**6.4 Measurement procedures**

The basic concepts of a measurement and the associated calibration procedures are the same for spectroradiometric measurements as presented in Section 5 above. A measurement is a

directly views the input radiation from the source. The baffles interior to the assembly are only used to prevent scattered radiation from the interior walls of the baffle assembly from re-entering the input beam to the sphere. The limiting aperture is large enough that it does not define, or vignette, the final size of the input radiation beam that enters the sphere. Its purpose is to limit as much as possible the amount of off-angle stray radiation that enters

The multiple reflections at the interior of the sphere cause a change in the relative spectral

wavelength will become amplified in the sphere output radiation. With the typical white diffusers used in integrating spheres, such as PTFE or BaSO4, this is usually observed in the lower wavelengths below approximately 400 nm. If a more uniform behaviour with

In summary, although the integrating sphere input configuration has several disadvantages, the advantages that it provides in reducing the spatial non-uniformities of sources and detectors outweigh the disadvantages. The disadvantages may be mitigated by careful consideration of

The purpose of the output optics is to couple the dispersed radiation from the monochromator, at the monochromator output slit, onto the detector. To obtain the maximum signal-to-noise at the detector, the detector is often placed as close to the output slit as possible in order to collect all the radiation. If the detector must be placed at some distance from the output slits of the monochromator, some optics will be needed to collect the radiation and re-image it onto the detector. Note that if the beam is focused too intensely onto the detector, local overloading of the conversion process from photons to the output

The spectroradiometer shown in Figure 15 is designed to enable various detectors to be used depending on the wavelength range of interest. Each of these detectors requires different output optics of the spectroradiometer to couple the radiation from the monochromator to the sensitive area of the detector. For the VIS and NIR wavelengths, a silicon (Si) photodiode and a InGaAs photodiode can be mounted directly behind the slits. For the UV and VIS wavelengths, a photomultiplier (PMT) is used with a lens assembly to focus the radiation from the slits onto the PMT cathode. The assembly for the infrared (IR) detectors (Ge and InSb) is a bit more complex since these detectors are often cooled with liquid nitrogen and prefer to be operated in an upright position. In addition, their sensitive areas are usually quite small. An elliptical mirror may be used to change the direction of the radiation beam, to focus the radiation onto the detector, and to avoid the problem of a change in the focal

The basic concepts of a measurement and the associated calibration procedures are the same for spectroradiometric measurements as presented in Section 5 above. A measurement is a

( ) /(1 ( ))

 , where ( ) 

( ) 

is the reflectance of

( ) 

from its high values

with

the material of the sphere wall (CIE 084, 1989). Any irregularities or changes in

near 99% to approximately 85% by addition of dark absorbers into the coating.

each of the components of the system when assembling a measurement system.

(electrical) signal may occur, causing non-linearity in the detector response.

wavelength is desired, a compromise is to reduce the reflectance

**6.3 Spectroradiometer output optics and detector** 

position with wavelength (Gaertner & Boivin, 1995).

**6.4 Measurement procedures** 

the integrating sphere.

distribution of the sphere by a factor of

comparison between our unknown spectral quantity and a similar quantity of known magnitude. The comparison device or transfer device is now a spectroradiometer, which is a little more complex than the single detectors or photometers we discussed. The input optics to the spectroradiometer must define the geometric quantity that we wish to measure, but the spectroradiometer itself only puts out a signal, such as the current from the detector, which is related to the radiant flux at the input to the spectroradiometer. The basic measurement Equation (34) now becomes a function of wavelength, to be applied at each wavelength that is measured.

$$\boldsymbol{S}^{\mathrm{T}}\left(\boldsymbol{\lambda}\right) = \frac{\boldsymbol{i}^{\mathrm{T}}\left(\boldsymbol{\lambda}\right)}{\boldsymbol{i}^{\mathrm{S}}\left(\boldsymbol{\lambda}\right)} \cdot \boldsymbol{S}^{\mathrm{S}}\left(\boldsymbol{\lambda}\right) \cdot \frac{\boldsymbol{T}^{\mathrm{S}}\left(\boldsymbol{\lambda}\right)}{\boldsymbol{T}^{\mathrm{T}}\left(\boldsymbol{\lambda}\right)}\tag{39}$$

