**2.2. Radiometry**

Radiometry is the science of electromagnetic (EM) radiation measurement. The spectrum covered by the science of radiometry is the range from 100 to 2500 nm.

#### *2.2.1. Radiant flux (*Φ*<sup>e</sup> )*

Radiant flux is defined as power emitted, transmitted or received in the form of radiation as shown in **Figure 3** [4]. The International System of Units (SI unit) of radiant flux is Watt.

#### *2.2.2. Radiant intensity (I<sup>e</sup> )*

Quotient of the radiant flux (*d*Φ*<sup>e</sup>* ) leaving the source and propagated in the element of solid angle (*d*) containing the given direction divided by the element of solid angle. The SI unit for radiant intensity is Watt/steradian (Watt/sr) as shown in **Figure 4** [4].

**Figure 2.** Solid angle [5].

**Figure 3.** Radiant flux [6].

**Figure 4.** Radiant intensity [6].

$$I\_e = \frac{d\,\Phi\_e}{d\alpha} \tag{1}$$

**Figure 5.** Radiance.

*ω*0

(Watt/m<sup>2</sup>

= 1 sr unit of solid angle.

*2.2.5. Exitance (M) [4]*

**2.3. Photometry**

*E<sup>e</sup>* = ∫ 2*π Le*

amount of radiant flux per unit area leaving a plane surface in W/m<sup>2</sup>

**Figure 6.** Illustrating the definition of the irradiance produced on a plane by a distributed source [7].

= ∫ *ϕ*=0 2*π* ∫ *ε*=0 2*π Le*

where the angles *ε* and *ϕ* are as shown in **Figure 6**.

), as shown in **Figure 7**.

(*ε*, *ϕ* ) cos *ε dω* (*ε*, *ϕ* )

The amount of incident radiant flux per unit area of a plane surface in Watt/square meter

It is the radiant flux emitted by a surface per unit area. The SI unit of radiant exitance is the

Photometry has a unique position in the science of physics. It is influenced by vision science and is a branch of optical radiometry. The science of photometry has been developed to quantify light and its properties accurately [9, 10]. The human eye reacts to electromagnetic

(*ε*, *ϕ* ) cos *ε* sin *ε dε dϕ ω*<sup>0</sup>

(3)

79

, as shown in **Figure 8**.

Optical Radiation Metrology and Uncertainty http://dx.doi.org/10.5772/intechopen.75205

#### *2.2.3. Radiance (L<sup>e</sup> )*

Quotient of the radiant flux **(**Φ*<sup>e</sup>* **)** leaving, arriving at or passing through an element of surface at this point and propagated in directions defined by an elementary cone containing [7]:

$$L\_{\epsilon} = \frac{d^2 \Phi\_{\epsilon}}{d\omega \cdot dA. \cos \varepsilon} \tag{2}$$

where is the angle between the normal *of* the surface element and the direction *of* propagation under question. The SI unit for radiance is Watt/square meter steradian (Watt/m<sup>2</sup> sr), as shown in **Figure 5**.

#### *2.2.4. Irradiance (E<sup>e</sup> )*

Flux per unit area passing through a plane from all directions in one hemisphere [7].

**Figure 5.** Radiance.

$$\begin{aligned} E\_{\varepsilon} &= \int\_{2\pi} \mathcal{L}\_{\varepsilon} \{ \varepsilon, \varphi \} \; \; \; \cos \varepsilon \, d\omega \, \{ \varepsilon, \varphi \} \\ &= \int\_{\varphi=0}^{2\pi} \int\_{\varepsilon=0} \mathcal{L}\_{\varepsilon} \{ \varepsilon, \varphi \} \; \; \; \; \cos \varepsilon \, \sin \varepsilon \, d\varepsilon \, d\varphi \, \, \omega\_{0} \end{aligned} \tag{3}$$

*ω*0 = 1 sr unit of solid angle.

where the angles *ε* and *ϕ* are as shown in **Figure 6**.

The amount of incident radiant flux per unit area of a plane surface in Watt/square meter (Watt/m<sup>2</sup> ), as shown in **Figure 7**.

#### *2.2.5. Exitance (M) [4]*

It is the radiant flux emitted by a surface per unit area. The SI unit of radiant exitance is the amount of radiant flux per unit area leaving a plane surface in W/m<sup>2</sup> , as shown in **Figure 8**.

#### **2.3. Photometry**

*I*

*)*

*)*

Quotient of the radiant flux **(**Φ*<sup>e</sup>*

*2.2.3. Radiance (L<sup>e</sup>*

**Figure 4.** Radiant intensity [6].

**Figure 3.** Radiant flux [6].

78 Metrology

shown in **Figure 5**.

