CN102636459B - Forward scattering and transmission combined visibility measuring instrument and measuring method thereof - Google Patents

Abstract

Translated fromChinese

本发明公开了一种前向散射与透射结合的能见度测量仪及其测量方法，包括发射器、透射接收器、散射接收器和控制器，发射器用于向透射接收器和散射接收器发射光信号；透射接收器用于将接收到的光信号转换为透射电信号；散射接收器用于将接收到的光信号转换为电信号；控制器用于接收所述透射接收器和散射接收器发来的电信号，并根据两电信号计算得到能见度。通过散射信号与透射信号对比测量得到大气消光系数，从而测得大气能见度。在前向散射测量的基础上增加一路透射光的测量，以透射测值作为参考对能见度进行修正，以减小环境灰尘对镜头的污染和发光管老化引起的功率下降等因素对仪器测量结果的影响。提高仪器的测量精度延长镜头的清理周期。

The invention discloses a visibility measuring instrument combined with forward scattering and transmission and a measurement method thereof, which comprises a transmitter, a transmission receiver, a scattering receiver and a controller, and the transmitter is used to transmit optical signals to the transmission receiver and the scattering receiver The transmission receiver is used to convert the received optical signal into a transmission electrical signal; the scattering receiver is used to convert the received optical signal into an electrical signal; the controller is used to receive the electrical signal sent by the transmission receiver and the scattering receiver , and calculate the visibility according to the two electrical signals. The atmospheric extinction coefficient is obtained by comparing the scattering signal with the transmission signal, so as to measure the atmospheric visibility. On the basis of the forward scatter measurement, a transmission light measurement is added, and the visibility is corrected with the transmission measurement value as a reference, so as to reduce the pollution of the lens by environmental dust and the power drop caused by the aging of the luminescent tube and other factors that affect the measurement results of the instrument. Influence. Improve the measurement accuracy of the instrument and prolong the cleaning cycle of the lens.

Description

Translated fromChinese

一种前向散射与透射结合的能见度测量仪及其测量方法A Visibility Measuring Instrument Combining Forward Scattering and Transmission and Its Measurement Method

技术领域technical field

本发明涉及一种能见度测量仪及其测量方法，尤指一种前向散射与透射结合的能见度测量仪及其测量方法。The invention relates to a visibility measuring instrument and a measuring method thereof, in particular to a visibility measuring instrument combining forward scattering and transmission and a measuring method thereof.

背景技术Background technique

能见度是气象观测中一个非常重要的要素，它的测报不仅用于气象部门的天气分析，还用来描述大气的污染程度，是对大气污染情况的一个直接反映；随着科技的发展，各种能见度自动测量仪器在不断更新。我国对能见度自动测量仪器的需求越来越大，尤其是现阶段高速公路建设迅猛发展和森林火灾检测等方面的需求，研制性价比高，体积小，重量轻，便于装校的能见度仪有重大意义。Visibility is a very important element in meteorological observation. Its forecast is not only used for weather analysis of meteorological departments, but also used to describe the degree of air pollution, which is a direct reflection of air pollution; with the development of science and technology, various Automatic visibility measuring instruments are constantly being updated. my country's demand for automatic visibility measuring instruments is increasing, especially the rapid development of highway construction and forest fire detection at the present stage. It is of great significance to develop a visibility instrument with high cost performance, small size, light weight, and easy installation and calibration. .

目前市场上的流行能见度仪器主要分为透射式和散射式。透射式能见度仪因需要基线，占地范围大，安装复杂，不适合高速公路沿线、森林及海岸台站，主要应用在民航系统。散射式能见度仪又分为后向散射式和前向散射式：后向散射式取样体积较大，结构简单，但前方不能有高的遮挡物；前向散射式以其体积小和低廉的价格，广泛应用于码头、高速公路等系统。能见度仪同其它气象仪器一样，一旦开动便需要不停地工作，同时这是一种装调精密且在外场工作的仪器。从整个能见度测量仪来看，仪器发光管老化和镜头污染会影响到仪器的测量精度，即便是可以更换光源和清理镜头，更换和清理一次也是非常麻烦的。The popular visibility instruments currently on the market are mainly divided into transmission type and scattering type. The transmissive visibility meter requires a baseline, occupies a large area, and is complicated to install. It is not suitable for stations along expressways, forests, and coasts. It is mainly used in civil aviation systems. Scattering visibility meter is divided into backscattering type and forward scattering type: the backscattering type has a large sampling volume and simple structure, but there cannot be high obstructions in front; the forward scattering type is characterized by its small size and low price. , Widely used in docks, highways and other systems. Like other meteorological instruments, the visibility meter needs to work continuously once it is started. At the same time, it is a precision-adjusted instrument that works in the field. From the perspective of the entire visibility measuring instrument, the aging of the instrument's luminescent tube and the contamination of the lens will affect the measurement accuracy of the instrument. Even if the light source and lens can be replaced, it is very troublesome to replace and clean it once.

