Unidirectional signal detection in time-resolved rotational anisotropy experiments has been known to affect the time zero and time infinity (persistent alignment) values because these measurements can overestimate the parallel or perpendicular components of the signal. Here we demonstrate that the well-known expression for obtaining the rotational anisotropy, a quantity that is typically calculated to measure the alignment, rotational energy, or rotational constants of molecules, is not applicable for some of the most common experimental configurations. We report new formulations that take into account different unidirectional detection schemes and the f-number of the collection optics. Femtosecond time-resolved anisotropy measurements on iodine vapor were obtained, with typical right-angle detection, to illustrate how the new expression corresponding to this configuration yields the expected time zero and time infinity values; Fits to the observed anisotropy are shown to provide quantitatively accurate results.