176 CALIFORNIA ACADEMY OF SCIENCES [Proc. 4th Ser. 



I. Spherical Aberrations 



Nearly every treatise on lenses illustrates the characteristic 

 appearance of one of the five spherical aberrations, namely 

 distortion, but the remaining four are referred to if at all 

 only by rather vague, indefinite descriptions. As a consequence 

 very few have any definite conception of the distinctions be- 

 tween them. 



All of these are shown in the accompanying figure which 

 represents eight sections of the field as seen in a microscope 

 or telescope, each one of these sections illustrating an instru- 

 ment with a different correction or adjustment. The two sec- 

 tions illustrating positive and negative distortion show the 

 two familiar effects when this aberration is under or over 

 corrected. 



Curvature is shown in the two phases dependent on the 

 adjustment of the instrument. It is the effect so familiar to 

 users of the microscope, because a certain amount of curvature 

 is uncorrected in some of the best and most expensive instru- 

 ments. In such a case, when the edge of the field is in focus 

 the center shows as out of focus, lines and points becoming 

 broad and vague, and when the fine adjustment is turned the 

 central portion of the field becomes sharp and clear while the 

 edge is indistinct. 



Axial aberration is rarely seen because this is the distortion 

 to which first attention is given in designing an instrument 

 and is perhaps the easiest aberration to correct. When it is 

 present, due to the use of an instrument under conditions for 

 which it was not designed, it is usually associated with one of 

 the lateral aberrations, coma or astigmatism. 



Astigmatism resembles in some particulars the appearance 

 of curvature, when the focus is made sharp on the center of 

 the field, but differs most strikingly by the fact that radial 

 lines remain sharp as shown at three parts of the letter S 

 in the figure. This aberration is due to the fact that the 

 portions of the image produced by the different zones of the 

 lens are displaced radially and shifting of this kind would 

 not increase the width nor therefore decrease the sharpness 

 of a radial line. This kind of aberration is entirely different 

 in character from the out of focus effect due to curvature. 



