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BELL SYSTEM TECHNICAL JOURNAL 



This difficulty may be entirely obviated by the introduction of a diffusion 

 screen directly adjacent to the pinhole.^- 



It might be noted that if it be desired to project or photograph the pin- 

 hole figure, one must focus on the virtual image which lies between the top 

 and bottom surfaces of the etched specimen. In the simple case dia- 

 grammed in Fig. 5.10, it is assumed that the camera lens is at a distance from 

 the section and directly over the section, so that the rays to the lens are essen- 

 tially normal to the section. For a section of thickness T, and index of 

 refraction n, the elevation E of the virtual image from the bottom surface 

 of the section is given by: E/T = 1 — Vl + R-/T-/n. Here R is the radial 

 displacement of the virtual image from the axis of the pinhole and is readily 

 observed and measured. Also, R may be calculated from the thickness of 

 the quartz T, the angle 6 between the facets and the gross surface, and the in- 



Fig. 5.10 — The elevation E of the virtual image may be calculated from the thickness 

 of the etched section T, the radial displacement of the image R, and the index of refraction 

 n; or from T, n, and d, the angle between the facets and the gross surface. 



dex w, (or d may be calculated from T, R, n) by: R/T = tan {d — sin~H(sin~^ 

 6)/n\). Commonly, pinhole figures from quartz which is weakly to moder- 

 ately etched (up to one hour in concentrated HF) have a maximum diameter 

 (or double radial displacement) 2R, nearly equal to the thickness of the 

 section. Since the elevation of the image, £, depends upon its displace- 

 ment R, an extended virtual image is not in a single plane and cannot be 

 exactly focused (the elevation is commonly about one-fourth to one-third 

 of the thickness of the section). The diameter of the pin-hole must always 

 be kept small compared to the thickness of the section to give sharp figures 

 (and the length of the pinhole must be small compared to its diameter). 



'^ The diffusion screen may be a sheet of white paper placed over the pinhole, or a piece 

 of flashed glass placed under the pinhole, with the flashed side against the pinhole. In 

 either case it is usually necessary to increase the light intensity by focusing a concentrated 

 light source onto the pinhole with a lens. 



