## 5 Conclusions  
In summary, the in-depth exploration of frequency-dependent contrast in EIT has significantly advanced the understanding of imaging methodologies, particularly in scenarios involving materials with distinct electrical properties, as demonstrated by acrylic resin and copper. The conducted experiments offer insights into empirical frequency ranges for enhanced contrast, considering variables such as object position, adjacent materials, and heterogeneous environments. These findings contribute to essential considerations for optimizing EIT imaging strategies, deepening the understanding of contrast dynamics. As the intricacies of EIT applications are revealed, this research establishes a foundation for enhanced precision and applicability across diverse environments, unlocking the full potential of this imaging technique in real-world scenarios.  
Optimized frequency selection in EIT holds promise for improving non-destructive inspection of copper welds in industries like energy and aerospace, potentially revolutionizing safety standards. Similarly, monitoring fluid flow in acrylic resin pipes could be transformed in sectors such as chemical processing, ensuring the safe and efficient handling of sensitive materials. The results reveal distinct empirical frequency bands for enhancing contrasts in specific materials: 15-38 kHz for conductive materials (copper) and 45-75 kHz for non-conductive materials (acrylic resin). Moreover, the potential for early skin cancer detection through EIT's sensitivity to conductivity differences between healthy and cancerous tissues presents exciting possibilities in the medical field. Additionally, environmental applications, such as monitoring saltwater intrusion in coastal areas or detecting buried pipes and cables, could greatly benefit from EIT's precision and non-invasive nature with optimized frequency selection.  
Future EIT research should aim to enhance the applicability and understanding of this imaging technique. There is a compelling need to explore diverse sample geometries beyond the current focus on cylindrical samples so as to broaden generalizability. Additionally, investigating the frequency-dependent contrast behavior of a more extensive range of materials will provide insights, deepening the understanding beyond the current focus on acrylic resin and copper. Additionally, future endeavors should evaluate the adaptability of specific empirical frequency ranges in real-world applications, ensuring the practical relevance and robustness of the findings in various scenarios.  
Conceptualization, T.N.T. and H.N.H.; methodology, T.N.T.; software, H.N.H. and A.T.T.; validation, Q.T.N.D.; analysis, Q.T.N.D.; investigation, T.V.H. and H.N.H.; resources, T.N.T.; data curation, M.Q.C.D. and H.N.H.; writing--original draft preparation, H.N.H.; writing--review and editing, T.V.H. and T.N.T.; visualization, H.N.H.; supervision, T.N.T.; project administration, A.T.T. and T.N.T.; funding acquisition, A.T.T. and T.N.T. All authors have read and agreed to the published version of the manuscript.  
This research is funded by the Vietnam National University, Ho Chi Minh City (VNU-HCM) under grant number B2024-20-16/HD-KHCN.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.