4. Results and discussion

crystal modules to deliver a laser beam at 266 nm (4th harmonic) for the off-wavelength. A practical reason for choosing fourth harmonic of Nd:YAG laser as off-wavelength is its reliability, compactness, long lifetime, and low running costs. However, its main drawback is the

Figure 3. Schematic diagram of the combined differential absorption/Raman lidars for simultaneously remote detection

A frequency-tripled Nd:YAG-pumped Coumarin 450 dye laser using a Littrow grating mounting operates in the frequency doubled mode for the on-wavelength, 245 nm. The grating is invariably used to allow tuning the laser across the wide gain bandwidth of the laser, the biggest advantage of dye lasers. Use of a diffraction grating alone as a wavelength selector (with suitable beam expanding optics allowing utilization of a large area of the grating surface) renders a spectral width of 0.01 nm. To reduce linewidth, an intracavity etalon is often included in the optical path. Use of an etalon along with a diffraction grating can render spectral widths as low as 0.0005 nm [21]. Coumarin 450 dye lasers with the spectral emission 427–488 nm is considered because of tunability, compactness, output stability, design simplicity, and good beam quality.

The laser output radiations are expanded by a beam expander (BE). The expanded beams are folded 90 by UV-enhanced aluminum-coated mirrors which have a good reflectivity in the region of 250–300 nm (R > 86%) and subsequently steered them toward the UF6 and hydrolyzed products plume released into the atmosphere. After interaction with particles and molecules of the atmosphere and plume, the elastic and inelastic backscattered radiations at 266, 245, and 297.3 nm are collected by a Newtonian-type telescope. It has an aspheric primary mirror with the focal length F. A secondary flat mirror reflects the converging light through a

Coumarin 450 has an absorption peak at 366 nm and an emission peak at 440 nm.

strong absorption by ozone at 266 nm [20].

96 Uranium - Safety, Resources, Separation and Thermodynamic Calculation

of UF6 and HF.

The total photon counts received by the elastic-DIAL at the distance R from both the aerosol and molecular backscattering species, Nsig(R), is given by the general lidar equation:

$$\mathbf{N}\_{\rm sig}(\lambda\_L, \mathbf{R}) = \frac{\mathbf{E}\_L(\lambda\_L)}{\mathbf{h}\nu} \eta\_{\rm bot} \mathbf{\hat{p}}(\lambda\_L, \mathbf{R}) \Delta \mathbf{R} \, \frac{A}{\mathbf{R}^2} \exp[-2\pi(\lambda\_L, \mathbf{R})] \tag{11}$$

Nspecies <sup>¼</sup> <sup>109</sup>

0.05 + (9.7 � 1.5) � <sup>10</sup>�<sup>3</sup>

sphere, described as:

2NatmΔσ

where the aerosol size gradient is large.

the atmosphere for detection UF6 can be obtained as:

Erroratm ppb <sup>¼</sup> <sup>1</sup>:<sup>3</sup> � 108

∂

<sup>∂</sup>Rln Nsig <sup>λ</sup>off ð Þ ; <sup>R</sup> Nsigsð Þ λon; R 

.<sup>T</sup> - (4.2 � 1.1)10�<sup>5</sup>

� <sup>10</sup><sup>9</sup> 2NatmΔσ

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Here Δσ ¼ σabsð Þ� λon σabsð Þ λoff is the differential absorption cross-section of the species of interest, and Natm = 2.55 � 1019 cm�<sup>3</sup> is the total number density of molecules in the atmosphere at sea level. At 266 nm, the absorption cross section of UF6 appears to be constant, <sup>σ</sup> = (1.15 � 0.01) � <sup>10</sup>�<sup>18</sup> cm2 from 0 to 100�C. The absorption cross section at 245 nm over the same temperature range may be represented with the empirical polynomial σ = [1.37 �

One can obtain the differential absorption cross section of Δσ = 4.2 � <sup>10</sup>�<sup>19</sup> cm<sup>2</sup> at room temperature T = 23�C for λon = 245 nm and λoff = 266 nm. Since aerosol concentration is typically high enough near the ground surface, it is reasonable to approximate β = βas. For the horizontal homogenous atmospheric path, βas is a slowly decreasing function of wavelength; therefore, the second term on the right hand side of the Eq. (15) can be negligible. However, for wavelengths below 300 nm, the wavelength dependent aerosol backscatter coefficient, βas, can significantly deviate from λ�<sup>1</sup> law, depending on the aerosol type. Therefore, a long distance between λon and λoff can introduce noticeable systematic error in regions of the atmosphere,

In Eq. (15), Δαatm ¼ αatmð Þ� λoff αatmð Þ λon is the differential extinction coefficient of the atmo-

Δαatm ¼ Δαma þ Δαms þ Δαas ¼ αma λoff ½ � ð Þ� ;R αmað Þ λon;R

where Δαma, Δαms, and Δαas are the differential molecular absorption, molecular scattering, and aerosol scattering coefficients, respectively. The measurement accuracy of DIAL depends very strongly on accuracy of species absorption cross-section and evolution of atmospheric extinction. The main errors of the measurement gas concentration lie with the high aerosol and air molecule concentrations in the troposphere, and errors are caused by the large wavelength separation between the "on" and "off" signals and different absorption by gases other than the species of interest and scattering caused by aerosols and molecules. Simplifying conditions can be hold when the "on" and "off" wavelengths are much more close together, and differential extinction coefficient of the atmosphere is negligible. In addition, differential backscatter error is negligible under the condition of spatially homogeneous backscatter. If the simplifications cannot be made, each of the error terms must be considered [20]. The total error caused from

Among the expected noise from constituents in the atmosphere, O3 is considered as the dominant constituent in the UV region. Figure 4 shows ozone absorption extinction as a function of

] � <sup>10</sup>�<sup>18</sup> cm<sup>2</sup>

.T2

∂

<sup>∂</sup>Rln β λoff ð Þ ; <sup>R</sup> β λð Þ on;R 

þ αms λoff ½ � ð Þ� ;R αmsð Þ λon;R þ αas λoff ½ � ð Þ� ; R αasð Þ λon;R

ð Þ Δαms þ Δαma þ Δαas (17)

� Δαatm NatmΔσ

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, where T is in degrees Celsius [24].

