Aperture Grid Diffraction Simulation

A Taichi-based simulation demonstrating diffraction patterns from a grid of circular apertures.

Overview

This project simulates diffraction patterns for multiple aperture-grid lattices (square, triangular, and hexagonal). The simulation displays both the aperture mask and the resulting diffraction pattern side-by-side.

Grid Types

• Square grids: 3x3, 4x4, 5x5
• Triangular grids:
  • Small triangular: 8 apertures
  • Large triangular: 31 apertures
• Hexagonal grids:
  • Small hexagonal: 7 apertures (center + 6 neighbors)
  • Large hexagonal: 24 apertures

Use the buttons in the left control panel to switch between grid types.

Physics Background

The simulation implements the physical optics calculation for:

• Single aperture diffraction: Uses Bessel functions to compute the Airy disk pattern
• Multi-aperture interference: Calculates phase differences between apertures in the grid
• Far-field approximation: Assumes Fraunhofer diffraction conditions

Features

• Interactive parameters: Real-time adjustment of aperture size, separation, distance, and wavelength
• Visual comparison: Side-by-side display of aperture mask and diffraction pattern
• Color mapping: Diffraction pattern colored according to the incident light wavelength
• High performance: GPU-accelerated computation using Taichi

Parameters

• Aperture diameter (W): Size of each circular aperture (meters)
• Center-to-center separation (d): Distance between adjacent apertures (meters)
• Distance to screen (z): Propagation distance from apertures to observation plane (meters)
• Wavelength (λ): Wavelength of incident light (meters)
• Screen size: Physical size of the observation area (meters)

Usage

Run the simulation:

python main.py

Use the interactive sliders to adjust:

• Distance (1.0 - 40.0 m)
• Aperture size (0.01 - 0.10 mm)
• Separation (0.0 - 0.2 mm)
• Wavelength (400 - 700 nm)

Implementation Details

• Bessel function computation: Custom implementation using series expansion and asymptotic approximation (see physics.py)
• Phase calculation: Accounts for geometric path differences between apertures
• Color rendering: Wavelength-to-RGB conversion for visual representation (see color.py)
• Normalization: Intensity scaling for proper display

Project Structure

• main.py: Entry point, configuration, Taichi field definitions, kernels, GUI loop
• physics.py: Airy/Bessel-related Taichi functions
• color.py: Wavelength to RGB Taichi function
• grids.py: Grid constants (point sets and offsets) and grid title helper

Dependencies

• Taichi: For high-performance GPU computing (Install via your Python environment manager or pip install taichi.)

Mathematical Foundation

The diffraction pattern combines:

1. Airy pattern from individual apertures: J₁(x)/x envelope function
2. Interference pattern from aperture array: Complex amplitude summation
3. Phase factor: (2π/λ) * (aperture_positions · direction) / z

Where J₁ is the first-order Bessel function of the first kind.