## 4 Results
### Close-Ups in Simulation  
One way to observe the accuracy of the calibration is by projecting a simple two-colored integral image and taking a closer look at the light reflected on a micromirror scale. Figure 5 gives closeups for cases using a ground-truth alignment, no calibration, calibration using the approach from [13], which does not utilize markers, and the approach presented in this section that introduces the transparent diffusive markers. All close-ups are obtained using a simulation program used to develop the calibration software. In our setup, both projector and camera were located at a less than optimal position. The projector was given an extra tilt around its projection axis, while the camera was located 2.5 cm to the left of the viewing zone its center. In this simulation, we projected a test pattern onto the micromirror array. The used pattern is an integral image in which each elemental image is given a single solid color. These differently colored rectangles help to visualize the correctness of the alignment. In our tests, each elemental image occupied \(22\times 11\) pixels, since the micromirrors are only half as high as they are wide. Most elemental images are colored red or blue to visualize their borders. Some are given a different color (yellow or green) to check whether the mapping between elemental images and micromirrors is correct. Please note that this pattern is not to be confused with a Bayer mosaic. Ideally, the resulting grid should align perfectly with the borders of the rectangular micromirrors, as can be seen in the ground-truthcase. The ellipse-shaped gradients show the regions of the mirrors that reflect light towards the camera. For illustration purposes, the mirrors were made more diffuse than the actual real-life material. The intensity corresponds to the amount of light being reflected in the direction of the camera for that point. A sudden cut-off of the circle corresponds to a transition to a neighboring mirror: e.g., the light at the left side of a micromirror is reflected to a completely different direction than the light at the right side. The same goes for bottom and top. The elemental images in a different color (e.g., green and yellow) helps to determine whether the elemental images project on the correct micromirror. In the case of the ground-truth, we can see that each micromirror has a single color for the whole micromirror. This indicates that the setup is accurately calibrated and has no distortion. In the case of the uncalibrated setup, most mirrors show a combination of more than one color, indicating that two or more elemental images are projected on the same micromirror. In some cases, micromirrors turn blue where in the ground-truth case they are red. This indicates that the elemental image is being projected on the wrong micromirror. This is reinforced by the fact that neither the green nor the yellow elemental images are projected on their corresponding micromirrors, and are even not visible at all in the provided close-ups. The borders of the test pattern its elemental images are also not parallel to the borders of the micromirrors, since the projector is also slightly tilted around its projection axis. In the case that we use the calibration without diffusers, the grid lines are parallel to the borders of the mirrors. This shows us that the projector tilt has been compensated for. However, there is a clear shift of the grid. This shift is caused by the fact that the camera was not located at the viewing zone's center, but towards the left of it. This shift will cause the observer to see the opposite side of the scene when moving to the border of the viewing zone. The highlighted yellow and green elemental images roughly project on the same micromirror as in the ground-truth case, proving that the micromirror and elemental image mapping is correct.