**2. Measurements, quantities, units and the SI**

As our measurements become more precise and more accurate, it becomes more and more important that we define precisely what we are measuring and what we mean by the terms that we are using to describe the measurements. We must also realize that the purpose of all measurements is to convey information—either to ourselves for some later use, or to someone else somewhere in the world. It is therefore critical that the meanings we associate with the terms we use are the same as the meanings used by the rest of the world. There are four documents that are of particular importance in optical radiation measurements:


The concept of measurement involves several important aspects. The basic definition (VIM, Section 2.1) gives measurement as "process of experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity". In addition to the 'process' of the measurement, some examples of which we will discuss in later sections of this chapter, there is the important requirement of a purpose or result to our process, and of a certain form to this result. We must consider a quantity and some means of attributing a value to this quantity. The definitions of quantity and quantity values are given (VIM, Sections 1.1 and 1.19) as:

A *quantity* is a "property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference". In this chapter we will discuss the measurement of several specific properties of optical radiation that determine the absolute amount of optical radiation that is available. In particular, we will consider the most important geometrical configurations for the amount of optical radiation (flux, intensity, irradiance, exitance, and radiance) and the spectral quantities associated with each of these geometrical quantities. We will also consider the quantities of optical radiation that are used to describe and measure the response of the human visual system to optical radiation (photometry, colorimetry). These latter quantities are the basis for the design and construction of lighting systems and facilities used for most human endeavors.

A *quantity value* is a "number and reference together expressing magnitude of a quantity".

In addition to stating that a quantity is something that must have a value, it states the form of a value as containing two parts: a number, and a reference. In all the examples we will be considering, a reference will be an entity called a *measurement unit*, which is defined (VIM, Section 1.9) as a "real scalar quantity, defined and adopted by convention, with which any other quantity of the same kind can be compared to express the ratio of the two quantities as a number". It can be seen from this definition that measurement units are the basis of our measurements. They are a quantity, just like the one that we are trying to measure ('same kind'), and they are the particular quantity that we use as the basis to obtain the magnitude

As our measurements become more precise and more accurate, it becomes more and more important that we define precisely what we are measuring and what we mean by the terms that we are using to describe the measurements. We must also realize that the purpose of all measurements is to convey information—either to ourselves for some later use, or to someone else somewhere in the world. It is therefore critical that the meanings we associate with the terms we use are the same as the meanings used by the rest of the world. There are

1. the VIM (JCGM 200:2008), which provides a vocabulary for the basic concepts and

2. the GUM (JCGM 100:2008), which provides a guide to the expression of uncertainty in

3. the SI brochure (BIPM, 2006), which provides a description of the International System

4. the CIE Vocabulary (CIE S017, 2011), which provides the vocabulary for optical

The concept of measurement involves several important aspects. The basic definition (VIM, Section 2.1) gives measurement as "process of experimentally obtaining one or more quantity values that can reasonably be attributed to a quantity". In addition to the 'process' of the measurement, some examples of which we will discuss in later sections of this chapter, there is the important requirement of a purpose or result to our process, and of a certain form to this result. We must consider a quantity and some means of attributing a value to this quantity. The definitions of quantity and quantity values are given (VIM,

A *quantity* is a "property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference". In this chapter we will discuss the measurement of several specific properties of optical radiation that determine the absolute amount of optical radiation that is available. In particular, we will consider the most important geometrical configurations for the amount of optical radiation (flux, intensity, irradiance, exitance, and radiance) and the spectral quantities associated with each of these geometrical quantities. We will also consider the quantities of optical radiation that are used to describe and measure the response of the human visual system to optical radiation (photometry, colorimetry). These latter quantities are the basis for the design and

construction of lighting systems and facilities used for most human endeavors.

A *quantity value* is a "number and reference together expressing magnitude of a quantity". In addition to stating that a quantity is something that must have a value, it states the form of a value as containing two parts: a number, and a reference. In all the examples we will be considering, a reference will be an entity called a *measurement unit*, which is defined (VIM, Section 1.9) as a "real scalar quantity, defined and adopted by convention, with which any other quantity of the same kind can be compared to express the ratio of the two quantities as a number". It can be seen from this definition that measurement units are the basis of our measurements. They are a quantity, just like the one that we are trying to measure ('same kind'), and they are the particular quantity that we use as the basis to obtain the magnitude

radiation, radiometry, photometry, lighting and colorimetry.

four documents that are of particular importance in optical radiation measurements:

**2. Measurements, quantities, units and the SI** 

terms of metrology,

measurement,

of Units, and

Sections 1.1 and 1.19) as:

of the quantity we are trying to measure. For example, the quantity of optical radiation flux is measured in terms of a specific amount of optical radiation flux–the watt.

