تحديد الثوابت الضوئية وسمك الاغشية الرقيقة من بياناتا لنفاذية الضوئية بطرق التحسين الرياضية

Abstract

films using only transmission spectra. The approach is based on a constrained pointwise optimization technique, where a nonlinear programming problem is formulated with linear constraints reflecting prior physical knowledge. Notably, the method does not rely on the presence of interference fringes in the data, making it suitable for a wide range of film types. Optimization techniques such as Newton’s method and gradient descent were used to minimize a nonlinear least squares cost function. The proposed method was validated through numerical experiments on synthetic data and applied to CdS thin films deposited via chemical bath deposition under various thiourea concentrations at El Oued University laboratories. The optimization process enabled accurate retrieval of refractive index, absorption coefficient, and film thickness. The extracted thickness values ranged from 221:55 nm in sample 1 to 247:84 nm in sample 4, with intermediate values of 238:39 nm and 241:85 nm for samples 2 and 3. This consistent increase in thickness correlates well with thiourea dosage, validating the numerical model's physical accuracy. Overall, this work demonstrates the effectiveness of combining physical modeling with constrained optimization in the analysis of thin films and provides a flexible MATLAB-based tool for further experimental and theoretical