*2.2.4. Irradiance (E<sup>e</sup>*

*<sup>e</sup>* <sup>=</sup> \_\_\_\_ *d* Φ*<sup>e</sup>*

at this point and propagated in directions defined by an elementary cone containing [7]:

*<sup>L</sup><sup>e</sup>* <sup>=</sup> *<sup>d</sup>* \_\_\_\_\_\_\_\_\_\_\_\_ <sup>2</sup> *<sup>Φ</sup><sup>e</sup> <sup>d</sup><sup>ω</sup>* <sup>⋅</sup> *dA*. cos*<sup>ε</sup>* (2)

where is the angle between the normal *of* the surface element and the direction *of* propagation under question. The SI unit for radiance is Watt/square meter steradian (Watt/m<sup>2</sup> sr), as

Flux per unit area passing through a plane from all directions in one hemisphere [7].

*<sup>d</sup>* (1)

**)** leaving, arriving at or passing through an element of surface

Photometry has a unique position in the science of physics. It is influenced by vision science and is a branch of optical radiometry. The science of photometry has been developed to quantify light and its properties accurately [9, 10]. The human eye reacts to electromagnetic

**Figure 6.** Illustrating the definition of the irradiance produced on a plane by a distributed source [7].

**Figure 7.** Irradiance [8].

radiation only in a certain part of the spectrum, that is, to a limited range of wavelengths or frequencies. The radiation of sufficient power within a wavelength range of approximately 380–830 nm only can stimulate the eye, and it is called light. Light enters the human eye through the cornea, a tough transparent membrane on the front of the eye as shown in **Figure 9**. It is refracted by the cornea and lens to form an image on the retina at the back of the eye. The sensitivity of the human eye to radiation is not the same for each of the wavelengths. This subjective nature of the visual system sets photometric quantities apart from purely physical quantities.

incident radiant power as a function of wavelength, normalized to unity at the maximum of the function [13] (see **Figure 10**). Special optical filters are used to give photometers nearly

The photometric quantities are related to the corresponding radiometric quantities by the CIE standard luminosity function. We can think of the luminosity function as the transfer function of a filter which approximates the behaviors of the average human eye as shown in **Figure 11**.

upon the **CIE** standard photometric observer, as shown in **Figure 12** [4]. The unit is lumen

(*λ*) functions [14].

**)** by evaluating the radiation according to its action

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the same response as the average eye.

**Figure 9.** Human eye structure [11].

*)*

**Figure 10.** The photopic vision *V*(*λ*) and the scotopic vision *V'*

Quantity derived from radiant flux **(**Φ*<sup>e</sup>*

*2.3.2. Luminous flux (*Φ*<sup>v</sup>*

(lm) = 683 × W (Watt) × V(λ).

#### *2.3.1. Photopic and scotopic vision*

The human eye adapts to the changes in brightness and color conditions, but a lux meter does not. [12]. CIE measured the light-adapted eyes of a sizeable sample group and compiled the data into the CIE standard luminosity function. During the daytime, the cones of the eye are the primary receptors and the response is called photopic vision*,* . During the nighttime, the rods become the primary receptors, and the eye's response changes to scotopic vision,. Relative spectral sensitivity here means the ratio of the perceived optical stimulus to the

**Figure 9.** Human eye structure [11].

radiation only in a certain part of the spectrum, that is, to a limited range of wavelengths or frequencies. The radiation of sufficient power within a wavelength range of approximately 380–830 nm only can stimulate the eye, and it is called light. Light enters the human eye through the cornea, a tough transparent membrane on the front of the eye as shown in **Figure 9**. It is refracted by the cornea and lens to form an image on the retina at the back of the eye. The sensitivity of the human eye to radiation is not the same for each of the wavelengths. This subjective nature of the visual system sets photometric quantities apart from

The human eye adapts to the changes in brightness and color conditions, but a lux meter does not. [12]. CIE measured the light-adapted eyes of a sizeable sample group and compiled the data into the CIE standard luminosity function. During the daytime, the cones of the eye are the primary receptors and the response is called photopic vision*,* . During the nighttime, the rods become the primary receptors, and the eye's response changes to scotopic vision,. Relative spectral sensitivity here means the ratio of the perceived optical stimulus to the

purely physical quantities.

**Figure 8.** Exitance [8].

**Figure 7.** Irradiance [8].

80 Metrology

*2.3.1. Photopic and scotopic vision*

incident radiant power as a function of wavelength, normalized to unity at the maximum of the function [13] (see **Figure 10**). Special optical filters are used to give photometers nearly the same response as the average eye.

