Spatial Frequency

Table of Contents:

  1. The Concept
  2. Gaussian Beams

The Concept

We will use the concept of spatial frequencies to further highlight the usefulness of the angular spectrum. First, the definition of spatial frequency is the number of periods per unit length, often in units of lines/mm. The difference between low and high spatial frequency is shown below.

This concept of spatial frequency can be useful when we consider the propagation of a plane wave at an angle to some plane A. In the figures below, we can consider the origin to be plane A.

In the first image, there are no discrete waves passing the plane A, so we would be better off just describing this as a plane wave. However, in the second and third images on the right, we can see that there are several waves of the plane wave that pass the plane at A. If we are given this distribution at plane A, then we can express the distribution as an integral over a set of periodic functions that satisfy the periodicity requriements. Note that the highest spatial frequency in the x-direction would be when the field propagates directly along the x-axis, which corresponds to

\begin{equation} (k_x)_{max} = \frac{2\pi}{\lambda} \end{equation}

GAUSSIAN BEAMS

Gaussian beams can also be represented as an angular spectrum distribution!

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