Examination of Validity of Paraxial Approximation in Second Harmonic Generation Microscopy under Low Numerical Aperture

By using a vectorial approach, the validity of paraxial approximation in second harmonic generation (SHG) microscopy under low numerical aperture (NA) is examined when the sample is a collagen fibril. Due to the larger value of d_zzx and tensorial nature of SHG, the component E_z of the focused field may have strong effect on the radiation pattern of SHG. Numerical results indicate that when the value of NA exceeds 0.3, the effect of E_z can not be neglected, which results in the invalidation of paraxial approximation in SHG microscopy despite the fact that SHG microscopy is still under low NA focusing.