发明内容Contents of the invention

针对现有技术存在的问题，本发明的目的在于提供一种测量精度高、受仪器发光管和环境影响较小的能见度测量仪及其测量方法。Aiming at the problems existing in the prior art, the purpose of the present invention is to provide a visibility measuring instrument and its measuring method with high measurement accuracy and little influence from the instrument luminescent tube and the environment.

为实现上述目的，本发明的前向散射与透射结合的能见度测量仪，包括发射器、透射接收器、散射接收器和控制器，发射器用于向透射接收器和散射接收器发射光信号；透射接收器用于将接收到的光信号转换为电信号；散射接收器用于将接收到的光信号转换为电信号；控制器用于接收所述透射接收器和散射接收器发来的电信号，并根据两电信号计算得到能见度。In order to achieve the above object, the visibility measuring instrument combining forward scattering and transmission of the present invention includes a transmitter, a transmission receiver, a scattering receiver and a controller, and the transmitter is used to transmit optical signals to the transmission receiver and the scattering receiver; the transmission The receiver is used to convert the received optical signal into an electrical signal; the scattering receiver is used to convert the received optical signal into an electrical signal; the controller is used to receive the electrical signal sent by the transmission receiver and the scattering receiver, and according to Visibility is calculated from two electrical signals.

进一步，所述发射器、透射接收器和散射接收器的光轴在同一个水平面上，透射接收器设置在发射器的正对面；散射接收器设置在发射器的侧对面，并与发射器呈一散射角；发射器到透射接收器的光程和发射器到散射接收器的光程相等。Further, the optical axes of the transmitter, the transmission receiver and the scattering receiver are on the same horizontal plane, and the transmission receiver is arranged directly opposite to the transmitter; A scattering angle; the optical path from the emitter to the transmitted receiver is equal to the optical path from the emitter to the diffuse receiver.

进一步，所述发射器与散射接收器间的散射角为20°-50°。Further, the scattering angle between the transmitter and the scattering receiver is 20°-50°.

进一步，所述发射器与散射接收器间的散射角优选为35°。Further, the scattering angle between the transmitter and the scattering receiver is preferably 35°.

本发明的前向散射与透射结合的能见度测量方法，包括以下步骤：1)控制发射器向透射接收器和散射接收器发射光信号；2)透射接收器和散射接收器分别将接收到的光信号转换为电信号；3)控制器接收透射接收器和散射接收器发来的电信号，并根据两电信号计算得到能见度。The visibility measurement method combining forward scattering and transmission of the present invention comprises the following steps: 1) controlling the transmitter to transmit light signals to the transmission receiver and the scattering receiver; 2) transmitting the light received by the transmission receiver and the scattering receiver respectively The signal is converted into an electrical signal; 3) The controller receives the electrical signal from the transmission receiver and the scattering receiver, and calculates the visibility according to the two electrical signals.

进一步，计算能见度首先需要根据透射接收器和散射接收器发来的电信号计算大气消光系数，大气消光系数的测量方程为：Further, to calculate the visibility, it is first necessary to calculate the atmospheric extinction coefficient according to the electrical signals sent by the transmission receiver and the scattering receiver. The measurement equation of the atmospheric extinction coefficient is:

其中，σ：消光系数；i：i取1表示散射接收器，i取2表示透射接收器；S_ri：接收器i的光电转换器的光谱灵敏度，单位：A/W；T_ri：接收器i的光学透过率；A_ri：接收器i的有效接收口径，单位：cm²；R_oi：接收器i的负载电阻；A_gi：接收器i的放大电路的增益，α为光束的发散角，θ为散射角。Among them, σ: extinction coefficient; i: i takes 1 to indicate the scattering receiver, and i takes 2 to indicate the transmission receiver; S_ri : the spectral sensitivity of the photoelectric converter of receiver i, unit: A/W; T_ri : the receiver Optical transmittance of i; A_ri : effective receiving aperture of receiver i, unit: cm² ; R_oi : load resistance of receiver i; A_gi : gain of amplifier circuit of receiver i, α is divergence of light beam angle, θ is the scattering angle.