The term *T*( ) indicates the effect of all the components of the spectroradiometer, from the input optics to the detector (Figure 16), upon the input source flux *S*( ) . Usually we assume that the effect of *T*( ) upon the measurements is the same for both the test and the standard sources, which reduces Equation (39) to the familiar form of Equation (34) for each wavelength. In spectroradiometric measurements the terms that must remain constant between the measurement of the standard and the test quantity are quite complex. Characteristics of the monochromator such as the large peaks in the grating reflectance and the reproducibility of the wavelength scale place greater demands on the ability of the instrument to reproduce its settings. The effects of these two particular characteristics can be mitigated by performing the measurements on both sources at each wavelength, before adjusting the monochromator to the next required wavelength. This requires that switching the monochromator between the test source and the standard source can be done in an accurate and reproducible manner. In addition to requiring the reproducibility of the monochromator, the entire optical system must 'evaluate' the flux in the same manner for the two measurements. This means that nothing in the behaviour of *T*( ) should depend on the magnitude of *S*( ) , nor its initial direction or position within the defined path.

#### **7. Primary radiation sources and calibration chains**

In Section 3 we introduced the concept of a metrological traceability chain that enables our measurements to be accurate and reproducible worldwide. The primary measurement standards used for optical radiation measurements may be traceable to either detector standards or source standards that provide a procedure by which the reference quantity is the definition of the measurement unit through its practical measurement. The two sources that are typically used in the source-based method are (1) blackbody radiators, whose output is calculated from the Planck equation when the temperature of the blackbody is known (Mielenz et al, 1990), and (2) synchrotron radiators, whose output can be determined from the calculable radiance of accelerating charged particles (Ulm, 2003). The detectorbased method depends upon the measurement of absolute quantities of radiant flux by absolute radiometers (Boivin & Gibb, 1995), which compare the heating caused by the absorption of the radiant flux with the heating caused by a known amount of electrical power. A comparison of the basic optical radiation calibration chain (Gaertner, 2009) for each of these methods, using a high temperature blackbody radiator source (HTBB), is given in Figure 19.

Fig. 19. Detector-based and HTBB Source-based calibration chains for optical radiation measurements.

This calibration chain indicates that HTBB primary source based calibrations are based upon primary detector measurements. The absolute temperature of a HTBB must be determined by the absolute measurement of the radiance of the HTBB. This is done using filter radiometers that measure the radiance or irradiance of the HTBB within a limited wavelength range. The filter radiometers used for irradiance measurements (Boivin et al, 2010) are basically constructed from detectors with a wavelength-limiting filter that allows the spectral responsivity of the filter radiometer to be accurately calibrated from measurements traceable to the absolute cryogenic radiometer. The measurement of the radiance of the HTBB is performed using the geometry described in Section 4.1.7.4, with a calibrated filter radiometer as the receiver. After the temperature of the HTBB is determined, the spectral radiance of the HTBB may be calculated for the desired wavelength range using the Planck equation. The HTBB may then be used for spectral irradiance calibrations using the geometry described in Section 4.1.7.4. With HTBB operating temperatures from 2500 K to 3500 K, known spectral irradiances may be produced from wavelengths of 200 nm to over 2500 nm to calibrate standard incandescent lamps, such as the 1000 W FEL lamps that are commonly used as spectral irradiance measurement standards. Since the radiation output of an incandescent lamp is quite low in the UV, deuterium arc lamps are often used in the wavelength range from 200 nm to 350 nm. These can be calibrated using HTBB sources operating in the upper range (3400 K to 3500 K) of their temperature limits.

Whereas the transfer from detector-based to source-based measurements is very useful for spectral radiation measurements, the calibration of sources that are used for photometric measurements is best performed using filter radiometers directly to calibrate the standard incandescent lamps (Gaertner et al, 2008). For this purpose, the filter radiometer is constructed with a combination of filters that results in a filter radiometer with a spectral responsivity that approaches the photometric functions as closely as possible.

#### **8. Uncertainties**

A measurement is not complete until an estimate of the uncertainties has been made and an uncertainty budget prepared. The GUM (JCGM, 2008a) and related documents (JCGM, 2009)

temperature measurement

Fig. 19. Detector-based and HTBB Source-based calibration chains for optical radiation

responsivity that approaches the photometric functions as closely as possible.

