Methods

Geometry of the Coordinate System:

Figure 2 shows the relationship between the camera coordinate system and translation along the X and Y axis of the goniometer for a fixed magnification. For a given starting position, translating the X axis of the goniometer results in a vector displacement, V_x, in the camera coordinate system. We define the slew rate, |V_x|, of the goniometer to be the magnitude of V_x measured in units of nm/tick of requested goniometer movement. We define the heading, Q_x, as the direction of this vector. Similarly, the motion of the y axis of the goniometer is characterized by V_y, |V_y|, and Q_y. The manufacturer nominally defines the slew rate for both axes to be 1nm/tick and the headings for both axes are nominally fixed and perpendicular to each other.

Figure 2: The relationship between the camera coordinate system and translation along the X and Y axis of the goniometer for a fixed magnification. For a given starting position, translating the X axis of the goniometer results in a vector displacement, Vx, in the camera coordinate system. We define the slew rate, |Vx|, of the goniometer to be the magnitude of Vx measured in units of nm/tick of requested goniometer movement. We define the heading, Qx, as the direction of this vector. Similarly, the motion of the y axis of the goniometer is characterized by Vy, |Vy|, and Qy. The manufacturer nominally defines the slew rate for both axes to be 1nm/tick and the headings for both axes are nominally fixed and perpendicular to each other.

Measurement Techniques:

Our goal was to characterize the behavior of the goniometer over the entire range of goniometer movement for both the x and y axes. As we wanted to measure many hundreds of data points we used the software developed as part of the Leginon system to design a system which automatically measures the response of movements along each of the goniometer axes. This is achieved by acquiring an image, moving the goniometer a specified number of ticks (defined nominally as 1nm/tick), acquiring a new image, and using cross correlation techniques to determine the displacement between the two images. The result is a measure of the displacement in nm for each tick of the goniometer axis movement. In order to do this automatically over the entire goniometer range we used single slot copper grids (Electron Microscopy Sciences, Fort Washington, PA) covered with a nitrocellulose supporting film (0.35% nitrocellulose in amyl acetate), carbon-coated to increase the stability of the film and onto which pigment granules were deposited to serve as reference points in the acquired images. The pigment granules were melanin from Xenopus laevis melanophores which were suspended in water and applied to the grids. The granules are roughly 0.2 micron on average and spread consistently over the entire grid to provide a field of view with sharp contrast to ensure accuracy in the cross correlation measurements.

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