本发明的前向散射与透射结合的能见度测量仪及其测量方法，通过散射信号与透射信号对比测量得到大气消光系数，从而测得大气能见度。在前向散射测量的基础上增加一路透射光的测量，以透射测值作为参考对能见度进行修正，以减小环境灰尘对镜头的污染和发光管老化引起的功率下降等因素对仪器测量结果的影响。提高仪器的测量精度延长镜头的清理周期。The visibility measuring instrument combined with forward scattering and transmission and the measurement method thereof of the present invention obtain the atmospheric extinction coefficient by comparing and measuring the scattering signal and the transmission signal, thereby measuring the atmospheric visibility. On the basis of the forward scatter measurement, a transmission light measurement is added, and the visibility is corrected with the transmission measurement value as a reference, so as to reduce the pollution of the lens by environmental dust and the power drop caused by the aging of the luminescent tube and other factors that affect the measurement results of the instrument. Influence. Improve the measurement accuracy of the instrument and prolong the cleaning cycle of the lens.

附图说明Description of drawings

图1为本发明能见度测量仪的结构示意图；Fig. 1 is the structural representation of visibility measuring instrument of the present invention;

图2为本发明能见度测量仪的测量光路原理图；Fig. 2 is the schematic diagram of the measurement optical path of the visibility measuring instrument of the present invention;

图3为本发明能见度测量方法的流程图。Fig. 3 is a flow chart of the visibility measurement method of the present invention.

具体实施方式Detailed ways

如图1所示，本发明的前向散射与透射结合的能见度测量仪，包括发射器1、透射接收器2、散射接收器3和控制器4，发射器1用于向透射接收器2和散射接收器3发射光信号；透射接收器2用于接收来自发射器1的光信号，并将该光信号转换为电信号；散射接收器3用于接收来自发射器1的光信号，并将该光信号转换为电信号；控制器4用于接收来自透射接收器2和散射接收器3的电信号，并根据两电信号计算得到能见度。As shown in Fig. 1, the visibility measuring instrument of the combination of forward scattering and transmission of the present invention comprises a transmitter 1, a transmission receiver 2, a scattering receiver 3 and a controller 4, and the transmitter 1 is used to transmit to the transmission receiver 2 and The scattering receiver 3 transmits an optical signal; the transmission receiver 2 is used to receive the optical signal from the transmitter 1, and converts the optical signal into an electrical signal; the scattering receiver 3 is used to receive the optical signal from the transmitter 1, and The optical signal is converted into an electrical signal; the controller 4 is used to receive the electrical signal from the transmission receiver 2 and the scattering receiver 3, and calculate the visibility according to the two electrical signals.

如图2所示，发射器1、透射接收器2和散射接收器3的光轴在同一个水平面上，透射接收器2设置在发射器1的正对面；散射接收器3设置在发射器1的侧对面，并与发射器1呈一散射角；发射器1与透射接收器2和散射接收器3的光程相等均为1.2米。发射器1与散射接收器3间的散射角为20°-50°，为了更好的接受散射光，发射器1和散射接收器3优选呈35°夹角，其采样容量是大约200cm³(0.2公升)。As shown in Figure 2, the optical axes of the transmitter 1, the transmission receiver 2 and the scattering receiver 3 are on the same horizontal plane, the transmission receiver 2 is set directly opposite the transmitter 1; the scattering receiver 3 is set on the transmitter 1 The side is opposite to the emitter 1, and has a scattering angle with the emitter 1; the optical path of the emitter 1, the transmission receiver 2 and the scattering receiver 3 are equal to 1.2 meters. The scattering angle between the transmitter 1 and the scattering receiver 3 is 20°-50°. In order to better accept the scattered light, the transmitter 1 and the scattering receiver 3 are preferably at an angle of 35°, and the sampling capacity is about 200cm³ ( 0.2 liter).

