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In this paper, we study how a displacement of a quantum system appears undera change of relativistic reference frame. We introduce a generic method inwhich a displacement operator in one reference frame can be transformed intoanother reference frame. It is found that, when moving between non-inertialreference frames there can be distortions of phase information, modal structureand amplitude. We analyse how these effects affect traditional homodynedetection techniques. We then develop an in principle homodyne detection schemewhich is robust to these effect, called the ideal homodyne detection scheme. Wethen numerically compare traditional homodyne detection with this in principlemethod and illustrate regimes when the traditional homodyne detection schemesfail to extract full quantum information.

Universal Transformation of Displacement Operators and its Application to Homodyne Tomography In Differing Relativistic Reference Frames