THE OPTICS OF PHOTOGRAPHIC LENSES 



33 



Vignetting in a lens affects the astigmatism of very oblique pencils, because, 

 when vignetting is present, the effective aperture of the lens is the intersection of two 

 ellipses as shown in Fig. 28, and hence the lens aperture in the radial direction is 

 smaller than in the tangential direction. This small radial aperture makes the 

 radial focal line short, but it also gives great depth of focus to the tangential line; 

 similarly, the large tangential aperture makes the tangential focal line long but gives 

 the radial line very little depth of focus. Generally speaking, the result of this is 

 that the radial lines have a definite focal position, whereas tangential lines are equally 

 sharp over a considerable range of positions, and indeed often it is impossible to say 

 where is the plane of best definition of tangential lines in the corners of the picture. 



Curvature of Field. — If all the tangential focal lines in the image of a plane object 

 are joined, they are found to lie on a surface called the "tangential field curve" of the 

 lens; similarly the radial focal lines all lie on the "radial field curve" or, as it is more 

 usually called, the "sagittal field curve" of the lens. These two field curves touch 

 at the center of the field since the astigmatism always vanishes there, and in a well- 

 corrected lens they both approximate reasonably to the plane of the plate. The 

 field curves of a typical lens are shown in Fig. 29. Stopping down the lens does not 



Fig. 



29. — The field curves of a typical lens. The particular curves shown, apply to the 

 Cooke wide-angle //8 lens. 



affect the positions of these image curves, but it increases the depth of focus and 

 shortens the focal lines themselves, so in practice it considerably reduces the effect 

 of astigmatism on the image. 



The Angular Field of a Lens. — This is limited by the state of correction of the lens 

 aberrations, and generally the limits of the iiseful field of a lens become very evident 

 in a photograph of some flat object (the front of a building, for instance) taken at full 

 aperture on a large plate. The limit is usually expressed as the useful angular field 

 measured outward from the axis before definition becomes too bad to be tolerated; 

 this should strictly be called the "semifield." Sometimes the whole angular extent 

 of the usable field is specified, and sometimes the field is indicated by stating the size 

 of plate covered by a lens of given focal length. For ordinary lenses, a semifield of 

 22 or 25° is considered normal. For wide-angle lenses, 45° is a reasonable limit, i.e., 

 a 90° total field. Motion-picture lenses have smaller fields, for instance a lens of 

 1-in. (25.4-mm.) focal length for use with 16-mm. motion-picture film need only 

 cover a semifield of 13°50', as each frame has the dimensions 7.5 by 10 mm., giving 

 a diagonal length of 12.5 mm. The 35-mm. film has a frame of dimensions 18 by 24 

 mm., with a diagonal of 30 mm., and hence, when used with a lens of 2-in. focal 

 length, the semifield is 16°30'. In the Leica and other miniature cameras covering 

 two adjacent frames of 35-mm. film, the picture size is 24 by 36 mm., giving a diagonal 

 of 43.2 mm., and hence with a 2-in. lens the semifield to be covered is 23°. With a 