如图3所示，发射器1、透射接收器2和散射接收器3均采用与现有能见度测量仪中相应部件相同的结构。发射器1采用波长为850nm的红外发光管(LED)为光源，光信号在前向散射方向比较微弱，为了能够在较大的噪声背景下提取出前向散射信号，用3.6KHZ的方波对发射光源进行调制，并为散射接收器3的锁相放大电路提供参考信号。接收器包括包括光学系统，光电探测器，放大电路，滤波电路，锁相放大电路，其功能是实现对光信号的准确提取与精确测量，散射接收器3与透射接收器2设计成电路结构相同但参数不同。能见度仪工作时由光电转换器将接收到的光能变换处理成电信号，经过放大滤波等模拟处理后，输出至控制器4。控制器4中包括AT89S8285微处理器，除了数据接收和内部控制外，还负责其串口RS-232的通信，同时监控发射器和接收器的供电情况以及控制发射器中加热器的通断。散射接收器3接收经前向散射得到的散射光，光信号经滤光片滤除杂散光后，由光电转换电路转换为电信号，经前置放大、带通滤波以及相敏检波等模拟处理后，再由模-数转换电路转换后送入微处理器；同理，透射信号经光电转换后再经放大滤波等处理，由模数转换电路转换后送入微处理器，透射信号作为参考信号与前向散射信号比较测量，进行数值计算。控制器4的核心功能是对能见度信号进行有效地运算，能见度需要实时准确地测量，单片机控制每分钟测一次数据然后通过RS232串口发送一次，其中每100ms采样一次，存于数组，由于外界的干扰等因素的影响，对数据排序后去掉最大、最小值取平均，此平均值计算出的结果作为此时的能见度值。每分钟测一次能见度值，然后发送一次数据。As shown in FIG. 3 , the transmitter 1 , the transmission receiver 2 and the scattering receiver 3 all adopt the same structure as the corresponding components in the existing visibility measuring instrument. Transmitter 1 uses an infrared light-emitting tube (LED) with a wavelength of 850nm as the light source, and the light signal is relatively weak in the forward scattering direction. In order to extract the forward scattering signal in a large noise background, a 3.6KHZ square wave is used to The light source is modulated and provides a reference signal for the lock-in amplifier circuit of the scattering receiver 3 . The receiver includes an optical system, a photodetector, an amplifier circuit, a filter circuit, and a lock-in amplifier circuit. Its function is to achieve accurate extraction and precise measurement of optical signals. The scattering receiver 3 and the transmission receiver 2 are designed to have the same circuit structure But the parameters are different. When the visibility meter is working, the photoelectric converter converts the received light energy into an electrical signal, and outputs it to the controller 4 after analog processing such as amplification and filtering. The controller 4 includes an AT89S8285 microprocessor. In addition to data reception and internal control, it is also responsible for the communication of its serial port RS-232, while monitoring the power supply of the transmitter and receiver and controlling the on-off of the heater in the transmitter. Scattering receiver 3 receives the scattered light obtained by forward scattering, and the optical signal is filtered by a filter to filter out stray light, then converted into an electrical signal by a photoelectric conversion circuit, and processed by analog processing such as pre-amplification, band-pass filtering, and phase-sensitive detection. After that, it is converted by the analog-to-digital conversion circuit and sent to the microprocessor; similarly, the transmitted signal is converted by the photoelectric conversion and then processed by amplification and filtering, and then sent to the microprocessor after being converted by the analog-to-digital conversion circuit. The transmitted signal is used as a reference signal and Forward scatter signal comparison measurement, numerical calculation. The core function of the controller 4 is to effectively calculate the visibility signal. The visibility needs to be measured accurately in real time. The single-chip microcomputer controls the data to be measured once per minute and then sent once through the RS232 serial port. The data is sampled every 100ms and stored in the array. Due to external interference Influenced by other factors, after sorting the data, remove the maximum and minimum values and take the average, and the calculated result of this average value is used as the visibility value at this time. The visibility value is measured every minute, and then the data is sent once.

