This work addresses the problem of uniquely determining a rotational motion from continuous time-dependent measurements within the frameworks of parallel-beam and diffraction tomography. The motivation stems from the challenge of imaging trapped biological samples manipulated and rotated using optical or acoustic tweezers. We analyze the conditions under which the rotation of the unknown sample can be uniquely recovered using the infinitesimal common line and circle method, respectively. We provide explicit criteria for the sample's structure and the induced motion that guarantee unique reconstruction of all rotation parameters. Moreover, we demonstrate that the set of objects for which uniqueness fails is nowhere dense.

翻译：本研究探讨了在平行束层析和衍射层析框架下，如何从连续时间依赖的测量数据中唯一确定旋转运动的问题。该问题的研究动机源于对受困生物样本进行成像的挑战，这些样本通常通过光镊或声镊操控并旋转。我们分别利用无穷小公共线方法和无穷小公共圆方法，分析了未知样本的旋转运动能够被唯一重建的条件。我们为样本的结构及其诱导运动提供了明确的判据，以保证所有旋转参数均可被唯一重建。此外，我们证明了无法实现唯一重建的对象集合是稀疏的。