Fourier Optics Lab (4f microscope): data analysis + uncertainty propagation

This repository turns a 4f microscope lab into a reproducible Python analysis project. Starting from raw CSV measurements, it reproduces the report numbers, propagates uncertainties analytically, exports machine-readable results, and generates figures that GitHub can render directly.

Project Overview

This project is a compact example of reproducible model comparison. It evaluates three measurement routes, carries uncertainty through each chain, exports structured outputs, and makes the figures inspectable without opening the report.

At a Glance

• Data workflow: raw measurement tables are converted into processed CSV/JSON outputs, figures, and a report-facing notebook.
• Methods signal: constrained regression, method comparison, analytic uncertainty propagation, and systematic-vs-random error discussion.
• Reproducibility signal: the analysis can be rerun from a single script or Makefile target and produces GitHub-renderable artifacts.

The project keeps alternative measurement definitions visible rather than collapsing everything into one final reported value. Beyond the optics result, it is structured as a compact empirical replication package: raw measurements, uncertainty assumptions, intermediate outputs, figures, and final reported numbers are linked through rerunnable code.

The most important methodological result is that the slit-cutoff route has the smallest reported random uncertainty but is dominated by systematic uncertainty. In this dataset, the camera-calibration route is the most defensible estimate once that distinction is made explicit.

What this repo shows

• Data analysis in numpy, pandas, and matplotlib
• Constrained regression for the screen-angle method
• Analytic uncertainty propagation across multiple measurement chains
• Comparison of independent experimental methods, not just a single final number
• Reproducible outputs in notebook, CSV, JSON, and PDF form

Scientific question

How consistent are three independent estimates of the grating period in a Fourier optics lab, and which method is most defensible once random and systematic uncertainty are separated?

Key results

Measurement route	Result for grating period d (um)	Main idea	Interpretation
Screen-angle geometry	9.87 +/- 0.26	Through-origin regression of diffraction spacing vs screen distance	Good consistency, but largest random uncertainty
Camera calibration	9.92 +/- 0.11	Calibrated object-plane pixel scale and period counting	Best overall method in this dataset
Fourier-plane slit cutoff	10.83 +/- 0.05	Spatial-frequency cutoff inferred from slit width	Reported sigma is random-only; systematics dominate

Additional quantitative result:

• Abbe-limit estimate: dx_min ~= 3.96 um, consistent with resolving the 6 um feature more clearly than the 4 um feature.

Analysis outputs

Screen-angle regression

Method comparison with propagated uncertainties

Uncertainty propagation strategy

The Python workflow does more than fit a line. It carries uncertainty through each calculation chain.

For the screen-angle method:

y = mL
theta = arctan(m)
d = lambda / sin(theta)
sigma_theta = sigma_m / (1 + m^2)
sigma_d = |dd/dtheta| sigma_theta

For the camera method, the script propagates uncertainty from calibration pixels to object-plane scale and then into the final period estimate. For the slit-cutoff method, it reports the random component directly and also computes a simple systematic cross-check against the camera-based estimate.

Reproduce the analysis

python -m venv .venv
pip install -r analysis/requirements.txt
python analysis/analyze.py

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

make all

Smoke test:

python -m unittest discover -s tests

Main outputs:

• analysis/FourierOptics_Analysis.ipynb: executed notebook rendered by GitHub
• data/processed/results.json: structured summary for all experiments
• data/processed/grating_results.csv: compact comparison table
• analysis/output/*.png: regression, residual, and uncertainty figures
• report/main.pdf: polished lab report with derivations and discussion

Repository structure

analysis/        Python scripts, notebook, and generated figures
data/raw/        Raw measurements with assigned uncertainties
data/processed/  Machine-readable outputs generated by the analysis
report/          LaTeX source and compiled PDF report
docs/            Supporting notes

Attribution

Report author: Hongyu Wang, with Maya Kang-Chou and Sidharth Kannan.
Code and reproducible analysis pipeline maintained by Hongyu Wang.