PHYSICAL ASPECTS OF IMAGE FORMATION 



19 



exhibited by a perfect objective. The first minimum is five times lower 

 than that of a fluorite objective and seven times lower than that of 

 an achromatic one. 



Naturally, the structure of diffraction patterns may vary slightly 

 with the chromatic correction of a given objective. Accordingly, the 

 curves (Fig. 1.20) should merely be considered as showing the general 

 aspect of the phenomena involved. 



6. LUMINOUS POINT IMAGED IN THE PRESENCE OF ABERRATIONS 



All the foregoing results apply to a perfectly corrected aberration- 

 free objective, the chromatism merely bringing about defective focusing 

 but no wave-front deformation. When the objective is not perfectly 

 aberration-corrected, the wave surface is no longer spherical thus 

 entailing an altered diffraction disk. A portion of the luminous energy 

 of the central diffraction disk is transferred to the rings which spread 

 the image and lessen contrasts throughout. In Fig. 1.21, the sphere 



0, A 

 Fig. L2L Wave surface in presence of aberrations: .T/ is deformed. 



Zj represents the ideal surface-wave that would be achieved were the 

 objective O^ free from aberrations. As a matter of fact, aberrations 

 distort the surface wave which becomes I[ . The distance between 

 Lj and El is denoted by J and is the path difference between the 

 actual wave Z/ and the reference sphere -/. The J values and variations 

 are determined by the aberrations of the microscope objective. Going 

 into the alterations brought about by aberrations in the diffraction 

 disk structure is very helpful. Such alterations need investigating for 

 they take effect on image formation and, hence, in their interpretation. 



Spherical aberration 



Let us assume that, notwithstanding its deformations the actual 

 wave E'i is a wave of revolution about the axis AA'^. In this case, 



