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This study proposed a non-iterative phase tilt interferometry (NIPTI) for the tilt shift calculation and phase extraction, which can solve the random tilt-shift problem caused by external vibration. The method approximates the higher order terms of the phase to make it suitable for linear fitting. Then according to an estimated tilt, the accurate tilt shift can be obtained by least squares method without iteration, and the phase distribution can be calculated by it. The simulation results indicated that the root mean square error of the phase calculated by the NIPTI can reach up to 0.0002λ. The experimental results showed that the calculated phase exhibited no significant ripple when using the NIPTI for cavity measurements in a time-domain phase shift Fizeau interferometer. Moreover, the root mean square repeatability of the calculated phase reached up to 0.0006λ. It indicates that the NIPTI provides an efficient and high-precision solution for random tilt-shift interferometry under vibration.