MATLAB Implementation of Ray Tracing Algorithm: Modeling Light Refraction and Attenuation

Ray tracing algorithm serves as a core technology in computer graphics and optical simulation, generating photorealistic images or analyzing optical system performance by simulating light propagation paths through media. When implementing in MATLAB, special attention should be paid to modeling three key physical phenomena: refraction, attenuation, and aberrations.

Refraction Modeling Light refraction behavior follows Snell's Law, where the ratio of sines of incidence and refraction angles equals the inverse ratio of refractive indices between two media. In MATLAB implementation, this can be achieved through vector operations: calculating refraction direction vectors based on incident light direction vectors and interface normal vectors. When light transitions from higher to lower refractive index media, additional critical angle checking for total internal reflection must be implemented using conditional statements and trigonometric calculations.

Attenuation Models Light intensity attenuation typically considers two mechanisms: Distance Attenuation: Following the inverse square law, intensity decreases inversely proportional to the square of propagation distance, implemented using distance-based scaling factors in energy calculations. Medium Absorption: Modeled using Beer-Lambert Law, where exponential decay functions describe wavelength-specific energy loss through media, requiring wavelength-dependent absorption coefficient arrays and exponential computation functions.

Aberration Handling For high-precision optical scenarios, five primary aberrations require simulation: Spherical Aberration: Difference in focal points between marginal and paraxial rays, implemented through ray height-dependent focal length adjustments. Coma: Comet-tail shaped distortion for off-axis point sources, modeled using asymmetric point spread functions. Astigmatism: Separation between tangential and sagittal focal lines, requiring directional ray tracing analysis. Field Curvature: Curved imaging surfaces, implemented through curved focal plane modeling. Distortion: Geometric image deformation, corrected using distortion mapping functions and coordinate transformations.

Implementation recommends modular design: decoupling ray tracing, medium interaction, and energy calculation components. For complex optical systems, recursive algorithms can handle multiple reflection/refraction paths with depth control parameters. MATLAB's matrix operation advantages enable efficient batch ray calculations through vectorized operations, while visualization toolkits facilitate real-time observation of ray paths and energy distributions through plotting functions and interactive displays.