� 109 (15)

99

(16)

where EL is the transmitting energy, h and ν are Planck's constant and the laser frequency, ηtot = ηtηrηFOVηIFηPMT is the total efficiency of the lidar, η<sup>t</sup> is the transmitting efficiency owing to the beam expander and mirrors, η<sup>r</sup> is the receiving efficiency owing to the mirrors, lenses, and telescope, ηFOV and ηIF are the efficiency of the FOV and interference filters, ηPMT is the quantum efficiency of the PMT, ΔR is the range resolution of the photon counter, β(R) is the total backscatter coefficient of molecules and aerosols, A is the area of the telescope, and the optical depth or optical thickness <sup>τ</sup>ð Þ¼ <sup>λ</sup>; <sup>R</sup> <sup>Ð</sup> <sup>R</sup> <sup>0</sup> α λð Þ ;r dr is the integral of the extinction coefficient α(λ, r) along the path which is a function of the laser wavelength and distance.

Usually backscatter coefficient β for elastically backscattered light consists of contribution of both air molecules and aerosols, i.e., βð Þ¼ R βmsð Þþ R βasð Þ R . For molecular species, backscatter and extinction coefficient differs by a constant factor βms = (3/8π)αms and can easily be substituted. While for the aerosol species, this procedure is not possible and must define "lidar-ratio" [22, 23]:

$$\mathbf{S(R)} = \frac{\alpha\_{\rm as}}{\beta\_{\rm as}} \tag{12}$$

The result of the inversion is the backscatter ratio which is defined as:

$$\mathbf{B(R)} = \frac{\beta\_{\rm as} + \beta\_{\rm ms}}{\beta\_{\rm ms}} = \frac{8\pi\alpha\_{\rm as}}{3\alpha\_{\rm ms}}\frac{1}{\mathbf{S}} + 1\tag{13}$$

For a lidar system with a narrow FOV and a separation between transmitter and receiver optical axes, the incomplete overlap between the laser beam and the receiver FOV significantly affects lidar observation in the short range. When separation of the laser and telescope axes is negligible or small enough in which the area of the laser illumination lies totally within the receiver-optical FOV or vice versa, the overlap distance and efficiency may be adjusted by controlling the FOV of the telescope or the divergence of the laser beam (DIV). As the transmitting laser has nearly a TEM00 mode Gaussian shape, for a given beam divergence, the FOV receiving efficiency, ηFOV, increases with FOV and saturates for FOV ≥ 1.5DIV as described in Eq. (14), which can be derived from the integral of the radial intensity distribution of TEM00 mode:

$$\eta\_{\text{FOV}} = 1 - \exp\left(-2\frac{\text{FOV}^2}{\text{DIV}^2}\right) \tag{14}$$

It indicates that the FOV of the telescope optics must be larger than the laser beam divergence so that the lidar can see the entire illuminated volume.

The volume density Nspcies (in ppb) of the measurement target species in the range between R and R + ΔR can be derived from Eq. (15), which is known as the DIAL equation:

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$$\text{N}\_{\text{species}} = \frac{10^9}{2 \text{N}\_{\text{atm}} \Delta \sigma} \frac{\partial}{\partial \mathbf{R}} \ln \left[ \frac{\text{N}\_{\text{sig}}(\lambda\_{\text{off}}, \mathbf{R})}{\text{N}\_{\text{sig}}(\lambda\_{\text{on}}, \mathbf{R})} \right] - \frac{10^9}{2 \text{N}\_{\text{atm}} \Delta \sigma} \frac{\partial}{\partial \mathbf{R}} \ln \left[ \frac{\beta(\lambda\_{\text{off}}, \mathbf{R})}{\beta(\lambda\_{\text{on}}, \mathbf{R})} \right] - \frac{\Delta \alpha\_{\text{atm}}}{\text{N}\_{\text{atm}} \Delta \sigma} \times 10^9 \tag{15}$$

Nsigð Þ¼ <sup>λ</sup>L;<sup>R</sup> <sup>E</sup>Lð Þ <sup>λ</sup><sup>L</sup>

98 Uranium - Safety, Resources, Separation and Thermodynamic Calculation

the optical depth or optical thickness <sup>τ</sup>ð Þ¼ <sup>λ</sup>; <sup>R</sup> <sup>Ð</sup> <sup>R</sup>

"lidar-ratio" [22, 23]:

mode:

<sup>h</sup><sup>ν</sup> <sup>η</sup>totβð Þ <sup>λ</sup>L; <sup>R</sup> <sup>Δ</sup><sup>R</sup> <sup>A</sup>

where EL is the transmitting energy, h and ν are Planck's constant and the laser frequency, ηtot = ηtηrηFOVηIFηPMT is the total efficiency of the lidar, η<sup>t</sup> is the transmitting efficiency owing to the beam expander and mirrors, η<sup>r</sup> is the receiving efficiency owing to the mirrors, lenses, and telescope, ηFOV and ηIF are the efficiency of the FOV and interference filters, ηPMT is the quantum efficiency of the PMT, ΔR is the range resolution of the photon counter, β(R) is the total backscatter coefficient of molecules and aerosols, A is the area of the telescope, and

coefficient α(λ, r) along the path which is a function of the laser wavelength and distance.

Usually backscatter coefficient β for elastically backscattered light consists of contribution of both air molecules and aerosols, i.e., βð Þ¼ R βmsð Þþ R βasð Þ R . For molecular species, backscatter and extinction coefficient differs by a constant factor βms = (3/8π)αms and can easily be substituted. While for the aerosol species, this procedure is not possible and must define

> S Rð Þ¼ <sup>α</sup>as βas

For a lidar system with a narrow FOV and a separation between transmitter and receiver optical axes, the incomplete overlap between the laser beam and the receiver FOV significantly affects lidar observation in the short range. When separation of the laser and telescope axes is negligible or small enough in which the area of the laser illumination lies totally within the receiver-optical FOV or vice versa, the overlap distance and efficiency may be adjusted by controlling the FOV of the telescope or the divergence of the laser beam (DIV). As the transmitting laser has nearly a TEM00 mode Gaussian shape, for a given beam divergence, the FOV receiving efficiency, ηFOV, increases with FOV and saturates for FOV ≥ 1.5DIV as described in Eq. (14), which can be derived from the integral of the radial intensity distribution of TEM00

ηFOV ¼ 1 � exp �2

and R + ΔR can be derived from Eq. (15), which is known as the DIAL equation:

so that the lidar can see the entire illuminated volume.

