Computational Optimization of Lens-Based Imaging Systems

📄 Links

Full paper: Computational Optimization and Selective Reconstruction in Lens-Based Imaging Systems

Github: Repository

🔍 Overview

This project treats an optical imaging system as a linear transformation pipeline. Light rays are represented in matrix form and propagated through:

• Free space
• A convex thin lens
• A sensor plane

By tuning physical and sensor parameters, the system can focus and reconstruct clear images from overlapping ray data. A structured optimization workflow was used to maximize image sharpness and selectively capture different objects by translating the lens.

Gaussian smoothing was applied as a final post‑processing step to reduce noise while preserving structural details.

✨ Features

🧮 Linear Optical Modeling

• Matrix-based ray tracing through free space and a thin lens
• Rays represented as state vectors transformed via linear system matrices

🎯 Imaging System Optimization

• Numerical sweep to optimize lens-to-sensor distance
• Custom sharpness metric based on edge strength using convolution filters

🖼 Selective Image Reconstruction

• Lateral lens translation isolates rays from different objects
• Enables recovery of multiple distinct images from overlapping data

📐 Sensor & Resolution Tuning

• Sensor width adjusted to properly frame each image
• Pixel count tuned to balance resolution and brightness

🌫 Post‑Processing Enhancement

• 1D Gaussian smoothing filter applied horizontally and vertically
• Reduces noise while preserving edges and structure

🔬 Lens Necessity Validation

• Demonstrated that free-space propagation alone cannot produce focused images
• Verified mathematically and experimentally that a lens is required for ray convergence

🛠 Tools Used

• MATLAB (ray tracing, simulations, parameter sweeps)
• Linear algebra & state-space modeling
• Convolution-based image processing

👨‍💻 Authors

Rex Paster
Adam Fleischman