Considerations in choosing a lens
In practice, as the polychromatic nature of white light is taken into consideration, and as imaging conditions depart from the Gaussian optics approximations that have framed our representations so far, optical aberrations get introduced into images formed by lenses.
Aberrations fall into two main categories: aberrations caused by wavelength variations (chromatic), and aberrations caused by the lens's spherical construction (these are known as Seidel's aberrations: spherical, coma, astigmatism, field curvature, and distortion) .
From fsu.edu 
Axial chromatic aberration and achromat doublet correction
- Axial chromatic aberration is due to dispersion by the lens's medium whose index of refraction effectively varies with the light wavelength: the blue part of the spectrum is refracted to a greater extent than the red portion.
- Lateral chromatic aberration manifests itself by a difference in magnification of blue vs. red images of white-light-illuminated objects, which causes color ringing at the outer regions of the field of view.
- An achromatic doublet combination (the association of a converging lens with a weaker diverging lens) can correct chromatic aberrations for certain wavelengths.
Longitudinal and transverse spherical aberrations
- Peripheral rays and axial rays have different focal points, because the former are actually refracted to a greater degree than the latter.
- Spherical aberrations arise from the higher-than-first-order terms in the sin θ and cos θ expansions that become non-negligible as the incident light angle θ increases.
- Spherical aberration causes the image to appear hazy or blurred and slightly out of focus.
- This effect significantly degrades the resolution of the lens because it affects the coincident imaging of points on and off the optical axis.
Coma and astigmatism
In coma and astigmatism, parallel off-axis oblique
rays do not focus at one point in the image plane, but rather at distinct points in the sagittal and meridional planes, causing image distortion.
- Comatic aberration results in off-axis point objects appearing asymmetrical and taking a comet-like shape. Comatic aberration is most commonly encountered when a microscope is out of alignment.
- Astigmatism engender ellipses or blurred lines as images of speciment points. Depending on the angle of the off-axis rays entering the lens, the line image may be oriented either tangentially or radially.
Petzval distortion or field curvature
Petzval distortion results in image curvature.
- Instead of generating image points of a flat object onto a flat screen as we have idealized so far in ray tracing estimations, a simple lens focuses these image points onto a spherical surface, shaped as a curved bowl whose curvature, the Petzval curvature, is the reciprocal of the lens radius.
- ↑ http://micro.magnet.fsu.edu/primer/anatomy/aberrationhome.html
- ↑ http://micro.magnet.fsu.edu/primer/anatomy/aberrations.html