It indicates that the FOV of the telescope optics must be larger than the laser beam divergence

The volume density Nspcies (in ppb) of the measurement target species in the range between R

<sup>¼</sup> <sup>8</sup>παas 3αms

1

FOV<sup>2</sup> DIV<sup>2</sup> � �

The result of the inversion is the backscatter ratio which is defined as:

B Rð Þ¼ <sup>β</sup>as <sup>þ</sup> <sup>β</sup>ms βms

<sup>R</sup><sup>2</sup> exp -2½ � τ λð Þ <sup>L</sup>;<sup>R</sup> (11)

<sup>0</sup> α λð Þ ;r dr is the integral of the extinction

<sup>S</sup> <sup>þ</sup> <sup>1</sup> (13)

(12)

(14)

Here Δσ ¼ σabsð Þ� λon σabsð Þ λoff is the differential absorption cross-section of the species of interest, and Natm = 2.55 � 1019 cm�<sup>3</sup> is the total number density of molecules in the atmosphere at sea level. At 266 nm, the absorption cross section of UF6 appears to be constant, <sup>σ</sup> = (1.15 � 0.01) � <sup>10</sup>�<sup>18</sup> cm2 from 0 to 100�C. The absorption cross section at 245 nm over the same temperature range may be represented with the empirical polynomial σ = [1.37 � 0.05 + (9.7 � 1.5) � <sup>10</sup>�<sup>3</sup> .<sup>T</sup> - (4.2 � 1.1)10�<sup>5</sup> .T2 ] � <sup>10</sup>�<sup>18</sup> cm<sup>2</sup> , where T is in degrees Celsius [24]. One can obtain the differential absorption cross section of Δσ = 4.2 � <sup>10</sup>�<sup>19</sup> cm<sup>2</sup> at room temperature T = 23�C for λon = 245 nm and λoff = 266 nm. Since aerosol concentration is typically high enough near the ground surface, it is reasonable to approximate β = βas. For the horizontal homogenous atmospheric path, βas is a slowly decreasing function of wavelength; therefore, the second term on the right hand side of the Eq. (15) can be negligible. However, for wavelengths below 300 nm, the wavelength dependent aerosol backscatter coefficient, βas, can significantly deviate from λ�<sup>1</sup> law, depending on the aerosol type. Therefore, a long distance between λon and λoff can introduce noticeable systematic error in regions of the atmosphere, where the aerosol size gradient is large.

In Eq. (15), Δαatm ¼ αatmð Þ� λoff αatmð Þ λon is the differential extinction coefficient of the atmosphere, described as:

$$\begin{aligned} \Delta \alpha\_{\text{atm}} = \Delta \alpha\_{\text{ma}} + \Delta \alpha\_{\text{ms}} + \Delta \alpha\_{\text{as}} &= [\alpha\_{\text{ma}}(\lambda\_{\text{off}}, \mathbb{R}) - \alpha\_{\text{ma}}(\lambda\_{\text{on}}, \mathbb{R})] \\ &+ [\alpha\_{\text{ms}}(\lambda\_{\text{off}}, \mathbb{R}) - \alpha\_{\text{ms}}(\lambda\_{\text{on}}, \mathbb{R})] \\ &+ [\alpha\_{\text{as}}(\lambda\_{\text{off}}, \mathbb{R}) - \alpha\_{\text{as}}(\lambda\_{\text{on}}, \mathbb{R})] \end{aligned} \tag{16}$$

where Δαma, Δαms, and Δαas are the differential molecular absorption, molecular scattering, and aerosol scattering coefficients, respectively. The measurement accuracy of DIAL depends very strongly on accuracy of species absorption cross-section and evolution of atmospheric extinction. The main errors of the measurement gas concentration lie with the high aerosol and air molecule concentrations in the troposphere, and errors are caused by the large wavelength separation between the "on" and "off" signals and different absorption by gases other than the species of interest and scattering caused by aerosols and molecules. Simplifying conditions can be hold when the "on" and "off" wavelengths are much more close together, and differential extinction coefficient of the atmosphere is negligible. In addition, differential backscatter error is negligible under the condition of spatially homogeneous backscatter. If the simplifications cannot be made, each of the error terms must be considered [20]. The total error caused from the atmosphere for detection UF6 can be obtained as:

$$\text{Error}\_{\text{atm}}\left(\text{ppb}\right) = 1.3 \times 10^8 (\Delta\alpha\_{\text{ms}} + \Delta\alpha\_{\text{ma}} + \Delta\alpha\_{\text{as}}) \tag{17}$$

Among the expected noise from constituents in the atmosphere, O3 is considered as the dominant constituent in the UV region. Figure 4 shows ozone absorption extinction as a function of

where Nbg, Nn, and Nsig are the detected background, dark counts accumulated over the laser pulsewidth, and the detected signal photons, respectively. From Eq. (18), the SNR is maximum

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The total detector noise counts within the laser pulsewidth, N, which is caused by the detected

where dNd/dt is the detector dark noise count rate (Hz), τPMT is the PMT response time constant or receiver pulse integration time, usually slightly larger than the laser pulsewidth, and Nbg is the photon counts of the background light received by the lidar is expressed by:

where Bbg is the sky background radiation that is negligible in the solar blind region, ΔλBIF is

angle. For a low dark count detector in the solar blind region, total detector noise count can be approximated as N ≈ 0. After accumulating photon counts for an integration time Tint, the

where f(λ)las is the laser repetition rate at wavelength λ, and f(λ)lasTint is the total number of pulse measurements averaged. For a low dark count detector in the solar blind region, we can

