SUBJECTIVE SHARPNESS OF IMAGES 581 



screen. Assuming for the moment that the optical imagery was per- 

 fect, each point of the film gave rise to a pyramidal volume of light 

 whose base was the opening of the external aperture and whose apex 

 was the point's image in the new focal plane beyond the screen. The 

 intersection of this pyramid with the viewing screen was the geo- 

 metrical figure of confusion for that point. The shape of the figure 

 was geometrically similar to that of the aperture, and the side of the 

 figure was to the corresponding side of the aperture as the distance 

 from focal plane to screen was to the distance from focal plane to 

 aperture. 



The distance of the focal plane beyond the screen was related to the 

 displacement of the lens from the "in focus" position by means of the 

 simple lens formula, and this relation was verified by actual measure- 

 ment of the distances. The geometrical area of the figure of confusion 

 was thus known in terms of the lens displacement, as shown in Fig. 9. 



Efforts to check this relationship by direct measurement of the 

 dimensions of the figure of confusion in the plane of the screen were 

 nullified by the aberrations of the optical system, especially by the 

 residual chromatic aberration. A comparison method was therefore 

 devised in which the out-of-focus image of a very thin vertical slit was 

 compared with an actual slit in the plane of the screen. In the film 

 gate was placed a glass plate bearing a sputtered layer of gold with a 

 razor-blade scratch not wider than 0.0001 inch in selected portions. 

 In the plane of the screen was placed a back-lighted slit made by 

 cementing the two halves of a cut piece of thin black paper onto a piece 

 of translucent white paper. This slit had sharp, parallel edges and 

 uniform brightness over its width, which was easily made as small as 

 0.005 inch. A set of these slits was prepared, ranging in width up to 

 0.100 inch, and each one was observed, without optical aid, close beside 

 the projected out-of-focus image of the scratch in the gold film. The 

 apparent brightnesses were equalized by means of neutral-tint filters 

 behind the paper slit. 



The ranges of values of lens displacement and of external aperture 

 shape which were used in the experiments were tested in this way, by 

 adjusting the out-of-focus images to subjective equality with the sharp- 

 edged slits. In every case the measured width of the comparison slit 

 turned out to be about 15 per cent less than the calculated geometrical 

 width of the projected image. This seeming a not unreasonable meas- 

 ure of the effect of the aberrations, it was adopted as a factor for con- 

 verting geometrical sizes into subjective sizes of the figures of confusion. 



Figure 9 shows both the calculated geometrical area and the observed 

 subjective area of the figure of confusion in terms of the displacement 



