## 1 Introduction  
Volume gratings, which are formed by introducing a periodic refractive index modulation within the volume of a bulk material, are of great importance and popularly used in optical physics for data storage [1], optical elements [2], as well as optical communications [3]. Many kinds of materials, such as crystals [4], fused silica [5; 6], photo-thermo-refractive (PTR) glass [7; 8; 9], and polymers [10; 11], have been employed as the recording media. In order to achieve larger refractive index modulation as well as higher data storage density in flexible devices with lightweight [12; 13; 14], polymer nanocomposites, with doped nanoparticles [15; 16; 17; 18; 19; 20; 21; 22; 23; 24], has attracted special attentions. Other than common grating structures that can be easily observed using techniques such as microscopy, volume grating does not exhibit structural characteristics such as grating groove and ridge physically. Therefore, metrology of a volume grating is challenging. [PERSON] and [PERSON] avoided the limit of resolution and achieved the image of the volume phase gratings recorded in polymer using an optical microscopy [25]. [PERSON] and co-workers had tried to monitor the eventual status of nanoparticle distribution in the holographic gratings using transmission electron microscopy (TEM) [26]. Although insightful information has been achieved, it is highly desirable to observe the volume gratings non-destructively. In practice, diffraction efficiency has been used comprehensively by many researchers to evaluate volume gratings [27; 28]. However, since the spatial distribution is not the only factor affecting the diffraction efficiency [29], it was not always a good predictor on nanoparticle distribution. [PERSON] et al. proposed a method based on angular selectivity curves to measure the refractive index modulation (RIM, i.e., the refractive index difference between bright and dark regions) of a volume grating recorded in photo-thermo-refractive glass and achieved high precision [9]. [PERSON] et al. measured the thickness, RIM and duty ratio of a volume diffraction grating using a commercial Fourier-transform spectrometer (FTS) combined with multi-incident angle measurement [30]. Recently, considering the advantages such as nondestructive to the samples, high sensitivity on anisotropy, as well as the capability of dealing with depolarization, we introduced Mueller matrix ellipsometry (MME) to characterize the volume holographic gratings recorded in a composite of poly(acrylate-co-acrylamide) and 5-nm zinc sulfide (ZnS) nanoparticles, and further studied the process of nanoparticle diffusion upon holography [31]. The time-dependent parameters had been achieved, such as the bright and dark region width, refractive index and nanoparticle volume fractions, which pave the way for the quantitative study of the nanoparticle diffusion process. However, due to the absence of general refractive index distribution model, an assumption of rectangular cross-section of the grating has been made, which may degrade the fidelity of the metrology, especially in the cases when the distribution of refractive index is not sinusoidal [32; 33] or significant absorption exists [34]. In this work, based on the rigorous coupled-wave analysis (RCWA) theory [35], we proposed a distributed dielectric constant model to interpret the interaction between the incident light and volume grating and calculate the Mueller matrices. In such a model, the dielectric constant of the volume grating is described by a general periodic spatial function, and two-dimensional discretization in one period have been carried out. By a regression analysis with the objective to best match the measured Mueller matrices, the refractive index distribution function can be reconstructed, as well as the thickness of the grating. The proposed method has been demonstrated using a series of simulations of measuring the volume gratings with different dielectric constant distribution functions.