Optical Cross Correlation for Similarity Detection
Optical wave interference can perform instantaneous operations, such as: addition, subtraction, multiplication, and more complex operations like Fourier transform [1]. Being able to develop an optical computer that directly executes these operations without the need for a digital representation could bring substantial benefits, e.g. being able to optically detect similarity versus the need for Euclidian distance calculations.
By simulating the optical cross correlation between input signals using COMSOL Multiphysics® and its Wave Optics module such direct optical similarity matching is demonstrated. The input signals were created by modulating a coherent incident wave using a metallic material (blue in Figure 1) with a number of air gaps (grey in Figure 1). The different dimensions of these gaps, resulting in different input signals.
According to [2], if an object is illuminated by a coherent plane wave and the light passes through a lens, then the Fourier transform is reconstructed exactly at a focal distance behind that lens. Therefore, a focusing lens is used in the setup as it eliminates the need for these objects to be in exactly the same location.
The simulation itself consists of two stages. The first stage stores the input signal on a photographic material located to the right of the lens (see Figure 1). Then a second input is directed toward the previously stored one. The resulting interaction, a cross correlation between the signal stored in the photographic plate (reference signal) and the second input, indicates the amount of similarity between the input and the stored signal. The resultant cross correlation will alternate between maximum intensity, in case of an exact match (Figure 2 (a)), intermediate intensity in case of a partial match (Figure 2 (b)), or minimum intensity in case of no match (Figure 2 (c)).
Compared with optoelectronic hybrid systems, this fully optical system will not suffer from the bottleneck of having to convert data from the optical to the electrical domain and vice versa [3]. Additionally, the proposed system is fully relying on the physical properties of optical materials to achieve the cross correlation instead of mathematical computations, consequently, allowing for dealing with data in its more natural format.
References
[1] M. C. Marshall C. Yovits, “Advances in Computers. Volume 28,” Academic Press, 1989, p. 155.
[2] J. Watson, “Fundamentals of Photonics,” in Optics & Laser Technology, Vol. 24, No. 3, Wiley, 1992, p. 130.
[3] D. D. Nolte, “Mind at Light Speed : a New Kind of Intelligence,” Free Press, 2001, p. 34.
