###### Abstract  
Although digital holography is used widely at present, the information contained in the digital hologram is still underutilized. For example, the phase values of the Fourier spectra of the hologram are seldom used directly. In this paper, we take full advantage of them for characterizing the phase modulation of a spatial light modulator (SLM). Incident plane light beam is divided into two beams, one of which passes the SLM and interferes with the other one. If an image with a single grey scale loads on the SLM, theoretical analysis proves that the phase of the Fourier spectra of the obtained hologram contains the added phase and a constant part relative to the optical distance. By subtracting the phase for the image with the grey scale of 0 from that for the image with other grey scales, the phase modulation can be characterized. Simulative and experimental results validate that the method is effective. The SLM after characterization is successfully used for coherent imaging, which reconfirms that this method is exact in practice. When compared  
It is well known that, based on the liquid-crystal birefractive property, SLM has been widely applied in many disciplines, such as optical information processing [9], holographic and/or color display [10; 11], pattern recognition [12], and vector beams [13; 14; 15]. The modulation is usually achieved by displaying a gray value map to an SLM. Different gray scale values correspond to the different directions of the liquid-crystal optical axis. As the optical axis is changed, the phase and/or intensity of the light beam passing through the SLM is modulated [16]. However, as the birefractive property can be affected by the wavelength of the incident light and the environment, it is necessary to characterize the phase and/or intensity modulation, i.e., to get the relationships between the changes of phase and/or intensity and the gray values [17; 18]. The intensity modulation can be easily characterized by an optical power meter, whereas the phase modulation may not be acquired directly. Usually, the phase modulation is characterized using interferometry, such as the Mach-Zehnder [18; 19], the Michelson [20], or even the simple double-beam interference [21]. Plane wave is always used as the incident beam; it is divided into two beams, one of which passes through the SLM (named as object wave) and interferes with the other one (named as reference wave) to form the patterns. Usually, two-part gray-scale maps are loaded on the SLM in the phase measurement. The gray scale in one part of the maps keeps the same (usually it is zero), and that in another part varies during the measurement. As the gray value changes, the phase added to the object wave is also changed, which bring on the relative shifts in interference patterns. Then, the phase variation can be obtained by measuring the shift and comparing it with the period of the fringes [16; 17; 18; 20; 21]. This traditional method is convenient, but sometimes it is time consuming to compare the intensity of the patterns to determine the real shifts. It may not be suitable for fast characterization of the phase modulation. [PERSON] et al. performed a one-dimensional correlation product to determine fringe displacement, as well as period [19]. This method is more convenient than the traditional method, but the procedure still seems a slightly complicated. [PERSON] et al. acquired the relationship of the phase shift and the gray value by writing a Ronchi grating pattern for the SLM, but the accuracy was limited by the quantization levels of the image board [22]. Recently, ptychography has been used to characterize SLM with excellent phase accuracy; however, owing to the mechanical shift in the experiment and the iterative algorithm used in the data process, this method is not suitable for fast characterization [23].