Theory: from signal to claim¶
This portal explains the physical models SPM-Kit implements, the assumptions that make them usable and the evidence currently attached to each code path. It is written for readers who want to understand what a parameter means before clicking Run.
Learning path¶
- AFM principles: tip, cantilever, optical lever, feedback, scanner, coordinates and calibration.
- Operating modes: contact, tapping, non-contact, force volume, quantitative imaging and KPFM context.
- Force-distance curves: approach/retract, baseline, snap-in, contact, adhesion, hysteresis and segmentation.
- Contact mechanics: Hertz/paraboloid, Sneddon, DMT, JKR, reduced modulus and fit limits.
- KPFM: contact-potential difference, work function, null feedback and sign conventions.
- Roughness and surface metrology: reference surface, leveling, Sa/Sq/Sz/Ssk/Sku, sampling and filters.
- Spectral and self-affine analysis: Fourier transform, radial PSD, Hurst exponent, fractal dimension and bandwidth.
- Resonance and mass sensing: SHO response, Q, thermal noise, effective mass and declared evaporation model.
- SPM-Kit implementation map: module, Fathom perspective, CLI/API, evidence and limitation for each concept.
- Glossary and primary references.
How to read an equation here¶
Every model is accompanied by:
- symbols and SI units;
- assumptions and common failure conditions;
- the current SPM-Kit code path and operating surface;
- the strongest retained evidence level for that path;
- a limitation that remains after the test passes.
An equation is not an endorsement for every sample. A fitted number is only as defensible as the calibration, geometry, preprocessing, fit window and evidence behind the path that produced it.
Evidence vocabulary¶
CLAIMED → SOFTWARE_VERIFIED → NUMERICALLY_VERIFIED → CROSS_VALIDATED → PHYSICALLY_VALIDATED → REPRODUCIBILITY_VALIDATED.
The same project can contain Level 1, Level 2 and Level 3 capabilities at once. No current public evidence supports a general Level 4 or Level 5 claim.