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 = ky^{4}/f^{3 }

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’.

Configuration |
Material |
Comar series |
k factor |

BK7 | PQ, PB, PI, PK | 0.0685 | |

BK7 | PQ, PB, PI, PK | 0.135 | |

BK7 | PQ, PB, PI, PK | 0.269 | |

S< |