552 



NA TURE 



[October 8, 189] 



PHOTOGRAPHIC DEFINITION. 



I. 



T T is a matter of some interest to determine what are the limits 

 to the definition obtainable in photographs. In examining 

 this question, three distinct classes of problems present them- 

 selves — namely : — 



(i) Those depending on the wave-length of light, and the 

 action of a perfect lens on such wave-lengths, 



(2) The various aberrations of real lenses. 



(3) The qualities of the different sensitive surfaces on which 

 the pictures are formed. 



Taking these divisions of the subject in the order given, I will 

 inquire first what is the limit to photographic definition on the 

 supposition that the lens has no aberration of any kind, i.e. that 

 all the waves which reach it from any point arrive at the image 

 of that point in the same phase. 



The image thus formed consists, as is well known, of a bright 

 disk surrounded by alternate dark and bright rings, the intensity 

 of the illumination of the rings decreasing rapidly at each suc- 

 cessive ring, reckoning outwards from the centre. 



In order that the images of two neighbouring points may 



Points nearer to, or further from, the lens than that which has 

 its image on the plate will be represented on the latter by round 

 patches of light ; these being the sections by the plate of the 

 cones of rays which have for their summits the geometrical foci 

 of the points, and for their slant the radius of the aperture -f- 

 focal length. 1 Thus, if e is the distance before or behind the 

 plate of the focus of a point, it will be represented on the plate 

 by a patch of light of diameter 



A 



This diameter can be diminished by the use of a diaphragm, 

 i.e. by diminishing A, but this at the same time increases the 

 diameter of the images of points whose foci are on the plate. 

 And the resulting average definition will be improved by dimin- 

 ishing A until the patch of light, representing the point most 

 out of focus, has the same diameter as the diffraction disk of 

 the image point in focu=. 



If we suppose the photographic plate to be placed at such a 

 distance from the lens that the focus of the nearest object is as 

 much behind the plate as the focus of very distant objects is 

 in front of it, we shall have, to determine the diameter of 





appear separated from one another, the central disks of their 

 images ought not to overlap. If the disks are just in contact, 

 it is possible that they would appear as a double object in the 

 photograph, and this may be taken as the limit of the defining 

 power of a lens. (See Airy "On Light," and Lord Rayleigh 

 •' On the Theory and Manufacture of Diffracti jn Gratings," 

 Phil. Mag., 1874.) 



But, in ordinary photography, objects at very various distances 

 have to be simultaneously represented, and it is to the definition 

 attainable under these circumstances that I wish now to direct 

 attention. 



On referring to the papers above-:nentioned, it will be seen 

 that the diameter of the central disk is 



I •219 — , 

 A 



where \ is the wave-length of ligh% 

 F the focal length of the lens, 

 A the aperture of the lens. 



This gives the effective diameter of the image of a point truly in 

 ;ocus when not far removed from the axis of the lens. 



NO. 1 145. ^■0L. 44] 



the stop giving the best average definition, the following 

 equation : — 



Putting F = principal focal length, 



D = distance of nearest object, 

 q = I'219A, 



.(F_±i)^.A^ 



(I) 



but, by the ordinary formulae, connecting the conjugate foci of 

 lenses, we have, if D = F -h ^, 



2g 2(U - !<) 



' This is an approvimate statement only. The true expression involves, 

 an investigation of the intensity of the light iinjiediateiy in front of and 

 behind a caustic. 



