652 



HANDBOOK OF PHYSIOLOG\' 



NEUROPHYSIOLOGY I 



TABLE I . Optical Constants of the Helmholtz Schematic Eye 



Distance from cornea to front of lens 



I'hickness of lens 



Radii of curvature: 



Cornea 



Front surface of lens . . 



Back surface of lens 



Indices of refraction (sodium light) 



Aqueous i .333 



Lens 1 .45 



Vitreous 1 .333 



FIG. 8. The reduced eye devised by Laurance. 



aspects of image formation as will become ob\ious 

 later. 



Role of Pupil in Image Formation 



The pupil is an aperture in the iris which lies in 

 contact with the front surface of the lens. The pupil 

 varies in size because the muscles in the iris can make 

 it either contract or dilate. The pupil is important in 

 the formation of an image on the retina because by 

 changing its size it can aflfect the illuminance and the 

 blur of the image. It does this by limiting the size 

 of the ray bundle which enters the eye from each 

 object point. In terms of geometrical optics this 

 means that it serves as the aperture stop of the 

 system. 



In order to understand the role of the pupil in 

 image formation, it simplifies matters to make use of 

 the imaginary entrance- and exit-pupils of the eye. 

 The entrance-pupil is conjugate to the real pupil 

 with respect to refraction at the cornea, and the exit- 

 pupil is conjugate to the entrance-pupil with respect 

 to the complete refracting mechanism of the eye. The 

 entrance-pupil is larger than the real pupil and lies 

 slightly in front of it. The exit-pupil lies behind the 

 real pupil and is not quite as lai-ge as the entrance- 



pupil. The entrance-pupil is the pupil which we see 

 when we look at another person's e\e. This is the 

 pupil on which direct measurements can be made in 

 \isual experiments. Its position and diameter can be 

 directly determined. The positions and sizes of the 

 real and of the cxit-piipil have to be calculated. 



Chief Rays 



Another concept which is needed in explaining the 

 role of the pupil is that of a chief ray. The chief rav 

 of a bundle of rays entering the pupil of the eye from 

 a given object point is the one which is directed 

 through the center (0) of the entrance-pupil and 

 which, after refraction at the cornea, passes through 

 the center of the real pupil. After emerging into the 

 vitreous, it is directed through the center (0') of the 

 exit-pupil, as shown in figure 9. 



Blur Circles in Eye Free from Astigmatism 



The major role of the pupil is to limit the size of 

 the blur circles and ellipses formed on the retina when 

 an eye is out of focus. The schematic and reduced eyes 

 referred to above are all free from astigmatism for 

 object points close to the optic axis because the re- 

 fracting surfaces are assumed to be spherical and also 

 centered on the optic axis. In this eye free from 

 astigmatism, the bundle of rays from a given object 

 point emerges into the vitreous as a cone or pencil of 

 rays with the exit pupil forming the base and with the 

 rays coming to a focus at the apex as shown in figure 

 10. This point is called the optical image and may 

 lie on, in front of, or behind the retina. If the retina 

 intercepts the bundle at the optical image so that the 

 optical image falls on the retina, the retinal image in 

 terms of geometrical theory is a point image; but if 

 the optical image ()' falls in front of or behind the 

 retina, the retinal image at Q.' is an out-of -focus blur 

 circle. As is obvious from figure 10, the size of the 

 blur circle is determined by the size of the exit-pupil. 



Astigmatism 



The bundle of rays from a point source does not 

 always come to a focus at a point. The most common 

 deviation from this ideal is called astigmatism. Figure 

 I I illustrates an astigmatic bundle of rays emerging 

 from the exit-pupil. The planes which intersect at the 

 chief ray constitute the meridians of the bundle. The 

 vertical and horizontal meridians are the principal 

 meridians because the ravs come to a focus in these 



