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# Interpretation of the detection performance index of telemetry equipment

### Interpretation of the detection performance of telemetry equipment

#### 1.1 Sensitivity

Sensitivity refers to the degree of change in the response of a method to unit concentration changes. It can be described by the ratio of the response of the instrument or other indicator to the concentration of the corresponding substance to be measured (slope).

Through the calibration curve, the response of the instrument can be quantitatively linked with the concentration of the substance to be measured, and the linear part of it can be expressed by the following formula.

A=k C + a

In the formula, A is the response value of the instrument; C is the concentration of the substance to be tested; a is the intercept of the calibration curve; k is the sensitivity, that is, the slope of the calibration curve.

#### 1.2 Detect Limit

"The detection limit is expressed as a concentration, which refers to the lowest concentration obtained from the smallest analytical signal that can be reasonably detected by a specific analysis step." —— International Union of Pure and Applied Chemistry（IUPAC）

cL=k Sb/S

In the formula, Sb is the standard deviation of the average value of the blank. The blank refers to a sample that has the same composition as the sample to be tested but does not contain the component to be tested. IUPAC stipulates that the standard deviation should be determined through experiments with a sufficient number of determinations, for example, 20 times. S is the slope (sensitivity) of the analytical calibration curve in the low concentration range, and Sb/S is the calibrated concentration value (unit ppm.m). k is a constant selected according to the required confidence. IUPAC recommends k=3 as the detection limit calculation standard. For a strict one-sided Gaussian distribution k=3, the corresponding confidence is 99.6%. Since S is based on a finite number of measurements, the confidence level corresponding to k=3 is usually about 90%.

#### 1.3 Other key indicators

The static performance indicators of the instrument also include indicators such as accuracy, resolution, and repeatability.

Accuracy: The degree of agreement between the display of the instrument and the measured true value is the probability limit of the correlation between the instrument output and the measured true value. Accuracy degradation may be caused by a series of factors such as non-linearity, hysteresis, temperature impact, and drift.

Resolution: Resolution generally has two meanings. The first definition is the amount of input change required to make the instrument display a certain amount of change. If there is no hysteresis, the resolution is equal to the inverse of the sensitivity. The second definition is commonly found in digital display instruments, usually by the distance of the last digit of the displayed value.

Repeatability: Repeatability is an important static characteristic of the instrument. It represents the closeness between a group of measurements made by the same observer using the same measurement conditions, methods, and instruments for the same measurement. It characterizes the degree to which the random error of the instrument is close to zero, also called the error limit.

It can be approximated that the unit concentration is the concentration obtained by uniformly "compressing" or "expanding" the methane molecules on the straight line (laser detection line) between the telemeter and the reflective target into an area with a thickness of 1 meter.

#### 1.4 Performance characteristics of laser telemetry products

The characterization of static detection performance of telemetry products takes into account the following problems in the actual detection environment of the detector:

1. The uneven distribution of the measured methane gas mass in space and time;

2. The reflecting surface cannot be determined;

3. The situation of the intermediate interface cannot be determined;

4. The detection distance cannot be determined

It is difficult to use one or several parameters to describe the actual performance. In this case, a common practice in the instrumentation industry is to set a group of determined measurement conditions and measurement methods and give the detection performance under certain conditions. The static detection limit selected here as the feature is based on the following characteristics of the equipment used in leak detection applications:

1. Portable detection equipment is generally not in a continuous concentration gas environment and pay more attention to the sudden change in concentration caused by sweeping the air mass during the detection process.

2. The leakage detection capability is the priority, the instrument is supposed to find smaller leakages, that is, have a lower detection limit.

3. Due to the uncertainty of the measured target itself and the uncontrollability of the environment, the accuracy requirements of the instrument are not as high as those of fixed optical path products.

The recommended measurement method for static detection limit is: Fixes a well calibrated device in a certain distance to the standard reflecting surface and the space between the device and the reflecting surface is air (without methane). The instrument starts to measure the concentration value Sb/S after 20 minutes of operation. Multiply the standard deviation of 1000 points by 3, and the value obtained is the static detection limit.