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Light-pulse atom interferometers are powerful quantum sensors, however, their accuracy for example in tests of the weak equivalence principle is limited by various spurious influences like stray magnetic fields or blackbody radiation. Improving the accuracy therefore requires a detailed assessment of the size of such deleterious effects. Here we present a systematic operator expansion to obtain phase shift and contrast analytically in powers of a perturbation potential. The result can either be employed for robust straightforward order-of-magnitude estimates or for rigorous calculations. Together with general conditions for the validity of the approach, we provide a particularly useful formula for the phase including wave-packet effects.