# Deep Learning for Computational Mode Decomposition in Optical Fibers
## 4 Discussion  
First, the results using synthetic data for mode weight prediction show that with the SMC training data design, a significant improvement of a complex-valued MD can be achieved. The DNN was trained with a dataset containing \(\approx\) 60,000 ensembles using predefined step sizes. With smaller step sizes, the amount of data would increase, which would lead to an improvement of the performance. This would also lead to a longer training phase of the DNN. The chosen step sizes resulted from a trade-off between performance and computational load. For the MD, an FMF was assumed, which can guide 3 modes. Increasing the number of modes and, thus, the complexity of the problem would also have an effect on the result. In this case, the DNN had to be trained with more data or had to be designed more deep to achieve equivalent results.  
Second, the DNN-based MD was applied to an experimental environment using the same synthetic SMC dataset. The aim is to create a measurement system, which can evaluate the mode weights in phase and amplitude with intensity-only measurements. An SLM was used to generate random mode combinations of the 3 modes the assumed FMF can guide. The light field distributions are then imaged to a CMOS camera, where holograms are captured and evaluated using the angular spectrum method. To ensure a fair comparison between the DNN and the DH method, the amplitude distributions from the holographic measurement were used as input for the DNN. Both the DNN and DH are utilized to run a complex MD. In the determination of the individual mode weights, it could be shown that the phase determination has a mean deviation of 4.20% using DH and 9.45% using the SMC-based DNN. The amplitude determination could be carried out with DH with a mean deviation of 3.32% and with the SMC-based DNN with a mean deviation of 6.02%. Although the phase determination with DH is better by a factor of 2, similar correlation values can be achieved with the original images. With DH, a mean correlation coefficient of 96.91% and 95.10% with the SMC-based DNN could be achieved. These results clearly show that a DNN shows equivalent results to an established measurement technique like DH. Although neither a phase measurement was carried out nor were sources of error of optical components learned in the training process, the results are comparable. These relationships clearly emphasize the potential of DNNs. Nevertheless, it can be observed that the results with measured data are significantly below the results using simulation data. This is mainly due to the fact that the optical system for collecting the measured data is not perfect. One source of error is the simultaneous amplitude and phase modulation with the phase-only SLM using superpixels. Only a discrete number of pixels can be used for the individual superpixels. An optimum of \(6\times 6\) pixels was found for this. Additionally, SLMs are known for their phase flicker property [33] and have a modulation efficiency \(<1\), which leads to unwanted background light and errors. Therefore, the superpixel phase-mask is superimposed with a diffraction grating. The actual modulated light is spatially separated in the Fourier plane of L1 (1 st diffraction order) and can therefore  
Figure 5: (**a**) Illustration of the scheme for data acquisition. (**b**) Correlation coefficients using DH and the prediction of a DNN, respectively.  
be filtered with a pinhole. Further, imaging errors, aberrations of optical components, and quantization noise are additional possible error sources in the optical setup. These sources of error are significant for both DH and the DNN. It is therefore important to find out how these error terms can be compensated in the future when using DNN with the help of suitable training data. However, it can already be stated at this point that the DNN reacts extremely robustly to experimental error sources which have not been learned in advance during the training process.