**2.2 Proposed alternative**

This alternative to the traditional types of devices for measurement is a modern technology used in manufacturing industry called 3-D co-ordinate metrology. It has been very difficult to accurately measure the taper produced and these previous methodologies may have had errors. The use of the Co-ordinate Measuring Machine (CMM) is an attempt to more formally, consistently and accurately measure dimensional changes due to tooth preparation either at the margin of the crown, the angulation of that margin or the taper of the walls of the preparation. It characterises and defines the geometry of objects.

Free form surface measurement involves two key procedures, data acquisition and development of the correct fitting algorithm (Summerhays *et al.*, 2002). Each of these problems has numerous solutions which largely depend upon the specified application. For example, the application of non-contact measurement methods has expanded into many new areas from traditional industrial applications; to the medical field, such as measurements of the human face and other parts of the human body (Aung *et al.*, 1995; Shahrom *et al.*, 1996; Fan, 1997). Gradually, researchers have required the process to be used on more complicated surfaces such as in the quantification of tooth morphology.

There are number of techniques currently used to obtain accurate surface measurements, each has its own strengths, weaknesses and areas of applicability. With surface form (shape) measurements, Co-ordinate Measuring Machines (CMMs) are more suited for the inspection of automotive parts in industry since the 1950's (Bosch, 1995). Since the late 90's, along with the development of new technology in optics and computing, numerous applications have been advanced in the fields of medicine and dentistry (Chadwick, 1989; Seymour *et al*. 1996; Kabban, *et al.* 2001; Zou, *et al.* 2001, 2009; Cherukara GP *et al.* 2002; Theocharopoulos *et al.*, 2010**;** Morris *et al.* 2011 ).

The interface between the CMM and the measurement object or surface is a probe. The probe plays a very important role in obtaining the co-ordinates of a surface, and there are several kinds of probes commercially available at the present time. **Touch trigger probes** are by far the most commonly used with CMMs due to their simplicity and low cost. One of the problems with touch probes is that even under well-controlled conditions and at a generally accepted measuring speed and force, damage to the surface being scanned can occur because of the inertia effects of some probe parts (Win *et al.*, 1998). Win also indicated that initial plastic yielding of a surface can easily occur when probing with a sphere, and at higher probing speeds, multiple bouncing of the probe may occur, which reduces the accuracy for all mechanical probe systems. **The optical probe** has the great advantage of non-contact with the surface being measured. By the late 1980's, non-contact laser probes were widely accepted for surface measurement, especially in free form surface digitisation techniques due to its fast speed in the digitisation. However the accuracy in measurement when using optical probes is affected by the reflectivity of the surface, for example, a rough or dark coloured surface which is often encountered, results in empty or distorted data readings at areas due to the surface low reflectivity.
