Dispersion represents a critical parameter influencing optical transmission performance, and its control technology has been widely applied to ultrafast optics, nonlinear optics, and fiber optic communication. Precise dispersion measurement systems are essential for developing accurate dispersion compensation schemes and optimizing optical system designs. Among various measurement techniques, white light interferometry emerges as particularly advantageous due to its high temporal and spatial resolution, broad spectral range, and straightforward experimental setup. Measurement accuracy remains a primary consideration for dispersion measurement systems. The spectrometer resolution and light source bandwidth constrain the number of interference fringes in the spectrum, while the delay difference between reference and measurement arms affects interference fringe density, subsequently impacting data processing sampling points. Addressing these challenges requires establishing a theoretical model to systematically evaluate how these factors affect measurement accuracy, analyze suitable delay differences and effective bandwidth for measurement systems, and experimentally demonstrate how appropriate parameter selection enhances system measurement accuracy.

This article presents a theoretical model for a white light spectral interference dispersion measurement system that processes the interference spectrum through normalization and phase information extraction using Hilbert transform (Fig. 2), and investigates the effects of bandwidth and time delay on measurement accuracy (Fig. 3). Concurrently, a measurement system was constructed to evaluate SF66 and F2 glass samples with a thickness of 10 millimeters (Fig. 1). The investigation involved varying spectral bandwidth and time delay, comparing experimental results with simulation outcomes (Fig. 5). The root mean square error (RMSE) served as the measurement accuracy metric.

Simulation analysis reveals that for ideal Gaussian light sources, RMSE remains below 7 fs² when time delay exceeds 8 ps and effective bandwidth surpasses 12 dB. For actual light sources, RMSE stays below 20 fs² with 20 dB effective bandwidth and delays between 7 to 12 ps (Fig. 3). This occurs because increased bandwidth generates spectral noise that adversely affects phase extraction accuracy. While time delay correlates positively with interference fringe quantity, the spectrometer’s wavelength resolution imposes an upper limit on interference fringe numbers. Experimental results demonstrate RMSE values not exceeding 30 fs² when using 20 dB bandwidth and time delays between 5 and 10 ps (Fig. 5). Furthermore, Fourier transform analysis of the interference signal explains the time delay upper limit (Fig. 6). The analysis indicates that increasing time delay progressively reduces the interference spectrum’s signal-to-noise ratio, potentially due to light spot shape differences during beam combination. The experimental data demonstrates strong correlation with theoretical simulation results.

This study establishes a dispersion measurement system for white light spectral interferometry and investigates the effects of bandwidth and time delay on phase extraction both theoretically and experimentally. The research develops a theoretical model based on system wavelength resolution, utilizing ideal Gaussian spectra and actual measured spectra to calculate dispersion RMSE curves through varying bandwidth factors and time delays. Simulation results indicate optimal performance with a bandwidth factor of 2 (corresponding to 20 dB calculated bandwidth) and time delays between 7?12 ps. Experimental validation through measuring standard optical glass dispersion curves of SF66 and F2 samples under various time delay conditions confirms the simulation trends. Through optimization of time delay and bandwidth factors, measurement errors for both glass samples remained below 50 fs2 throughout the 42 nm spectral range.