干涉型分数傅里叶变换计算全息及其数字再现

Interference type computer-generated hologram of fractional Fourier transform and its digital reconstruction

根据Lohmann I型分数傅里叶变换(FRFT)光学单元,在FRFT数值算法的基础上获得了物光波在FRFT域的离散复振幅分布,以干涉型计算全息编码方法制作出了分数傅里叶变换计算全息图(CGH),并在计算机中进行了数字再现。仿真实验结果表明:干涉型CGH能记录下物光波的振幅和相位的完整信息,输入平面上的物光波经过任意阶次FRFT后,按照干涉型CGH编码方式产生的全息图能够通过相应阶次的逆FRFT实现再现。

According to the Lohmann I type fractional Fourier transform（FRFT） optical unit and based on the numerical algorithm of FRFT, the discrete complex amplitude of object wave in the FRFT domain is obtained. The computer generated hologram （CGH） of FRFT is made out with the discrete complex amplitude by using the coding method of interference type CGH. The digital reconstruction of the hologram was performed in the computer. The results of simulating experiments show that the interference type CGH can record the whole information of the object wave, and the hologram, which is generated by using the coding method of interference type CGH, records the complex amplitude of the object wave obtained through arbitrary fractional order Fourier transform from the input plane and the object wave can be reconstructed through corresponding converse fractional order Fourier transform.