I would like some help with this optics problem.

Question 1 Stopping down a system. You are designing a system to focus a laser beam that will work only on axis, that is with a single spot. Analysis of your first design reveals that the transverse ray aberration at the paraxial image plane is a factor of x larger than the diffraction limited spot size. By what factor must you reduce radius of the laser beam to reduce the ray aberration to be equal to the diffraction limited spot size if you are also allowed to defocus the system?

In the previous problem, let x = 8, that is the TSA at paraxial focus is eight times the diffraction-limited spot size. After the aberration correction methods have been applied, by what percentage will the diffraction limited spot be larger than the original design?

Repeat the calculation assuming you had a system with only coma, not spherical aberration. By what factor must you reduce radius of the laser beam to reduce the ray aberration to be equal to the diffraction limited spot size if you are also allowed to also defocus the system?

Again, let x = 8 for this system with only coma. After the aberration correction methods have been applied, by what percentage will the diffraction limited spot be larger than the original design?

Thank you for the help!