## 3 Results and Discussion
### The Avoidance of Secondary Gratings  
There are several possibilities to avoid the appearance of secondary gratings. The most generic approach is to use antireflection coating on the substrate to attenuate reflection of the recording waves. A more sophisticated way exploits the correlation between recording geometry and grating period, described by Equation (1). Accordingly the grating period \(\Lambda\) converges to infinity if the angle between the recording beams is approaching zero. As a consequence, no secondary transmission grating should arise in case of symmetric exposure geometry. As can be seen from Figure 1 this technique cannot be applied to avoid parasitic reflection gratings. Even in case of a perfectly unslanted transmission grating secondary reflection gratings may arise, namely with the smallest possible period \(\Lambda\) = 130 nm. Another possibility to avoid secondary transmission gratings is to apply a single beam exposure. In this case the incident beam forms a reflection grating with its own reflection. This technique was applied in case of the reflection grating shown in Figure 4 (right side). In this event the grating period is determined by the incidence angle of the recording beam only. According to the suboptimal visibility of the interference pattern (see Equation (3)) false-color display was used to improve the visibility of the grating in the microscopic image.  
The possibilities mentioned above particularly apply to uni-directional secondary gratings and are expected to show only little effect on noise gratings. Caused by scattered light, such multi-directional secondary gratings may only be affected by means of addressing the material response. A corresponding approach is to apply short exposure time. A minimum deposited energy density is needed to trigger material response [7]. If the scattered or reflected waves, potentially forming secondary gratings, exhibit sufficiently low intensity the corresponding exposure dose falls short of the threshold. This connection is capable to explain the observation that secondary gratings do not appear if the exposure is stopped at an early stage [19]. The transmission grating without secondary reflection grating, shown in Figure 4 (left side), likewise corresponds to a small exposure dose (200 mJ/cm\({}^{2}\)).  
Figure 3: Microscopic images of transmission gratings (diagonal lines) and secondary reflection gratings (vertical lines) for different recording geometries. Transmission grating periods \(\Lambda\) are 7.6 μm (left side) and 2.3 μm (right side) and sectional grating periods \(\Lambda_{\mathrm{s}}\) are 42 μm (left side) and 9 μm (right side), respectively.  
To take full advantage of the correlation described by Equation (2), two of the parameters \(\{\Lambda\), \(\Lambda_{\mathrm{s}}\), \(\varphi\}\) are required, yielding a complete description of the spatial hologram characteristics. In case of the single beam exposure discussed above, \(\Lambda_{\mathrm{s}}=32\)\(\upmu\)m was read from the image (Figure 4, right). This corresponds to \(\Lambda=130\) nm and a slant angle of \(\varphi=0.25^{\circ}\). However, in the more general case of two-beam exposure the determination of the respective slant angle appears to be less trivial.