## 4 Conclusions  
Based on the methods introduced here, lateral scanning of the grating parameters was demonstrated. Results from spatially resolved investigations of the grating constant reveal a distinct influence of the recording intensity and exposure duration on the Bragg selectivity:  
\[\lim_{t_{\text{exp}}\to 0}\frac{\partial\Lambda}{\partial I}=0\,;\ \frac{\partial\Lambda}{\partial I}<0\,;\ \frac{\partial\Lambda}{\partial t_{\text{exp}}}>0\,;\ \lim_{l\to\infty}\frac{\partial\Lambda}{\partial t_{\text{exp}}}=0\,;\frac{ \partial^{2}\Lambda}{\partial l\,\partial t_{\text{exp}}}=\frac{\partial^{2} \Lambda}{\partial t_{\text{exp}}\,\partial l}<0\] (2-8)  
First, it was shown that the grating period is independent of the recording intensity in the case of short exposure duration (Equation (2)) and independent of the exposure duration in the case of high recording intensity (Equation (7)). Second, the grating period shows a decrease with increasing recording intensity (Equation (3)). This effect is enhanced with increasing exposure duration (Equation (4)). Third, an increase of the grating constant with increasing exposure duration was found (Equation (5)). This effect is, in turn, increasingly pronounced with decreasing recording intensity (Equation (6)). Such countervailing effects of positive and negative optical shrinkage have already been reported with respect to time resolved investigations [13]. Results are in accordance with those obtained with other methods [9,13,29] and with other photopolymer systems [28,29]. Thus, it appears a general characteristic that lower shrinkage is observed with recordings at high intensities and short exposure duration. In view of the recently demonstrated  
Figure 4: Influence of the exposure duration on the grating slant difference: \(\Delta\Phi(t_{\text{exp}})\) for low viscosity (below, blue squares) and high viscosity (on top, orange circles). The different material’s viscosity notwithstanding, the curve progressions are highly similar in terms of quality. Quantitatively they differ with regard to the scaling of the abscissa. In the case of high viscosity, the \(\Delta\Phi(t_{\text{exp}})\)–minimum is observed for shorter exposure durations. correlation between photo-induced crosslinking and mechanical shrinkage [13], this can be interpreted in terms of advantageous conditions for monomer diffusion in case of short exposure. Investigations, based on the periodicity of transmission type gratings, are intrinsically limited, yielding only two-dimensional information on optical shrinkage in the direction of the grating vector. Therefore, to complete the picture on spatially resolved analysis of the Bragg selectivity, the modification of optical shrinkage perpendicular to the sample surface was also accomplished. Results from lateral scanning of the volume holographic grating slant angle are consistent with spatially resolved investigations of the periodicity. A distinct influence of recording intensity, exposure duration and material viscosity on the 3D Bragg selectivity was found. Furthermore, the presence of countervailing effects of positive and negative optical shrinkage is confirmed [13]. It was demonstrated that optical shrinkage occurs not only in the direction perpendicular to the sample surface. Moreover, the optical shrinkage shows characteristic changes through the depth of the layer. Accordingly, lateral progressions of the grating slant revealed a decreasing grating period towards the substrate in case of short exposure duration and an increase in the case of long exposure duration, while an intermediate behavior arises in between. The overall strength of the modification of optical shrinkage through the layer was investigated and a characteristic influence of the exposure duration was found, while the material's viscosity affects the influence of the exposure duration not in terms of quality, but in terms of quantity.