THE IMAGE-FORMING MECHANISM OF THE EYE 653 



Fig. 10 



Fic. 9. Chief ray. 



FIG. 10. Out-of-focus blur circle. 



meridians. The rays in the vertical meridian focus at 

 Q,' and the rays in the horizontal meridian at QJ'. 

 Cross sections of the bundle at various distances 

 from the exit-pupil are also shown in the figure. The 

 cross section is in general elliptical but at Q,' it be- 

 comes a horizontal line and at QJ' a vertical line. At 

 one point in between it becomes a circle; and when 

 this part of the bundle is intercepted by the retina, 

 the effect is the same as throwing out of focus an 

 eye which is free from astigmatism. 



There are two principal causes of astigmatism. 

 On the one hand the chief ray of the bundle may be 

 oblique to one or more of the refracting surfaces. On 

 the other hand one or more of the surfaces may be 

 toroidal, i.e. a given surface may be shaped like the 

 side of a barrel which is more curved in the direction 

 around the barrel than up and down. It is obvious 

 that in a multisurface system like the eye, there may 

 be many comijinations of toroidal and tilted surfaces 

 and it becomes impractical to try to analyze all these 

 various combinations. 



In practice the resultant astigmatism is measured 

 and treated without analyzing the contributions 

 made by the separate surfaces. However, the toroidic- 

 ity of the cornea may be independently measured and 

 gross observations may be made of the tilt of the re- 

 fracting surfaces. 



Lines of Sight 



Object points which lie on the incident path of a 

 chief ray produce concentric blur circles or ellipses 

 on the retina, and because of this the incident path of 

 a chief ray is also called a line of sight. 



Primary Line of Sig/it and Foveal Chief Ray 



Of all of the lines of sight (or chief rays) which 

 converge at the center of the entrance-pupil, there is 



CHIEF 

 RAY 



CIRCLE OF 

 LEAST CONFUSION 



FIG. 1 1. .-Xstigmatic blur ellipses. 



one which is all-important in the use of the eyes. When 

 a person is told to fixate a given point with one of his 

 eyes while the other is covered, he points that eye 

 at the object. The pointing is not steady because the 

 eye is subject to a fine tremor and also weaves back 

 and forth and makes occasional jerks awa\' from the 

 object, but we can nevertheless think of the average 

 fixating position of the normal eye as one in which the 

 retinal image is centered on a given part of the retina 

 which falls somewhere near the center of the fo\'ea. 

 The chief ray which penetrates this point is the fo\eal 

 chief ray and the incident path of this ra\ is the pri- 

 mary line of sight. 



Pupillary Axis am! Angle X 



It is customary to specify the location of the fo\enl 

 line of sight in terms of its relation to the pupillary 

 axis which can be easily located by ol)jective methods. 

 The pupillary axis is a line normal to the front surface 

 of the cornea and directed through the center of the 

 entrance-pupil. It forms an angle X with the primary 

 line of sight which also passes through the center of 



