分别从球面和椭球波前推导伽利略和相对论多普勒/像差效应
Galilean and relativistic Doppler/aberration effects deduced from spherical and ellipsoidal wavefronts respectively
摘要：
传统上用于说明多普勒效应的偏心嵌套球体的图示是误导性的，并且其三角分析导致关于光的误差，因为电磁多普勒效应和像差效应符合波前表面，该波前表面不是球体而是沿着源的轨迹拉伸的椭圆体。球面和椭球波前的笛卡尔和极坐标方程在这里进行了比较，并与它们各自的角多普勒函数。由于波前表面直接将帧间坐标变换与它们产生的像差联系起来，因此对其几何形状的简单分析足以找到狭义相对论的精确结果，并顺便修正经典像差公式。
英文摘要：
The diagram showing off-center nested spheres which is traditionally used to illustrate the Doppler effect, is misleading and its trigonometric analysis leads to errors concerning light, because electromagnetic Doppler and aberration effects conform to a wavefront surface that is not a sphere but an ellipsoid stretched along the trajectory of the source. The Cartesian and polar equations of the spherical and ellipsoidal wavefronts are compared here and related to their respective angular Doppler functions. As wavefront surfaces directly link inter-frame coordinate transformations to the aberrations they generate, the simple analysis of their geometry is sufficient to find exact results of special relativity and incidentally to revise the classical aberration formula.
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