A Brief History of Lens Design
"|8oFf)l@B Since about 1960, the way lenses are designed has changed profoundly as a result of the introduction of electronic digital computers and numerical optimiz-ing methods. Nevertheless, many of the older techniques remain valid. The lens designer still encounters terminology and methods that were developed even in previous centuries. Furthermore, the new methods often have a strong classical heritage. Thus, it is appropriate to examine, at least briefly, a history of how the techniques of lens design have evolved.
?#K.D vGJ [KK
|_ A.2.1 Two Approaches to Optical Design
?),b902C 072C !F The equations describing the aberrations of a lens are very nonlinear func-tions of the lens constructional parameters (surface curvatures, thicknesses, glass indices and dispersions, etc.). Boundary conditions and other constraints further complicate the situation. Thus, there are only a few optical systems whose con-figurations can be derived mathematically in an exact closed-form solution, and these are all very simple. Examples are the classical reflecting telescopes.
#|b*l/t8 This predicament has produced two separate and quite different approaches to the practical task of designing lenses. These are the analytical approach and the numerical approach. Historically the analytical dominated at first, but the numer-ical now prevails.
{fXkbMO| Neither approach is sufficient unto itself. A lens designed analytically using aberration theory requires a numerical ray trace to evaluate its actual perfor-mance. In addition, an analytically designed lens can often benefit significantly from a final numerical optimization. Conversely, a lens designed numerically cannot be properly understood and evaluated without the insight provided by ab-erration theory.
NpH8=H9 9[.HWe, A.2.2 Analytical Design Methods
^~H}N$W"-q KOy{? The first lenses made in quantity were spectacle lenses (after about 1285).
i|^Q{3?o# Later (after 1608), singlet lenses began to be made in quantity for telescopes and microscopes. Throughout the seventeenth and eighteenth centuries, optical instru-ments were designed primarily by trial and error. As might be expected, optical flaws or aberrations remained. Note that, aberrations are fundamental design shortcomings, not fabrication errors. Eventually it became clear that understand-ing and correcting aberrations required greater physical understanding and a more rigorous analytical approach.
!J7`frv"( At first, progress was slow and the methods largely empirical. Later, math-ematical methods were introduced, and these were much more effective. The most outstanding early work on optical theory was done by Newton in 1666. Among the somewhat later pioneers were Fraunhofer, Wollaston, Coddington, Hamilton,and Gauss. A major advance was made by Petzval in 1840. Petzval was a mathemati-cian, and he was the first to apply mathematics to the general problem of design-ing a lens with a sizable speed and field for a camera. The techniques he devised were new and fundamental. His treatment of field curvature based on the Petzval sum is still used today. Just as unprecedented, he was able to completely design his very successful Petzval Portrait lens on paper before it was made.
L jy797{f In 1856, Seidel published the first complete mathematical treatment of geo- metrical imagery, or what we now call aberration theory. The five primary or third-order monochromatic aberrations are thus known today as the Seidel aber-rations. They are:
G WIsT\J 1. Spherical aberration
=
7y-o 2. Coma
R0- 0 3. Astigmatism
40kAGs>_ 4. Field curvature
oV%:XuywT 5. Distortion.
jSem/; There are also two primary chromatic aberrations. These are wavelength-de-pendent variations of first-order properties, and they are often included with the Seidel aberrations. They are:
Y7t#)? 6. Longitudinal chromatic aberration
P)Adb~r 7. Lateral chromatic aberration.
0<m7:D
Gd Petzval, Seidel, and many others in subsequent years have now put aberra-tion theory and analytical lens design on a firm theoretical basis.注釋1
7h
54j Until about 1960, the only way to design lenses was by an analytical ap-proach based on aberration theory. Unfortunately, by its nature, aberration theory gives only a series of progressively better approximations to the real world. Thus, the optical designs derived from aberration theory are themselves approximate and usually must be modified to account for the limitations in the process.
ZsP
