Wenderoth P, Beh H
Perception. 1977;6(1):57-75. doi: 10.1068/p060057.
Orientation illusions occur when the inducing figure is a line or grating (the tilt illusion) or a square outline frame (the rod-and-frame illusion). In the range of inducing figure tilts between vertical and horizontal, the tilt illusion describes one cycle of positive (direct) and negative (indirect) effects but the rod-and-frame illusion describes two such cycles. In two experiments, angular functions of illusions were measured with the six possible inducing figures which result when two of the four sides of a square inducing frame are deleted. As expected, the parallel-side frame amputations induced angular functions similar to the tilt illusion and these functions differed from those induced by the orthogonal-sided amputations. In agreement with previous findings on the nonadditivity of tilt illusions, the sum of angular functions induced by frame amputations, which together form a complete frame, were not always equivalent to the angular function induced by a complete frame, and there were asymmetries in the data fro which neither of two simple hypotheses could adequately account. The discussion focuses upon properties of inducing figures which psychophysical hypotheses might need to consider in order to account for the shapes of angular functions of orientation illusions and, in particular,a distinction is drawn between the global orientation of the inducing figure and the orientations of it (local) component features. It is suggested that it might be fruitful if the tilt illusion and the rod-and-frame illusion were conceived of as illusions resulting from inducing figures composed of all or part of n gratings of spatial frequency fn intersecting at angles of 180 degrees/n.
当诱导图形为一条线或一个光栅（倾斜错觉）或一个方形轮廓框架（棒框错觉）时，就会出现方向错觉。在诱导图形倾斜角度介于垂直和水平之间的范围内，倾斜错觉描述了一个由正向（直接）和负向（间接）效应组成的周期，但棒框错觉描述了两个这样的周期。在两个实验中，使用从方形诱导框架的四条边中删除两条边后得到的六种可能的诱导图形，测量了错觉的角度函数。正如预期的那样，平行边框架切除诱导出的角度函数类似于倾斜错觉，并且这些函数与正交边切除诱导出的函数不同。与先前关于倾斜错觉非叠加性的研究结果一致，由框架切除诱导出的角度函数之和（这些切除共同构成一个完整框架）并不总是等同于由完整框架诱导出的角度函数，并且数据中存在不对称性，两种简单假设都无法充分解释这种不对称性。讨论集中在诱导图形的特性上，心理物理学假设可能需要考虑这些特性，以便解释方向错觉角度函数的形状，特别是，在诱导图形的全局方向与其（局部）组成特征的方向之间做出了区分。有人提出，如果将倾斜错觉和棒框错觉设想为由空间频率为fn的n个光栅的全部或部分以180度/n的角度相交组成的诱导图形所产生的错觉，可能会有成果。
