Phase Contrast Imaging Simulation

This repository contains a Python implementation of phase contrast microscopy simulation using the Transport of Intensity Equation (TIE) for phase retrieval.

Images

Overview

Phase contrast microscopy is a powerful technique for visualizing transparent specimens (like biological cells) that do not absorb light but alter its phase. This simulation demonstrates:

1. Generation of transparent phase objects
2. Wave propagation using the angular spectrum method
3. Phase retrieval using the Transport of Intensity Equation (TIE)
4. Phase contrast microscopy simulation

How It Works

Phase Object Generation

• Creates synthetic phase objects with Gaussian profiles
• Transparent objects that only modify the phase of light

Wave Propagation

• Simulates light wave propagation using angular spectrum method
• Calculates defocused images at different z-planes

Transport of Intensity Equation (TIE)

• Uses intensity measurements at different focal planes to recover phase information
• Solves TIE using Fourier methods

Phase Contrast Microscopy

• Simulates the effect of a phase plate in a phase contrast microscope
• Converts invisible phase variations into visible intensity contrast

Requirements

• numpy
• matplotlib
• scipy
• scikit-image

Usage

python phase_contrast_simulation.py

The simulation will:

1. Generate synthetic phase objects
2. Calculate intensity images at different focal planes
3. Reconstruct the phase using TIE
4. Simulate phase contrast microscopy imaging
5. Display comparison of bright-field and phase contrast images

Results

The code generates visualization of:

• Original phase object
• Defocused images (front, in-focus, and back focal planes)
• Reconstructed phase using TIE
• Phase contrast microscope simulation

Comparing the bright-field image (where transparent objects are invisible) with the phase contrast image demonstrates how phase contrast microscopy makes transparent objects visible.

Theory

Transport of Intensity Equation

The TIE relates the intensity gradient along the optical axis to the phase distribution:

∇⊥ · [I(x,y,0) ∇⊥φ(x,y)] = -k ∂I(x,y,z)/∂z|z=0

Where:

• I is the intensity
• φ is the phase
• k is the wave number (2π/λ)
• ∇⊥ is the gradient operator in the transverse plane

Phase Contrast Microscopy

Phase contrast microscopy works by:

1. Separating the direct (unscattered) and diffracted light
2. Advancing/retarding the phase of the direct light by π/2
3. Recombining the light to create amplitude contrast from phase differences

References

• Teague, M. R. (1983). Deterministic phase retrieval: a Green's function solution. JOSA, 73(11), 1434-1441.
• Paganin, D., & Nugent, K. A. (1998). Noninterferometric phase imaging with partially coherent light. Physical review letters, 80(12), 2586.
• Zernike, F. (1942). Phase contrast, a new method for the microscopic observation of transparent objects. Physica, 9(7), 686-698.