M. Herzberger

Refractive Indices of Infrared Optical Materials and Color Correction of Infrared Lenses

The senior author’s interpolation formula for computing the dispersion of glass has been appropriately modified and applied to infrared materials. Indices of refraction for 14 optical materials that are suitable for practical refracting systems have been fitted by the modified formula and have been tabulated at increments of 0.5 μ for the useful transmittance range of each material. The method of applying the dispersion formula is discussed and is illustrated by the design of two three-element superachromats corrected for the region of 2.0–5.0 μ.

Light Distribution in the Optical Image

A method is proposed for obtaining information about the light distribution in an optical image. The characteristic function of the optical system is approximated by a polynomial, containing terms up to the fifth or seventh order. The coefficients of this function having been found, a large number (about 100) of rays from an object point are chosen, so that they are evenly spaced in the aperture of the system. By means of the function, the intersection points of the rays can be calculated in any desired image plane, to a close approximation. The intersection points were plotted, representing each ray by a small dot. The figures show that these plots are very similar to photographs of the image of a point light source. The image of a line element can be obtained by integration of a series of such figures.

Gaussian Optics and Gaussian Brackets

Gauss invented an algorithm for certain arithmetical purposes, which has various applications in optical problems. For instance, it is sometimes of value to see how the focal length, magnification, and back focus of a lens system vary with the change of one of the construction elements (thickness, radius, or refractive index). It is sometimes very useful to have explicit expressions for these significant lens characteristics as functions of the construction elements. However, the usefulness of these Gaussian brackets is not limited to Gaussian optics. The image errors for finite rays in the new form recommended by the author can be expressed with their help.

The Design of Superachromatic Lenses

The history of achromatic lenses is briefly reviewed. The latest development is the superachromat, which is corrected for four colors. Since the dispersion of glass can be represented by an equation containing four constants, the superachromat is practically corrected for all colors. The application of the superachromatic principle to thick lenses is described and it is shown that a compound lens can be made superachromatic by making each of its separate components superachromatic.

Optics from Euclid to Huygens

The salient contributions of writers on optics from Euclid to Newton and Huygens are outlined, with a workable bibliography, to encourage present-day workers to restudy the classical writings and to find ideas that lie outside the paths that orthodox optical science has taken.

Precalculation of Optical Systems

A necessary and sufficient condition is derived for a system of thin lenses with finite distances, in which image position and magnification can be corrected simultaneously for two colors. As an example, a nomogram is given for all color-corrected photographic triplets.

The Calculation of Aspherical Correcting Surfaces

A straightforward and reasonably quick method is described for the calculation of the aspherical correcting surface of the Schmidt camera, or other optical system in which the aspherical surface is adjacent to the object or image. An extension of the method is also described for cases where the correcting surface is in the interior of the system, and the rays must be refracted to match a given non-spherical wave surface, instead of meeting at a point. The procedure involved in the actual numerical calculation is described in detail, and selected figures are quoted from a representative system for which the calculation has been carried out.

Analysis of Spot Diagrams

A method has been described previously whereby, as a result of tracing relatively few rays through an optical system, the intersection points of a large number of rays from an object point with any assumed image plane can be found by means of an interpolation formula. When these latter rays are distributed equally over the exit pupil, the resulting spot diagram indicates the distribution of illuminance in the image of the point. The interpolation formula is of the fifth degree. In the present paper, the coefficients of this formula are grouped according to increasing powers of the aperture, thus giving a new type of image theory for large aperture and field. This new analysis of the image errors leads to simple geometrical patterns that enable the designer to ascertain the effect of changes in the constructional data on the complex spot diagrams. The analysis is applied to an actual lens, and an example of the way it is used to improve the lens is given.

Color Correction in Optical Systems and Types of Glass

The authors suggest that the optical qualities of a transparent material are given with the help of three graphs, one a plot of the reciprocal dispersion 1/(nF−nC) against the ν-value, the other two giving two data ρA and ρh signifying the deviation of the dispersion of the glass toward the red and violet ends of the spectrum from the regular standard. A universal dispersion formula is given which permits one (a) to calculate the refractive index for any given wave-length if the above data are given; and (b) to compute the above data if the refractive index is given for four or more values.The dispersion formula is linear with respect to the given data.The graphs so designed permit one to estimate immediately the powers of a doublet corrected for two wave-lengths and the amount of the secondary spectrum in the red and violet ends for any two given glasses.Testing these formulas for different types of glass and other optically important materials (fluorite, quartz, lithium fluoride, salt, etc.) shows an agreement with the measurements throughout the spectrum which is sufficient for optical calculation (±2×10−5).

A New Theory of Optical Image Formation

A report including the generalization of Gaussian theory of image formation with regard to an arbitrary ray; the location of points with a sharp image, and points whose image caustics are symmetrical; the derivation of the angle eiconal W for systems with certain special qualities; and a discussion of the qualities of ideal optical systems.