When longitudinal chromatic aberration has been corrected, we normally find that the focal positions for three wavelengths still do not coincide. This effect is known as secondary spectrum and is due to the nonlinearity of the curve of refractive index as a function of wavelength. It stems from a difference between the nonlinearity of the positive (crown) element and the negative (flint) element of an achromat. The basic Petzval lens consists of two positive components, spaced apart so that the astigmatism is controlled to be either zero or slightly positive. Usually the two components are achromats, typically doublets. Secondary spectrum is reduced in Petzval lenses because the second doublet operates at a lower aperture than the first.
The original Petzval lens was designed by Joseph Petzvel of Slovakia in 1839 as a portrait lens for the Daguerrotype camera and, at a speed of about f/3.5. Its purpose was to reduce the extremely long exposure times of the daguerreotype camera from about 30 minutes to about 30 seconds, using a wide aperture. The Petzval lens was optimized for large apertures and indeed could only operate at one fixed aperture. Petzval lenses were the mainstay of camera and projection lenses for almost 40 years during the dawn of photography. They are very rare now.Telephoto lens
When moderately long focal lengths are required, design similar to normal 50mm local length systems are often use. The basic power arrangement of a positive component followed by a negative component, can produce a compact system with an effective focal length F which is longer than the overall length L of the lens. The ratio of L/F is called the telephoto ratio, and a lens for which this ratio is less than unity is classified as a telephoto lens. By definition, many camera lenses which are sold as telephoto lenses are simply long-focal-length lenses and are not true telephotos. Since the system is unsymmetrical, each component must be individually achromatized if both axial and lateral color are to be corrected. The aperture stop is usually at the front member or part way toward the rear. Since a telephotos lens covers only a relatively small angular field, coma, distortion, and lateral color (which in many lenses are reduced by an approximate symmetry about the stop) are not as troublesome as they would be with a wider field. Simple telephoto lenses are formed by two cemented or closely airspaced achromatic doublets. Additional degree of freedom can be gained by splitting the doublets into widely airspaced components.
Telephoto lenses
Long-focal-length lenses
Wide-angle lenses for SLR camera
In modern SLR camera, a back focus of about 38mm to 40mm is required for mirror mechanism. This means the earlier forms of wide-angle lens are not acceptable, and the inverted telephoto construction is necessary. The arrangement of a negative component following a positive component has a back focal length which is longer than the effective focal length. Although the lens is much larger than the Biogon, correction for field curvature is very good because of the separated negative power at the front of the lens. The simplest fully corrected form is a pair of achromatic components. For the negative front component, the crown glasses (used for the negative elements) should be high-index and the flint glasses (in the positive elements) should be low-index; this reduces the overcorrected Petzval contribution from this component. For the positive rear component, the ordinary glasses should be low-index crowns and high-index flint. This combination increases its negative, inward-curving contribution to the Petzval sum. Usually the aperture stop is at the rear component; the natural shape for the front negative achromat is then that of a meniscus, concave toward the stop.
Double-meniscus anastigmat (Hypergon, Topogon, Dagor, Dogmar)
The Hypergon lens consists of two identical meniscus elements, symmetrical about a central stop. The concave and convex radii differ by less than 0.7 percent so that the Petzval contributions of the convex surfaces are almost completely offset by the Petzval of the concave surfaces. The astigmatism is controlled by the distance of the lens from the stop, and the symmetrical construction almost completely eliminates the coma, distortion, and the lateral color. The lens covers an astonishing field of 135 degree. Rapid rectilinear lens is a double meniscus system in which two achromatized meniscus lenses are arranged symmetrically on either side of the aperture stop, reducing or eliminating distortion, coma and lateral color.
The obvious way to improve the Hypergon is to add negative flint elements to correct the spherical aberration and axial chromatic aberration. The Topogon covers a field of about 100 degree at a speed of f/6.3, using dense barium crown and extra-dense flint glasses, retaining the symmetrical construction and the strong meniscus configuration for all the elements.The Dagor combines both the old achromat and the new achromat into a cemented triplet construction. If we visualize the central negative element of the triplet split into two parts, then the outer high-index element and the outer part of the middle (medium-index) element can be seen to make up a new achromat. The inner low-index crown element and the other part of the middle element make up the old achromat. The symmetrical construction about the stop minimizes the coma and distortion, while the spacing from the stop and the cemented surfaces control the astigmatism.
The Dogmar lens is also a member of the double-meniscus family. It can be realized if one considers each half to be a triplet with a center air lens. The Dogmar form is used as an excellent general-purpose camera lens, and its symmetry and stability of correction make it eminently suitable for an enlarger lens.
