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This section describes two methods to calibrate the *Pattern Center*, or in other words, to determine the position of the point on the phosphorus screen seen by the CCD camera at which the normal of the screen intersects the specimen at the electron beam location (see Figure 1 in the General Description section). All the angle calculations are made using a reference centered at this point on the screen, with the X and Y axis being horizontal and vertical, respectively. The Z axis is along the normal of the screen.

A simple way to determine the *Pattern Center* is to use a Si (001) single crystal wafer oriented so that one of the [001] directions is perfectly horizontal. For a specimen holder oriented so that the normal of the wafer is at 70? of the vertical toward the phosphorus screen, the [114] pole of the Si wafer becomes horizontal and thus coincides with the *Pattern Center*, see Figure 2 below. By finding the coordinate of the [114] pole in the pattern in pixels, you can find the position of the *Pattern Center*. The vector *up* in the patcenter.m file is the coordinate of the *Pattern Center* in pixels for a 640x480 image with the origin at the lower left corner. To calculate Z, the distance specimen-Pattern center, you should measure the distance *d* in pixels between the [114] pole and another known pole in the pattern, e.g [112]. After calculating the angle teta between the two known poles, Z becomes Z=*d*/tan(teta). The value of *up* and Z can then be entered in the patcenter.m file which will be called each time you will run ebsp.m.

**Indexed EBSP of a Si (100) wafer, with a [100] direction horizontal, and the specimen normal at 70?[sgl dagger]of the vertical**

To refine the determination of the pattern center, I have written a Matlab application, calibnew.m, which optimizes the coordinates of the pattern center mathematically. This application takes advantage of the Matlab 3d optimization function "fmin". You must first enter in the file patcenterfunct.m (by editing the file) the coordinates of the projection of three known poles, u1, u2, u3, and the angles, alpha1, alpha2 and alpha3, which are the angles in degrees between the poles u1 and u2, u2 and u3, u1 and u3 respectively. The Z coordinates of the three poles are taken from the calibnew.m file and do not need to be entered.

You must then edit in the file calibnew.m the position of the pattern center (the value found by the Si(001) method for example), as well as the angles alpha1, 2, 3 that you have entered in the patcenterfunct.m file.

You can now run the optimization routine, calibnew.m.

The pattern center coordinates are optimized by minimizing the error delta2 (see the end of the patcenterfunct.m file) between the pole angles calculated from the pole positions in the pattern and the *pattern center* position, and the true pole angles (calculated or found in tables). calibnew.m gives you a new pattern center coordinates, the number of iteration and the value of the error paramater delta2. Those new values of the pattern center can then be edited in the patcenter.m file.