An equal area projection pole figure is a standard representation of crystallographic orientation data where the hemisphere of orientations is projected onto a 2D plane in a way that preserves spherical area.
Pole figures are used to visualize the distribution of crystallographic poles (like crystal directions or plane normals) from many grains in a material onto a projection sphere. The resulting plot shows the density of these poles across the sphere's surface.
Why Equal Area Projection is Used
The core reason for using equal area projection for pole figures is directly related to their definition and interpretation. As stated in the reference:
- Pole figures are defined as relative frequency by area. This means that the intensity or color at any point on a pole figure represents how many crystallographic poles fall within a specific unit area on the original projection sphere.
- An equal area projection preserves the spherical area. Unlike projections that preserve angles (like stereographic projection), an equal area projection ensures that equal areas on the sphere map to equal areas on the 2D plot.
Therefore, using an equal area projection ensures that the visual density shown on the pole figure plot accurately reflects the true density of orientations per unit area on the original spherical space. This makes it straightforward to interpret the relative abundance of different orientations by simply looking at the colored areas on the figure.
Characteristics
- Preserves Area: The defining characteristic is that areas on the sphere correspond proportionally to areas on the projection plane.
- Default Standard: Because of the "relative frequency by area" definition of pole figures, equal area projection is the default projection in many materials science software packages, such as MTEX.
- Alternative Names/Flags: It is sometimes referred to or set using specific flags or terms like
eareaorschmidtin software.
Comparison to Other Projections
While equal area projection is standard for density plots (pole figures), other projections exist:
| Projection Type | Characteristic | Common Use Case | Pole Figure Suitability |
|---|---|---|---|
| Equal Area Projection | Preserves Area | Density plots (Pole Figures) | Standard/Default |
| Stereographic Projection | Preserves Angles | Plotting individual points | Less common for density |
In summary, an equal area projection pole figure is a specific type of pole figure plot where the underlying projection method ensures that the visual density accurately represents the area density of crystal orientations. This is essential for correctly interpreting texture strength and distribution in polycrystalline materials.
