Data-bearing halftone images are an aesthetically pleasing alternative to barcodes. A frequency-based method has been proposed to determine the scale, orientation and the location of such images [1]. However, we find that the introduction of periodic shifting of halftone dots complicates the detection of fundamental peaks in the frequency domain. In order to analyze and solve the problem, we develop solutions based on mathematical analysis and simulation. We also perform experiments to detect the peaks in the frequency domain using camera-captured halftone images. Based on this work, a potential optimal design for data-bearing halftone images will be proposed enabling the fundamental peaks to be detected more accurately. We also provide a theoretical proof that this design is optimal.