Solve Fourier Optics Output with Fresnel Transform

[chenrim]

1. I have the following setting of free space than a lense and again free space
i need to solve for the output field as in the figure attached.
3. i used the fresnel transform once and then multiplied the field with the exponential and then convolved all the field. still couldn't make it to the final solution as stated at the output.

 

[Asim Riaz]

The output field can be found by solving the Fresnel diffraction equation. The Fresnel diffraction equation states that the amplitude of the output field is the Fourier transform of the input field multiplied by a transfer function. In this case, the transfer function is a complex exponential representing the propagation of the light through the two sections of free space.To solve for the output field, we first need to calculate the Fourier transform of the input field. Once we have the Fourier transform, we multiply it by the transfer function and take the inverse Fourier transform of the result. This will yield the output field.