Principal Rays Research Articles

The Frequency Response of Optical Systems

In optical systems the pencils forming images of extra-axial object points are generally oblique to both the object and image planes. The diffraction image of a point source observed in an oblique image plane differs significantly from that obtained in a plane normal to the image-forming pencil. The theory of the frequency response of optical systems is formulated for this more general case. The resulting formulae are used to relate the response obtained between object and image planes perpendicular to the optical axis to that obtained between planes perpendicular to the principal rays. It is shown that no loss of generality is introduced by the restriction to unidimensional objects. Some general properties of the response function for optical systems having aberration are derived.

Tracing a Normal Congruence through an Optical System

A method is given for tracing a wave surface through an optical system having rotational symmetry. The approximation used is valid for rays in the neighborhood of a principal ray lying in a meridian plane.

The Virtual Optics of the Median Plane of Axially Symmetric Magnetic Prisms

The angle between the asymptotes of a ray is developed as a power series in its impact parameter about some value which characterizes the `principal ray' When this value is zero, the principal points of the equivalent lens coincide at the axis of symmetry; in all other cases it is `thick' The focal length is here associated with the coefficient of the linear term, the transverse aberrations with those of the higher terms The quadratic aberration vanishes for a wide range of relative Hρ if the principal ray is suitably chosen. Foci with quadratic aberration are intercepts of the caustic curve, whose cusp lies at the cubic focus The dependence of aberration upon magnification and the conditions in which the cubic as well as the quadratic aberration vanish are discussed

A Note on the Calculation of Principal Ray Aberration

An expression for the spherical aberration of the principal rays is derived. If the primary aberrations are calculated the principal ray aberration may be found with very little additional effort

Correction of pupil aberration in Kellner-type eyepieces.

THE steeply curved surface of the field lens of a Kellner-type eyepiece usually introduces considerable spherical aberration of the principal rays. Frequently, this aberration cannot be corrected elsewhere in the system and, in consequence, there is no well-defined exit pupil of the instrument. In the case of a visual instrument, this pupil aberration may cause variations of brightness across the field of view, due to vignetting of the image-forming pencils at the observer's eye pupil. It has been found possible to correct the pupil aberration in a Kellner eyepiece by employing an aspherical surface on the field lens.

The General Theory of Isoplanatism for Finite Aperture and Field

In the introduction we have generalized the definition of isoplanatism and established the corresponding representation for centered systems. In Part I we explain the theory for the meridional bundles, applying the general differential law for two independent wave surfaces. The angle of field may have any finite magnitude. After having found Eq. (35), we transform it conveniently, so that there appear in it only the intrinsic variables which are introduced for the bundles under consideration and the total aberration of aperture, obtaining the condition (42) in invariant form. This is a necessary and sufficient condition.The explained theory is valid for optical systems more general than centered systems, viz., for those which have only a single plane of symmetry, in which the isoplanatic, linear element can have any direction.Though we defer the general discussion of the conditions to a later paper in which the theory will be extended to extra-meridional bundles, we make a first analysis of formula (42) deducing from it (Sections II.9–17) some characteristic laws. The extension of the validity of the form of some conditions, for instance those of Herschel and Lihotzky-Staeble, for general values of fields, shows the principal ray is an axis of bundle even more important than the optical axis in the centered systems.In the Appendix we shall present some comments on main aspects of the theory.

The Diffraction Structure of the Elementary Coma Image

The integrations reported in this paper domonstrate conclusively that the elementary coma image is of the size and shape determined by ordinary geometrical optics, and that the only effect of diffraction is to break up the image into an elaborate fine structure of dots and lines of light. Practically all the light in the image is confined within the triangular space between the principal ray at the tip of the figure and the sagittal focus. Between the sagittal and tangential foci there is a small amount of light broken up into a series of approximately concentric curved bands of darkness and light, centred about the brightest part of the image. Even when the amount of coma is very small, comparable to the Rayleigh Limit, the characteristic shape of a typical coma-image is already making its appearance. The accuracy of the theoretical predictions is fully and completely borne out by the actual photographs of a comatic image.

Image Error Theory for Finite Aperture and FieldI The Image of a Point; Geometry of the Wave Surface*,†

The author here suggests the replacement of the customary image error theory by a new one which permits the analysis of the symmetry qualities of the image by means of a few diagrams. Three new functions are introduced: the deformations function, D, the asymmetry function, A, and the spherical aberration function, S. The distance, τ, of the caustic from the diapoints is given by τ2+Sτ+Dζ2=0,and D=S=0 gives a system free from aberration. S, D, and A, are developed as functions of a special kind of variable, for which the author suggests η−η0, ζ−ζ0. Here, ζ and η are the direction cosines of the image ray with the optical axis and the perpendicular to it in the meridian plane; ζ0 and η0 are the corresponding angles for the principal ray of the bundle to be investigated.Formulas are given for the development of these functions and for their connection with the characteristic function of the system.

The diffraction theory of optical aberrations: Part II: Diffraction pattern in the presence of small aberrations

In this paper the diffraction theory for arbitrary aberrations of a symmetrical optical system is developed for the case that the amount of aberration is small. The aberration function, which measures the deviation of the actual wave-front from a sphere, is expanded in a series of the so-called circle polynomials, which were introduced by Zernike in a problem closely related to the one treated here. This new expansion appears to have considerable advantages as compared to the customary one. So, for instance, the problem of the counter-balancing of aberrations of various orders can be solved now completely. Formulae are given, from which the intensity distribution of the diffraction pattern in a receiving plane perpendicular to the principal ray in the neighbourhood of the Gaussian image can be numerically determined without much labour. The formulae are applied to the diffraction patterns of astigmatism and coma. The results of the numerical computations are given in diagrams showing the lines of equal intensity.

