IMAGE FORMATION BY A FRESNEL ZONE PLATE 



was 0.00053 radian, which is 1.68 ^„,in for 

 that wavelength. 



The center picture of Fig. 6 was made at 

 p = 47 cm, q = 12.5 cm, at a wavelength 

 of 4358 A. A Baird interference filter with a 

 total pass band of about 100 A was used. 

 Here the angular separation between adja- 

 cent centers is 2.59 ^min . An improvement 

 in resolution is apparent. 



Fig. 6 (right) shows an image of the same 

 mesh taken at 2537 A. The value of p re- 

 mained fixed at 47 cm, q was 27 cm and the 

 angular separation between object centers 

 was now 4.44 ^min • The source was a General 

 Electric germicidal lamp number GT4/1. 

 The manufacturer states that this lamp 

 yields 60 % of its energy at 2537 A. A filter 

 was used to remove the visible radiation, 

 but the monochromatic effect at 2537 A is 

 due only to the relative intensity of this 

 line. This demonstrates a point about zone 

 plate focusing that may be useful in ultra- 

 violet and x-ray astronomy: a relativel}^ in- 

 tense and isolated spectral line may preclude 

 the use of filters. These pictures lead us to 

 believe that the resolution will continue to 

 improve in a predictible way as we go down 

 first to 1000 A and later to 100 with our zone 

 plate. 



Comparison of Zone Plate with Pinhole 

 and Lens 



Next we compared the image-forming 

 qualities of our zone plate with those of a 

 pinhole. The pinhole size was calculated 

 to give the optimum resolution for the 

 chosen values of X, p, and q. The optimum 

 diameter for such a pinhole is given by the 

 expression (17) 





# t • ^ « # ' 







• «**-••. 









d = 2 



0.9pg 



(7) 



This may also be written d = 2\/o.9/X 

 which, interestingly enough, is very close 

 to the diameter of the innermost circle of a 

 zone plate that gives good focus at the same 

 distances and for the same wavelength. In 



Fig. 6. The pictures of Fig. 5 are here enlarged 

 to produce equal image sizes. From left to right, 

 they were made at 6700 A, 4358 A, and 2537 A. The 

 angles subtended at the zone plate by two adja- 

 cent midpoints of the open area of the object mesh 

 were 1.68 (9min , 2.59 ^min , and 4.44 ^min , where 

 ^minis the theoretical minimum angle of resolution 

 computed at the respective wavelengths. The im- 

 provement in resolution with shorter wavelength 

 is apparent. 



other words, the pinhole behaves like a zone 

 plate with a single circular opening. 



Fig. 7 is a picture of a mesh with 4 lines 

 per mm framed by the lines of a coarser 

 screen with 0.7 lines per mm, made with the 

 pinhole at a wavelength of 4358 A. With 

 the same screens as an object and all other 

 factors the same, a picture was taken with 

 the zone plate instead of the pinhole, with 

 the results shown in Fig. 8. The angular 

 separation, at p = 26.7 cm, between adjacent 

 centers of the smaller screen pattern was 

 5.3 X 10~* radian or 4.5 ^min , as computed 

 for the zone plate. Theoretically, the im- 

 provement in resolution of the zone plate 

 over that of the pinhole is a factor \/n or 

 6.23 for our zone plate of 38 rings. The actual 

 improvement as demonstrated in Figs. 7 and 

 8 is quite apparent. 



The zone plate has another advantage 

 over a pinhole in that the light flux reaching 

 the image is greater with the zone plate, so 

 that much less exposure time is required 

 if all other factors have been left unchanged. 

 In our notation, n stands for the number of 

 circles in the zone plate pattern. Hence n/2 

 is the number of open zones or bands. The 

 expected improvement in exposure should 



557 



