Improved temporal speckle contrast model for slow and fast dynamic: effect of temporal correlation among neighboring pixels.

Significance: Speckle contrast analysis, whether spatial or temporal, is a valuable optical technique extensively utilized in medical and engineering domains owing to its simplicity, affordability, and noninvasive nature. It relies on statistical analysis of the dynamic speckle pattern produced by the sample under examination, offering insights into the sample's dynamics. However, challenges persist in precisely measuring temporal speckle contrast, particularly for slow dynamic samples. Existing mathematical models fail to accurately reflect the experimental data, which could result in misinterpretation of the analyzed results.

Aim: To overcome these constraints, we present a mathematical model that incorporates the correlation between adjacent pixels. We specifically concentrate on temporal correlation, i.e., the relationship between neighboring frames, to compute the temporal speckle contrast.

Approach: We theoretically replicate the statistical analysis typically conducted to compute temporal speckle contrast in a series of consecutive raw speckle images. Unlike previous models, our calculations account for the potential correlation between neighboring pixels across successive frames. To validate this model, we apply it to the analysis of the dynamics of Escherichia coli ATCC 25922 colonies.

Results: By considering the probable temporal correlation between neighboring pixels, the proposed model notably improves the precision of temporal speckle contrast measurements, particularly for slow dynamic samples. Analytical expressions for the contrast are derived, incorporating both Gaussian and Lorentzian correlation functions, which exhibit excellent agreement with experimental findings conducted on E. coli colonies. Conversely, for fast dynamic samples where neighboring pixels lack correlation, our model aligns with the outcomes of the previously reported models.

Conclusions: The proposed model is well-suited for computing temporal contrast in both slow and fast dynamics, rendering it applicable to a wide range of biological and industrial systems.