What you would see the moving rod look like on a photo of a length contraction experiment, as opposed as using two locally measured separate spacetime events to measure its length.
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The apparent rotation of a moving object arises when length contraction is combined with different light emission times for photons arriving at a camera together. For an edge-on plane lamina moving along x, let X,Y be its rest coordinates and put a distant camera on the negative y axis. Simultaneous reception requires . Since , its transverse image coordinate is . This is the projection of a stationary lamina rotated through with , . It describes a photographic projection; simultaneous laboratory positions retain length contraction. The simple angle formula assumes the transverse distant-camera geometry.