Procedure

Experiments 1, 2, and 3 included practice and main trials. The practice trials were administered until participants demonstrated comprehension of the task. The stimuli for the practice trials were randomly selected from those in the main trial. Participants indicated the number of overlapping surfaces before each main trial in Experiments 1 and 3. In all the experiments, no time limit was imposed for stimulus observation based on our preliminary observations; when a POTS configuration was presented with short durations, some participants had difficulty perceiving stereo-transparent surfaces, as reported in the literature^21,22, and judging the perceived depth magnitude confidently. In Experiments 1 and 3, the participants could move their eyes, and in Experiment 2, they were instructed to maintain fixation on the fixation cross on the monitor. We discussed the possible role of the eye position on the perceived depth measured in this study in the “Discussion” section. The participants were allowed to take breaks whenever their eyes felt fatigued.

In Experiment 1, we asked participants to report the surface number of the POTS configuration and accurately replicate the extent of depth between the outer surfaces of the configuration. Participants held a tape measure and reproduced the depth magnitude by alternatively looking at the stereoscope and the measure at hand. They completed four experimental sessions. Each session's frames, total disparities, and surface numbers were randomly selected from four different frames, three different total disparities, and three different surface numbers of POTS, respectively, with one repetition. Thus, each participant had 144 trials (4 frames × 3 total disparities × 3 surface numbers × 4 repetitions).

In Experiment 2, participants were required to (1) assess the perceived depth between the outermost surfaces for the right and left side stimuli on the screen and (2) indicate which exhibited a superior magnitude of depth. The stimuli were visible until participants finished providing their estimates. The experiment consisted of twelve blocks that differed in two disparities of the frame, three total disparities of the frameless POTS, and two surface numbers of POTS. Each block comprised five sessions. For each session, the total disparities of the framed two-POTS or three-POTS stimulus and their spatial positions (right or left) were randomly drawn from five disparities and two locations, respectively, with one repetition. Consequently, each participant completed a total of 600 trials (2 frames × 3 total disparities of a frameless POTS × 2 surface numbers × 5 disparities of a framed POTS × 2 position × 5 repetitions).

In Experiment 3, participants performed a depth reproduction task as in Experiment 1. They completed ten sessions, and the frames, total disparities, and surface numbers for each session were randomly selected from four different frame sizes, three different total disparities, and two different surface numbers of a POTS, with one repetition. Thus, each participant had a total of 240 trials (4 frame sizes × 3 total disparities × 2 surface numbers × 10 repetitions).