KR100223031B1 - The binery phase hologram formation method using genetic algorithm - Google Patents

Abstract

In order to form a binary phase hologram that can be useful for free space optical coupling and optical information processing, it is necessary to determine the phase value of each cell of the two-dimensional binary phase hologram. The phase value of each cell depends on the shape of the target pattern, and the cost function is determined by the shape and phase value of the target pattern. In order to form the hologram corresponding to the desired target pattern, an algorithm that minimizes the cost function is required.

Accordingly, the present invention discloses a method for forming two-dimensional binary phase holograms having high efficiency and uniformity by using genetic algorithms to minimize cost functions.

Description

Binary Phase Hologram Formation Method Using Genetic Algorithm

The present invention relates to a method for forming a binary phase hologram having higher efficiency and uniformity by using a genetic algorithm to determine a phase value required for each cell in forming a two-dimensional binary phase hologram.

The hologram scans a laser beam onto an object and records the pattern of the reflected light and the transmitted light emitted from the object by using interference with the direct light of the laser beam. While a general photographic film cannot display a stereoscopic effect by recording only the amplitude of light, a hologram can record not only the amplitude of the light but also the phase. Holograms can be widely used in three-dimensional stereoscopic images because the phase of light stores information about the perspective of distance.

Recently, researches on binary phase holograms that can be usefully used in the field of free space optical connection or optical information processing have been actively conducted. The binary phase hologram is constructed by dividing one period of the hologram into K and L cells, respectively, as shown in FIG. 1, and then assigning each cell a phase value of 0 or π. Since each cell has two possible phase values, a hologram composed of K * L cells has a total of 2 ^{K * L} cases.

For the phase values Ψ _{K, L} of a given cell (k, l), the hologram transmission function g (x, y) is given by Equation 1 below.

Given that the hologram is a periodic function, the hologram transmission function g (x, y) can be Fourier-developed, and the Fourier coefficient G (m, n) is the amplitude of the diffraction beam at the output plane and is given by have.

In Equation 2, sinc (x) = sin (πx) / πx, and constants K and L represent the number of cells divided into x and y axes in one period of the hologram. The square of the Fourier coefficients G (m, n) gives the intensity of the diffracted beam at the output plane, where m and n represent the frequencies of the x and y axes, respectively. The method of forming the hologram is to make the intensity of the diffraction beam and the intensity of the diffraction beam of the target pattern coincide. However, in order to exactly match the intensities of the two diffraction beams, the number of cells must be infinite, which is practically impossible. Therefore, the method of forming the hologram is based on a few of the target pattern diffraction beam intensities. The efficiency of the output surface, denoted by, and the uniformity between the diffraction beams depending on the frequencies m and n must be taken into account at the same time.

In order to simultaneously consider such efficiency and uniformity, a cost function such as Equation 3 below is considered.

Here, T _{m, n} represent the diffraction beam intensity of the target pattern,

Is defined as By using the cost function in Equation 3, efficiency and uniformity can be considered simultaneously. This is because Equation 3 can be decomposed as shown in Equation 4 below, and the first term of Equation 4 represents efficiency and the second term represents uniformity.

In all possible cases finding the phase value of each hologram cell for the desired pattern results in an optimization problem that minimizes the cost function. Simulated Annealing has generally been used to solve this optimization problem.

However, this method is not only time consuming, but also requires a large number of cells. In addition, efficiency and uniformity could not be considered at the same time by using a cost function and another cost function proposed in Equations 3 and 4 above.

Accordingly, the present invention provides a method for forming a binary phase hologram that satisfies high efficiency and uniformity even with a small number of cells using a genetic algorithm as an appropriate cost function and an algorithm that minimizes this function in order to overcome the aforementioned difficulties. Its purpose is to.

In order to achieve the above object, the present invention is to determine the target pattern and the number of cells, and to determine the population (population), applying a genetic algorithm using the parameters determined in the step, and every iteration Investigating whether the efficiency and uniformity of the desired pattern is satisfied, characterized in that the step of determining the phase value of the hologram corresponding to the desired pattern.

Genetic algorithms are based on biological natural selection and evolution and consist of three stages of operations:

1) Reproduction

2) Crossover

3) Mutation

1 is an exemplary diagram for determining a phase value of a two-dimensional hologram.

2 is a flowchart of a genetic algorithm.

3 is an exemplary diagram illustrating the role of a crossover operator in a genetic algorithm.

4 is a graph showing the optimization process of cost function obtained by genetic algorithm.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

The genetic algorithm according to the present invention will be described in detail with reference to FIGS. 2 and 3 as follows.

First step: determine the target pattern and the number of cells of the hologram. (21 in Fig. 2)

Step 2: Apply genetic algorithm That is, an appropriate number of populations are constructed (21 in FIG. 2) to obtain the cost function for each individual in the population. Based on the obtained cost function, a new population is formed by giving a probability that the lower cost function is selected. That is, two objects are selected to obtain respective cost functions. Among them, select the individuals with low cost functions to form members of the new population. This process is repeated until the number of individuals selected is equal to the number of populations. This process is called cloning (22 in Figure 2). From the constructed population, we arbitrarily choose two parents to intersect (22 in Figure 2). This intersection selects blocks of constant size from the two ancestors, as shown in Figure 3, and selects the phases within the convex. Replace. This process is called a crossover operation. Store offsprings generated after the crossing and continue this crossing process until the number of offspring produced is equal to the number of populations. Compute the cost function of the population of the generated offspring and take the minimum of them (Figure 23).

Step 3: Check whether the minimum value (C _min ) obtained in the second step satisfies the efficiency and uniformity of the desired target pattern (C _limit ) (24 in FIG. 2). If satisfied, stop the genetic algorithm, if not satisfied, apply the mutation operation to the population (25 in Figure 2) and go back to step 2 and continue the genetic algorithm.

4 is a graph illustrating a process of minimizing a cost function when obtaining a phase value of a hologram for a target pattern using the genetic algorithm described above. As shown in this graph, as we continue to apply the genetic algorithm, the cost function decreases, which means that the efficiency and uniformity are improved at the same time. By applying the above algorithm to the design of binary phase hologram, it has high efficiency even with a small number of cells (about 70 ) And uniformity (about 5 You can form a hologram with).

As described above, according to the present invention, by using a genetic algorithm as an appropriate cost function and an algorithm that minimizes this function, there is an excellent effect of forming a binary phase hologram satisfying high efficiency and uniformity even with a small number of cells. .

Claims (1)

A first step of setting a population by determining a target pattern and the number of cells of the hologram; a second step of obtaining a cost function for each individual in the population, and performing a cross operation based on the obtained cost function; Continue to repeat until the number of generated progeny is equal to the number of populations, calculate the cost function of the population of the generated progeny and take the minimum of them, and the minimum value obtained in the second step A fourth step of checking whether the desired target pattern satisfies the efficiency and uniformity; and if the result of the check in the fourth step is satisfied, the genetic algorithm is stopped, and if not satisfied, a mutation operation is applied to the population. Binary phase using a genetic algorithm, characterized in that it comprises a fifth step of repeating the genetic algorithm How to program formation.