Optimization of lens spacing for collimation magnification in the defocused two-lens system

Precise lens-spacing control is critical for two-lens laser collimation, yet the conventional afocal condition does not necessarily provide the maximum collimation magnification when defocus is introduced. This study proposes the defocused two-lens collimation design method that exploits the defocus effect to optimize beam expansion. In the proposed Galilean configuration, the incident beam waist is intentionally displaced from the object-side focal plane of the secondary lens, allowing the lens spacing to depart from the afocal spacing and the defocus amount to serve as an optimization parameter. Based on Gaussian-beam propagation, the analytical condition for maximizing the collimation magnification is derived and experimentally verified using the He–Ne laser. Camera-captured spot images are processed by constrained elliptical Gaussian fitting, and the finite-range effective divergence angle is used to evaluate the collimation performance. The results show that the maximum magnification is achieved when the waist of the beam emerging from the secondary lens is located at the object-side focal plane of the primary lens. The measured optimum spacing and magnification agree well with theoretical predictions, with the magnification error within 3%. These findings provide a reliable basis for the precise design and lens-spacing optimization of defocused two-lens collimation systems, with potential applications in high-magnification beam expansion, lens-spacing optimization, and precision laser measurement.