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with only four open surfaces would be desirable for projection purposes, but the production of such an objective of sufficiently large aperture does not seem compatible with the corrections required, although some of the objectives designed by Hugh L. Aldis of Birmingham, England, are suggestive efforts along this line.
In respect of cemented surfaces, the Cooke lens has none, being ideal in this respect for projection with high power illuminants which generate considerable heat; the Tessar has one cemented surface which would doubtless hold up well as no trouble is ever experienced with the cemented surface in the Petzval type objectives now commonly in use. The Cooke and the Tessar objectives are both of compact construction and are therefore superior in this respect to the Petzval objective, an advantage which will be again referred to.
The corrections for coma, astigmatism and curvature of field are carried out to a high degree in these two modern types of objectives; there being no noticeable departure from the sine condition, and the field being almost perfectly flat and free from any noticeable trace of astigmatism for upwards of io° away from the axis, thus allowing the projection of a sharp stigmatic image of 20° or more in angular extent.
Distortion, the seventh aberration on our list, has been deferred until the last because under the conditions generally met with at present wherever motion pictures are projected, the elimination of distortion would appear to be an almost needless refinement in a projection objective, although, of course, this correction should be carried out to the utmost extent possible in a large aperture objective, and is carried out by all reputable opticians.
Distortion in a photographic or a projection objective may be briefly described as an increasing or a decreasing scale of reproduction from the center to the edges of the images produced by objectives of either simple or compound type, and it results from the refractive effect on rays incident at increasing angles with respect to the axis being such as to cause the angles made with the axis by the chief-rays after refraction to differ from the angles made by the same rays, with respect to the axis, before refraction.
(Note — A chief -ray is the representative ray of a pencil; it is the ray which passes through the center of the diaphragm of an objective and therefore through the center of the entrance-and exit-pupils ?)
In order that an objective may be free from distortion, and yield an orthoscopic, or rectilinear, representation of the object projected, Airy's condition must be fulfilled, which requires that the ratio of the tangents of the angles made with the axis by corresponding chief-rays on the object side and on the image side of the objective must be constant, or
y a tan w
— = ^ -= N
y' a' tan w'
where jy and jy' represent the size of the object and the image respectively; a and a' are the distances of the entrance and exit-pupils from the plane focussed for {the film image in motion picture projection) and the image plane {or lantern screen); w and w' are the angles made with
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