A simple and cost-efficient method for extending a projector's depth-of-field (DOF) is proposed. By leveraging liquid lens technology, we can periodically modulate the focal length of a projector at a frequency that is higher than the critical flicker fusion (CFF) frequency. Fast periodic focal length modulation results in forward and backward sweeping of focusing distance. Fast focal sweep projection makes the point spread function (PSF) of each projected pixel integrated over a sweep period (IPSF; integrated PSF) nearly invariant to the distance from the projector to the projection surface as long as it is positioned within sweep range. This modulation is not perceivable by human observers. Once we compensate projection images for the IPSF, the projected results can be focused at any point within the range. Consequently, the proposed method requires only a single offline PSF measurement; thus, it is an open-loop process. We have proved the approximate invariance of the projector's IPSF both numerically and experimentally. Through experiments using a prototype system, we have confirmed that the image quality of the proposed method is superior to that of normal projection with fixed focal length. In addition, we demonstrate that a structured light pattern projection technique using the proposed method can measure the shape of an object with large depth variances more accurately than normal projection techniques.