一种菲涅尔全息图的快速算法

通过分析菲涅尔全息图计算模型,发现大量的平方运算和三角函数运算是计算速度的瓶颈,提出了一种菲涅尔全息图的快速计算方法.根据菲涅尔全息图的数学模型,利用三角函数的和差化积公式,将全息图的数学模型变换为由仅与水平或垂直方向有关的独立分量,通过四则运算来表示.在菲涅尔全息图的计算中,用少量的三角函数、平方运算和大量的四则运算代替原来大量的三角函数和平方运算,减少了全息图的运算量.实验表明,采用该算法后全息图的计算速度提高了9倍以上.

A Fast Computation Method for Fresnel Hologram

The mathematical model of Fresnel hologram is analyzed,and it is found that the speed bottleneck of generating CGH is the operation of square and trigonometric function.A method for fast computation of Fresnel hologram is proposed.The mathematical model of Fresnel hologram is transformed to the form which is expressed as the four arithmetic operations of components related to horizontal direction and vertical direction of hologram,according to trigonometric identity.Then,the great amount of operation of square and trigonometric function is replaced by little amount of operation of square and trigonometric function and great amount of arithmetic operation.The computational amount of Fresnel hologram is reduced and the computational speed will be increased clearly.The experimental results show that the speed of Fresnel hologram computation is accelerated over 9 times by using the method of separation of variables.