Longitudinal Aberration Research Articles

Relative Star Positions from Overlapping Photographic Plates

An account is given of an investigation to obtain accurate relative star positions from overlapping photographic plates. The method described is quite general, but in the first instance is to be applied to plate material obtained with the new Cape astrometric camera.The Cape 4-component f/10 20-cm astrometric camera produces a field of 5° square with a scale of 100″ per mm in the focal plane. The telescope is fitted with a yellow filter 12 mm from the focal plane, which in combination with the Ilford-R40 emulsion used, transmits more or less uniformly in the range 5300<λ<6500 and little elsewhere. Within this spectral range, the maximum longitudinal aberration is only 0·75 mm and the images sensibly round out to the edge of the plate. The instrument is currently being used to obtain a complete coverage of the Southern hemisphere down to mv~11·5 such that each plate, effectively 4° square, has overlapping plates centred at each corner and at the middle of each side. In practice, this system of overlapping is applied to a number of zones in declination each about 10° broad. Each plate is taken within 30m of the meridian and is given two 3m exposures above and below the 1950 standard positions, the geometrical plate centre being estimated to be within 20″ of the tangential point. At the time of writing, coverage of the zone −30° to −52° is almost complete, and preparations for the zone 0° to −30° well advanced.

Highly Accurate Nonspherical Reflectors for the Millimeter and Submillimeter Wavelength Region

A method of fabricating nonspherical reflectors for the millimeter and submillimeter wave region with a precision greater than that afforded by normal machining techniques yet less costly than optical grinding has been devised. The heart of the technique lies in bonding a thin foil of aluminum to a slip cast fused silica mold with epoxy cement. Both paraboloidal and prolate spheriodal reflectors have been built. The surface of a 30.5 cm paraboloidal reflector fabricated by this method has been found to vary by no more than ±12 μ which was the limit of resolution of the longitudinal aberration test used for checking the finished surface.

On the Errors of Testing and a New Method for Surveying Optical Surfaces and Systems

A systematic study of the precision required and of the errors committed in testing parabolic mirrors by the longitudinal aberration and by the transversal aberration methods is made, showing that these methods do not possess in general the necessary accuracy of a hundredth of a wave-length per zone. A new method is developed, which consists in determining the caustic or line of the centers of curvature of the surface elements. With this method, a precision of better than a hundredth of a wave-length per zone can easily be obtained. The zones can be comparatively wide. Secondary zones and surface detail can be detected just as well, or even better than by using a plane mirror in conjunction with the parabolic. The use of master flats is thus superfluous. The experimental procedure is explained and results of actual tests are given. By using a thin wire instead of a knife-edge systematic errors are avoided and higher precision is obtained. The caustic method can be applied to the quantitative test of convex surfaces, like Cassegrain mirrors, to the determination of astigmatism, to the study of single lenses, lens systems, Schmidt correcting plates, etc. Its accuracy does not depend on the value of the aberrations, so that surfaces departing considerably from a sphere can be tested just as well as spherical surfaces. It will thus be possible to figure such surfaces with high precision.

A New Method for Testing Cassegrain Mirrors

A new arrangement for testing Cassegrain mirrors is described which does not require the use of large mirrors as auxiliaries. It consists in placing a convergent lens in front of the mirror so as to form a real image of the illuminating pinhole and measuring the resulting aberration. The aberration of the lens is numerically eliminated after an independent measurement with the help of a small plane mirror placed at an appropiate distance. The longitudinal aberration of the Cassegrain alone can also be directly obtained by displacing the small plane mirror. The method permits high precision. It can be applied to any convex surface.

