Camera Length in EBSD

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Camera Length in EBSD

Figure 2333a shows EBSD geometry together with camera length (L).

EBSD geometry together with camera length (L)

Figure 2333a. EBSD geometry together with camera length (L).

The camera length influences the projected image of crystal planes on the detector. Longer camera lengths improve sensitivity to certain shear components (U13, U23) but reduce sensitivity to others (U31, U32), due to the inverse relationship between these components and the camera length. The projected image components on the detector plane can be given by, [1]

---------------------------------------------------------------- [2333a]

------------------------------------------------------------- [2333b]

where,

U₁₃, U₂₃, U₃₁, and U₃₂ are out-of-plane shear components.

In Equations 2333a and 2333b, the terms involving and are divided by , indicating that the sensitivity to these components decreases with increasing camera length. Conversely, the terms involving U₁₃ and U₂₃ are multiplied by , showing that the sensitivity to these components increases with longer camera lengths.

Figure 2333b compares the original grid with the deformed grid based on Equations 2333a and 2333b. Figures 2333b (a) and (c) show the original positions, while Figures 2333b (b) and (d) illustrate how the grid is deformed by applying the two equations, with deformation components that are dependent on the camera length . The blue arrows in the right panel show the direction and magnitude of the deformations according to the equations.

In Equations 2333a and 2333b

(a)

(b)

In Equations 2333a and 2333b

(c)

(d)

Figure 2333b. Camera length = 2: (a) Original grid, and (b) Deformed grid based on Equations 2333a and 2333b, and camera length = 0.5: (c) Original grid, and (d) Deformed grid.

The relationship between camera length and the sensitivity to different strain components, in Equations 2333a and 2333b of the EBSD measurements, creates a balance where an optimal camera length exists for strain measurements, balancing signal strength and blurring effects. Errors in pattern center calibration, including camera length, can lead to "phantom strains," which can affect the accuracy of stress state measurements in the crystal.

In addition to the effects of camera length on strain sensitivity, some other impacts of camera length on EBSD measurements are:

Effect on Image Projection: The camera length affects the projection of the crystal directions onto the detector plane. The projected image of crystal directions depends on the camera length d, influencing the positions of Kikuchi bands. Errors in camera length calibration can lead to shifts in the projected patterns and introduce inaccuracies in the interpretation of strain and stress states.
Pattern Sensitivity: Longer camera lengths increase sensitivity to in-plane shear components U13 and U23 but reduce sensitivity to out-of-plane components U31 and U32. This means that specific strain components can be more easily detected at certain camera lengths, while others become less detectable. Thus, we need to dentify an optimal camera length for strain measurement, considering both geometrical factors and practical issues like signal quality and image blurring.
Pattern Center Calibration: Errors in the calibration of the camera length (along with errors in the pattern center location) can lead to phantom stresses. These phantom stresses are artificial strains that arise from miscalibrations and can mimic real strain components, complicating the interpretation of the data. Therefore, accurate calibration of the camera length is crucial for obtaining reliable strain measurements.
Impact on Measurement Accuracy: Since stress effects on the width of Kikuchi bands are second-order effects, errors in the camera length can significantly impact the accuracy of EBSD measurements. The ambiguity in solving crystal strain states due to incorrect camera length calibration makes it difficult to determine the absolute stress state of a crystal in a single-detector configuration. This ambiguity can only be resolved using multiple detectors or EBSD patterns recorded at different camera lengths.

[1] Jon Alkorta, Limits of simulation based high resolution EBSD, Ultramicroscopy 131 (2013) 33–38.

Practical Electron Microscopy and Database

An Online Book, Second Edition by Dr. Yougui Liao (2006)

Camera Length in EBSD