### #55 Fundamentals--Farunhofer Diffraction-II 常識集_夫朗和斐繞射_中

In this episode we will integrate the formula we left in the previous episode and introduce the concept of impulse response. Knowledge about Dirac delta function is required.

#50常識集_Dirac_delta_function    https://goo.gl/lTv7CE

## Fresnel approximation 菲涅耳近似

Recall that we expressed the electric field in (x, y, z) of a light passing through a transparent in terms of the summation of light with various spatial frequencies, or the Fourier transform of the transparent:

And now we are going to deal with it. We have previously mentioned that kz = (k^2-kx^2-ky^2)^1/2 =2π (1/λ^2 - νx^2 - νy^2)^1/2. Now let:

We post this figure again in case of you might forget:

Substitute it back and we could express kz as:

and we substitute it back to the exponential and do some Taylor expansion:

## 脈衝響應(impulse response)

除了剛剛說我們可以把通過透明片的影像想成是很多不同方向的光的總和之外，我們也可以換回我們一開始所說的，把透明片上的每一點當成新的點波源，看點波源發出的光的總和。點波源用數學來表示就是一個delta function。