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We describe a microscope that preferentially displays moving objects. This all-optical device operates in real-time using the nonlinear coupling of optical beams in a photorefractive crystal of barium titanate. A holographic image is continuously written and compared with the real image, and any discrepancy between the two images is immediately visible. The device can be used to highlight moving objects, such as protozoans, while suppressing the image of any stationary objects in the background. The device needs only milliwatts of laser power, and can detect objects moving at velocities of a few micrometres per second.