Moiré effect is a well-known interference phenomenon occurred between repetitive structures. Conventional moiré fringes are produced by superposing gratings or dots arrays. However, when the micro-image array as base layer and the corresponding micro-focusing elements as revealing layer overlap each other, a special kind of moiré effect, so-called moiré magnifier, can be observed. Micro-image units in the base layer are enlarged and projected to moiré space. To our knowledge, there has no complete design methodology for the realization of the moiré magnifier. With the combination of the Fourier transform and spectral approach, a new algorithm based on transfer matrix is investigated, which is capable of predicting the location of any arbitrary point in the base layer mapping to the moiré space, thus it provides a simple way to explore the physical insight into the field of moiré imaging. The magnification factor and the orientation of the synthetically enlarged image are determined not only by the scaling ratio but also by the interrelation between the primitive vectors in the base and revealing layers. Experimental results are in good agreement with theoretical predictions. By using the proposed method, the moiré magnifier can extend appealing applications in esthetic security devices, highly accurate measurements and precise color printing.