32 



PROGRESS IN MICROSCOPY 



whose vibratory motions are totally unrelated. To every constituent 

 source, e.g. B, corresponds the diffraction disk B'^. The image P' of 

 the object P is the outcome of the superimposition of all diffraction 

 disks the centres of which are A'^^, B'^, Q, etc. It follows that in- 

 tensity in the centre of a diffraction disk depends on the light-intensity 

 of the relevant object point hnes. In areas where the object is dark, 

 the constituent sources transmit but little light and the relevant 

 diffraction disks are likewise but slightly illuminated. To better illumi- 

 nated areas correspond better illuminated diffraction disks. The image 

 P' is achieved by sunmiing all the intensities originated by all the 

 diffraction disks. Figure 1.37 shows the imaged plane P' of object P. 



Fig. 1.37. Image formation of an incoherent extended object. 



Required: to determine the light-intensity at any point B^ of the 

 image. Were only the source B involved, the intensity at B^ would merely 

 be the peak ordinate of the 5^ diffraction disk. If the source A takes 

 effect simultaneously, the light diffracted by A[^ and reaching 5^', must 

 be taken into account. In fact the image A'^^ is a diffraction disk ex- 

 tending in the plane P'. To determine the light-intensity at B^^, 

 originated by the sources A and B, requires summing together the 

 intensity originated by the source B (peak ordinate of 5,', centre 

 diffraction disk) and the intensity originated by the light diffracted 

 by the image A^^. Effect of yf,', on B^^ increases as distance A^^B'^^ is 

 short in relation to the diffraction-disk size. To determine the structure 

 of the whole P image the operation is resumed for all the points of 

 the image P', taking into account the relevant intensities of the object 

 points. Thus is derived the distribution of imaged light-intensities. 

 The structure of images can be derived mathematically. In many cases 

 a deft application of the Fourier transformation enables one to calcu- 

 late the phenomena in a comparatively simple manner. Owing to the 



