Lens Distortion Measurement and Correction

This repository contains a grid-based lens distortion measurement and image correction workflow developed for Mitutoyo CF 2X, 3X, and 5X lenses. The project uses ThorLabs 0.125 mm pitch dot-grid target images to estimate geometric residual distortion, fit a mathematical correction model for each lens, and apply the model to new images using inverse remapping.

The full TIFF datasets are not included in this repository in order to keep the repository lightweight. A small sample subset is provided for demonstration purposes.

Project Goals

• Detect dot-grid centers from microscope/lens images.
• Estimate the ideal grid position using planar homography.
• Compute residual displacement vectors between measured and ideal grid points.
• Fit a separate 5th-degree two-dimensional polynomial displacement model for each lens.
• Correct distorted images using cv2.remap and inverse mapping.
• Compare residual error before and after correction.
• Provide reproducible scripts and compact result files for review and further development.

Lab Test Environment

The experimental setup was tested in a laboratory environment using microscope optics and a dot-grid calibration target.

Mathematical Model

Pixel coordinates are first normalized with respect to the image center:

X = (x - cx) / s
Y = (y - cy) / s

For each lens, the displacement field is modeled separately in the x and y directions:

d_x(x,y) = sum_{i+j<=5} a_ij * X^i * Y^j
d_y(x,y) = sum_{i+j<=5} b_ij * X^i * Y^j

The corrected image is generated by inverse remapping:

I_corrected(x,y) = I_distorted(x + d_x(x,y), y + d_y(x,y))

In other words, for each pixel (x,y) in the corrected image, the model computes the corresponding sampling location in the original distorted image.

Repository Structure

lens-distortion-correction/
  README.md
  requirements.txt
  .gitignore
  data/
    README.md
    sample/
      2x/
      3x/
      5x/
  docs/
    Distorsiyon_Modelleme_Raporu.md
    Distorsiyon_Modelleme_Raporu.pdf
    lab_test_environment.jpeg
  results/
    2x/
      summary.json
      distortion_model.json
    3x/
      summary.json
      distortion_model.json
    5x/
      summary.json
      distortion_model.json
    lens_distortion_type_analysis.json
    runtime_benchmark/
      3x_runtime_benchmark.json
  scripts/
    analyze_grid_distortion.py
    apply_distortion_model.py
    benchmark_distortion_runtime.py

Installation

python -m venv .venv
.\.venv\Scripts\Activate.ps1
pip install -r requirements.txt

Usage

1. Grid Distortion Measurement

Place the input TIFF images under data/. Example command:

python scripts\analyze_grid_distortion.py `
  --input data\3x `
  --glob "3x Lens v2_*.tiff" `
  --output output\3x_v2_distortion `
  --grid-pitch-mm 0.125 `
  --rows 59 `
  --cols 59

This step produces files such as:

summary.json
distortion_points.csv
radial_summary.csv
visual validation images

2. Polynomial Model Fitting and Image Correction

python scripts\apply_distortion_model.py `
  --points output\3x_v2_distortion\distortion_points.csv `
  --summary output\3x_v2_distortion\summary.json `
  --input data\3x `
  --glob "3x Lens v2_*.tiff" `
  --output output\3x_v2_correction_model `
  --degree 5

This step writes:

distortion_model.json
distortion_model_equation.txt
corrected_images/
comparisons/

3. Runtime Benchmark

python scripts\benchmark_distortion_runtime.py `
  --model results\3x\distortion_model.json `
  --image "data\sample\3x\3x Lens v2_1.tiff" `
  --output output\benchmark\3x_corrected.tiff `
  --json-output output\benchmark\3x_runtime.json `
  --iterations 25 `
  --threads 1

On the reference PC, the remapping-only correction time for one 2048 x 2048 16-bit image was measured at approximately 85 ms. The target PolarFire hardware was not available during this work; therefore, final hardware timing must be verified on the target using readmcycle().

Summary Results

Lens	Dataset	Grid points	P95 before	P95 after	Distortion type interpretation
2X	v2	2116	0.7812 px	0.6626 px	Mixed / asymmetric
3X	v2	3481	0.4708 px	0.1535 px	Mixed / mustache-like
5X	v2	1681	0.6603 px	0.2541 px	Mixed / mustache-like

Sample Dataset Policy

The full raw TIFF datasets are not tracked in this repository. To avoid filling GitHub storage with large image data, only a small sample subset is included:

Lens	Source dataset	Sample images included
2X	v2	5
3X	v2	5
5X	v2	5

The full measurements reported in results/ were generated using the complete 100-image v2 datasets for each lens. The data/sample/ folder is intended only for demonstration and small-scale testing.

Notes and Limitations

• The polynomial coefficients are valid for the same lens, sensor geometry, working distance, focus condition, and image resolution.
• If the optical setup changes, the distortion model should be recalibrated.
• The residual field may include lens distortion, target alignment error, target flatness error, illumination effects, and point-detection noise.
• The included PDF report in docs/ provides the detailed mathematical explanation and experimental interpretation.

Main Scripts

• analyze_grid_distortion.py: detects grid points, estimates homography residuals, and exports distortion metrics.
• apply_distortion_model.py: fits the polynomial displacement model and applies image correction using inverse remapping.
• benchmark_distortion_runtime.py: measures remapping runtime for a selected image and model.