As a consultant, this author has reviewed the design and performance of numerous instruments and three common problems were found: ignorance of physical optics, negligence of aberrations, and absence of a tolerance budget. At least one member of the design team should indentify the type of aberration within the lens. Spherical aberration grows with NA, coma grows with field angle and NA, and astigmatism grows with tilt of the optic. These are important considerations for an optical system design.
4.1 Seidel Aberrations
A polynomial expression for the ray height at an image is expressed as follows:
y = Mh
+ B0p3 + B1h1p2 + B2h2p1 + B3h3
+ ∑50Cihip5−i + ...,
where h is the object height and p is the pupil position. The first line indicates the paraxial image height, which is simply the product of the magnification M and the object height h. The paraxial image height specifies an image system without aberration. The second line indicates a first-order aberration: defocus A1. The third line indicates third-order aberrations: spherical aberration B0, coma B1, astigmatism and Petzval curvature B2, and distortion B3.
Defocus occurs in several formats: an axial error in the position of the sensor creates defocus across the entire image; a curved image surface creates variable defocus across the field; a tilted surface creates astigmatism; a variation in refractive index creates axial color. Defocus is indicated by a dependency on p1.
Figure 4.1 displays a report for a spherical lens with spherical aberration. There is a dependency on p3. Spherical aberration is created by an increased power of the marginal focus with respect to the axial focus. The marginal rays are bent too much due to the spherical shape of the surface.