surface or thin section made, parallel to the original section, and the process
repeated. Clearly, the sample is either destroyed or reduced to a series of
thin sections. The resolution of the method is limited by the spacing of the
sections and the resolution of each image, which should ideally be equal
(Marschallinger, 1998b, Marschallinger, 1998a). The images can be processed
as for surface methods to separate out the different minerals (see Sections 2.6.2
and 2.6.3). The processed images can then be combined into a data volume (3-D
image) to establish the complete shape of each crystal (Marschallinger, 2001).
Serial sectioning can give excellent results, especially for small numbers of
irregularly shaped objects, but it is very time consuming and its resolution is
limited by the spacing of the sections. For example, 500 successive images must
be obtained and combined to match an image with a resolution of 500 500
pixels. This is rarely done and the vertical resolution is generally much less
than the resolution in the plane of the images. If the sample is ground away
(‘lapped’) to make the separate images then a resolution as small as 40 mm has
been achieved (Marschallinger, 1998a). If thin sections are used then a much
larger spacing is needed, typically several mm. Of course, the vertical resolu-
tion must be balanced by the need and ability to distinguish individual crystals.
Some textural parameters do not need crystals to be separated (e.g. intercept
orientation method) and in some rocks crystals can be readily isolated in plane
surfaces without optical orientation. However, if crystals must be separated
then it is generally easier to do in a thin section than on a flat surface.
Serial sectioning has been used more extensively in biological and palae-
ontological studies where the interest is in small numbers of very irregular
objects – whereas petrology is more unusually concerned with large numbers
of similarly shaped objects, like crystals.
2.2.2 Optical scanning and confocal microscopy
Optical scanning and confocal microscopy are special techniques that can be
used for the measurement of small proportions of grains in transparent mate-
rials. They give a result similar to serial sectioning, but without destroying the
sample. In optical scanning the section is examined at high magnification with
a large aperture. In this situation the depth of field is small and a narrow range
of depths in the section are focused. A photograph is taken and the sample–
objective distance increased. The process is repeated to build up a complete
3-D reconstruction of the section. The matrix of the crystals must be sufficiently
transparent and the crystal number density must be sufficiently low that the
whole crystal can be observed; hence it can only be applied in special circum-
stances, for instance microlites in a glassy volcanic rock (Castro et al., 2003).
2.2 Complete three-di mensional analytical methods 11