Digital speckle photography is a displacement field measurement method that employs laser speckles as surface markers. Since the approach requires only one reference image without a preparation of the sample and provides a fast, single-shot measurement with interferometric precision, the method is applied for in-process measurements in manufacturing engineering. Due to highly localized loads, higher-order displacement gradients occur in manufacturing processes and it is an open research question how these gradients affect the measurement errors of digital speckle photography. We simulate isotropic Gaussian surface topographies, apply a displacement field and then generate laser speckle patterns, which are evaluated with digital image correlation and subsequently the resulting random and systematic errors of the displacement field are analyzed. We found that the random error is proportional to the first-order displacement gradient and results from decorrelation of the laser speckles. The systematic error is mainly caused by the evaluation algorithm and is linearly dependent on the second-order gradient and the subset size. We evaluated in-process displacement measurements of laser hardening, grinding and single-tooth milling where we determined the relative error caused by displacement gradients to be below 2.5% based on the findings from the simulative study.