## 4 Discussion  
In the analysis presented in the previous paragraphs, we show the effects of wavelength drift on the performance of a VGG classifier of speckle patterns at the output of a 10-cm long GRIN MMF. Although 10 cm is considered short for certain applications, such as telecommunications, it is often sufficient for medical imaging (e.g., brain imaging and diagnosis). It is observed that DNNs can recognize the digits used of the phase image inputs on the proximal facet of a GRIN fiber from their corresponding speckle patterns with high accuracy. These results were presented in our previous work and accurately verified here [16]. However, the trained DNN model with a dataset collected at a certain wavelength can efficiently perform classification of a speckle pattern that is generated using inputs recorded at the same wavelength only. For the fiber length used, drifting of the wavelength of the laser source by 3 nm causes the speckle patterns recorded at this new wavelength value to be incorrectly classified by the trained model. The performance of the DNN degrades and the classification accuracy abruptly drops, as reported in Figure 5b (red circles). Consequently, it is important that the DNN model is trained to in a way which allows classification of an input even if the corresponding speckle pattern is generated at different wavelengths. We found that one solution, which was also proposed for the case of bending by [PERSON] et al. [20], is to include the potential perturbations in the measurements of the training dataset so that the DNN learns to interpolate correctly and properly classify the speckle outputs. However, it is observed that the classification accuracy saturates at values dependent on the size of the wavelength drift bandwidth, and even when increasing the size of the dataset, they never reach the maximum of 90%, which is the measured accuracy in the absence of drift. One possible reason for this result is the randomization of the input-output mapping; the large wavelength drift, the speckle pattern of a specific digit captured at a certain wavelength can be very similar to the speckle pattern of another digit captured at another wavelength. Another interesting observation based on the measurements reported in the presence of wavelength drift, is that the classification accuracy does not notably deteriorate after increasing the drift bandwidth further than 60 nm approximately. MMFs support modes whose shape is independent of the wavelength within a certain bandwidth. These modes are called principal modes [32; 33]. However, this effect is usually observed for longer fibers of few meters and further investigation is necessary to evaluate if there is any contribution in the results presented in this work.  
Until this point, we have discussed the aspect of training a DNN algorithm to recover information through a MMF system despite the wavelength changes by including the noise in the dataset. Nevertheless, there are cases where sensitivity in the wavelength change is actually crucial; for example, MMFs have been proposed as suitable systems for high-resolution spectrometers [34; 35]. In those previous works, the speckle decorrelation with wavelength is used for distinguishing different wavelengths and the resolution is dependent on the speckle decorrelation bandwidth of the specific fiber, which becomes narrower with increases in the fiber length. In the results presented in this work, we observed that the classification efficiency of a trained DNN with data recorded at a single wavelength is sensitive to wavelength changes and deteriorates within a significantly narrower bandwidth (Figure 5b, red circles) than the decorrelation bandwidth of the system (Figure 5a). Therefore, what is considered unwanted for information recovery through the system under a wavelength drift situation, it could potentially be desired for achieving a resolution which is higher than the one given by the decorrelation bandwidth and has been previously proposed in the literature for spectroscopic applications.