Simple spherical aberration control in the direct laser writing deep under the plane surface of dielectrics

The algebraic equation established shows the focusing depths with compensated spherical aberrations under high-aperture focusing through the planar surface in materials with different refractive indices and the same pre-compensation settings of spherical aberration (SA) in focusing optics. Typically, the focusing objective possesses the correction collar calibrated for a single specific material. The developed relation allows the calculation of the depth at which SA pre-compensation is applied for any material.