Switchable holographic optical elements (HOEs) can used in systems and methods for projecting three-dimensional images, or for projecting two-dimensional tiled images with increased size and / or resolution. One of the methods may include sequentially displaying first, second, and third color components of a first two-dimensional image at an object plane. The first two dimensional image represents a first slice of a three-dimensional image. As the first, second, and third color components are displayed, first, second and third HOEs may be activated so that the activated first switchable HOE focuses the first color component of the first two-dimensional image onto a first image plane, the activated second switchable HOE focuses the second color component of the first two-dimensional image onto the first image plane, and the wherein the activated third switchable HOE focuses the third color component of the first two-dimensional image onto the first image plane. It is noted that the first, second, and third HOEs may be activated concurrently or sequentially with the display of the first, second, or third color components of the first two-dimensional image. After the first, second, and third color components are displayed, the first, second and third switchable HOEs are deactivated. Then, first, second, and third color components of a second two-dimensional image are sequentially displayed. The second two-dimensional image represents a second slice of the three-dimensional image. A fourth switchable HOE may be activated to focus the first color component of the second two-dimensional image onto a second image plane. The second image plane is adjacent to the first image plane.