Cavendish torsion balance: laser tracking and time-series analysis

This repository documents a Cavendish torsion balance experiment using video-based laser-spot tracking, calibrated position reconstruction, and uncertainty-aware analysis of the gravitational constant.

Project Overview

This project highlights reproducible time-series analysis from imperfect observational data. The workflow turns raw tracking outputs into calibrated measurements, records systematic-error assumptions, and regenerates report tables from code.

At a Glance

• Data workflow: video-derived laser-spot tracks are converted into calibrated displacement series and report-ready summary tables.
• Methods signal: computer-vision preprocessing, time-series reconstruction, calibration metadata, and systematic-error accounting.
• Reproducibility signal: one script rebuilds processed CSVs, summary tables, and the data catalog used by the report.

The main emphasis is traceability: raw tracking files, calibration choices, processed position series, and report-facing tables remain linked through code. Beyond the physics result, it is structured as a compact empirical replication package: raw tracking logs, calibration choices, fit metadata, systematic-error assumptions, and reported tables are linked through rerunnable code.

Key results

Method II refers to the equilibrium-center method: laser-spot time series are calibrated into displacement, fitted before and after the source-mass swap, and converted into an estimate of G using the PASCO torsion-balance formula.

The report treats the spread below as a diagnostic result rather than a precision measurement. The Method II estimates are above the accepted value, and the report attributes that gap mainly to run-to-run systematics and the shortened apparent period.

Quantity	Value
Method II G0 range	(1.53--3.48) x 10^-10 m^3 kg^-1 s^-2
Accepted reference value	6.674 x 10^-11 m^3 kg^-1 s^-2
Equilibrium shift Delta S	5.908--13.427 cm
Period used in Method II	292.3 +/- 12.8 s
Statistical uncertainty by run	9.4%--10.0%
Dominant limitation	shortened apparent period, drift/creep, and environmental perturbations

What the code does

• Track the reflected laser spot from video with OpenCV
• Convert pixel coordinates to physical displacement
• Reconstruct equilibrium shifts and oscillation behavior across multiple runs
• Recompute Method II results and the systematic-error table used in the report
• Export processed datasets and summary tables from the raw inputs

Analysis preview

The summary figure below is regenerated from results/method2_summary.csv and results/systematics_table3.csv by the reproducibility script.

Laser-spot tracking diagnostics

The diagnostic figure below shows a clean Method II damped-wave simulation for the three runs, alongside the raw centroid path and recovered points from the tracking workflow.

Reproduce the analysis artifacts

pip install -r requirements.txt
python scripts/reproduce_report_artifacts.py

If make is available, the same artifacts can be regenerated with:

make all

Smoke test:

python -m unittest discover -s tests

Generated outputs include:

• data/processed/*.csv
• results/method2_summary.csv
• results/systematics_table3.csv
• results/data_catalog.csv
• figures/method2_overview.png
• figures/tracking_diagnostics.png

Repository structure

data/raw/        Raw laser-spot tracking CSVs
data/metadata/   Calibration and fit metadata used by the report
data/processed/  Generated calibrated position tables
figures/         Key plots used in the report
results/         Recomputed summary tables
scripts/         Reproducibility scripts
src/             Core tracking and analysis code
reports/         Final PDF report and LaTeX source

Raw data fields

The tracking CSV files contain:

• Frame: video frame index
• Time_Sec: time in seconds
• X, Y: laser-spot centroid in pixels
• Mode: TRACKING or RECOVERED
• Area, Circularity: blob-shape diagnostics

Report

• Final report: reports/latex/main.pdf
• Compiled report copy: reports/G.pdf

Attribution

Authors: Hongyu Wang and Cici Zhang.
Code, tracking workflow, and reproducible analysis pipeline maintained by Hongyu Wang.