML transfer functions into GWexpy containers |
Physics Validation (Case Study) |
Container test suite |
Quality assurance |
Broad physics invariant assertions |
Core Mathematical Conventions#
Coupling Response: \(C(f) = Y_{\text{count}}(f) / X_{\text{m}}(f)\) with physical unit \(\text{ct}/\text{m}\).
Complex Spectrum Calibration: \(X(f) = Y(f) / C(f)\) restoring physical displacement in meters.
Amplitude Spectral Density (ASD): \(A_x(f) = A_y(f) / |C(f)|\) with unit \(\text{m}/\sqrt{\text{Hz}}\).
Power Spectral Density (PSD): \(P_x(f) = P_y(f) / |C(f)|^2\) with unit \(\text{m}^2/\text{Hz}\).
Strain Sensitivity: \(h(f) = X(f) / L\) given detector arm length \(L\).