The feasibility of the system is simulated by taking into account the contribution of molecules and aerosols in the backscatter lidar photon rate. The aerosol backscatter has been included in the simulation considering the lidar ratio of 50 Sr corresponding to extinction and back-

results are organized using the parameter introduced in Table 1. In Figure 5, the minimum detectable concentration of UF6 as a function of range for a typical detector having a low SNR of 1.5 is depicted. It can be seen that the minimum detectable concentration of UF6 is limited to 1.21 ppm for range of 1000 m. Note that each system parameter should be carefully considered in a trade-off analyses, including the distances (or ranges) from which the measurements are to be taken, to determine the best overall solution for a given lidar application. In other words, if the determined set of lidar parameters yields a SNR that is below specification, it may be adjusted simply by reducing the DIV, and thus, the SNR will increase, or by increasing the integration time (number of shots) as shown in Figure 6. It may also possibly increase the

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>f</sup>ð Þ <sup>λ</sup><sup>i</sup> lasTint <sup>q</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>f</sup>ð Þ <sup>λ</sup><sup>i</sup> lasTint <sup>q</sup> ffiffiffiffiffiffiffiffiffi

Nsig <sup>q</sup>

Sr�<sup>1</sup>

•

N ¼ Nbg þ Nd

Nsig p . The SNR decreases rapidly once the received light

<sup>h</sup><sup>ν</sup> <sup>η</sup>rηIFηPMTBbgΩAΔλBIFτPMT (20)

τPMT (19)

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101

/4 is the viewing solid

(21.b)

SNRi (21.a)

, respectively. The simulation

when Nn = Nbg = 0; i.e., SNRmax <sup>¼</sup> ffiffiffiffiffiffiffiffiffi

intensity drops below the noise intensity.

sunlight and the detector dark noise, is given by:

averaged SNR at each wavelength is given by:

simplify Eq. (21.a) as below:

Nbg <sup>¼</sup> <sup>1</sup>

the bandwidth of the narrow-band interference filter, and Ω = πFOV2

SNRð Þ¼ λ<sup>i</sup>

SNRð Þ¼ λ<sup>i</sup>

scattered coefficients of 5 � <sup>10</sup>�<sup>4</sup> <sup>m</sup>�<sup>1</sup> and 1 � <sup>10</sup>�<sup>5</sup> <sup>m</sup>�<sup>1</sup>

Figure 4. The ozone absorption extinction as a function of wavelength [20].

wavelength in the UV region. The ozone concentration near the surface is considered to be about 0.8 � 1012 cm�<sup>3</sup> , corresponding to 30 μg/cm�<sup>3</sup> or 30 parts in 109 volumes (ppbv). From ~200 to ~310 nm, the ozone absorption coefficient is large with a maximum absorption extinction ~1 km�<sup>1</sup> at 255 nm, and it reduces rapidly to ~10�<sup>6</sup> km�<sup>1</sup> by increasing wavelength near 360 nm [20, 25].

Before designing a DIAL system, the differential absorption of the target species must be known to derive the necessary parameters such as laser energy, linewidth, and detector area. Also, the sensitivity and lower detection limit of the DIAL measurement are directly dependent on the accuracy of the differential absorption cross-section. From Eq. (15), it follows that if differential extinction and backscatter coefficients of the atmosphere as a function of wavelength are known, a measurement of backscatter power is adequate to precisely determine concentration.

In photodetectors, such as PMT or APD, that have an internal gain, both signal and noise are amplified. Usually, in photon counting regime, the random errors caused by shot noise is the dominant factor to fluctuate the detected signal and background. The SNR at each wavelength can be computed for each laser shot from:

$$\text{SNR}\_{i} = \frac{N\_{\text{sig}}}{\sqrt{N\_{\text{sig}} + N\_{\text{bg}} + N\_{\text{n}}}} \tag{18}$$

where Nbg, Nn, and Nsig are the detected background, dark counts accumulated over the laser pulsewidth, and the detected signal photons, respectively. From Eq. (18), the SNR is maximum when Nn = Nbg = 0; i.e., SNRmax <sup>¼</sup> ffiffiffiffiffiffiffiffiffi Nsig p . The SNR decreases rapidly once the received light intensity drops below the noise intensity.

The total detector noise counts within the laser pulsewidth, N, which is caused by the detected sunlight and the detector dark noise, is given by:

$$N = N\_{b\text{\text\textquotedblleft}} + \stackrel{\bullet}{N} \tau\_{PMT} \tag{19}$$

where dNd/dt is the detector dark noise count rate (Hz), τPMT is the PMT response time constant or receiver pulse integration time, usually slightly larger than the laser pulsewidth, and Nbg is the photon counts of the background light received by the lidar is expressed by:

$$\mathbf{N\_{bg}} = \frac{1}{\mathbf{h}\mathbf{v}} \boldsymbol{\eta}\_{\mathbf{r}} \boldsymbol{\eta}\_{\text{IF}} \boldsymbol{\eta}\_{\text{PMT}} \mathbf{B\_{bg}} \boldsymbol{\Omega} \mathbf{A} \boldsymbol{\Delta} \boldsymbol{\lambda}\_{\text{BIF}} \boldsymbol{\tau}\_{\text{PMT}} \tag{20}$$

where Bbg is the sky background radiation that is negligible in the solar blind region, ΔλBIF is the bandwidth of the narrow-band interference filter, and Ω = πFOV2 /4 is the viewing solid angle. For a low dark count detector in the solar blind region, total detector noise count can be approximated as N ≈ 0. After accumulating photon counts for an integration time Tint, the averaged SNR at each wavelength is given by:

$$\text{SNR}(\lambda\_i) = \sqrt{\mathbf{f}(\lambda\_i)\_{\text{las}} \mathbf{T}\_{\text{int}}} \text{SNR}\_i \tag{21.a}$$

where f(λ)las is the laser repetition rate at wavelength λ, and f(λ)lasTint is the total number of pulse measurements averaged. For a low dark count detector in the solar blind region, we can simplify Eq. (21.a) as below:

wavelength in the UV region. The ozone concentration near the surface is considered to be

Figure 4. The ozone absorption extinction as a function of wavelength [20].

