by the lens and mirror mount shown in fig. 9. T represents the lens under test, U a convex mirror in such a position that it reflects back along their own paths the rays received from T. The mirror U can be moved by a screw motion

actuated by the handle V, so that its distance from T can be varied at will. It will be seen that when the adjustment of this part of the apparatus is correct, the whole lens addition will, if the lens T be perfect, receive the beam of plane wavefront and deliver it back again with a plane wave-front. If it does not do so the departures from planeness of the so delivered wave-front will form a contour map of the corrections which have to be applied to the lens in order to make its performance, when in actual use, perfect.

The general procedure is the same as in the case of prisms, namely, to choose such an adjustment as presents a favourable aspect for working and to polish off those portions of the surface corresponding with the parts of the contour map which represent hills.

2. Various Uses of the Interferometers.

(a) Control of "retouching."

The instruments were primarily designed for the correction by retouching of object-glasses and prisms.

The process of retouching (viz. local polishing away of the glass) appears to have been adopted by all the great constructors

of large astronomical lenses*. Although the necessity for this device has not generally been referred by them to the want of homogeneity of the glass, yet the almost invariable presence of such heterogeneity would render retouching essential even were there no other causes of optical imperfection. The method of carrying out the process with the aid of this apparatus has been sufficiently described above. It has been found both speedy and effective in the manufacture of prisms and lenses where the highest accuracy is desired.

Many other methods of testing telescope or camera objectives have been devised with a view to the control of retouching. With each of the well-known methods results have been attained of an excellence commensurate with the reputation for optical work of high quality which has distinguished the individual exponents; but none of the methods appear to give indications upon which the optician could take action without a more or less complex process of reasoning.

The apparatus here described, on the other hand, produces, as has been shown above, a system of interference-bands which may be regarded as a "contour map" of the imperfections. This contour map can for practical purposes be considered as located at any of the optical surfaces involved; and in the case of the control of retouching, the observer may, if he likes, draw this map upon the surface under treatmeat. He is then in a position without further preliminary to remove the superfluous material from the prominences by polishing with pads of suitable size and shape, the "contour map" giving all that is necessary for him to know both as to the location and the magnitude of the sources of the imperfections.

(b) The testing of lens systems.

The apparatus obviously affords, when applied to any optical system, all the data necessary for a complete and precise statement of the degree of optical perfection of that system. As regards small aberrations it is sufficient to quote the well-known and valuable generalization :

"An obvious inference from the necessary imperfection of optical images is the uselessness of attempting anything like

The opinions of Schroeder, Grubb, Czapski, and Alvan Clark on this subject are cited in a summary by H. Fassbender of the then known methods of testing object-glasses: "Ältere und neuere Methoden zur Prüfung von Objektiven," Deutsche Mechaniker Zeitung, July 1913, pp. 133-138 & 149-155. This report should be read by all interested in the subject. It omits, however, an ingenious method due to Dr. Chalmers, see Proc. of the Optical Convention, vol. ii. p. 56 (1912).

an absolute destruction of aberration. In an instrument free from aberration the waves arrive at the focal point in the same phase. It will suffice for practical purposes if the error of phase nowhere exceeds λ. This corresponds to an error of in a reflecting and λ in a (glass) refracting surface, the incidence in both cases being perpendicular "*.

In the case of larger aberrations (implying by that word the effect on the "image" of the deviation from sphericity of the wave-front) the writer is firmly of the opinion that the departure (expressed in wave-lengths) of the wave surface as it leaves the dioptric element from a spherical wave surface, should form the basis of all statements of imperfections of definition, and believes that such a procedure, besides being most rational according to our present knowledge, is at the same time very convenient in application by the manufacturer.

The co-ordination of the phenomena observed on this interferometer with the image-forming properties of the optical system under test is one of the objects of Dr. L. Silberstein's investigations, part of which appear in another paper in this Magazine.

(c) The use of aspherical surfaces.

In spite of the great advances in the technique of optical manufacture during the past thirty years, the definition of actual optical systems still leaves ample room for improvement. Even if we confine our remarks to the best makers, it is only in certain of the smaller optical instruments that the imperfections of definition are inconsiderable, and even then only on the best part of the field of view. This is in great part due to the difficulty with a limited choice of suitable dioptric materials (for, although extensive, the choice is not as varied as the lens designer could wish) of obtaining the results desired by calculations based on the utilization of spherical surfaces alone.

If we look for the reason why opticians have so far almost entirely limited themselves to the production of dioptric elements bounded by spherical surfaces, we find it at once in the comparative ease with which such surfaces can be generated with precision. But, given a sufficient incentive, it cannot be doubted that surfaces other than spherical could be produced. Indeed this has already been done with an

Scientific Papers of John William Strutt, Baron Rayleigh, vol. ii. Article on Optics, Encyclopædia Britannica, xvii. 1884.

accuracy suitable for the purpose in the case of a few exceptional types of lenses, for instance the special spectacle lenses designed by Von Rohr for those whose eyes have been operated on for cataract*; and with considerable accuracy (though with a smaller departure from true sphericity) in the "figured " lenses or mirrors for large telescopes and for other special purposes.

Now, experience has shown that with the aid of this apparatus, and even with the ordinary means of retouching, the optician can face without dismay the task of making with precision quite considerable departures from the sphericity of his surfaces. It appears to the writer certain that by modifying from true sphericity the surfaces of systems which have been suitably computed for the purpose, results will be attained more perfect than has hitherto been possible in, for instance, camera lenses. It is even likely that valuable results may be attained at some future time by using apparatus of this kind to assist the correction to a pitch of high accuracy of lens systems wherein definitely aspherical surfaces have been generated by processes essentially different from those ordinarily used by opticians.

(d) The experimental study of lens systems.

There are probably few interested in optical systems who have not felt disappointment at the comparative lack of success which has attended attempts to deal with the passage of light through such systems by means of the Wave Theory. The difficulties are mathematical, and not of course to be directly relieved by such instrumental aids as those now described.

But it is perhaps not too much to hope that the existence of means of direct demonstration of the effect on wave surfaces of passage through optical systems may attract the attention of mathematicians to this aspect of the subject of dioptrics, with good result.

Research Department,
Adam Hilger Ltd.

* See Proc. of the Optical Convention, 1912, p. 118.