# Michelson Interferometric Methods for Full Optical Complex Convolution
## 1 Introduction  
Modern computing faces increasing demands for high-speed and efficient data processing, driven by the exponential growth in data generation and the complexity of computational tasks. Traditional electronic computing systems, while continuously improving, are approaching physical limitations in terms of processing speed and energy efficiency. This is particularly evident in data-intensive applications such as artificial intelligence, big data analytics, and real-time signal processing, where the large volume of information to be processed poses significant challenges. The bottleneck in these systems often lies in data movement and complex mathematical operations, especially in convolutional processes central to many machine learning algorithms. Additionally, the energy consumption and heat generation of dense, high-performance computing clusters presents both economic and environmental concerns. These challenges have spurred research into alternative computing paradigms that can potentially overcome the limitations of traditional electronic systems. Optical computing, leveraging the properties of light for information processing, emerges as a promising avenue. It offers the potential for parallel processing, reduced energy consumption, and faster computation of certain mathematical operations. However, realizing these benefits in practical systems requires overcoming several technical hurdles, including the development of efficient optical components and the integration of optical and electronic systems. In this study, we examine the potential of optical computing to address current technological challenges in data processing methodologies. We present a comparative analysis of classical electronic convolution techniques and optical passive convolution, highlighting the specific characteristics of each approach. This comparison aims to provide insights into their respective roles and limitations within current computing paradigms. Our research focuses on the development of hardware solutions for heterogeneous data processing, specifically exploring the application of optical methods. We investigate how optical computing techniques can potentially overcome certain limitations of traditional electronic systems, particularly in the context of convolution operations [1; 2; 3; 4; 5]. These approaches, with a particular emphasis on their impact on accelerating computational tasks, represent a significant leap in computing architecture diversity [6; 7; 8]. Our experimental work demonstrates a convolution-based processor capable of modulating both phase and amplitude across two million pixels independently. We present the design, implementation, and performance metrics of this processor, discussing its capabilities and limitations within the context of current optical computing challenges. Our focus is on developing and analyzing an SLM-based Reconfigurable Simultaneous Optical Full Complex Convolution Module. We also investigate potential applications, including an Optical Hashing Module based on the SWIFFT algorithm [9]. This study examines the principles and applications of the free-space Fourier 4F system in optical computing. We analyze its potential advantages in data processing, particularly for convolution operations. Our investigation also addresses the current limitations in optical computing approaches. We specifically focus on the trade-offs between resolution and processing speed in optical systems and the constraints imposed by commercial spatial light modulators (SLMs) with their 60 Hz refresh rate limitation. These challenges are critical factors affecting the practical implementation and performance of optical computing systems. By identifying these limitations, we aim to provide a foundation for future research directions in overcoming these obstacles. We introduce the Reconfigurable Complex Convolution Module (RCCM), an approach for optical computing based on established theoretical principles.