本发明中能见度的计算是通过以下公式推导得出的：The calculation of visibility in the present invention is derived by the following formula:

透射接收器2的电压输出：Transmissive receiver 2 voltage output:

${\mathrm{<span><span>V</span>V</span>}}_{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>o</span>o</span>}}<span><span>=</span>=</span>{\mathrm{<span><span>S</span>S</span>}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>R</span>R</span>}}_{\mathrm{<span><span>o</span>o</span>}\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>A</span>A</span>}}_{\mathrm{<span><span>g</span>g</span>}\mathrm{<span><span>2</span>2</span>}}{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>e</span>e</span>}}{\mathrm{<span><span>T</span>T</span>}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>2</span>2</span>}}\frac{{\mathrm{<span><span>A</span>A</span>}}_{\mathrm{<span><span>r</span>r</span>}\mathrm{<span><span>2</span>2</span>}}}{{\mathrm{<span><span>l</span>l</span>}}^{\mathrm{<span><span>2</span>2</span>}}}<span><span>*</span>*</span>\frac{{\mathrm{<span><span>P</span>P</span>}}_{\mathrm{<span><span>0</span>0</span>}}}{{\mathrm{<span><span>\&Omega;</span>\&Omega;</span>}}_{\mathrm{<span><span>t</span>t</span>}}}<span><span>*</span>*</span>\mathrm{<span><span>exp</span>exp</span>}<span><span>(</span>(</span><span><span>-</span>-</span>\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}<span><span>*</span>*</span>\mathrm{<span><span>l</span>l</span>}<span><span>)</span>)</span>$

散射接收器3的电压输出：Voltage output of scatter receiver 3:

易得，能见度仪大气消光系数的测量方程：It is easy to get, the measurement equation of the atmospheric extinction coefficient of the visibility meter:

$\mathrm{<span><span>\&sigma;</span>\&sigma;</span>}<span><span>=</span>=</span>\mathrm{<span><span>C</span>C</span>}<span><span>*</span>*</span>\frac{{\mathrm{<span><span>V</span>V</span>}}_{\mathrm{<span><span>1</span>1</span>}\mathrm{<span><span>o</span>o</span>}}}{{\mathrm{<span><span>V</span>V</span>}}_{\mathrm{<span><span>2</span>2</span>}\mathrm{<span><span>o</span>o</span>}}}$

其中，P₀：发射器的发射功率，单位：W；Among them, P₀ : the transmitting power of the transmitter, unit: W;

T_e：发射器的光学透过率；T_e : optical transmittance of the emitter;

i：i取1表示散射接收器，i取2表示透射接收器；i: i takes 1 to indicate the scattering receiver, and i takes 2 to indicate the transmission receiver;

T_ri：接收器i的光学透过率；T_ri : optical transmittance of receiver i;

A_ri：接收器i的有效接收口径，单位：cm²；A_ri : effective receiving aperture of receiver i, unit: cm² ;

S_ri：接收器i的光电转换器的光谱灵敏度，单位：A/W；S_ri : spectral sensitivity of the photoelectric converter of receiver i, unit: A/W;

R_oi：接收器i的负载电阻，单位Ω；R_oi : load resistance of receiver i, unit Ω;

A_gi：接收器i的放大电路的增益；A_gi : the gain of the amplifier circuit of receiver i;

σ：消光系数。σ: extinction coefficient.

上式中只有散射接收器和透射接收器的光学透过率是不确定量。但是，我们选择参数完全相同的两个接收透镜，在各项同性假设下安装在相同环境下的两个镜片的光学透过率可以认为一致，所以其比值为1，通过以上公式分析可知：双光路测量消光系数σ的计算只与系统的固有参数有关，与发射端P₀无关，故其测量结果不受发光管老化的影响。相同环境下三个镜头污染情况相似，两者相比降低了镜头污染对测量结果的影响，延长清理周期。In the above formula, only the optical transmittance of the scattering receiver and the transmission receiver are uncertain quantities. However, we choose two receiving lenses with exactly the same parameters. Under the assumption of isotropy, the optical transmittance of the two lenses installed in the same environment can be considered to be consistent, so the ratio is 1. Through the analysis of the above formula, we can know: double The calculation of the optical path measurement extinction coefficient σ is only related to the inherent parameters of the system, and has nothing to do with the transmitter P₀ , so the measurement results are not affected by the aging of the luminous tube. The pollution of the three lenses in the same environment is similar, and the comparison between the two reduces the impact of lens pollution on the measurement results and prolongs the cleaning cycle.