100 Uranium - Safety, Resources, Separation and Thermodynamic Calculation

~200 to ~310 nm, the ozone absorption coefficient is large with a maximum absorption extinction ~1 km�<sup>1</sup> at 255 nm, and it reduces rapidly to ~10�<sup>6</sup> km�<sup>1</sup> by increasing wavelength near

Before designing a DIAL system, the differential absorption of the target species must be known to derive the necessary parameters such as laser energy, linewidth, and detector area. Also, the sensitivity and lower detection limit of the DIAL measurement are directly dependent on the accuracy of the differential absorption cross-section. From Eq. (15), it follows that if differential extinction and backscatter coefficients of the atmosphere as a function of wavelength are known, a measurement of backscatter power is adequate to precisely determine

In photodetectors, such as PMT or APD, that have an internal gain, both signal and noise are amplified. Usually, in photon counting regime, the random errors caused by shot noise is the dominant factor to fluctuate the detected signal and background. The SNR at each wavelength

SNRi <sup>¼</sup> Nsig ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Nsig þ Nbg þ Nn

<sup>p</sup> (18)

, corresponding to 30 μg/cm�<sup>3</sup> or 30 parts in 109 volumes (ppbv). From

about 0.8 � 1012 cm�<sup>3</sup>

360 nm [20, 25].

concentration.

can be computed for each laser shot from:

$$\text{SNR}(\lambda\_i) = \sqrt{\text{f}(\lambda\_i)\_{\text{las}} \mathbf{T}\_{\text{int}}} \sqrt{\mathbf{N}\_{\text{sig}}} \tag{21.b}$$

The feasibility of the system is simulated by taking into account the contribution of molecules and aerosols in the backscatter lidar photon rate. The aerosol backscatter has been included in the simulation considering the lidar ratio of 50 Sr corresponding to extinction and backscattered coefficients of 5 � <sup>10</sup>�<sup>4</sup> <sup>m</sup>�<sup>1</sup> and 1 � <sup>10</sup>�<sup>5</sup> <sup>m</sup>�<sup>1</sup> Sr�<sup>1</sup> , respectively. The simulation results are organized using the parameter introduced in Table 1. In Figure 5, the minimum detectable concentration of UF6 as a function of range for a typical detector having a low SNR of 1.5 is depicted. It can be seen that the minimum detectable concentration of UF6 is limited to 1.21 ppm for range of 1000 m. Note that each system parameter should be carefully considered in a trade-off analyses, including the distances (or ranges) from which the measurements are to be taken, to determine the best overall solution for a given lidar application. In other words, if the determined set of lidar parameters yields a SNR that is below specification, it may be adjusted simply by reducing the DIV, and thus, the SNR will increase, or by increasing the integration time (number of shots) as shown in Figure 6. It may also possibly increase the


Table 1. Major parameters of the lidar system considered in simulation.

receiver diameter; however, it increases both the received signal and noise in the same proportion. An increase in the laser beam diameter will increase the received signal, as well as SNR. Despite the advantage of large Mie- and Rayleigh-scattering and therefore high SNR of the conventional elastic lidar systems, they cannot provide species selectivity. In contrast, inelastic Raman scattering where the frequency of the scattered radiation is shifted by an amount that is a unique of the molecule can be used like fingerprint to distinguish molecular species. In other words, the Raman spectrum contains characteristic signatures of each target molecules with high spectral resolution which makes the Raman spectroscopy a very powerful technique for characterization and identification of unknown species. The intensity of the Raman signal is directly proportional to the density of the scattering molecules independent of other molecular

Figure 6. Calculated SNR as a function of FOV/DIV for a UF6 cloud with 1.1 ppm concentration at 1 km. The integration

Remotely Monitoring Uranium-Enrichment Plants with Detection of Gaseous Uranium Hexafluoride and HF Using…

time is 300 second (3000 shots). Other parameters of the lidar system are shown in Table 1.

<sup>h</sup><sup>ν</sup> <sup>η</sup>totβRað Þ <sup>λ</sup>L;<sup>R</sup> <sup>Δ</sup><sup>R</sup> <sup>A</sup>

<sup>β</sup>Rað Þ¼ <sup>λ</sup>L; <sup>R</sup> NRað Þ <sup>R</sup> <sup>d</sup>σRað Þ <sup>π</sup>; <sup>λ</sup><sup>L</sup>

is the Raman backscatter coefficient, λ<sup>L</sup> and λRa are the wavelength of laser and Raman, respectively. The wavelength shift and also narrow spectral width of the Raman scattered

<sup>R</sup><sup>2</sup> exp -½ � τ λð Þ <sup>L</sup>; <sup>R</sup> -τ λð Þ Ra;<sup>R</sup> (22)

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103

<sup>d</sup><sup>Ω</sup> (23)

or particulate species:

where

Nsigð Þ¼ <sup>λ</sup>Ra;<sup>R</sup> ELð Þ <sup>λ</sup><sup>L</sup>

Figure 5. The minimum detectable UF6 concentration by DIAL (λon = 245 nm and λoff = 266 nm) versus range for one pulse for a very low dark count detector. The SNR is considered to be 1.5. Other parameters of the lidar system are shown in Table 1.

Remotely Monitoring Uranium-Enrichment Plants with Detection of Gaseous Uranium Hexafluoride and HF Using… http://dx.doi.org/10.5772/intechopen.73356 103

Figure 6. Calculated SNR as a function of FOV/DIV for a UF6 cloud with 1.1 ppm concentration at 1 km. The integration time is 300 second (3000 shots). Other parameters of the lidar system are shown in Table 1.

receiver diameter; however, it increases both the received signal and noise in the same proportion. An increase in the laser beam diameter will increase the received signal, as well as SNR.

