# Michelson Interferometric Methods for Full Optical Complex Convolution
## 3 Results and Discussion
### CNN Simulation Evaluation  
In our comprehensive study, we delved into the intricacies of optical modulation techniques, with a special emphasis on amplitude modulation and phase modulation, primarily facilitated through the use of spatial light modulators. Our investigation led us to employ neural network simulations to scrutinize the impact of our complex modulation approach, the Reconfigurable Simultaneous Optical Full Complex Convolution Module, on the performance metrics of optical neural networks. Remarkably, we discovered that the RCCM approach considerably boosts the efficiency and accuracy of these networks. This enhancement can be primarily attributed to the sophisticated nature of complex modulation, which introduces an additional degree of freedom over traditional modulation techniques by offering a complete optical modulation schema. This approach allows for more nuanced and precise control over the light's properties, which is paramount in optical computing. In our investigation, we conducted neural network simulations to assess the impact of our innovative complex modulation approach on the efficacy of optical neural networks. The findings were unequivocal: RCCM significantly amplifies the capabilities of these networks. This enhancement can be traced back to the comprehensive nature of complex modulation, which integrates both amplitude and phase modulation in a single framework. This integration provides a crucial additional degree of freedom, enabling more sophisticated manipulation of the optical signals than is possible with traditional modulation methods that treat amplitude and phase separately. The architecture of our simulated neural network was designed to include one optical layer followed by two fully connected layers, facilitating a comparison across three modulation strategies: complex modulation, amplitude modulation, and phase modulation. Our methodology involved the use of the CIFAR-10 dataset, a standard benchmark in machine learning for evaluating object recognition algorithms, to train and test the models. As the results shown in Figure 5, thecomplex modulation achieved an accuracy rate of 51.98%, surpassing amplitude modulation and phase modulation, which posted accuracy rates of 50.83% and 47.87%, respectively. This differential in performance underscores the superiority of the RCCM approach, particularly its ability to exploit the multidimensional nature of light for computational purposes fully. By leveraging the inherent properties of light in a more holistic manner, complex modulation facilitates a higher-dimensional space for information encoding and processing, leading to more efficient and accurate neural network operations. Moreover, these results highlight the potential of RCCM to serve as a cornerstone for the next generation of optical neural networks, offering a promising avenue for achieving high-speed, high-accuracy computations in an energy-efficient manner. The findings not only validate the theoretical advantages of complex modulation but also underscore its practical utility in enhancing the performance of optical neural networks, paving the way for its adoption in cutting-edge computational technologies [13; 22; 23; 24]. In the development of optical neural networks, manipulating the optical field typically involves altering either the phase or the amplitude independently. However, the complete optical field encompasses both phase and amplitude, presenting an additional degree of freedom. This holistic approach allows for more intricate control and interaction within the optical system, potentially leading to significant improvements in network performance. By leveraging both parameters simultaneously, researchers can achieve higher precision and flexibility in the modulation of light, which is crucial for the complex operations required in advanced optical neural networks. The inclusion of more adjustable parameters enhances the network's ability to learn and adapt, as it can represent and process a wider range of signal variations and complexities.