Spherical aberration correction of Gaussian beam

The relationship between the Strehl ratio and the standard deviation of the wave front aberration of a Gaussian beam is derived from the diffraction integral in the presence of aberrations. Let it be required to develop the spherical aberration of a Gaussian beam into an aberration polynomial. For the maximum value of the Strehl ratio, a set of linear equations is obtained. The optimum configuration of the balanced spherical aberration is obtained from the solution of this set of linear equations. The coefficients of the spherical aberration of a Gaussian beam for the optimum design are illustrated in terms of tables. A comparison is made between the Strehl ratio of the corrected spherical aberration of the Gaussian beam using the optimum design of the uniform beam for the minimum RMS wave front aberration and those for the minimum P-V wave front aberration. The Strehl ratio of the configuration using the optimum design of the uniform beam changes slightly. It turns out that the spherical aberration of the Gaussian beam can be balanced with the optimum configuration of the uniform beam. Finally, the correction of the spherical aberration of the Gaussian beam is illustrated with an example.