Abstract: It is quite natural that we perceive erroneously what we see, and we can hardly correct the image even if we have noticed we are wrong, which is how visual illusion occurs. Since last century researchers have studied the relationship between the figure image and human behavior, the perceptional processing and the neuron system. Ironically, however, few of them have considered the basic condition or elements required when we want illusion to occur, and few of them focus on the famous Z?llner illusion even they discovered how the optical features influence the illusion amount. In addition, there lies opposite opinions whether the Z?llner illusion can be viewed as accumulation of separate Z?llner figures. So what we are curious of is the least condition that determines it, in other words, we are to measure the absolute threshold of the Z?llner illusion. In experiment I the variable is the quantity of interfering lines (1 to 9 pairs). Six men and ten women participated in. We chose the minimal-change method. Participants need to answer whether it looks parallel or not according to their very first sensation. When it comes to data analyzing, we firstly focus on the watershed of participants’ responses, finding that the threshold is 7 pairs of interfering lines when it’s oriented 90° and 5 pairs when it’s oriented 45°. The threshold has significant difference between increasing and decreasing blocks. Then we focus on the accumulated accuracy of their response, finding that the more interfering lines, the more illusion. Meanwhile, figures with 45° orientation is generally more erroneously perceived. In experiment II the variable is the gap between the main line and the interfering lines (0 to 20 pixels). Six men and twelve women participated in. The rest is exactly the same as experiment I. According to the results, the threshold is a 4.48-pixel gap of 90° orientation and a 6.58-pixel gap of 45° orientation. Significant difference between increasing and decreasing blocks occurs as well. Finally, the smaller the gap, the more illusion. 45° causes more illusion too. In experiment III the variable is the distance between the two main lines (67 to 197 pixels). Five men and nine women participated in. The rest is exactly the same. Results show the threshold is 131.73-pixel distance of 90° orientation and 124.44-pixel distance of 45° orientation. Significant difference between increasing and decreasing blocks occurs at the same time. As the distance increases, the percentage of illusive perception decrease at first and increase later, which indicates that the Z?llner illusion cannot be viewed as simple accumulation of separated figures. Still, 45° generally causes more illusion. Comparing the three experiments, figures with 45° orientation is more falsely perceived, showing the same result with former findings and fMRI support. In addition, the quantity of interfering lines can mostly determine this illusion, followed by the main line distance and the gap. Anticipation error causes significant difference between increasing and decreasing blocks in all experiments. We further analyze the beginning figures, which are exactly the same, in three experiments, and surprisingly find them perceived completely different, supporting that anticipation error should not be ignored. We guess it is the false attention distribution that causes this error, and this error may be a remarkable feature to distinguish normal perception and illusive perception. To summarize, the Z?llner illusion only occurs when: 1) there are more than 5 or 7 pairs of interfering lines in 45° and 90° orientation; 2) the gap between the interfering lines and the main line is less than 6.58 or 4.48 pixels each; 3) and the distance between the two main lines is less than 124.44 or 131.73 pixels each. Besides, we find that: 4) the studied variables can determine the Z?llner illusion in this strong-to-weak order: the quantity of interfering lines, the distance between the two main lines, and the gap between the main line and the interfering lines; 5) when the orientation of the main lines is 45°, illusions occur generally easier than when it’s 90 degrees; 6) in the perception of the Z?llner illusion, anticipation error is quite severe.

Key words: the Z?llner illusion, absolute threshold, minimal-change method, anticipation error

摘要： 该研究选取大学生为被试，采用最小变化法，分别测量了干扰线对数、干扰线与主线之间的间隔、主线之间的间隔等三个变量导致Z?llner错觉产生的绝对阈限。每个变量中主线与水平面的夹角分为45°和90°两种条件。结果发现，若要产生Z?llner错觉：1）干扰线对数的阈限分别为5对、7对；2）干扰线与主线之间的间隔阈限分别为6.58像素、4.48像素，3）干扰线之间的间隔阈限分别为124.44像素、131.73像素。此外还发现：4）在Z?llner错觉形成的影响因素中，从大到小依次是：干扰线对数、主线之间的间隔、干扰线与主线之间的间隔；5）45°情况下比90°情况下更容易产生错觉；6）在Z?llner错觉知觉中，期望误差严重。

关键词: Z?llner错觉, 绝对阈限, 最小变化法, 期望误差