568 BELL SYSTEM TECHNICAL JOURNAL 



background, and was repeated every quarter minute. The observer 

 could have the lens moved whenever and as often as he wanted to 

 before reporting, so that he soon acquired the habit of observing only 

 the most critical portions of the scene. As soon as his report was 

 recorded, completing that observation, he was shown a new pair of 

 lens positions, the same reference one with a different neighboring one, 

 and asked again to report which he judged to yield the sharper image. 



We believe that there were no contaminating influences and that 

 only the size of the figure of confusion was varied. No change in 

 brightness or in magnification could be detected. A minute lateral 

 shifting of the image, because of play in the focusing mount of the lens, 

 was completely masked by the continual weave of the film in the gate 

 and the natural motion of the model. Any significance of the position 

 of the observer's control key was destroyed by reversing its connections 

 from time to time, between observations, without the observer's 

 knowledge. No tell-tale sound accompanied the small motion of the 

 lens, and none of the operator's movements could be seen by the 

 observer. 



Each one of 15 observers made 84 separate observations of sharpness 

 difference. Expressing the resolution in terms of the angle at the 

 observer's eye subtended by the side of the square figure of confusion, 

 there were four main reference values, namely 0.71, 1.1, 1.7 and 2.8 

 milliradians (1 milliradian is equal to 3.44 minutes of arc). At each 

 of these reference values there were seven neighboring values, namely 

 0, 0.045, 0.090, 0.13, 0.18, 0.22 and 0.27 milliradians greater than the 

 reference value. (The in that set means that the reference value 

 was shown against itself, or that the observer was asked to judge a null 

 change; this was intended to keep him on his guard and alert, not to 

 furnish primary data.) Each pair of values was presented to each 

 observer three times, so that there were 45 observations on every pair. 

 The pairs were presented in irregular order according to a schedule, 

 the variation about one reference value being completed before going 

 on to the next. The differences were set up on the basis of preliminary 

 trials to include some which almost none of the observers could detect 

 and some which almost all could. It was explained that some of the 

 differences to be judged would probably be too small for discernment, 

 and that a "no choice" response would be permitted whenever reason- 

 able effort failed to establish a definite choice. 



The primary data are shown in Fig. 2. Each point shows the pro- 

 portion of the observations in which the variable image, which had the 

 poorer resolution by reason of its larger figure of confusion, was never- 

 theless judged to be sharper than the reference image. Such a judg- 



