Rolling shutter speckle imaging (RSSI) is a single-shot imaging technique that directly measures the temporal dynamics of the scattering media using a low-cost rolling shutter image sensor and vertically elongated speckles. In this paper, we derive and validate a complete spatiotemporal intensity correlation (STIC) model for RSSI, which describes the row-by-row correlation of the dynamic speckles measured with a rolling shutter in the presence of static scattering. Our new model accounts for the finite exposure time of the detector, which can be longer than the sampling interval in RSSI. We derive a comprehensive model that works for all correlation times of rolling shutter measurements. As a result, we can correctly utilize all data points in RSSI, which improves the measurement accuracy and ranges of speckle decorrelation time and dynamic scattering fraction, as demonstrated by phantom experiments. With simulations and experiments, we provide an understanding of the design parameters of RSSI and the measurement range of the speckle dynamics.
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