The Fundamentals of Radiation Thermometers

Peter Coates, David Lowe

• Publisher: CRC Press
• Year: 2016
• ISBN:
  9781315349701
• Edition: 1
• Topic: Naturwissenschaften
• Subtopic: Physik

Authored by two highly respected experts in this specialist area, The Fundamentals of Radiation Thermometers is an essential resource for anyone intending to measure the temperature of an object using the radiated energy from that object. This readable, user-friendly book gives important background knowledge for anyone working in the field of non-contact thermometry.

The book begins with an accessible account of how temperature scales are set up and defined, and explores the historic development of temperature scales and Planck's radiation law. Through explaining the reliability of both emissivity values and extrapolation to different wavelengths and temperatures, the book provides a foundation for understanding when a valid measurement with realistic uncertainties has been made, or if an inappropriate emissivity value has been used with consequent unknown errors.

The book also presents the hardware of radiation thermometers, allowing the reader to specify an appropriate design for a particular measurement problem. It explores multi-wavelength radiation thermometry and its associated pitfalls, and a final chapter suggests strategies to minimise the uncertainties from unreliable emissivity data.

CHAPTER 1

The quantity ‘temperature’

1.1 INTRODUCTION

Radiation thermometry¹ may be defined as that field of science which deals with the measurement of the quantity ‘temperature’ using the characteristics, such as the intensity or the spectral distribution, of the thermal radiation emitted by the object undergoing measurement. The first step, then, is to be clear what quantity is being measured and how it should be expressed. In particular, we should be clear of the distinction between an empirical scale and thermodynamic temperature. It is the aim of this chapter to provide a brief introduction to the quantity ‘temperature’, and set the context of its measurement, before proceeding to discuss the fundamentals of making a measurement of radiant intensity (or intensities) and from there assigning a temperature value.

1.2 THE CONCEPT OF A SCALE

Objects and events in the world around us show a variety of characteristics or properties. Some of these possess magnitude, that is, some of the objects have the property to a greater or lesser extent than others. These properties, for example size and weight, are called quantities; shape and colour, on the other hand, are generally considered to be qualities. One of the basic assumptions of science, and one reason why it has proved so successful in describing the physical world, is that it is possible to measure quantities.

Measurement is the assignment of a number according to established objective rules or procedures, in such a way that the number represents the magnitude of the quantity concerned.

Quantities generally have a continuous range of values and cannot be determined exactly. There is always some uncertainty associated with the measurement of a physical quantity, and this greatly complicates both the theory of measurement and its application in the real world. In addition, the units in which physical quantities are measured characterise the quantity itself and are independent of the application. This is not to say that different units may not have been adopted for a given quantity, but the relationship between them is usually well known or even laid down by definition. The length of a molecule may be given in Angstrom units, that of a cricket pitch in yards, and the distance to the moon in kilometres, but all may be expressed if need be in metres.

Since in the physical sciences the fundamental concepts are well defined and the measurements of the corresponding quantities are limited only by the uncertainties associated with the measuring procedures, it is possible to state the conditions necessary for the existence of a physical quantity quite positively.

In the discussion which follows we restrict ourselves to scalar, as opposed to vector, quantities. The conditions required for a property of a system to be recognised as a quantity may be summarised as follows. First, the property must possess physical or theoretical significance. It is possible to invent quantities for which the following rules will apply, but which have no real meaning. For example, it is possible to assign quite accurate values to a variable which is formed by taking the product of a person’s height and age (their ‘hage’, measured in metre.years), but such a quantity is at present of no value whatsoever. The second requirement is that it shall be possible to find procedures which allow all of the objects or events that demonstrate the property to be ordered, that is, arranged in order of magnitude.

The ordering of objects in general is quasi-serial, that is, objects are divided into groups, or sub-sets, in which each member possesses the same magnitude of the quantity, and the groups are then arranged in ascending order. The next step is to establish a procedure which assigns to each sub-set a number. For physical quantities, the density of sub-sets is extremely high, and we may treat the quantity as essentially taking a range of continuous values. The range is not necessarily the whole range of real numbers, as many quantities are limited to positive values.

