This behaviour was described independently by both Roger Penrose and James Edward Terrell.
Since the Lorentz transform does not depend on the acceleration, the visual appearance of the object depends only on the instantaneous velocity, and not the acceleration of the observer.Terrell's and Penrose's papers pointed out that although special relativity appeared to describe an "observed contraction" in moving objects, these interpreted "observations" were not to be confused with the theory's literal predictions for the visible appearance of a moving object.
A previously popular description of special relativity's predictions, in which an observer sees a passing object to be contracted (for instance, from a sphere to a flattened ellipsoid), was wrong.
These papers pointed out that some existing discussions of special relativity were flawed and "explained" effects that the theory did not actually predict – while these papers did not change the actual mathematical structure of special relativity in any way, they did correct a misconception regarding the theory's predictions.
A representation of the Terrell effect can be seen in the physics simulator "A Slower Speed of Light," published by MIT.