定义：
决定衍射效应区域的参数。

菲涅尔数最初在衍射理论中提出来是用来描述光束传播的。如果光先通过大小为a的孔而后传播距离L后到达屏幕，这是采用菲涅尔数表达式为： 

其中 λ 是波长。 
当菲涅尔数小于1时，发生夫琅禾费衍射，屏幕上显示的为孔的远场衍射图像，与光场通过孔径后空间复振幅分布的傅里叶变换相关。 
菲涅尔数等于或者大于1表示发生的是菲涅尔衍射（或者近场衍射），这时数学表示非常复杂。当菲涅尔数和衍射角度不大时，可以采用菲涅尔近似。 
 
共振腔的菲涅尔数 
菲涅尔数在光学谐振腔（腔）中也有重要作用，尤其是激光器谐振腔中。同样采用方程： 

这里a是端反射镜的半径，L为谐振腔长度。 
具有比较大的菲涅尔数（大于1）的谐振腔表明对于普通的模式大小（即不在谐振腔的稳定限度，该处模式大小会变化），端反射镜的衍射损耗很小。这在稳定的激光器谐振腔中是正常的情况。相反的，如果菲涅尔数比较小，衍射损耗会很大，尤其是对于高阶模式，因此最好采用衍射极限工作。 

许多稳定的激光器谐振腔具有相对较大的菲涅尔数，不稳定谐振腔中的菲涅尔数较小，这通常用于高功率激光器。 在分析法布里珀罗干涉仪的模式时，菲涅尔数也是一个很重要的参数。
 

Definition: a parameter determining the regime of diffraction effects

Originally, the Fresnel number was introduced in the context of diffraction theory for beam propagation. If a light wave first passes through an aperture of size (e.g. radius) a and then propagates over a distance L to a screen, the situation is characterized with the Fresnel number

where λ is the wavelength.

For values of the Fresnel number well below 1, Fraunhofer diffraction occurs where the screen essentially shows the far-field diffraction pattern of the aperture, which is closely related to the spatial Fourier transform of the complex amplitude distribution of the light field after the aperture.

Fresnel numbers around 1 or larger characterize the situation of Fresnel diffraction (or near-field diffraction), where the mathematical description is more complicated. For not too large Fresnel numbers and diffraction angles, the Fresnel approximation can be used.

Fresnel Number of a Resonator

The concept of the Fresnel number has also been applied to optical resonators (cavities), in particular to laser resonators [1]. One again uses the equation

where a is now the radius of the end mirrors, and L is the resonator length.

A large Fresnel number (well above 1) of a resonator (cavity) means that diffraction losses at the end mirrors are small for typical mode sizes (i.e. not near a stability limit of the resonator, where mode sizes can diverge). This is the usual situation in a stable laser resonator. Conversely, a small Fresnel number means that diffraction losses can be significant – particularly for higher-order modes, so that diffraction-limited operation may be favored.

Most stable laser resonators have a fairly large Fresnel number, whereas small Fresnel numbers occur in unstable resonators, which are sometimes applied in high-power lasers.

The Fresnel number is also important for the analysis of the modes of (plane) Fabry–Pérot interferometers, which extend to the edges of the mirrors.

Bibliography