Efficient image cytometry of a conventional microscope slide means rapid acquisition and analysis of 20 gigapixels of image data (at 0.3-microm sampling). The voluminous data motivate increased acquisition speed to enable many biomedical applications. Continuous-motion time-delay-and-integrate (TDI) scanning has the potential to speed image acquisition while retaining sensitivity, but the challenge of implementing high-resolution autofocus operating simultaneously with acquisition has limited its adoption. We develop a dynamic autofocus system for this need using: 1. a "volume camera," consisting of nine fiber optic imaging conduits to charge-coupled device (CCD) sensors, that acquires images in parallel from different focal planes, 2. an array of mixed analog-digital processing circuits that measure the high spatial frequencies of the multiple image streams to create focus indices, and 3. a software system that reads and analyzes the focus data streams and calculates best focus for closed feedback loop control. Our system updates autofocus at 56 Hz (or once every 21 microm of stage travel) to collect sharply focused images sampled at 0.3x0.3 microm(2)/pixel at a stage speed of 2.3 mms. The system, tested by focusing in phase contrast and imaging long fluorescence strips, achieves high-performance closed-loop image-content-based autofocus in continuous scanning for the first time.