Locating Particle Positions via Gaussian Fitting of Approximately Circular Diffraction Spots in Images

In image processing, diffraction spots typically exhibit approximately circular brightness distributions, where the central point may correspond to the actual particle position. Gaussian fitting serves as a widely-used mathematical approach that accurately characterizes the brightness distribution profile of diffraction spots. Through fitting parameters, it determines the precise center location of the spot.

Spot Characteristic Analysis: Diffraction spot intensity generally attenuates radially from the center, adhering to Gaussian distribution properties. Implementing 2D Gaussian fitting using functions like scipy.optimize.curve_fit in Python or fitgmdist in MATLAB enables extraction of parameters including center coordinates, width (sigma), and peak intensity. The Gaussian model function typically follows: G(x,y) = A*exp(-((x-x₀)²/(2σ_x²) + (y-y₀)²/(2σ_y²))).

Gaussian Fitting Methodology: Optimization algorithms such as least-squares regression (e.g., Levenberg-Marquardt algorithm) adjust Gaussian parameters to minimize residuals between the model and actual intensity data. The fitted center coordinates (x₀, y₀) provide the estimated particle position. Code implementation often involves initial parameter estimation through centroid calculation or peak detection before refinement.

Circular Detection Enhancement: For near-circular spots, combining edge detection (e.g., Canny operator) or Hough circle transform with Gaussian fitting improves localization accuracy. Constraining Gaussian symmetry (σ_x = σ_y) during fitting further enhances precision for isotropic spots. This integration can be implemented through preprocessing segmentation or multi-stage fitting pipelines.

Application Scenarios: This technique is prevalent in optical measurement, biological imaging, and micro/nano-particle tracking, significantly improving positioning accuracy. It maintains robust performance even under low signal-to-noise conditions through regularization or weighted fitting approaches.

Gaussian fitting enables high-precision particle position extraction from complex diffraction images, providing reliable data support for subsequent tracking or quantitative analysis workflows. Implementation typically includes noise filtering, sub-pixel interpolation, and uncertainty quantification for production-level applications.