566 BELL SYSTEM TECHNICAL JOURNAL 



It is seen that the value of the limen is arrived at statistically, taking 

 into account the variability of individual judgments. Smaller differ- 

 ences than the limen are not always imperceptible, nor are larger 

 differences always perceptible. .'- 



The difference in sharpness, or in sensory response, which corre- 

 sponds to a difference of one limen in resolution may be said to be one 

 unit on the subjective scale of measurement. We shall designate this 

 as a liminal unit* It will be understood that the word liminal has 

 here a particular and precise significance, by reason of the one-to-one 

 correspondence between the liminal unit and the statistically-derived 

 value of the difTerence limen. A liminal unit of sharpness difference 

 may be considered as the median of a number of values of sensory 

 response to a difference of one limen in resolution, 



3. Sharpness and Resolution 



Figure 1 shows how we find the sharpness of an image to vary as the 

 number of elemental areas in the image is changed. Sharpness is 

 expressed in liminal units, based on measurements of the limen at four 

 different values of resolution, indicated by the four pairs of points on 

 the curve. Resolution is expressed as the number of figures of con- 

 fusion in a rectangular field of view whose width is 4/3 of its height 

 and which is viewed at a distance of 4 times its height.f This conven- 

 tional field of view was chosen as typical of viewing conditions for 

 motion pictures and television images. (The conventional field is 19° 

 wide by 14° high.) The range of the curve in Fig. 1 may be stated 

 very roughly as from 150-line to 600-line television images. 



The significant feature of this curve is its rapidly decreasing slope 

 with increasing sharpness. It shows that sharpness is by no means 

 proportional to the number of elemental areas in the image, and demon- 

 strates that the use of objective factors as indices of sharpness should 

 be regarded with more than the usual amount of caution. It shows 



that its meaning may be precisely defined in terms of the particular experimental 

 method under consideration, without the extraneous significance which might attach 

 to the more commonplace words. 



* There seems to be no accepted name for such a unit. Guilford ^ calls it simply 

 "a unit of measurement on the psychological scale." In discussing the measurement 

 of sensory differences which are equal to each other but not necessarily of liminal 

 size, the terms "sensory value" and "scale value" have been used. 



t We have used relative values here in order that our results might be applied to 

 other images not too different in size from the small ones we actually used. Other 

 values of aspect ratio in the neighborhood of 4 to 3, and other values of viewing dis- 

 tance in the neighborhood of 4 times the picture height, may be brought within the 

 scope of our data on the assumption that the sharpness is the same if the solid angle 

 subtended by the area of the figure of confusion is the same. For example, a square 

 field of view containing 60 thousand figures of confusion, and viewed at 5 times its 

 height, would be equal in sharpness to our conventional field containing 125 thousand 

 figures of confusion [125 = 60 X 4/3 X (5/4)^]. 