Despite the advantage of large Mie- and Rayleigh-scattering and therefore high SNR of the conventional elastic lidar systems, they cannot provide species selectivity. In contrast, inelastic Raman scattering where the frequency of the scattered radiation is shifted by an amount that is a unique of the molecule can be used like fingerprint to distinguish molecular species. In other words, the Raman spectrum contains characteristic signatures of each target molecules with high spectral resolution which makes the Raman spectroscopy a very powerful technique for characterization and identification of unknown species. The intensity of the Raman signal is directly proportional to the density of the scattering molecules independent of other molecular or particulate species:

$$\mathbf{N}\_{\rm sig}(\lambda\_{\rm Ra}, \mathbf{R}) = \frac{\mathbf{E}\_{\rm L}(\lambda\_{\rm L})}{\hbar \mathbf{v}} \eta\_{\rm bot} \beta\_{\rm Ra}(\lambda\_{\rm L}, \mathbf{R}) \Delta \mathbf{R} \, \frac{\mathbf{A}}{\mathbf{R}^2} \exp[-\mathbf{\tau}(\lambda\_{\rm L}, \mathbf{R}) \cdot \mathbf{\tau}(\lambda\_{\rm Ra}, \mathbf{R})] \tag{22}$$

where

Transmitting subsystems

Receiving subsystems

in Table 1.

Energy per pulse 300 mJ Repetition rate 10 Hz Pulsewidth (FWHM) 10 ns Pulse laser linewidth (FWHM) 0.1 nm Optical transmission efficiency 0.7

102 Uranium - Safety, Resources, Separation and Thermodynamic Calculation

Far-Field Full angle divergence (beam expanded) 100 μRad

Telescope aperture (diameter) 35 cm FOV 200 μRad Interference filter bandwidth 0.1 nm Receiving efficiency 0.5 PMT quantum efficiency 0.1 Range resolution of photon counter 30 m

Figure 5. The minimum detectable UF6 concentration by DIAL (λon = 245 nm and λoff = 266 nm) versus range for one pulse for a very low dark count detector. The SNR is considered to be 1.5. Other parameters of the lidar system are shown

Table 1. Major parameters of the lidar system considered in simulation.

$$\beta\_{\text{Ra}}(\lambda\_{\text{L}}, \text{R}) = \text{N}\_{\text{Ra}}(\text{R}) \frac{\text{d}\sigma\_{\text{Ra}}(\pi, \lambda\_{\text{L}})}{\text{d}\Omega} \tag{23}$$

is the Raman backscatter coefficient, λ<sup>L</sup> and λRa are the wavelength of laser and Raman, respectively. The wavelength shift and also narrow spectral width of the Raman scattered signal respectively at 266 and 297.3 nm allows distinguishing HF from the other species which elastically scatter 266 nm radiation [10]. Simultaneous measurement of the elastic-backscatter signals at 266 nm and 245 nm and the HF inelastic-backscatter signal at 297.3 nm permit the determination of the concentration of UF6 and HF, independently, and therefore detection and localization of UF6 leaks. Notice that both Rayleigh and Raman scattering are two-photon processes involving scattered incident light from a virtual state. The main problem of the Raman scattering is its weak interaction compared to Rayleigh scattering, with a cross-section that is typically 3–4 orders of magnitude smaller. Therefore, the strong Rayleigh scattered radiation must be eliminated when analyzing the weak Raman scattered radiation. The Raman lidar typically consists of an untunable laser excitation source, collection optics like a telescope to collect the rotational-vibrational backscattered radiation from the molecular HF, a spectral analyzer such as monochromator, and a high-sensitive detector such as PMT. The collection optics must be carefully designed to collect as much as the Raman scattered radiation from HF and transfer it into the monochromator. Using a high-sensitive PMT and a high-throughput monochromator with Rayleigh rejection filters may dramatically improve the performance of the Raman lidar. The low intensity of the Raman backscattered signal can be improved by using a high-power laser, high-efficient receiver, low-noise detector, and operation in the solar blind region. It is well known that tropospheric and stratospheric ozone absorb practically all of the incoming solar radiation in this region of the spectrum, providing a black background for detection of the weak Raman signals in the region of 200–310 nm. Natural ozone mainly occurs in the stratosphere between heights of 15 and 50 km. The solar blind region provides conditions that make it possible to operate lidar with a wide FOV telescope and sensitive quantum noise–limited photon counting detectors. The magnitude of the Raman shift is specific of the excited molecule, and the detected light is proportional to the concentration of molecule and Raman cross-section as well. At wavelengths greater than 310 nm, the background noise radiation is significant. Below 200 nm, absorption by oxygen is so strong that propagation is severely limited, and it is not feasible to operate within the atmosphere.

So far, a single grating monochromator and a double grating monochromator in combination with an interference filter have been employed to separate wavelengths effectively in practice [26]. Moreover, for further suppressing the elastic Mie- and Rayleigh-scattering signals, two sets of interference filters can be employed. To improve the optical efficiency of spectroscopic filters, the filters are designed with a peak transmittance at non-normal incidence angle. The function relationship between the central wavelength at normal incidence, λn, and wavelength at non-normal incidence angle of θ is given by:

$$
\lambda(\theta) = \lambda\_n \sqrt{1 - \left(\sin \theta / n\right)^2} \tag{24}
$$

used to construct a powerful spectroscopic system for achieving the required high rejection

Remotely Monitoring Uranium-Enrichment Plants with Detection of Gaseous Uranium Hexafluoride and HF Using…

The grating diffracts the spectra of the backscattered signal spatially according to the Fraunhofer diffraction. If the incident light beam is not perpendicular to the grooves, the grating

Here, m is diffraction order, α is the angle of incidence, λ is the diffracted light at angle of β, G = 1/d is the groove frequency or groove density, and γ is the angle between the incident light path and the plane perpendicular to the grooves at the grating center. If the incident light lies in this plane, γ = 0, and Eq. (25) reduces to the famous grating equation. In geometries for which γ 6¼ 0, the diffracted spectra lie on a cone rather than in a plane, so such cases are termed conical diffraction. In the most fundamental senses, both spectral bandpass and resolution are used as a measure of an instrument's ability to separate adjacent spectral lines called resolving power. The spectral bandpass is the wavelength interval passed through the exit slit or falls onto the detector. Resolution is related to the bandpass but determines whether the separation of two adjacent peaks can be distinguished. The spectral resolution Δλ is measured by convolution of the image of the entrance aperture with the exit aperture. It determines resolving power RP = λ/Δλ. However, the practical resolving power is limited by the spectral width of

