Cycloids for Sv

Use this probe to estimate the surface area per unit volume, sometimes referred to as the surface density.

The program displays sets of short test curves (cycloids) and test points in a grid pattern over the material to be examined. Place markers wherever the cycloids cross the boundaries of the surface of interest, or wherever a test-point appears in the region that represents the volume in the length per volume estimate.

Prerequisites

  • Vertical sections with a random rotation around the vertical axis, systematic random sampling with sections, and an identifiable vertical axis.
  • Isotropy for the third axis achieved by using a random test-line— this test-line is a cycloid to make the probe random in three dimensions.

Procedure

  1. Click Probes>All probes>Surface>Cycloids for Sv.
  2. Adjust the values for section cut thickness and cycloid width. You may need to experiment to determine an appropriate grid in order to obtain a statistically significant number of intersections.

    The cycloid width is the vector distance from endpoint to endpoint of the cycloid line segment.

  3. Right-click and select Define Vertical Axis.
    1. Drag the head of the arrow to align the vertical axis with the vertical axis of the tissue.
    2. Right-click and select Accept to confirm the alignment.
  4. Click all the test points (angle marks) inside the region of interest's volume.
  5. Click wherever the cycloid curves cross the boundary of the region of interest's surface.
  6. To end the probe, right-click and select Exit Cycloid.
  7. The results are immediately displayed in the Sampling Results window.

 

See Formulas & references, Sv-Cycloid Fractionator