The photometric quantities are related to the corresponding radiometric quantities by the CIE standard luminosity function. We can think of the luminosity function as the transfer function of a filter which approximates the behaviors of the average human eye as shown in **Figure 11**.

#### *2.3.2. Luminous flux (*Φ*<sup>v</sup> )*

Quantity derived from radiant flux **(**Φ*<sup>e</sup>* **)** by evaluating the radiation according to its action upon the **CIE** standard photometric observer, as shown in **Figure 12** [4]. The unit is lumen (lm) = 683 × W (Watt) × V(λ).

**Figure 10.** The photopic vision *V*(*λ*) and the scotopic vision *V'* (*λ*) functions [14].

**Figure 11.** Relationship between radiometric units and photometric units.

#### *2.3.3. Luminous intensity (I v )*

Quotient of the luminous flux **(**Φ*<sup>v</sup>* **)** leaving the source and propagated in the element of solid angle *dω* containing the given direction divided by the element of solid angle, as shown in **Figure 12** [4]. The unit is candela (cd).

$$I\_v = \frac{d\,\Phi\_v}{d\alpha} \tag{4}$$

*2.3.5. Luminance (L<sup>v</sup>*

where *<sup>d</sup>* <sup>Φ</sup>*<sup>v</sup>*

*)*

Quantity defined by the formula [4]:

**Figure 13.** The traceability chain [17].

*<sup>L</sup><sup>v</sup>* <sup>=</sup> \_\_\_\_\_\_\_\_\_\_\_ *<sup>d</sup> <sup>Φ</sup><sup>v</sup>*

*dA*.cos*θ*. *<sup>d</sup><sup>ω</sup>* (6)

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).

is the luminous flux transmitted by an elementary beam passing through the given

point and propagating in the solid angle *d* containing the given direction, *dA* is the area of a section of that beam containing the given point, B is the angle between the normal to that sec-

The traceability to the SI unit through a National Metrology Institute (NMI) is defined as the property of the result of measurement or the value of a standard whereby, it can be related to stated references, usually national or international standards, through an unbroken chain of comparisons all having stated uncertainties [16], as shown in **Figure 13**. Traceability only exists when metrological evidence is collected to document the traceability chain and quantify its associated measurement uncertainties. In most cases, the ultimate reference for a measurement result is the SI definition of the appropriate unit and the stated reference is usually a national laboratory that maintains a realization of the unit. This is a practical way of stating

tion and the direction of the beam. The unit is candelas per square meter (cd/m<sup>2</sup>

**3. Traceability and the accreditation of the laboratories**

traceability and reflects the usual chain of measurement comparisons.

#### *2.3.4. Illuminance (E<sup>v</sup> )*

Quotient of the luminous flux Φ *v* incident on asurface divided by the area *dA* of that element, as shown in **Figure 12** [4]. The unit is lux (lx) and is equal to lumen per square meter (lm/m<sup>2</sup> ).

$$E\_v = \frac{d\,\Phi\_v}{dA} \tag{5}$$

**Figure 12.** Luminous flux, luminous intensity, illuminance, and luminance [15].

#### *2.3.5. Luminance (L<sup>v</sup> )*

*2.3.3. Luminous intensity (I*

82 Metrology

*2.3.4. Illuminance (E<sup>v</sup>*

Quotient of the luminous flux **(**Φ*<sup>v</sup>*

**Figure 12** [4]. The unit is candela (cd).

*I*

*<sup>E</sup><sup>v</sup>* <sup>=</sup> \_\_\_\_

**Figure 12.** Luminous flux, luminous intensity, illuminance, and luminance [15].

*)*

*v )*

**Figure 11.** Relationship between radiometric units and photometric units.

**)** leaving the source and propagated in the element of solid

*<sup>d</sup>* (4)

*dA* (5)

).

angle *dω* containing the given direction divided by the element of solid angle, as shown in

*<sup>v</sup>* <sup>=</sup> \_\_\_\_ *d* Φ*<sup>v</sup>*

Quotient of the luminous flux Φ *v* incident on asurface divided by the area *dA* of that element, as shown in **Figure 12** [4]. The unit is lux (lx) and is equal to lumen per square meter (lm/m<sup>2</sup>

*d Φ<sup>v</sup>*

Quantity defined by the formula [4]:

$$L\_v = \frac{d\,\Phi\_v}{dA\cos\theta \,d\omega} \tag{6}$$

where *<sup>d</sup>* <sup>Φ</sup>*<sup>v</sup>* is the luminous flux transmitted by an elementary beam passing through the given point and propagating in the solid angle *d* containing the given direction, *dA* is the area of a section of that beam containing the given point, B is the angle between the normal to that section and the direction of the beam. The unit is candelas per square meter (cd/m<sup>2</sup> ).