It is important to realise that the procedures used do not imply any relationships between the numbers assigned in different parts of the permitted range, that is, the suggestion that such scales must be ‘linear’ in some way is meaningless. In addition, the magnitude of the unit interval, that is, the difference between two states whose assigned numbers differ by unity, cannot necessarily be related in different parts of the scale.

For a quantity without a solid theoretical background, scales based upon different operational definitions will give arbitrary values which are not necessarily related in any predictable way. One of the first indications that a quantity has real physical significance and is well understood is that it becomes apparent that there are simple numerical relationships between scales based on a variety of physical effects. Often, values on one scale may be converted to another with a linear transformation. Initially, the relationships may be obscured by experimental uncertainties and the presence of unsuspected systematic errors. But eventually, when the structure of the theory is sufficiently well established, it becomes possible to jettison the empirical system of arbitrary scales, and to replace it with a system of measurement based upon a standard amount of the quantity, known as the unit quantity. Different magnitudes of the quantity may then be built up from multiples and sub-multiples of the unit quantity, using any of the established relationships within the theoretical structure. The major advantage of adopting this approach is that of generality, as the concepts involved may be applied equally to new physical laws and experimental techniques, as the subject area develops and the theoretical superstructure is extended.

The adoption of a system of unit quantities removes the dependence on operational definitions of scales which must specify particular procedures and materials to be used in the measurement process, and allows the application of any of the physical laws which involve the quantities concerned. However, the point of contact with the real world then occurs in the need to be specific about the definition of the unit quantity itself. In classical physics the units or primary standards were realised in the form of material artifacts, such as the platinum-iridium metre bar and the kilogram. It was necessary to treat them with great care, and to bring them out for comparison with secondary or national standards on relatively rare occasions. Although the system was not so fragile that an accident to the primary standard would have led to a significant change in the unit quantity, it was extremely difficult to ensure that slow drifts in their absolute magnitude did not occur.

More recently some of the definitions of units have been changed, or are in the process of being changed, so that they refer to atomic rather than macroscopic properties. Of course, this has to be carried out without introducing a significant change in the magnitude of the unit. The constants of the atomic processes concerned should be at least as well known as the material standards they are proposed to replace. This approach has two very significant advantages. First, it is a fundamental tenet of quantum theory that atoms of a particular isotope and in a given state are not simply similar in their characteristics but identical. The unit quantity may be realised independently in laboratories around the world and should in principle be the same in each. It is therefore much more accessible than a single artifact, and much less prone to accidental change. In practice, of course, the distinction is blurred by the effects of systematic uncertainties which differ from one laboratory to the next. This leads to the establishment of systems for inter-comparing the national standards in order to assess the overall reproducibility of the unit. The second advantage is that there is no reason to suppose that atomic properties vary with time. Although some theories suggest that fundamental constants may change on a cosmological time scale, the effects are limited, very small in magnitude and have not been confirmed in practice.

1.3 THERMOMETRY – THE MEASUREMENT OF TEMPERATURE

The concept of the temperature of an object may be directly experienced as part of our everyday existence, but measurement of the temperature of an object by touch is a very subjective process and also depends on the properties of the object itself, in particular its thermal conductivity. What is sensed, of course, is the heat that flows from the object to, or from, the sensors in our fingers or hand. But temperature and heat are different quantities, and they are commonly distinguished by saying that “temperature is the degree of hotness,” though exactly what this means is not clear. The most general definition of temperature comes from the first law of thermodynamics², which considers heat flow between objects and establishes the idea of ‘thermal equilibrium’. It can be stated as “Temperature is the potential for heat flow,” or, more generally, “the potential for heat transfer” by conduction, convection or radiation. Thus a temperature difference causes heat to flow, much as a pressure difference causes water to flow in a pipe or an electric potential difference causes a current to flow in a wire.

Returning to our everyday sensation of temperature, the range of temperature which can be sensed by direct contact is very limited. At freezing temperatures, and those above about 60°C, physical contact becomes increasingly painful. As an alternative, the temperature of hot objects may be sensed by non-contact means: the thermal (heat) radiation may be detected by the warming sensation produced. When the source is at a very high temperature, enough radiation may be emitted at visible wavelengths to be detected by the eye. The apparent colour moves from a dull red to an intense white or even blue as the temperature increases, and this gives rise to such qualitative estimates...