A measurement is not complete until an estimate of the uncertainties has been made and an uncertainty budget prepared. The GUM (JCGM, 2008a) and related documents (JCGM, 2009)

This calibration chain indicates that HTBB primary source based calibrations are based upon primary detector measurements. The absolute temperature of a HTBB must be determined by the absolute measurement of the radiance of the HTBB. This is done using filter radiometers that measure the radiance or irradiance of the HTBB within a limited wavelength range. The filter radiometers used for irradiance measurements (Boivin et al, 2010) are basically constructed from detectors with a wavelength-limiting filter that allows the spectral responsivity of the filter radiometer to be accurately calibrated from measurements traceable to the absolute cryogenic radiometer. The measurement of the radiance of the HTBB is performed using the geometry described in Section 4.1.7.4, with a calibrated filter radiometer as the receiver. After the temperature of the HTBB is determined, the spectral radiance of the HTBB may be calculated for the desired wavelength range using the Planck equation. The HTBB may then be used for spectral irradiance calibrations using the geometry described in Section 4.1.7.4. With HTBB operating temperatures from 2500 K to 3500 K, known spectral irradiances may be produced from wavelengths of 200 nm to over 2500 nm to calibrate standard incandescent lamps, such as the 1000 W FEL lamps that are commonly used as spectral irradiance measurement standards. Since the radiation output of an incandescent lamp is quite low in the UV, deuterium arc lamps are often used in the wavelength range from 200 nm to 350 nm. These can be calibrated using HTBB sources operating in the upper range (3400 K to 3500 K) of their temperature limits. Whereas the transfer from detector-based to source-based measurements is very useful for spectral radiation measurements, the calibration of sources that are used for photometric measurements is best performed using filter radiometers directly to calibrate the standard incandescent lamps (Gaertner et al, 2008). For this purpose, the filter radiometer is constructed with a combination of filters that results in a filter radiometer with a spectral

Unknown Lamp

measurements.

**8. Uncertainties** 

Standard Lamp

(filter radiometer) Calibrated Detector

Absolute Radiometer

DETECTOR-BASED

Unknown Lamp

Standard Lamp

Primary Standard Source

high temperature blackbody (HTBB)

SOURCE-BASED

are excellent references. In addition, the CIE has published an extensive document on uncertainty determinations (CIE 198:2011).

The measurement configurations discussed in the preceding sections have served to define the typical types of optical radiation measurements. This means that we will be measuring radiation using internationally defined quantities and units. This requires that the actual measurement configurations and equipment that we use must adhere to the internationally accepted definitions.

There are many factors that will influence the results of our measurements. In addition to the difficulty of configuring our apparatus to measure the quantities we wish to measure, there will be influences of time, temperature, humidity and many other often unknown or unexpected factors upon the equipment we use to give us our results. The consequences are that the results we obtain are not exactly what we wish to obtain, nor are they what we would like to claim them to be. Our only recourse is to try to understand the behaviour of our equipment and how many of the conditions in our laboratory can influence the results. In many cases this will mean a deliberate attempt to change these variables to determine the subsequent change in our results. By this means we will come to know the influences that change the results by significant amounts, and are therefore important influences to control. If we cannot control them, we will at least have an idea as to how to correct our results to account for the error caused by them, or at minimum, the amount of an uncertainty to apply to our results.

The evaluation of measurement uncertainties has been divided into two different types: Type A and Type B (JCGM 100:2008, JCGM 104:2009, JCGM 200:2008).

#### **8.1 Type A uncertainty evaluation**

The Type A evaluation of a component of our measurement uncertainties is done by a statistical analysis of the measurement quantity values that are obtained by repeated measurements under the same defined measurement conditions. Each measurement value under these conditions is different from the previous measured value in a random manner such that the next measured value cannot be predicted exactly from the previous value. These uncertainties are usually analysed using Gaussian probability density functions, such as shown in Figure 20. If many repeated measurements are made, the distribution describing the quantity *x* will approach a curve similar to the black curve labeled 'distribution of data'. From these measured values, *mean x* , the mean value of x, and *data* , the standard deviation of the distribution of the measured data, can be calculated. Any single measured value of *x* is expected to be found within this distribution.

