## 1 Introduction  
Speckle photography, a technique that uses a random speckle pattern to quantitatively measure displacement and strain, is a major milestone in the archive of experimental mechanics. Speckle photography has found application in many fields of science and engineering. The basic principle of the white light speckle technique was first proposed in a 1968 paper by [PERSON] [1]. After the advent of laser, the laser speckle photography technique [2] was developed, followed by a major expansion of the white light speckle photography approaches [3]. The method's spatial resolution was significantly increased with the development of the electron speckle photography technique by [PERSON] et al., in 1997 [4], which employs submicron and nano-sized speckles. In addition, its ease of use and versatility were greatly enhanced by the development of the digital speckle photography (DSP) technique [5, 6]. DSP is a 2-D method in that only the deformation of a plane (either a surface plane or interior plane [7]) can be mapped. Since the genesis of experimental mechanics field, one of the major goals has always been to develop a true 3D experimental stress/strain analysis technique whereby one can probe into solids for detecting the interior deformation with ease. The invention of techniques such as frozen stress photoelasticity [8, 9], scattered light photoelasticity [10, 11], integrated photoelasticity and photoelastic tomography [12, 13, 14], etc. were major developments in this field. However all of these techniques are rather tedious and time consuming, some of which are even error prone. These techniques require transparent birefringent materials to simulate the real object, which limits their application. Many important solid mechanics problems cannot be modeled by a transparent material, the most obvious of which are the 3D deformation of rock materials and fiber-reinforced composites. Aside from photoelasticity, moire, laser speckle, and white light speckle photography techniques have also been attempted to investigate the internal strain of 3D objects [15; 16; 17; 18]. However, successes in such attempts have been restricted because only a few planes or sections can be probed. All of these techniques require the use of a transparent material. With the rapid growth and application of high-resolution X-ray computed tomography (nano, microfocus and synchrotron), it becomes much easier to acquire volumetric images of opaque materials with high spatial resolution. Based on volumetric images, digital volume correlation (DVC) method, a 3D extension of 2D digital image correlation (DIC), has been proposed by [PERSON] et al. for strain analysis of bone tissues exposed to compression loads [19]. This method has since been applied to many materials such as wood [20], compacted sugar [21], sand grains [22], cast iron [23], rock materials [24; 25; 26], concrete [27; 28], and composites [29; 30; 31]. In the DVC method, surrounding an interrogated point, a cubic subset (subvolume) of voxels is selected in the reference volumetric image, its corresponding position is registered in the deformed volumetric image, from which its 3D displacement vector is retrieved. The registration process can be carried out either in the spatial domain or the frequency domain. In the frequency domain, fast Fourier transform (FFT) is used to increase the calculation efficiency. As an extension of the 2D DSP (Digital Speckle Photography) method [5; 6], we have developed a 3D interior full field deformation measurement technique called digital volumetric speckle photography (DVSP) with the help of X-ray microtomography [32]. This technique has been successfully applied to mapping the internal 3D strain fields of rocks [33; 34; 35], concrete [36], and composites [37; 38; 39]. In applying the DVSP method, the reference volumetric image and deformed volumetric image are divided into subsets of certain 3D voxel arrays. Each corresponding pair of the subsets are \"compared\" via a two-step 3D FFT analysis, which is computationally highly efficient.