Since the Young's formula for spherical waves can't accurately describe the field curvature and astigmatism of Gaussian beams, this study derived a Young's formula suitable for the off-axis transmission of Gaussian beams, which aids in the calculation of field curvature and astigmatism of Gaussian beams. Through five sets of experiments, the accuracy of the formula was verified, revealing that the size of the incident beam waist, the position of the beam waist, and the beam quality factor M² are all key factors affecting the field curvature and astigmatism of Gaussian beams.
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Jiang et al. (2024) studied this question.
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