The accuracy or uncertainty with which we know both *mean x* and *data* depends upon how well we know the 'distribution of data' curve, which will depend upon how many data points we have taken. The accuracy of *mean x* is described by the standard deviation of the mean, *mean* , which is calculated from the datapoints by:

$$
\sigma\_{\text{mean}} = \sigma\_{\text{data}} \Big/ \sqrt{n} \tag{40}
$$

where *n* is the number of datapoints. The red curve labeled 'distribution of mean' in Figure 20 shows the uncertainty with which the mean value *mean x* is known from *n* measurements of *x*, all of which are assumed to be part of the distribution shown by the 'distribution of data' curve, and as calculated for a Gaussian distribution using equation (40). The value used for *n* was 10 in Figure 20.

Fig. 20. Gaussian probability density functions for Type A evaluation of uncertainties.

The distinction between *data* and *mean* is important for the estimation of the Type A uncertainties in the calibration and use of optical radiation detectors, such as photometers and spectroradiometers. During the calibration of the detector, a total of n measurements may be performed, resulting in a mean calibration value of *mean x* with a Type A uncertainty of *mean* . When the detector is later used for a single measurement of quantity x, using the calibrated value obtained from *mean x* , the Type A uncertainty in this single measured value will be given by *data* , the standard distribution of the probability distribution that describes the repeatability of the detector. The uncertainty in the calibration of the detector, which includes the *mean* obtained during the calibration, now becomes an uncertainty with a Type B uncertainty evaluation for the single subsequent measurement.

#### **8.2 Type B uncertainty evaluation**

The Type B uncertainty evaluation is defined as an evaluation of a component of measurement uncertainty determined by means other than a Type A evaluation uncertainty (JCGM, 2008b). This type of evaluation is used with systematic errors, which are themselves associated with the fact that a measured quantity value contains an offset from the true quantity value. These offsets have many origins, such as those indicated in Section 8.0 above. Determining actual and potential systematic errors requires critical evaluation of our measurement configuration.

As we have seen, optical radiation measurements involve the determination of the flux produced by a source into many different geometrical configurations. As a result, these measurements will require the use of working standard sources to either calibrate our detection system or to compare with our test source using the detection system. We noted in Section 4.2.5 the importance of comparing sources as similar as possible to reduce the spectral errors and uncertainties in photometric measurements. In Section 6.4 we discussed

of *x*, all of which are assumed to be part of the distribution shown by the 'distribution of data' curve, and as calculated for a Gaussian distribution using equation (40). The value

> distribution of mean

Fig. 20. Gaussian probability density functions for Type A evaluation of uncertainties.

uncertainties in the calibration and use of optical radiation detectors, such as photometers and spectroradiometers. During the calibration of the detector, a total of n measurements may be performed, resulting in a mean calibration value of *mean x* with a Type A uncertainty

 *mean* . When the detector is later used for a single measurement of quantity x, using the calibrated value obtained from *mean x* , the Type A uncertainty in this single measured value

the repeatability of the detector. The uncertainty in the calibration of the detector, which

The Type B uncertainty evaluation is defined as an evaluation of a component of measurement uncertainty determined by means other than a Type A evaluation uncertainty (JCGM, 2008b). This type of evaluation is used with systematic errors, which are themselves associated with the fact that a measured quantity value contains an offset from the true quantity value. These offsets have many origins, such as those indicated in Section 8.0 above. Determining actual and potential systematic errors requires critical evaluation of our

As we have seen, optical radiation measurements involve the determination of the flux produced by a source into many different geometrical configurations. As a result, these measurements will require the use of working standard sources to either calibrate our detection system or to compare with our test source using the detection system. We noted in Section 4.2.5 the importance of comparing sources as similar as possible to reduce the spectral errors and uncertainties in photometric measurements. In Section 6.4 we discussed

*data* , the standard distribution of the probability distribution that describes

*mean* obtained during the calibration, now becomes an uncertainty with a Type

*mean* is important for the estimation of the Type A

distribution of data

B uncertainty evaluation for the single subsequent measurement.

*data* and

used for *n* was 10 in Figure 20.

The distinction between

**8.2 Type B uncertainty evaluation** 

measurement configuration.

will be given by

includes the

of  the importance of accounting for the potential differing responses of the spectroradiometer (*T*( ) ) to the different sources. As may be expected, this 'like-with-like' principle is also

applicable to geometrical properties and in signal size comparisons. Therefore we should use a working standard lamp that is as similar in relative spectral output, geometrical size and shape, and flux output as the test lamp we wish to measure. By using all these techniques we will stack as many odds in our favor as possible.

However, as discussed below, there will still be aspects of our measurement that will cause us some errors and uncertainties.