Spectral bandpass resolved by a monochromator is the difference in wavelength between the points of the half-maximum intensity on either side of the intensity maximum. For an optical

where Rd is reciprocal of linear dispersion, and W is the width of the entrance or exit slit (larger one). An instrument with smaller bandpass can resolve wavelengths that are closer together than an instrument with a larger bandpass. Bandpass can be reduced by decreasing the width of the exit slit but usually at the cost of decreasing light intensity. The reciprocal linear dispersion represents the number of wavelength intervals (e.g., nm) contained in each interval

<sup>∂</sup><sup>x</sup> <sup>¼</sup> <sup>d</sup>cos <sup>β</sup>

where d is the ruled width of grating and f is the focal length of the grating (in the case of

Rd <sup>¼</sup> <sup>d</sup>

Rd <sup>¼</sup> <sup>∂</sup><sup>λ</sup>

curved grating). At small angles of diffraction, Eq. (27) is simplified as:

Gm<sup>λ</sup> <sup>¼</sup> cos<sup>γ</sup> sin<sup>α</sup> <sup>þ</sup> sin<sup>β</sup> (25)

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105

BP ¼ W:Rd (26)

<sup>f</sup> :<sup>m</sup> (27)

<sup>f</sup> :<sup>m</sup> (28)

rate of 107

.

equation is given by the modified equation as [27]:

the spectral lines emitted by the source.

of distance (e.g., mm) along the focal plane:

system, bandpass is given by:

where n is the effective refractive index of the filter. λ/λ<sup>n</sup> decreases slowly with angle from 1 to 0.75, as angle is increased from normal to 90� for the case of n = 1.5. In many applications, angle shifts can be safely ignored. Using a high-index material such as zinc sulfide (n = 2.355 at 632.8 nm), the feature of the spectrum shift to the shorter wavelength versus angle decreases. Sometime, two narrow-band interference filters combined with a high resolution grating are used to construct a powerful spectroscopic system for achieving the required high rejection rate of 107 .

signal respectively at 266 and 297.3 nm allows distinguishing HF from the other species which elastically scatter 266 nm radiation [10]. Simultaneous measurement of the elastic-backscatter signals at 266 nm and 245 nm and the HF inelastic-backscatter signal at 297.3 nm permit the determination of the concentration of UF6 and HF, independently, and therefore detection and localization of UF6 leaks. Notice that both Rayleigh and Raman scattering are two-photon processes involving scattered incident light from a virtual state. The main problem of the Raman scattering is its weak interaction compared to Rayleigh scattering, with a cross-section that is typically 3–4 orders of magnitude smaller. Therefore, the strong Rayleigh scattered radiation must be eliminated when analyzing the weak Raman scattered radiation. The Raman lidar typically consists of an untunable laser excitation source, collection optics like a telescope to collect the rotational-vibrational backscattered radiation from the molecular HF, a spectral analyzer such as monochromator, and a high-sensitive detector such as PMT. The collection optics must be carefully designed to collect as much as the Raman scattered radiation from HF and transfer it into the monochromator. Using a high-sensitive PMT and a high-throughput monochromator with Rayleigh rejection filters may dramatically improve the performance of the Raman lidar. The low intensity of the Raman backscattered signal can be improved by using a high-power laser, high-efficient receiver, low-noise detector, and operation in the solar blind region. It is well known that tropospheric and stratospheric ozone absorb practically all of the incoming solar radiation in this region of the spectrum, providing a black background for detection of the weak Raman signals in the region of 200–310 nm. Natural ozone mainly occurs in the stratosphere between heights of 15 and 50 km. The solar blind region provides conditions that make it possible to operate lidar with a wide FOV telescope and sensitive quantum noise–limited photon counting detectors. The magnitude of the Raman shift is specific of the excited molecule, and the detected light is proportional to the concentration of molecule and Raman cross-section as well. At wavelengths greater than 310 nm, the background noise radiation is significant. Below 200 nm, absorption by oxygen is so strong that propagation is severely limited, and it is not feasible to operate within the atmosphere.

104 Uranium - Safety, Resources, Separation and Thermodynamic Calculation

So far, a single grating monochromator and a double grating monochromator in combination with an interference filter have been employed to separate wavelengths effectively in practice [26]. Moreover, for further suppressing the elastic Mie- and Rayleigh-scattering signals, two sets of interference filters can be employed. To improve the optical efficiency of spectroscopic filters, the filters are designed with a peak transmittance at non-normal incidence angle. The function relationship between the central wavelength at normal incidence, λn, and wavelength

q

where n is the effective refractive index of the filter. λ/λ<sup>n</sup> decreases slowly with angle from 1 to 0.75, as angle is increased from normal to 90� for the case of n = 1.5. In many applications, angle shifts can be safely ignored. Using a high-index material such as zinc sulfide (n = 2.355 at 632.8 nm), the feature of the spectrum shift to the shorter wavelength versus angle decreases. Sometime, two narrow-band interference filters combined with a high resolution grating are

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � ð Þ sinθ=n

2

(24)

λ θð Þ¼ λ<sup>n</sup>

at non-normal incidence angle of θ is given by:

The grating diffracts the spectra of the backscattered signal spatially according to the Fraunhofer diffraction. If the incident light beam is not perpendicular to the grooves, the grating equation is given by the modified equation as [27]:

$$\mathbf{Gm}\lambda = \cos\gamma \left(\sin\alpha + \sin\beta\right) \tag{25}$$

Here, m is diffraction order, α is the angle of incidence, λ is the diffracted light at angle of β, G = 1/d is the groove frequency or groove density, and γ is the angle between the incident light path and the plane perpendicular to the grooves at the grating center. If the incident light lies in this plane, γ = 0, and Eq. (25) reduces to the famous grating equation. In geometries for which γ 6¼ 0, the diffracted spectra lie on a cone rather than in a plane, so such cases are termed conical diffraction. In the most fundamental senses, both spectral bandpass and resolution are used as a measure of an instrument's ability to separate adjacent spectral lines called resolving power. The spectral bandpass is the wavelength interval passed through the exit slit or falls onto the detector. Resolution is related to the bandpass but determines whether the separation of two adjacent peaks can be distinguished. The spectral resolution Δλ is measured by convolution of the image of the entrance aperture with the exit aperture. It determines resolving power RP = λ/Δλ. However, the practical resolving power is limited by the spectral width of the spectral lines emitted by the source.

