CAJ | 학술논문

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.
통과분석비열이전식도계산모형,발현대량적평방운산화삼각함수운산시계산속도적병경,제출료일충비열이전식도적쾌속계산방법.근거비열이전식도적수학모형,이용삼각함수적화차화적공식,장전식도적수학모형변환위유부여수평혹수직방향유관적독립분량,통과사칙운산래표시.재비열이전식도적계산중,용소량적삼각함수、평방운산화대량적사칙운산대체원래대량적삼각함수화평방운산,감소료전식도적운산량.실험표명,채용해산법후전식도적계산속도제고료9배이상.
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.