需要指出的是上述实施例只是示例性的对本发明加以说明，根据本发明的精神所做出的任意变形，均不应认为脱离本发明的保护范围。It should be pointed out that the above-mentioned embodiments are only examples to describe the present invention, and any modification made according to the spirit of the present invention shall not be regarded as departing from the protection scope of the present invention.

Claims (6)

1. the transmittance meter that forward scattering is combined with transmission, is characterized in that, comprises transmitter, transmission receiver, scattering receiver and controller, and transmitter is used for to transmission receiver and scattering receiver utilizing emitted light signal; Transmission receiver is for being converted to electric signal by the light signal receiving; Scattering receiver is for being converted to electric signal by the light signal receiving; The electric signal that controller is sent for receiving described transmission receiver and scattering receiver, and calculate visibility according to two electric signal; Obtain atmospheric extinction coefficient by scattered signal and transmission signal measurement of comparison, on the basis of measuring in forward scattering, increase the measurement of a road transmitted light, as a reference visibility is revised with transmission measured value; It is light source that transmitter adopts infraluminescence pipe, transmitting illuminant is modulated with the square wave of 3.6KHZ, and is provided reference signal for the phase-locked amplifying circuit of scattering receiver.

2. the transmittance meter that forward scattering as claimed in claim 1 is combined with transmission, is characterized in that, the optical axis of described transmitter, transmission receiver and scattering receiver is on same surface level, and transmission receiver is arranged on the right opposite of transmitter; Scattering receiver is arranged on the side opposite of transmitter, and is a scattering angle with transmitter; The light path of transmitter and transmission receiver, the equivalent optical path of transmitter and scattering receiver.

3. the transmittance meter that forward scattering as claimed in claim 2 is combined with transmission, is characterized in that, the scattering angle between described transmitter and scattering receiver is 20 °-50 °.

4. the transmittance meter that forward scattering as claimed in claim 3 is combined with transmission, is characterized in that, the scattering angle between described transmitter and scattering receiver is preferably 35 °.

5. a visibility measurement method for the transmittance meter as described in claim 1-4 any one, comprises the following steps: 1) control transmitter to transmission receiver and scattering receiver utilizing emitted light signal; 2) transmission receiver and scattering receiver are converted to electric signal by the light signal receiving respectively; 3) electric signal that controller reception transmission receiver and scattering receiver are sent, and calculate visibility according to two electric signal; Obtain atmospheric extinction coefficient by scattered signal and transmission signal measurement of comparison, on the basis of measuring in forward scattering, increase the measurement of a road transmitted light, as a reference visibility is revised with transmission measured value, it is light source that transmitter adopts infraluminescence pipe, transmitting illuminant is modulated with the square wave of 3.6KHZ, and provided reference signal for the phase-locked amplifying circuit of scattering receiver.

6. visibility measurement method as claimed in claim 5, is characterized in that, calculating visibility first needs the electric signal of sending according to transmission receiver and scattering receiver to calculate atmospheric extinction coefficient, and the measurement equation of atmospheric extinction coefficient is:

Wherein, σ: extinction coefficient; I:i gets 1 expression scattering receiver, and i gets 2 expression transmission receivers; S_ri: the spectrum sensitivity of the photoelectric commutator of receiver i, unit: A/W; T_ri: the optical transmittance of receiver i; A_ri: effective Receiver aperture of receiver i, unit: cm²; R_oi: the feedback resistance of the prime amplifier of receiver i; A_gi: the gain of the amplifying circuit of receiver i; V_1o: scattering receiver Voltage-output; V_2o: transmission receiver Voltage-output; A: optical axes crosspoint O point is to the distance of transmitter; L: the distance of transmission receiver and transmitter; Ω: the field angle of receiver is the half of transmitting light beam at surface level plane subtended angle;for constant,be that scattering θ direction scattering coefficient and total scattering coefficient are proportional; θ: scattering angle; α_s: beam divergence angle.