Fresnel Diffraction Geometry

Fresnel Geometry

弗雷斯涅几何

For the Fresnel case, all length parameters are allowed to take comparable values, so all must be included as variables in the problem. The usual geometry assumes a monochromatic slit source and the problem is set up in terms of a parameter v as defined below. This parameter is used with the Cornu spiral or a table of elliptical intgrals.

在弗雷斯nel情况下，所有长度参数都被允许取相近的值，因此都必须作为问题中的变量包括在内。通常的几何假设为单色缝光源，问题则通过下文定义的参数v来设定。该参数用于与科努螺旋或椭圆积分表一起使用。

To calculate the intensity at point P, the geometry is set up in terms of the parameter v which is used with the Cornu spiral.

为计算点P处的强度，几何结构以参数v来设定，该参数用于Cornu螺旋。

Fresnel v Parameter

弗雷斯nel参数

The v-parameter in Fresnel diffraction analysis can be thought of as the arclength along the amplitude vector diagram called the Cornu spiral. In the Fraunhofer diffraction case where the source wavefront was assumed to be planar, the different elements of the wavefront had a constant phase difference and the incremental amplitude elements added to form the arc of a circle. In the Fresnel diffraction case where the curvature of the wavefront is included, the relative phase is not constant and the amplitude elements bend into the spiral curve. Just as in the Fraunhofer case, the resultant amplitude is represented by the chord of the arc.

在菲涅耳衍射分析中，v参数可以看作是沿着幅度矢量图中的弧长，称为Cornu螺旋。在夫琅禾费衍射情况下，假设光源波前为平面，波前的不同部分具有恒定的相位差，增量幅度元素相加形成圆弧。在考虑波前曲率的菲涅耳衍射情况下，相对相位不恒定，幅度元素弯曲成螺旋曲线。正如在夫琅禾费情况一样，结果幅度由弧的弦表示。

The intent here is to show conceptually how the light amplitudes at different points on a screen can be obtained using the Cornu spiral or the expressions shown in the Fresnel geometry. The amplitude is then squared to get the relative intensity at that field point. It is typical in more advanced optics texts to provide tables of the Fresnel integrals, which could be used for a computer routine to plot the Fresnel diffraction pattern.

此处的意图是通过Cornu螺旋或Fresnel几何中所示的表达式，概念性地展示如何获得屏幕上不同点的光幅值。然后将幅值平方以得到该场点的相对光强。在更高级的光学教材中，通常会提供Fresnel积分的表格，这些表格可以用于编写计算机程序来绘制菲涅耳衍射图样。