## 3 Results
### Model error due to sensor induced noise levels  
To examine the sensor-induced noise levels in the HbA1c estimation models, we considered two sensors for PPG acquisition. One of the sensors is the Osram SFH7050 with AFE4404 and the other is the TCS34725 color sensor. The Osram SFH7050 and AFE4404 pair are considered as a discrete-LED/PD-based PPG acquisition system. On the other hand, the TCS34725 is considered to be a camera-sensor-based PPG acquisition system. According to our tests on these sensors, the standard deviation (SD) of error values generated by the AFE4404 front end is \(1.820\times 10^{-4}\) for transmission-mode PPG, and \(1.480\times 10^{-4}\) for reflection mode PPG signals. The TCS34725 sensor has an SD of \(3.640\times 10^{-5}\) and \(6.711\times 10^{-5}\) for transmission and reflection mode PPG signals, respectively.  
Figure 4: Molar concentration based SpO\({}_{2}\) approximation error for (17) from the model (8).  
Figure 5: Molar absorption coefficient based SpO\({}_{2}\) approximation error of (19) for (a) 465 nm, (b) 525 nm, and (c) 615 nm. The color bar represents the reference HbA1c values.  
Considering the method described in subsection C of the Methodology section, the width of the Gaussian function is set using the SD values obtained from the different sensors for different modes, as given previously. Figure 6 shows the HbA1c values estimated from the noise-prone ratio values (\(R_{1}\) and \(R_{2}\)) for the AFE4404 based sensor and PPG mode. On the other hand, Figure 7 illustrates the HbA1c estimation error for the TCS34725 sensor.  
In Figure 6, the estimation error of HbA1c is illustrated with respect to reference HbA1c values for model (7) (Figure 6a-b) and model (8) (Figure 6c-d), respectively. From all these figures it is evident that the estimation error level increases as the HbA1c level increases. This is due to the high light attenuation property of HbA1c molecules. An increment of HbA1c molecules inside a solution can lead to reduced amplitudes in received light signals, resulting in greater errors in estimation.  
The standard deviation (SD) of the erroneous estimation for the AFE4404-based sensor of the model (7) is found to be 0.258 and 0.317 for reflection and transmission modes, respectively. On the other hand, model (8) has an SD of 0.114 and 0.142 for reflection and transmission modes, respectively.  
Figure 7 also depicts similar illustrations to Figure 6. However, since the TCS34725 sensor receives less signal noise than the AFE4404, the SD of the estimation error of HbA1c is reduced greatly, which can be seen in Figure 7.  
Figure 6: HbA1c estimation error due to AFE4404-based sensor-induced noise. Model-(7)-based HbA1c estimation values are illustrated for (**a**) reflection-mode and (**b**) transmission-mode PPG signal. Model-(8)-based estimation values are given for (**c**) reflection-mode and (**d**) transmission-mode PPG signals. The color bar represents the reference SpO2 values.  
The SD of the erroneous estimation of the model (7) is found to be 0.117 and 0.063 for reflection and transmission modes, respectively. For model (8), SD is found to be 0.052 and 0.028, in reflection and transmission modes, respectively.