SUBJECTIVE SHARPNESS OF IMAGES 565 



originally abrupt edges in the image. The variety of such relations 

 assumed by others^- ^' ^' ^' ^ has led to a variety of conclusions with 

 respect to resolution in television. We find subjective comparison of 

 images to yield results of fairly small dispersion. 



Let us consider now the measurement of sharpness in subjective 

 terms. Here we find no familiar units of measurement, no scales or 

 meters. We find no agreement as to the meaning of a statement that 

 one image looks twice as sharp as another. We can say of two images 

 only that (a) one image looks sharper than the other, or {b) the two 

 images look equally sharp. When the images are quite dififerent, there 

 will be agreement by a number of observers that the one image is the 

 sharper. When the images are not different in sharpness, there may 

 be some judgments that one of them is the sharper, but these will be 

 counterbalanced in the long run by an equal number of judgments that 

 the other is the sharper. When the images are only slightly different 

 in sharpness, an observer may reverse his judgment from time to time 

 on repeated trials, and he may sometimes disagree with the judgment 

 of another observer. It is within this region of small sharpness differ- 

 ences, in the interval of uncertain judgments where the observer is 

 sometimes right and sometimes wrong with respect to the known ob- 

 jective difference, that it becomes possible to set up, on a statistical 

 basis, a significant quantitative measure of sharpness difference. 



Suppose that in judging two images of almost equal sharpness the 

 observers have been instructed to designate either one or the other of 

 the images as the sharper; that is, a judgment of "equally sharp" is not 

 to be permitted for the present. An observer who discerns no differ- 

 ence in sharpness is thus compelled to guess which image is sharper, 

 and his guess is as likely to be right as it is to be wrong, with respect 

 to the known objective difference. Suppose, further, that the sharp- 

 ness difference has been made so small that only 75 per cent of the 

 judgments turn out to be right, the remaining 25 per cent being wrong. 

 On the basis that these wrong judgments are guesses, we must pair 

 them off with an equal number of the right judgments, so that 50 per 

 cent of the total are classed as guesses. The other 50 per cent are 

 classed as real discriminations. (The pairing of an equal number of the 

 right judgments with the wrong judgments goes back to the equal 

 likelihood of right and wrong guesses; it affords the best estimate we 

 can make of the number of guesses.) When real discrimination is thus 

 evidenced in one half of the observations, that is, when 75 per cent of 

 the judgments are right and 25 per cent of them are wrong, we shall 

 designate the difference in resolution as the difference limen* 



* The term limen is frequently used in psychometry in lieu of older terms such as 

 just-noticeable-difference, threshold value, perceptible difference, etc. It has the virtue 