LV.—The Perciform Genera Gymnapogon and Nannatherina

YMN.POGON japonicus, a new genus and species of fishes, was described by me in 1905 (Regan, Ann. Mag. Nat. Hist., (7) 15: 19) from a number of specimens measuring up to 45 mm. in total length, from the Inland Sea of Japan. I considered it to belong to the Chilodipteridae (=Apogonidae), and using Jordan and Snyder's review of the Japanese fishes of this family (Proc. U. S. Nat. Mus., 22, 1901: 891-913), I put it near Telescopias, which it appeared to resemble in having the spines feeble, canines anterior in the upper jaw, and lateral in the lower, preoperculum produced into a thin flap, etc. In 1913 (Classification of the Percoid Fishes, Ann. Mag. Nat. Hist., (8) 12: 111-145) Telescopias, as a synonym of Scombrops, was placed in the Pomatomidae, and Gymnapogon was mentioned as related to it. I have for some time thought it likely that this was a mistake, but it was not until I had read Herre's description of Henicichthys philippinus (CoPEIA (4), 1939: 200), evidently a Gymnapogon, that I decided to reexamine the types, and to study the skeleton. This I have done by examining an alizarin preparation and by dissecting another specimen. Henicichthys foraminosus Tanaka, 1915 (Tomiyama, Japanese J. Zool., 7 (1), 1936: 50, fig. 9) is a synonym of Gymnapogon japonicus. Tomiyama's figure is good, except that the pectoral fin is too high, and the caudal rays are too divergent. He considers this fish to be a gobioid, but it differs from all known members of this group in having the gill membranes separate and two anal spines, and I find that the skeleton is typically perciform. In most respects Gymnapogon japonicus resembles the Chilodipteridae, especially Chilodipterus, but it differs from them in the following characters: No scales; sides of head with a network of series of small pores; 20 or more vertical series of similar pores on each side of body; lateral line represented by a series ending below soft dorsal, and another on middle of side of tail. Fin spines very slender. Pectoral higher, the upper end of its base about equidistant from dorsal and ventral profiles. Operculum connected by membrane to pectoral arch, the gill opening ending a little above the pectoral. No supramaxillary (or supplemental maxillary). There appear to be no other differences from the Chilodipteridae. The dentition is similar to that of Dinolestes and Synagrops. The preoperculum, produced backwards below as a large thin flap, is also much as in these genera. The dorsal fin has VI, I 10-11 rays, the anal II 9-10. The caudal has 17 principal rays, 15 branched, and a series of about 10 procurrent simple rays above and below, a structure approached in Synagrops. The pelvics, with I, 5 rays, are close together, a little in advance of the pectorals, which have 13 or 14 rays. The pectoral fin is supported by four hour-glass shaped radials. The skull is essentially similar to that of Dinolestes, as described by Starks (Proc. U. S. Nat. Mus., 12, 1899: 113-120, pls. VIII-XI), but with parietal crests scarcely developed, and with a short ethmoid region, ending

The path of rays in periscopes having an inverting system comprising two separated lenses

Foreword. Principal elements. The marginal beam, field of view, and magnification. Ray tracing as applied to periscopes. The principal rays and the centre of the effective stop. Illumination of the marginal beam and its relation to the field of view. The Collector Law. Determination of the collector lens. Periscopes with parallel path of principal rays in front of the eyepiece. Special numerical example. Calculation of the Ramsden eyepiece. Reduced top periscopes. The external form of the submarine periscope.

II. The spectroscopic properties of dust

The suggestion that the auroral spectrum, the principal ray in the spectrum of nebulæ, and other rays of unknown origin, might be due to meteoric dust induced us to investigate the problem whether solid particles of sufficient minuteness would act like gaseous molecules in an electric discharge and become luminous with their characteristic special radiation. The dust we employed was that thrown off from the surface of various electrodes by a disruptive discharge, and it was carried forward into the tube of observation by a more or less rapid current of air or other gas. The arrangement will be best understood from the annexed diagram, which represents a section of the glass vessel which was the principal part of the apparatus. A represents a bulb in which were the electrodes a , a to give the dust, connected by a widish tube d with the tube for observation B .

XII. Researches towards establishing a theory of the dispersion of light

The phenomena of prismatic dispersion, as originally discovered by Newton, and since examined throughout a vast range of transparent bodies by succeeding philo­sophers, especially Sir David Brewster, were principally considered with reference only to successive parts, or spaces, of the coloured spectrum, designated generally as the red, or violet, or mean rays. The increasing precision of modern science has been evinced in the elaborate and justly celebrated researches of M. Fraunhofer, who, availing himself of the dark and bright lines to mark and designate distinct points of the spectrum, by prismatic ob­servations for ten different media, solid and liquid, has determined in each the re­fractive indices for seven principal rays, thus always absolutely identifiable. We will use the term “definite rays” to signify the specific parts of the spectrum thus defined. As to the law of the phenomena, the first notion of a simple proportionality was soon disproved. The refrangibility was seen to vary considerably and irregularly for each ray and each medium ; and when Fraunhofer had assigned serieses of numbers as the accurate expressions of the varying refractive powers throughout the several spectra, the apparent absence of any law connecting these numbers was only ren­dered more palpable. All that could be said was, that the numbers increased from the red to the blue end of the scale, and in a different way in each medium.