Sphere Probes (Space Balls®) for unbiased estimation of object length.

 

Theory. The surface of a sphere provides the ideal probe for estimation of object length. In contrast to the surface of a plane, which must be randomized in 3-D space to achieve isotropy, all integral angles exist tangential to the surface of a sphere. The Space Balls® approach, developed by the SRC, is used to quantify the total length (total L) and length density (Lv) of linear features such as fibers, capillaries, etc. on tissue sections cut at any convenient orientation, e.g., coronal, sagittal.

Practical Application.
  The data collector focuses through the section in the Z-axis and clicks on intersections between the probe (sphere) and the linear features of interest as shown below.

Probe-Object Intersections On Multiple Z-Axis Planes Through Tissue Section

Space Balls

Since the Space Balls® probe is isotropic, tissue sections may be at any convenient orientation, e.g., coronal, sagittal, horizontal.
Reference 
Mouton PR, Gokhale AM, Ward NL, West MJ. Stereological Length Estimation Using Spherical Probes. Journal of Microscopy 206: 54-64, 2002.