In this paper, we calculate the transverse spherical aberration <i>TA</i> of a thin lens and defines a normalized aberration Y equal to <i>TA</i> divided by the theoretical resolution limit. As a rule of thumb, (a) a thin lens that suffers only from spherical aberration may be considered effectively diffraction-limited as long as <i>Y</i>< 1.6. Similarly, (b) the coupling efficiency of a Gaussian beam to a single-mode fiber may be high even when Y >1.6, and, specifically, (c) the lens need be diffraction-limited only over a radius approximately equal to the radius (to the 1/e-point) of the Gaussian beam.
© 2000 Optical Society of America
Matt Young, "Normalized Parameter Relating the Spherical Aberration of a Thin Lens to the Diffraction Limit and Fiber Coupling Efficiency," Appl. Opt. 39, 6519-6522 (2000)