IMAGE FORMATION BY A FRESNEL ZONE PLATE 



as an image-forming device. We can con- 

 clude that the zone plate image compares 

 favorably with that of the lens. 



The zone plate was about 20 times slower 

 than the lens for the folio w-ing reason: in 

 the vector diagram representing the ampli- 

 tude of the waves that pass through suc- 

 cessive Fresnel zones, the continually chang- 

 ing phase produces a spiral (Fig. 10). In 

 Fresnel's treatment of the contributions of 

 successive circular zones, the amplitude of 

 the contribution due to one zone is repre- 

 sented by the vector AB. The length of the 

 arc ABC, starting at A and ending at C, 

 would be proportional to the amplitude 

 produced by two zones of a lens (since the 

 lens has the property of orienting all the 

 infinitesimal vectors in the same direction). 

 The ratio of these amplitudes is approxi- 

 mately TT. The ratio of intensities would be 

 TT^. This argument would hold for a perfect 

 zone plate, that is, one in which the width 

 of an opaque band never exceeded the 

 mathematically computed value of s„ . 



With the real zone plate, the widths of all 

 the gold bands are greater than the theoreti- 

 cal value of Sn , thereby reducing the in- 

 tensity of the light gathered at the focus. A 

 perfect zone plate introduces the factor ir^ 

 and inaccm-acies in manufacture introduce 

 a factor of about 2, making the ratio ap- 

 proximately 2x2 which is about twenty. This 

 means that a single zone plate is not a very 

 efficient gatherer of light when compared 

 with a lens. However, with sufficiently in- 

 tense sources it can produce images with 

 good resolution. Certainly the resolution 

 and light gathering power are much better 

 than those of a pinhole. We conclude that 

 the zone plate is much better than a pin- 

 hole both in resolution and light -gathering 

 power; it is comparable to a lens in resolu- 

 tion but about twenty times slower than a 

 lens of similar aperture when used with 

 visible light. 



To overcome the intensity limitation the 

 method of superposition of images could be 



B 



/ 



/ 



y 



I 



\ 



\ 



\ 



V 



X 



\ 



\ 



/ 



Fig. 10. The vector AB represents the resultant 

 of the infinitesimal vectors contributed by the sub- 

 zones of one open Fresnel zone in a zone plate. The 

 length of the arc ABC represents the amplitude of 

 the contributions due to two successive Fresnel 

 zones in a lens. The continuously changing thick- 

 ness of a lens causes the infinitesimal vectors to 

 line up since they all have the same phase. The 

 ratio of the length of the arc ABC to the length 

 AB is approximate!}' ir. 



used. It has been shown (18) that n pictures 

 of the same object each exposed for a time 

 t (where t would yield an underexposed 

 negative) give negatives which when super- 

 imposed produce an image comparable in 

 exposure to that of a single picture exposed 

 for a time nt. Intead of photographic record- 

 ing some form of electronic readout might 

 be used to integrate the signals from n zone 

 plates and produce an exposm'e in / seconds 

 that ordinarily would have required nt 

 seconds. Because noise increases along with 

 the signal, the advantages in resolution are 

 not simply multiphed n times. Nevertheless, 

 a gain does result from this technique and 

 since zone plates may eventually be produced 

 fairly cheaply, it is conceivable that the 

 signals received simultaneously from many 

 zone plates could be integrated advanta- 

 geously. 



559 



