## 1 Introduction
Both plastic and elastic strain have been evaluated on the surface of a nickel-based superalloy [12]. However, the high-resolution method can be applied to a specimen loaded in the vacuum chamber of an SEM. On the other hand, optical-DIC has also been used to identify the deformation of various materials in air. Meso-scale plastic deformations of carbon steel [13] and pure titanium [14] specimens were investigated in detail. Strain heterogeneity and localization were evaluated and the effect of the representative volume element (RVE) size on the results was discussed. Furthermore, the three-dimensional digital image correlation (3D-DIC) method was applied to biological specimens [15] and the carbon fiber reinforced composite [16]. Though application of the conventional (two-dimensional) DIC is limited to the materials with negligible out-of-plane motion, 3D-DIC is applicable when considerable out-of-plane displacements are present. Similar analysis has been applied to the development of surface roughness during metal forming by [PERSON] et al. [17]. Two- and three-dimensional finite element simulations, using a number of square and cubic grains with different flow stresses, were performed. The results showed that surface roughness increased with an equivalent strain in both uniaxial and biaxial tensions, and analyses were well simulated. It was also found that grain size and the distribution of flow stress strongly influenced the development of surface roughness. In this case, the drastic simplification of the shapes and constitutive equations of grains made it possible to carry out simulations of whole polycrystalline specimens. Combined, recent studies on the inhomogeneous deformation and surface roughness of polycrystalline metals indicate that it is still difficult to investigate grain deformation when considering the three-dimensional geometries and crystal orientation of subsurface and interior grains. In an attempt to address this, we measured the changes in the nanoscopic height distribution of grains on the surface of pure titanium [18; 19] and pure copper [20] specimens under monotonic tension in air. We found that the microscopic inhomogeneity of surface grains appeared as a small change in the height distribution, and that this shift in height distribution under plastic deformation was strongly correlated with that under elastic deformation. A new non-destructive method, using a change in surface profile caused by a small external load, was also proposed [21; 22; 23], which is expected to facilitate the detection of small cracks initiated on the inner surface of the cooling passage of a turbine blade. In this paper, a cyclic tensile test is performed using a plate specimen of commercial pure titanium on a digital holographic microscope stage, and the height distribution is measured in a fixed area on the specimen surface. The results obtained are compared with those from a monotonic tension test [19]. We confirm that the strong correlation between elastic and plastic microscopic deformations seen under monotonic tension was also observed under cyclic tension. In addition, grain slip lines were observed after the test, and we discuss the overall plastic deformation behavior of surface grains.