PHYSICAL ASPECTS OF IMAGE FORMATION 



33 



small diameter, the image is virtually Airy's disk, whether coherently 

 or incoherently illuminated. 



Perception of a small white disk on black ground is a problem 

 which has not the same aspect as that of a black disk on white ground. 

 As the diameter of a small black disk shrinks, ingress of diffracted 

 light increases until the image is completely blotted out. When the 

 object is a small white disk on a black ground and its diameter de- 

 creases, the ultimate image is the conventional diffraction disk (Airy's 

 disk). If the disk still dwindles in size, the curve showing the intensity 

 distribution in the diffraction disk gradually gets flatter but the lateral 

 dimensions of the diffraction disk remain constant. Visibility of a small 

 white disk on black ground is, therefore, merely a matter of luminous 

 flux. The smaller the disk, the more light it must send forth. 



Black line on white ground imaged in incoherent illumination 



Now the object is a thin, long black line. It follows that light- 

 intensity is constant along a line parallel to the thin line and the 

 information required is merely the light-intensity changes taking place 

 along a straight line at right angles to it. The curves in Fig. 1.40 show 



Fig. 1.40. Black line on white ground imaged in incoherent illumination. 



the general aspect of the phenomena involved. The geometrical width 

 of the imaged black line is shown by A'^^B'^. Curve 2 shows how 

 intensity is distributed in the imaged black hne: this curve does not 

 extend to the horizontal line anywhere. The lowest contrast perceivable 

 to the eye for an object of this type is 002. As with the black disk, 

 there is a relationship between the contrast y of the imaged black line 

 and its width e. As the width of the line decreases so does the contrast 

 until the image contrast has dropped to 002, and the hne has reached 



