Optimization of intensity distribution in laser drilling

Optimization of the beam shape for laser drilling is theoretically discussed. Laser drilling is widely used in manufacturing vias on printed wiring boards. For that purpose, instead of an ordinary Gaussian beam, a flat-top beam is required at an object surface. An optimization method of the beam shape is proposed that uses the Fourier-Bessel series expansion of the complex amplitude distribution at an object surface. Each term of the series is related to a certain spatial frequency and the spatial frequency distribution of the beam at the object surface is related to the amplitude distribution at the lens. Terms having a spatial frequency lower than that related to the lens radius are used to optimize the beam shape so that the optimized beam shape is realized by an actual lens that has a finite aperture. The coefficients are determined such that they minimize the residual between the target shape and the beam shape. The optimization method is validated numerically using a CO2 laser drilling system, and the result shows that it is effective.