Digital holographic microscopy retrieves amplitude and phase information of an image which allows us to computationally correct for imperfections in the imaging optics. However, digital holographic microscopy is an interferometric technique that is inherently sensitive to undesired phase variations between object and reference beam. These phase variations lower the fringe contrast if they are integrated over a finite exposure time which leads to a reduced amplitude of the retrieved image. This results in significant errors in applications that rely on a stable and accurate amplitude measurement, such as optical overlay metrology in the semiconductor industry. We present experimental results on a computational vibration mitigation method for the application of overlay metrology using phase interpolation between a sequence of measured holograms and demonstrate its capability to improve metrology precision in an overlay metrology application that uses digital holographic microscopy.