# Michelson Interferometric Methods for Full Optical Complex Convolution
## 5 Conclusions  
In this study, we addressed the engineering challenge of implementing reconfigurable complex wavefront modulation for optical convolution through the development of the RCCM. Our approach focused on overcoming the limitations of current optical computing systems, particularly in terms of processing speed and versatility. The RCCM demonstrates the capability to independently modulate both phase and amplitude over two million pixels in real time. Our experimental results show that the RCCM can effectively perform complex convolutions through the interference of spatially modulated wavefronts in both phase and magnitude. In neural network simulations using the CIFAR-10 dataset, we achieved a top accuracy of 51.98%, outperforming traditional amplitude-only (50.83%) and phase-only (47.87%) modulation techniques. These results indicate the potential of our approach in improving the efficiency and accuracy of optical neural networks. Critical analysis of our results reveals both strengths and limitations of the RCCM. The primary advantage lies in its ability to perform complex convolutions optically, potentially reducing the computational load on electronic systems. However, the current implementation faces a significant limitation in terms of operational speed, primarily due to the 60 Hz refresh rate of the commercial SLMs used in our setup. The RCCM's capability for simultaneous phase and amplitude modulation opens up possibilities for multiple image recognition tasks. By leveraging the parallel processing nature of optical systems, the RCCM could potentially handle multiple input images simultaneously; each modulated onto different spatial regions of the wavefront. This parallelism could significantly enhance throughput in large-scale image recognition applications. Furthermore, the RCCM shows promise in the realm of encrypted data transmission, particularly in implementing optical hashing algorithms based on SWIFFT. The ability to perform complex wavefront modulation allows for the implementation of more sophisticated optical encryption schemes. By encoding data in both amplitude and phase, we can potentially create more secure optical hashing methods, enhancing data security in optical communication systems. Future work will focus on overcoming the current speed limitations of our system. We aim to explore faster modulation technologies, including novel materials for high-speed spatial light modulation. Additionally, we will investigate the integration of our RCCM technology with PICs to enhance compactness and scalability. In conclusion, the proposed RCCM shows great promise in advancing optical computing, particularly for complex data processing, image analysis, and secure communications. Our system's capacity to adjust both light intensity and phase across two million points simultaneously marks a significant advance in optical data handling. Ongoing research into self-designed ITO-based SLM could push the RCCM's operating speed into the GHz range. Such improvements may dramatically enhance processing speed and efficiency, enabling real-time data analysis in fields like machine learning and cryptography. This work establishes a strong basis for future developments in adaptable optical computing systems, paving the way for more efficient data processing solutions as computational needs evolve. Conceptualization, H.K., Methodology, H.K., H.W., J.Y., Z.H., J.K.G., V.J.S. and M.S.-G.; Software, H.K., H.W., J.K.G. and M.S.-G.; Validation, H.K. ; Formal analysis, M.S.-G.; Resources, J.K.G. and V.J.S. ; Data curation, H.K. ; Writing--original draft, H.K., H.W., J.Y. and Z.H. ; Writing--review & editing, H.K., H.W., J.Y. and Z.H. ; Supervision, V.J.S. and B.M.N. ; Project administration, B.M.N. ; Funding acquisition, B.M.N. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The raw data supporting the conclusions of this article will be made available by the authors on request.