Question 2 : Principle of the laser velocimeter

a) In order to lighten notations, we can choose that the amplitude of the electrical field equals the unity, as both beams are polarized in parallel in a point the total complex amplitude of the expression equals the complex amplitude sum of each of the two monochromatic plane waves of the same frequency:

For the first wave is :

For the second one.

The total electromagnetic field is given by the sum of both complex amplitudes, namely:

The luminosity on the screen is proportional to the square complex amplitude:

Let us consider that plane is located in , the components of the vector that finds the position of a point in plane are:

In the fluid, the wave vectors of both waves have the same module with ,  is the fluid refraction index. Their components respectively are:

Vector is oriented in accordance with and its coordinates are

So the intensity is expressed as:

The place with the same intensity points corresponds to a succession of planes that are parallel to axis , of abscissa regularly spaced from interfringe . The expression of that interfringe is:

b) If the particle moves at speed following the axis of the , then the interfringe is browsed during time so that: