Three-dimensional display technology has developed rapidly in recent years. This has been accompanied by increasing problems of visual complaints such as eye strain. There are also various types of digital signage, in which text information moves on a screen. In this paper, we conducted two experiments for the purpose of easy to read, dynamic characters that pop out when viewing 3D images, and safe and comfortable 3D viewing. We conducted a survey of accommodation and convergence of viewers when they watched a movie with a television opaque projector for large outward projection of characters. We also compared the results of a survey on the readability of characters that pop out and the proportion and the perception of the amount of protrusion. We examined the maximum distance in which subjects' eyes could recognize the 3D character representations without any difficulty or discomfort. The distance of the images as they popped out from the screen as a theoretical virtual target was compared with what the subjects recognized according to each age group. There was no significant difference between the theoretical and observed values in any age groups. In a second experiment, we performed objective measurements of accommodation and convergence for 3D character representation using original instruments. We then compared the values of the measurements of the subjects with the theoretical positions of emergence. When a subject recognized a 3D character representation, the position of his or her accommodative and convergent focus was closer to the theoretical position of the virtual object that projected out from the screen. Nearly all of the subjects recognized the 3D representation at even 3.8 degrees, which was the largest parallax condition. Cognitively, almost all of the subjects viewed the positions of the objects correctly without much difficulty.