TIE Phase Retrieval (MATLAB)

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Overview

This project implements the Transport of Intensity Equation (TIE) to reconstruct phase information from intensity-only measurements. The experiment characterizes a low-cost LCD-based spatial light modulator (SLM). By analyzing intensity changes across slightly defocused images, the algorithm reconstructs a 3D phase map of the LCD surface. I also included my senior thesis and results.

The phase reconstruction reveals:

• Surface texture and non-uniformities of the LCD
• Intensity variations from Arduino-controlled patterns
• Optical behavior of a low-cost SLM system

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Methods

Data Collection

To perform TIE reconstruction, capture three intensity images using an optical setup.

Equipment

• Light source (laser or LED)
• LCD (used as SLM)
• Lens
• Camera
• Optical rail (for precise positioning)

Procedure

1. Align the system: Light → LCD → Lens → Camera

2. Display a pattern on the LCD using Arduino

3. Capture the following images:

Image	Description	Action
I₀	In-Focus Image	Sharpest image (best focus)
I⁺	Forward Defocus	Move lens +5 mm forward, capture image
I⁻	Backward Defocus	Move lens –5 mm backward, capture image

Important:

• Keep lighting constant
• Ensure images are aligned
• Use small, controlled movements

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MATLAB Reconstruction

Files

File	Purpose
run_TIE.m	Main script
TIE_simple.m	Core TIE solver

How It Works

1. Loads intensity images
2. Applies preprocessing (noise reduction)
3. Computes intensity derivative ∂I/∂z
4. Solves the TIE
5. Outputs a 2D phase map and 3D surface

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How to Run

1. Open MATLAB
2. Navigate to the project folder
3. Place your images in the folder
4. Update filenames in run_TIE.m:

I_plus  = imread('zplus.JPG');
I0      = imread('I0.JPG');
I_minus = imread('zminus.JPG');

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Results Output

Includes:

• Phase map of the LCD
• 3D surface reconstruction
• Visualization of intensity variations

Applications:

• Analyze surface irregularities
• Study optical distortions
• Evaluate LCD pattern response

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Notes

• Ensure images are well-aligned
• Use consistent illumination
• Keep defocus distance small (~5 mm)
• Avoid vibrations during capture
• Normalize intensity if needed

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Future Work

• Test additional LCD patterns and voltages
• Improve noise filtering and stability
• Compare with interferometric methods
• Automate alignment and preprocessing

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Acknowledgements

• Dr. Hongbo Zhang — Mentorship and guidance
• Middle Tennessee State University (MTSU), Department of Physics and Astronomy