Laser Trackers: Defining Accuracy (Part 1)

Measurement instruments and systems evolve constantly, enabling the user to take advantage of a whole host of features. The technical specifications of most measurement systems may include reference to such entities as resolution and repeatability but will always include reference to the term accuracy.

Let’s explore the meaning of accuracy in the context of metrology in general and in particular for the use of a laser tracker instrument.

We’ll also explain the term and distinguish between in-line (or radial accuracy) and angular accuracy. Also described is the tendency for the angular errors to dominate during the measurement of a typical object and examples are offered to illustrate this.

Finally, we’ll illustrate the consequences of poor angular accuracy in particular.


Accuracy

Accuracy, or bias as it is sometimes called, is a term which can be described as the closeness of the agreement between the result of a measurement and a true value of the particular quantity being measured. In reality, we will never know the true value of the measured quantity which is why in cases where more certainty of the measured quantity is important, there tends to be an emphasis on ensuring that at least the accuracy of the measurement instrument is optimized.


Laser Tracking Instruments and Accuracy

Laser tracking measurement instruments are very versatile by nature, although their use is frequently for applications where there is a demand for the highest possible performance from the measurement system to characterize the object being measured.

One of the reasons why laser trackers have evolved into this high accuracy sector is because of their outstanding ability to accurately measure distances. This was initially due to the use of laser interferometers (IFM) followed later by Absolute Distance Meters (ADM).

Distance measurement capability on its own is not enough if a set of coordinates is required. In order to achieve this, the laser tracker instrument in its basic form is equipped with an angular measurement system to enable the distance measurement to be processed alongside two measured angles to arrive at the required coordinates.

It is clear then that in order for the ever-increasing customer specifications to be met, there has to be an emphasis upon the accuracy of both the distance and angular measurements of the instrument.


Specifications for Distance and Angular Measurement Accuracy

Dependent upon the manufacturer of the laser tracker, specifications over the last few years have varied in the sense of their presentation, usefulness and practicality to the user.

The introduction of the ASME B89.4.19-2006 standard has helped manufacturers to standardize the approach toward specifying, although there is some way to go in order that complete agreement is reached across continents.

The ASME standard offers the concept of Maximum Permissible Error (MPE) to the manufacturer and subsequently the user. MPE is useful in the sense that it encompasses the extreme values of error that are permitted by a specification.

The following is a typical distance measurement specification offered by a manufacturer. Please note that actual numbers are for reference only:

For the IFM system:
4 micrometers + 0.8 micrometers/meter

For the ADM system:
20 micrometers + 0.8 micrometers/meter

For the Angular or more often called the Transverse system
36 micrometers + 0.6 micrometers/meter

Note that in all cases there are two terms - the first term is the offset, while the second term is the slope or scale factor. The slope or scale factor is predominantly a function of distance; therefore it should encapsulate the range of specified environmental conditions together with the specified range of the instrument.

The MPE specifications can sometimes be offered as “Typical”, in which case they constitute a halving of the full MPE value for the purposes of portraying a value which will be typically achieved the majority of the time.

As for the relevance of the MPE specs to the user, it’s clear that the declared MPE values can be compared to assess the relevance of the purchase across manufacturers. If Point-to-Point accuracy is of interest to the user, some manufacturers publish the formulae used to calculate the MPE, making it possible for the user to calculate his or her own situation.

Some manufacturers also offer to certify the instrument with respect to the B89.4.19-2006 standard. If this is available, together with processes to protect or guard-band the MPE specifications, it can only be of benefit to the user.

Download the full white paper.