Spectral bandpass resolved by a monochromator is the difference in wavelength between the points of the half-maximum intensity on either side of the intensity maximum. For an optical system, bandpass is given by:

$$BP = W.R\_d \tag{26}$$

where Rd is reciprocal of linear dispersion, and W is the width of the entrance or exit slit (larger one). An instrument with smaller bandpass can resolve wavelengths that are closer together than an instrument with a larger bandpass. Bandpass can be reduced by decreasing the width of the exit slit but usually at the cost of decreasing light intensity. The reciprocal linear dispersion represents the number of wavelength intervals (e.g., nm) contained in each interval of distance (e.g., mm) along the focal plane:

$$R\_d = \frac{\partial \lambda}{\partial \mathbf{x}} = \frac{d \cos(\beta)}{f.m} \tag{27}$$

where d is the ruled width of grating and f is the focal length of the grating (in the case of curved grating). At small angles of diffraction, Eq. (27) is simplified as:

$$R\_d = \frac{d}{f.m} \tag{28}$$

By substituting Eq. (28) into Eq. (26), one can obtain:

$$BP = \frac{W.d}{f.m} \tag{29}$$

Author details

Switzerland

References

Inc; 2000

1991

420-433

Patent, No. 59319

Compounds. Oxford: Program Press; 1964

2010: St.-Petersburg. pp. 814-817

Wiley & Sons Ltd; 2002

Gholamreza Shayeganrad

Address all correspondence to: gholamreza.shayeganrad@unibas.ch; shayeganrad@yahoo.com

Remotely Monitoring Uranium-Enrichment Plants with Detection of Gaseous Uranium Hexafluoride and HF Using…

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107

[1] Knoll GE. Radiation Detection and Measurement. 3rd ed. New York: John Wiley & Sons,

[2] Safety requrements, Safety of nuclear fuel cycle facilities. IAEA, No. NS-R-5 (Rev.1) 2007 [3] Railly D, Ensslin N, Smith H, eds, Passive Nondestructive Assay on Nuclear Materials.

[5] Shayeganrad G, Parvin P. DIAL–phoswich hybrid system for remote sensing of radioactive plumes in order to evaluate external dose rate. Progress in Nuclear Energy. 2008;51:

[6] Rabinwitch E, Linn Belford R, Dunworth JV. Spectroscopy and Photochemistry of Uranyl

[7] Shayeganrad G, Mashhadi L. Remote leak detection of UF6 by UV-DIAL. 2009: Iranan

[8] Shayeganrad G, Mashhadi L. High speed remote monitoring of hazardous uranium hexafluoride by lidar. In: Proceedings of the 25th international laser radar conference.

[9] Shayeganrad G. On the remote monitoring of gaseous uranium hexafluoride in the lower

[10] Chalmers JM, Griffiths PK. eds, Handbook of Vibrational Spectroscopy. Chichester: John

[11] Grigoriev GY et al. Remote detection of HF molecules in open atmosphere with the use of

[12] Gibson G et al. Remote detection of HF molecules in open atmosphere with the use of tunable diode lasers. Applied Physics B: Lasers and Optics. 2010;101:683-688

[13] Hanna SR, Chang JC. Modeling accidental releases to the atmosphere of a dense reactive

atmosphere using lidar. Optics and Lasers in Engineering. 2013;51:1192-1198

tunable diode lasers. Applied Physics B. 2010;101:683-688

chemical. Atmospheric Environment. 1997;31:901-908

[4] Reilly TD, Walton RB, Parker JL. A-1 Progress Report LA-4605-MS. 1970. p. 19

Department of Biomedical Engineering, University of Basel, Gewerbestr, Allschwil,

For instance, considering G = 1200 gr/mm, W = 0.05 mm, f = 500 mm, and m = 1, the obtained bandpass is 0.083 nm. For selecting grating, one should consider that the grating equation reveals only the spectral orders for which |mλ/d| < 2 exist. This restriction prevents light of wavelength λ from being diffracted in more than a finite number of order m. Once angle of incidence has been determined, the choice must be made whether a small width grating should be used in a low order, or a large width grating such as an echelle grating should be used in a high order; though, the small width grating will provide a larger free spectral range, ΔλFSR = λ/m.

The minimum attainable spectral resolution is given by:

$$
\Delta\lambda = \lambda^2 / 2\text{D} \tag{30}
$$

regardless of the order m or number of grooves N under illumination. Here D = Nd is the rules width of the grating. This minimum condition corresponds to the grazing Littrow configuration. Noticeably when the grating is incorporated in a spectrometer or monochromator, however, aberrations and imperfections in other elements (e.g., lenses and mirrors) rather than grating and factors related to the size of the slits and detector elements may result in even wider spectral resolution. This means that the minimum wavelength difference Δλ that can be resolved will be larger that for the grating only defined by Eq. (30), and, in general, the resolving power for the optical system degrades.

#### 5. Conclusion

A sudden release of UF6 into the atmosphere can conceivably cause undesirable health effects to the workers and the public in general associated with high level of toxicity of the hydrolysis products HF and UO2F2. Although the hydrolyze reaction of UF6 is fast, however, after escaping of UF6 into the atmosphere, besides HF and UO2F2, UF6 may also be found in the atmosphere. Therefore, the combination of DIAL and Raman lidar for simultaneously detection of UF6 and HF can be a reliable technique for remotely detection and monitoring UF6 leaks and further improving the safety and economically operation of a uranium-enrichment plant. The DIAL provides information on UF6 concentration using the off- and on-wavelength at 266 and 245 nm, respectively, while Raman scattering of HF at 297.3 nm can identify and quantify HF as a probe for real-time detection and localization of toxic UF6 leaks. This system might be mounted on a helicopter for quickly and remotely surveying the leaks from the large facilities. Since the system is working in the solar blind ultraviolet (200–310 nm), the Raman signal may simply be enhanced by increasing FOV or increasing the integration time (or number of shots).
