There is considerable support for the hypothesis that perception of heading in the presence of rotation is mediated by instantaneous optic flow. This hypothesis, however, has never been tested. We introduce a novel method, termed "non-varying phase motion," for generating a stimulus that conveys a single instantaneous optic flow field, even though the stimulus is presented for an extended period of time. In this experiment, observers viewed stimulus videos and performed a forced choice heading discrimination task. For non-varying phase motion, observers made large errors in heading judgments. This suggests that instantaneous optic flow is insufficient for heading perception in the presence of rotation. These errors were mostly eliminated when the velocity of phase motion was varied over time to convey the evolving sequence of optic flow fields corresponding to a particular heading. This demonstrates that heading perception in the presence of rotation relies on the time-varying evolution of optic flow. We hypothesize that the visual system accurately computes heading, despite rotation, based on optic acceleration, the temporal derivative of optic flow.James Gibson first remarked that the instantaneous motion of points on the retina (Fig. 1a) can be formally described as a two-dimensional field of velocity vectors called the "optic flow field" (or "optic flow") (1). Such optic flow, caused by an observer's movement relative to the environment, conveys information about self-motion and the structure of the visual scene (1-15). When an observer translates in a given direction along a straight path, the optic flow field radiates from a point in the image with zero velocity, or singularity, called the focus of expansion (FOE; Fig. 1b). It is well known that under such conditions, one can accurately estimate one's instantaneous direction of translation or "heading" by simply locating the FOE (see SI Appendix). However, if there is angular rotation in addition to translation (by moving along a curved path or by a head or eye movement), the singularity in the optic flow field will be displaced such that it no longer corresponds to the true heading ( Fig. 1c, d). In this case, if one estimates heading by locating the singularity, the estimate will be biased away from the true heading. This is known as the rotation problem (14).Computer vision researchers and vision scientists have developed a variety of algorithms that accurately and precisely extract observer translation and rotation from optic flow, thereby solving the rotation problem. Nearly all of these rely on the instantaneous optic flow field (4, 9,(16)(17)(18)(19)(20)(21)(22)(23)(24)(25) with few exceptions (26-28). However, it is unknown whether these algorithms are commensurate with the neural computations underlying heading perception.The consensus of opinion in the experimental literature is that human observers can estimate heading (29, 30) from the instantaneous optic flow field, in the absence of additional information (5, 10,15,(31)(32)(33). Even so, there...