The Measurement of the Aberrations of a Microscope Objective

After outlining the methods that have been employed for measuring the spherical aberration of microscope objectives, a new method is described in which a thin metal plate having a small hole in it is mounted between the objective and the microscope tube in such a way that the hole may be traversed across the middle of the objective aperture by a micrometer screw. The point at which the small beam of light thus isolated intersects the image plane is located by means of a filar micrometer. This gives a direct measure of the transverse aberration of that zone of the lens which contains the sliding hole, from which either the optical path difference or the ordinary longitudinal aberration of the zone can be readily computed. The aberration is then plotted graphically against the numerical aperture of the zone. The limitations and the precision of the method are discussed. The Foucault knife-edge test was found to be readily adaptable to the measurement of the chromatic aberration of a microscope objective. Typical curves for all these tests are given.

Refraction of a Spherical Wave in a Spherical Interface

Transformation of a plane or spherical wave by refraction at a plane or spherical surface, treated vectorially.---The vector equation of the refracted surface is calculated completely in each of the following four cases: (1) Plane wave incident on plane surface, (2) plane wave on spherical surface, (3) spherical wave on plane surface and (4) spherical wave on spherical surface. In each case an exact expression for the longitudinal aberration is calculated and this is reduced to the usual formula by expansion in series.

Longitudinal Aberration in Aspherical Optical Systems

I. Introduction. Various references have been made to the use of aspherical lenses for reducing defects and new methods of analysis have been devised for studying such systems. The present paper extends certain well-known formulas from the case of spherical lenses to those not spherical, but symmetrical.II. The Coefficient of Form. The general surface of revolution generated by the curve x=x0+γ1y2+γ2y4 is characterized for present purposes by the coefficient of form B=1−γ2/γ13, which reduces to zero for the case of a sphere.III. Longitudinal Aberration. Since the longitudinal aberration is the only second order defect affected by the departure from sphericity, the results are restricted to this defect. Several formulas are derived, each depending on the coefficient of form.IV. Conclusion. The amount of retouching necessary to change a sphere of radius 1/k into a surface whose coefficient of form is B is (1/8) B k3h4, where h is the optical “height” i.e. distance from axis of the point concerned. For a Dallmeyer “Rapid Landscape” lens of focal length 102. 88 mm and semi-aperture 4.52 mm, the maximum amount of retouching necessary to completely remove the second order longitudinal aberration is found to be about 0.0026 mm, whether the initial or final surface is retouched.

The Transmission of Waves Through A Symmetric Optical Instrument.

Gaussian Parameter Method of Studying the Transmission of a Wave Surface through a Centered System of Symmetric Lenses.---Since for each point of an incident wave surface there is a corresponding point on the refracting surface, the parameter $\ensuremath{\alpha}$ of the refracting surface may be expressed in terms of the parameter $\ensuremath{\beta}$ of the wave surface, thus allowing the elimination of the parameter $\ensuremath{\beta}$. After expressing all quantities in terms of $\ensuremath{\alpha}$, certain invariant combinations are found among the coefficients of the wave and lens surfaces, these furnishing the determination of the refracted surface. This gives a point by point correspondence between all surfaces of the system. As an application, the focal distance and longitudinal aberration are calculated and a numerical case given. The method is applicable to aspherical surfaces as simply as to spherical ones, and it is hoped that many problems in practical optics may be simplified by the present method, combined with proper choices of the parameter.

On a theory of the second order longitudinal spherical aberra­tion for a symmetrical optical system

1. The object of this investigation is to establish a formula for the longitudinal spherical aberration of rays which traverse a symmetrical optical system in an axial plane that shall be capable of fairly easy computation for any combination of lenses, and at the same time shall be accurate to the second order and free from certain important difficulties of convergency which occur in certain neighbourhoods when we attempt to use for the longitudinal aberration the method of aberration of successive orders. From the point of view of the optical designer, the usual theory of aberrations, which, for all practical purposes, is largely restricted to the first order, is known to give an unsatisfactory approximation. In practice, the designer adopts a semi-empirical method of tracing a number of rays through the system by means of the trigonometrical equations, a method which is laborious and lengthy, and which can at best give only incomplete informa­tion and very limited guidance for effecting improvements.

The longitudinal aberration of prisms

The longitudinal aberration of prisms