Compressed sensing has been discussed separately in spatial and temporal domains. Compressive holography has been introduced as a method that allows 3D tomographic reconstruction at different depths from a single 2D image. Coded exposure is a temporal compressed sensing method for high speed video acquisition. In this work, we combine compressive holography and coded exposure techniques and extend the discussion to 4D reconstruction in space and time from one coded captured image. In our prototype, digital in-line holography was used for imaging macroscopic, fast moving objects. The pixel-wise temporal modulation was implemented by a digital micromirror device.

We have demonstrated two illustrative cases where 4D spatio-temporal data is recovered from a single 2D data. In the case of vibrating hairs, 2 depth layers and 10 video frames in time were recovered. The spatio-temporal compression is 20×. In the case of dropping glitter flakes, a 4D volume was reconstructed to track the motion of small particles. The spatio-temporal compression is 120 × 10. We call our technique “compressive holographic video” to emphasize the compressive sampling approach to acquisition of spatio-temporal information. We show that our technique affords a significant reduction in space-time sampling, enabling 4D events to be acquired using only a single captured image.

In our prototype implementation we use a DMD as a coded aperture that is imaged directly onto a sensor. While non-trivial to implement, in principle it is possible to fabricate a CMOS sensor with pixel-wise coded exposure control. The prototype showed that it is possible to simultaneously exceed the capture rate of imagers and recover multiple depths with reasonable depth resolution. In this paper, as an example, we presented a temporal increase factor of 10×. A potential factor can be 24× based on the DMD we used. By means of spatio-temporal modulator, one is able to significantly increase the frame rate of the sensors. Based on this idea, the recovered frame rate is redefined by the modulator’s frame rate. The coded-exposure technique enables high speed imaging with a simple frame rate camera. Digital in-line holography brings the capability of 3D tomographic imaging with simple experimental setup. Our Compressive Holographic Video technique is also closely related to phase retrieval problems commonly faced in holographic microscopy. Our space-time subsampling technique can be viewed as a sequence of coded apertures applied to a spatiotemporally varying optical field. In the future we plan to explore the connections between our CS reconstruction approach and the methods introduced in [33]. In our general model, we place a coded aperture between the sensor and scene. In our prototype implementation we use a DMD as a coded aperture that is imaged directly onto a sensor. While not explored in this paper, we believe that adding defocus between the coded aperture plane and sensor may be beneficial for phase retrieval tasks, as in [33]. In this work, we focus on a proof-of-principle demonstration of compressive holographic video. In the future, we hope to explore a diverse set of mask designs, as well as techniques for mask optimization.

Acknowledgments