Robust Estimation of Bump Height for Wafer-Level Packaging Using Optical Triangulation

Accurate bump height estimation is critical for ensuring the reliability of semiconductor devices. Traditional optical triangulation methods have utilized centroid-based calculations and thresholding, but they suffer from information loss, noise sensitivity, and estimation bias in low-SNR regions. To address these issues, we propose a framework that estimates the height at each location using Maximum a Posteriori (MAP) estimation with a smoothness prior. We model the noise distribution of observations as a zero-mean Gaussian with unequal variances that are related to the amount of reflected light. Additionally, the smoothness prior enforces structural consistency across multiple bumps and helps to accurately estimate the height in noisy regions by leveraging information from neighboring observations in high-SNR regions. By dynamically balancing bias and variance, our framework provides a robust and scalable solution for semiconductor manufacturing, enabling more accurate and reliable bump height estimation in high-precision applications.