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Figure 3
(a) Raw speckle images of the reference beam (left) and the reflected beam (right) from the optic being tested. The magnified speckle patterns from the sub-regions (red and green rectangular boxes), extracted from (a) are shown in (b). The red arrow shows the shift of the speckle pattern from the upper part of the image of the reference beam to the upper part of image of the reflected beam. Likewise, the green arrow shows the shift of the speckle pattern extracted from the lower parts of the reference and reflected images. Comparing the speckle pattern shifts from the upper part and the lower part of the two raw images together, we observe that the image of the reflected beam is rotated with respect to the image of the reference beam. Panel (c) demonstrates how the rotation angle affects the calculated y displacement. The y direction is along the mirror width. Since the optical surface of the X-ray mirror should be very smooth, the calculated y displacement iy should be small along the mirror length while the speckle generator is translated along the x direction. If the mirror is well aligned, the calculated iy should be close to zero. When the mirror is rotated about the z axis (not shown in the image), the reflected image will be rotated by the same angle. As shown in (c), the calculated iy will have a linear relationship with the x coordinates.

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