Note that these definitions of quantity and measurement unit contain one of the key parts of a measurement process, which is to compare the two quantities, the unit and the quantity we wish to measure.

The 'defined and adopted by convention' aspect of the definition of measurement unit leads us to the SI (BIPM, 2006). This reference quantity ('real scalar quantity…of the same kind') could be a quantity of any size that is convenient for our immediate use. However, if the measurement is to convey any information to anyone else—our clients, an industrial factory, another scientist—or even to ourselves at a later time, we need to put qualifications on the properties of this reference quantity. As a minimum, we can see that it needs to be stable over time, and it needs to be accessible to any user of our data. The other users need to either have access to the same unit that we used, or they need to be able to create (realize) one of their own. For true universality, all measurements will need to be based upon reference quantities that have been agreed upon internationally. The present basis of international agreement on units of measurement is the Convention of the Metre (Convention du Mètre), which "is a treaty that created the International Bureau of Weights and Measures (BIPM), an intergovernmental organization under the authority of the General Conference on Weights and Measures (CGPM) and the supervision of the International Committee for Weights and Measures (CIPM)" (http://www.bipm.org/en/ convention/). The BIPM presently has fifty-five member states, including all the major industrialized countries. The present agreements upon the basic quantities and their units are contained in the SI brochure (BIPM, 2006). This agreement also contains information on the general consensus on how unit symbols and names, quantity symbols, and quantity values should be expressed.

While all these definitions may seem pedantic, they clarify many concepts that we often take for granted without realizing. The length of a piece of wood seems rather straightforward: we have the quantity length (the property of the piece of wood), with its magnitude as a number, such as 2, and a reference (measurement unit), such as the metre. In optical radiation we get into problems quickly because there are so many measurements, quantities and references (measurement units), that it is often difficult to sort out which of the words we are using applies to which of these concepts. The definitions in the VIM and in the SI help us to understand the framework of the measurement process. The definitions in the CIE vocabulary help us to standardize the terms and concepts in optical radiation measurements.

#### **3. Traceability chains and measurement uncertainties**

The SI definitions of the basic reference quantities and their units provide the most accurate basis for measurement that is presently available. Although the definitions of these units are constructed such that the units may be realized in any laboratory with the required skills and facilities, the realization of any of these units is not necessarily a simple matter. In general, the primary realization is performed in dedicated national facilities, called National Measurement Institutes (NMIs). At the NMI, this primary measurement standard is established using a measurement procedure that obtains the measurement result, not by comparison with a reference quantity of the same kind, but by a procedure where the reference is the definition of the measurement unit through its practical realization. In this manner, that primary measurement standard can be said to be "traceable to the SI", rather than to any other laboratory or NMI. For example, the SI unit for luminous intensity, the candela, is defined in terms of a specific amount of radiant intensity (Section 4.2.2). Calibration of sources based upon the realization of the candela is discussed in Section 7.0.

In all these measurements, the establishment of the reference and our comparison to the reference will be subject to some errors. It is not possible to establish a reference exactly to definition, as it is not possible to compare two quantities exactly. These errors may be systematic or random, leading to a measurement uncertainty, which is defined (VIM, Section 2.26) as a "non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on the information used". This definition leaves it open as to the parameter used to describe the dispersion, as well as noting that the value depends upon the information used, implying that our information may not be complete and may include an element of belief rather than absolute knowledge (JCGM 104:2009). As a consequence, a measurement result becomes (VIM, Section 2.9) a "set of quantity values being attributed to a measurand together with any other available relevant information."

Since most measurements are carried out using references that are quantities of the same kind, and are not a primary measurement standard, these measurements and references must somehow be related to the primary measurement standard. This leads to a sequence of calibrations (calibration hierarchy, VIM Section 2.40) that leads from a reference to the final measuring system, where each calibration depends upon the outcome of the previous calibration. The metrological traceability chain is the sequence of measurement standards and calibrations that were used to relate the measurement result to the reference, and the metrological traceability is the property of the measurement result whereby the result can be related to the reference through a *documented unbroken* chain of calibrations, each contributing to the measurement *uncertainty*. An example of a calibration chain used at an NMI is discussed in Section 7.0.
