## 5 Conclusions  
In this study, we performed a quantitative analysis on two models for the non-invasive estimation of glycated hemoglobin (HbA1c). Comparing the two models, by taking one as a reference for different parametric states, the two-wavelength model was found to have errors in the range of \(-1.306\%\) to \(0.047\%\) of HbA1c, depending on the amount of oxygenated and deoxygenated hemoglobin compounds present in the blood solution. On the other hand, the three-wavelength model's HbA1c-estimation error was found to have a magnitude of \(10^{-14}\)\(\%\). From the approximation of the blood oxygenation (SpO\({}_{2}\)) value of the two-wavelength model, it can be seen that a lower error can be attained by using the molar concentration based SpO\({}_{2}\) approximation technique, as compared to the molar absorption coefficient based method. The method based on the molar absorption coefficient depends on the wavelength of the light and, in our experiment, we observed that the light at a wavelength of \(465\) nm produced the lowest error for the two-wavelength-based SpO\({}_{2}\) approximation. Finally, from the estimation error of HbA1c due to sensor noise level, it can be seen that the two-wavelength-based model has a higher resistance to sensor noise, and that the three-wavelength-based model is more susceptible to noise due to the higher complexity of the model. Though the two-wavelength based model has a low error level even when the sensor noise is high, the model performs poorly (error range varies between \(-1.306\%\) and \(0.047\%\) with the change in SpO\({}_{2}\) values) when estimating the glycated hemoglobin as compared to the three-wavelength based model. This is because the two-wavelength based model does not consider the two major hemoglobin components of blood. S.H. : conceptualization, methodology, software, validation, data curation, visualization. C.A.H. : software, validation, data curation, investigation. K.-D.K. : conceptualization, validation, supervision, formal analysis, funding acquisition. All authors have read and agreed to the published version of the manuscript. This research was supported by the Basic Science Research Program through the National Research Foundation (NRF) of Korea, funded by the Ministry of Education (NRF-2019R1F1A1062317), and was also supported by the National Research Foundation of Korea Grant, funded by the Ministry of Science, ICT, and Future Planning [2015R1A5A7037615]. The authors hereby declare that they have no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript; or in the publication of the results. [PERSON] was born in Dhaka, Bangladesh, on 10 May 1994. He received a Bachelor of Science (B.Sc.) degree in Electrical and Electronic Engineering from the Khulna University of Engineering and Technology, Bangladesh, in 2017. Later he received his Master of Science (M.Sc.) degree in 2021 from Department of Electronics Engineering, Kookmin University, Seoul, South Korea. He is currently appointed as a full-time researcher in the Department of Electronic Engineering, Kookmin University. He worked as a Lecturer with the Department of Electrical and Electronic Engineering, Daffodil International University from September 2018 to February 2019. His current fields of study are machine learning algorithms and computational biomedical engineering. \\ \end{tabular} \ \begin{tabular}{c} [PERSON] received a Bachelor of Science (B.Sc.) degree in electrical and electronic engineering from Khulna University of Engineering and Technology (KUET), Bangladesh, in 2019. He is currently pursuing a Master of Science (M.Sc.) degree in electronics engineering with Kookmin University, Seoul, Korea. His current research interests include biomedical signal processing and Monte Carlo simulations in computational biomedical engineering. \\ \end{tabular}