Linear gratings are only suitable for the amplitude modulation of images. To overcome this limitation, the anti-counterfeiting technology for phase-modulated latent images is studied based on the frequency-modulated image. The latent image is hidden in an error diffusion-screened image using the phase modulation method. Mutual information is considered to be the evaluation index of the hiding effect. An irregular grating is designed based on the grating extraction principle. Further, the application scope of the amplitude-modulated images is explored based on the concept of irregular grating design. The experimental results show that irregular gratings can clearly extract latent images from the frequency-modulated image and are suitable for the different tonality of the amplitude-modulated image. Thus, the applicability of the anti-counterfeiting technology based on phase-modulated grating for the frequency-modulated screening mode and amplitude-modulated full-tone latent image extraction is verified. The irregular grating obtained by relying on the original manuscript exhibits the property of anti-duplication, and endows the technique with natural anti-counterfeiting capability.