Spherical aberration

To calculate the spherical aberration of a system and evaluate its effect proceed as follows.

1. Calculate element contributions

For each lens element work out the wavefront aberration A:

A = ky⁴/f³

where y is the semi-aperture, or maximum ray height at the element (from an on-axis object); f is the element focal length, and the coefficient k depends on material, shape and conjugates and is given in the relevant section of this catalogue.

2. Sum contributions

Simply add the contributions algebraically to give the total wavefront aberration ΣA (deviation from the best-fit sphere).

3. Evaluate effect

If ΣA is less than λ/4 the system is diffraction-limited and aberration can usually be neglected. For larger aberration, the geometrical spot diameter D is given by:

D = 8 ΣAv/y

where y is as above, for the last element, and v is the distance from this element to the image. For further detail request our Technical Note ‘Spherical aberration’.