Display field communication (DFC) is an unobtrusive display-to-camera technology that transmits data within the frequency domain of images, ensuring that the embedded data are hidden and do not disrupt the viewing experience. The display embeds data into image frames, while the receiver captures the display and extracts it. Two-dimensional DFC (2D-DFC) focuses on embedding data in the width and height of an image. This study explores two methods to minimize the error rate in 2D-DFC without affecting the quality of the displayed image. The orthogonal method embeds data in the orthogonal direction of an image. On the other hand, the diagonal embedding method strategically embeds the data in the diagonal direction. Experiments show the diagonal method maintains a higher peak signal-to-noise ratio and surpasses the orthogonal embedding method in terms of bit error rate. 2D-DFC is expected to have practical applications in digital signage, advertising and informational displays at airports and train stations, as well as at large-scale displays for events, sports arenas, and performance venues.