Aplanatic Lens:

Aplanatic lenses are designed to correct spherical distortions at the outer edges of an image. They differ from simple magnifiers being constructed from two bi-convex lenses, which provide significantly better image properties, because the aberrations usually present around the edges are eliminated.  Example: Peak 1961 Loupe magnifier

Aspheric Lens:

Aspheric hand-held magnifiers are excellent for short term tasks, such as reading labels, menus or maps. Aspheric lenses are also used to correct spherical aberration but, unlike Aplanatic lenses, they are made from a single element with a complex front surface that gradually changes in curvature from the centre of the lens out to the edge. The reduction in lens elements helps decrease the size, weight and assembly cost.  Example: Eschenbach Vario Plus

Achromatic Lens:

An Achromatic lens is one of the most popular lens type for high quality magnifiers. Used to correct or eliminate chromatic aberration which occurs when a lens fails to focus all colours in the same plane, the design of an achromatic lens bring two wavelengths (typically red & blue) into focus in the same plane. Achromatic lenses also minimise spherical aberrations. Made from cementing or mounting two lenses together, one positive and one negative, an Achromatic lens creates smaller spot sizes and superior image quality than a comparable single lens. Example: Peak 1983 Scale Loupe

Anastigmatic Lens:

Often used for checking items such as X-ray films or in the field of dermatology, anastigmatic magnifiers are the ideal tool for all applications requiring a large field of view, in addition to providing distortion-free, true-colour images. An observer can evaluate the entire image field by moving only his eye rather than his head, making anastigmatic magnifiers excellent tools for checking images, printing and slides or measuring lengths and distances up to 40 mm.
Anastigmatic lenses provide images with correct colour, crisp sharp edges and extremely high contrast over the entire visible surface, compared with conventional magnifiers which are corrected only in the centre of the image.  Example: Peak 1990-4 Anastigmatic Scale Loupe

Telecentric Lens:

A  Telecentric  system has a small opening at the focal point of the lens system, allowing measurement of the length and width of flat objects, as well as measurement of three-dimensional objects such as spheres, cylinders, etc. without parallax errors.  Example: Peak 1999 Telecentric Scale Loupe