Achromatic lens
Achromatic lenses are corrected to bring two wavelengths (typically red and blue) into focus on the same plane.
The lens elements are mounted next to each other, often cemented together, and shaped so that the chromatic aberration of one is counterbalanced by that of the other.
Together they form a weak positive lens that will bring two different wavelengths of light to a common focus.
Credit for the invention of the first achromatic doublet is often given to an English barrister and amateur optician named Chester Moore Hall.
[1][2] Hall wished to keep his work on the achromatic lenses a secret and contracted the manufacture of the crown and flint lenses to two different opticians, Edward Scarlett and James Mann.
He realized the two components were for the same client and, after fitting the two parts together, noted the achromatic properties.
[6] In the late 1750s, Bass mentioned Hall's lenses to John Dollond, who understood their potential and was able to reproduce their design.
[2] Dollond applied for and was granted a patent on the technology in 1758, which led to bitter fights with other opticians over the right to make and sell achromatic doublets.
Dollond's son Peter invented the apochromat, an improvement on the achromat, in 1763.
In the following, R denotes the radius of the spheres that define the optically relevant refracting lens surfaces.
Historically, this was indeed a driving concern for lens makers up to the 19th century and a primary criterion for early optical designs.
However, in the mid 20th century, the development of advanced optical coatings for the most part has eliminated the issue of ghost images, and modern optical designs are preferred for other merits.
A Littrow doublet can produce a ghost image between R2 and R3 because the lens surfaces of the two lenses have the same radii.
In a Fraunhofer doublet, the dissimilar curvatures of −R2 and R3 are mounted close, but not quite in contact.
[7] This design yields more degrees of freedom (one more free radius, length of the air space) to correct for optical aberrations.
After the late 1860s, they changed to the Littrow design, approximately equiconvex crown, R1 = R2 , and a flint with R3 ≃ R2 and R4 ≫ R3 .
By about 1880, Clark lenses had R3 set slightly shorter than R2 to create a focus mismatch between R2 and R3, thereby avoiding ghosting caused by reflections within the airspace.
It can also increase light transmission slightly and reduce the impact of errors in R2 and R3 .
(for the refractive index at the Fraunhofer "d" spectral line wavelength), and the Abbe number
In order to correct other aberrations, the front and back curvatures of each of the two lenses remain free parameters, since the color correction design only prescribes the net focal length of each lens,
This leaves a continuum of different combinations of front and back lens curvatures for design tweaks (
Normally, the free parameters are adjusted to minimize non-color-related optical aberrations.
Lens designs more complex than achromatic can improve the precision of color images by bringing more wavelengths into exact focus, but require more expensive types of glass, and more careful shaping and spacing of the combination of simple lenses: In theory, the process can continue indefinitely: Compound lenses used in cameras typically have six or more simple lenses (e.g. double-Gauss lens); several of those lenses can be made with different types of glass, with slightly altered curvatures, in order to bring more colors into focus.
The constraint is extra manufacturing cost, and diminishing returns of improved image for the effort.
