Air refractive index measuring method and system

Abstract

The invention provides an air refractive index measurement method and system, and the method comprises the steps: S1, collecting environment temperature data, humidity data and air pressure data through a temperature and humidity sensor and an air pressure sensor, packaging the data into a data packet, and transmitting the data packet to a test computer; s2, the test computer receives the data packet, and temperature data, humidity data and air pressure data are separated; and S3, calculating and displaying the air refractive index according to the separated temperature data, humidity data and air pressure data. The method can realize rapid measurement of the air refractive index, and can be used in the fields of precision measurement, laser communication, optical remote sensing and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of atmospheric parameter measurement, and specifically, to a method and system for measuring the air refractive index. Background Art

[0002] The air refractive index is one of the important factors affecting the measurement accuracy in laser remote sensing and laser ranging. Under the conditions of a standard atmospheric pressure, a temperature of 20 °C, a relative humidity RH% = 50%, and a CO 2 concentration of 450 ppm, the refractive index of air for a laser with a wavelength of 633 nm is approximately 1.0002713733. When performing precise distance measurement, according to the relationship between the optical path, the air refractive index, and the actual geometric distance, if the refractive index is regarded as 1, the measurement error introduced by the air refractive index will reach 4 cm per 100 m. Experiments show that temperature, humidity, and air pressure fluctuations all have varying degrees of influence on the air refractive index. Taking temperature as an example, near 20 °C, for every 0.1 °C increase in temperature, the air refractive index approximately decreases. The temperature change within a day can reach 10 °C, and the fluctuation of the air refractive index will bring an error of approximately 2 mm to the measurement result. In order to improve the measurement accuracy and achieve a sub-millimeter measurement accuracy at the 100-meter distance scale, it is necessary to correct the error introduced by the air refractive index, and it is particularly important to accurately measure the air refractive index.

[0003] The existing invention patent with the publication number CN108426858A discloses an air refractive index gradient measurement system, including an LED lamp, a glass gas chamber, and a light-shielding box. A first convex lens and a second convex lens are provided on the glass gas chamber, and a light inlet window is provided on the light-shielding box. A knife edge and a CCD are provided inside the light-shielding box. The light emitted by the LED lamp becomes parallel light after passing through the first convex lens, and the parallel light beam irradiates the second convex lens after passing through the glass gas chamber. The parallel light converges at the focal point after passing through the second convex lens; when the pressure in the glass gas chamber is changed, the air in the glass gas chamber is disturbed, and the parallel light is no longer parallel when passing through the glass gas chamber, and the light rays will be deflected. After the light rays pass through the second convex lens, some of the light rays no longer converge at the focal point. The knife edge in the light-shielding box intercepts light rays of a certain frequency spectrum to obtain different schlieren images, and the air refractive index gradient is obtained by comparing the schlieren images through a computer.

[0004] Directly measuring the air refractive index by experimental methods requires strict experimental conditions, a large system, and is relatively difficult to implement. In 1966, Edlén proposed a calculation formula for the air refractive index based on temperature, humidity, and air pressure. Later, Birch et al. modified it. Precise experiments show that the modified Edlén has a -8 precision.

[0005] When measuring the refractive index of air using the Edlén formula, the accuracy of the sensor must be ensured. Traditional sensors require complex signal conditioning circuits and are susceptible to interference. Although the traditional method has high measurement accuracy, the system is large and not conducive to miniaturization. Summary of the Invention

[0006] In view of the defects in the prior art, the present invention provides a method and system for measuring the refractive index of air.

[0007] According to a method and system for measuring the refractive index of air provided by the present invention, the solution is as follows:

[0008] In a first aspect, a method for measuring the refractive index of air is provided, and the method includes:

[0009] Step S1: Use a temperature and humidity sensor and a barometric pressure sensor to collect ambient temperature data, humidity data, and barometric pressure data, and package them into a data packet for transmission to a test computer;

[0010] Step S2: The test computer receives the data packet and separates the temperature data, humidity data, and barometric pressure data;

[0011] Step S3: Calculate and display the refractive index of air based on the separated temperature data, humidity data, and barometric pressure data.

[0012] Preferably, Step S1 includes: The temperature and humidity sensor and the barometric pressure sensor are controlled by a single-chip microcomputer and communicate using a serial interface;

[0013] First, reset the temperature and humidity sensor and the barometric pressure sensor, then configure the temperature and humidity sensor to the temperature and humidity measurement mode, configure the barometric pressure sensor to the high-precision mode and start measuring. After the measurement is completed, wait for the completion of the measurement signal to be established and then read the measurement data.

[0014] Preferably, in Step S1, the specific method of packaging and transmitting the temperature data, humidity data, and barometric pressure data to the test computer is: The test computer sends a transmission command to the single-chip microcomputer, and after receiving it, the single-chip microcomputer sequentially transmits the temperature data, humidity data, and barometric pressure data stored in its internal memory, and each data is represented in floating-point type.

[0015] Preferably, in Step S2, the specific method for the test computer to receive the data packet and separate the temperature, humidity, and barometric pressure data is:

[0016] Use the VISA module of LABVIEW software to read the serial port data and intercept it byte by byte in sequence.

[0017] Preferably, step S3 includes: when calculating the refractive index, first calculate the saturated water vapor partial pressure, and then use the Edlén formula to calculate the refractive index of air;

[0018] The Edlén formula is:

[0019]

[0020] If the volume fraction of CO 2 in the air is not 0.0003, the refractive index needs to be corrected, and the correction formula is as follows:

[0021] (n - 1) x = [1 + 0.540(x - 0.0003)](n - 1) s

[0022] where, (n - 1) x is the difference between the corrected refractive index and 1; (n - 1) s is the difference between the refractive index before correction and 1; x is the volume fraction of CO 2 ; σ is the wave number in vacuum, unit: μm -1 , p is the pressure, unit: Pa; t 90 is the temperature, unit: °C; f is the partial pressure of water vapor, unit: Pa; (n - 1) tp represents the difference between the intermediate refractive index after introducing pressure and temperature and 1; n tpf represents the final refractive index value; n tp represents the intermediate refractive index after introducing pressure and temperature.

[0023] In a second aspect, an air refractive index measurement system is provided, and the system includes:

[0024] Module M1: Using a temperature and humidity sensor and a pressure sensor to collect ambient temperature data, humidity data, and pressure data, and packaging them into data packets for transmission to a test computer;

[0025] Module M2: The test computer receives the data packets and separates the temperature data, humidity data, and pressure data;

[0026] Module M3: Calculate and display the refractive index of air according to the separated temperature data, humidity data, and pressure data.

[0027] Preferably, module M1 includes: the temperature and humidity sensor and the pressure sensor, which are controlled by a single-chip microcomputer and communicate using a serial interface;

[0028] First, reset the temperature and humidity sensor and the barometric pressure sensor. Then, configure the temperature and humidity sensor to the temperature and humidity measurement mode, configure the barometric pressure sensor to the high-precision mode and start the measurement. After the measurement is completed, wait for the completion of the measurement signal to be established and then read the measurement data.

[0029] Preferably, in the module M1, the specific method for packing and transmitting the temperature data, humidity data, and barometric pressure data to the test computer is as follows: The test computer sends a transmission command to the single-chip microcomputer. After receiving it, the single-chip microcomputer sequentially transmits the temperature data, humidity data, and barometric pressure data stored in its internal memory, and each data is represented in floating-point type.

[0030] Preferably, in the module M2, the specific method for the test computer to receive the data packet and separate the temperature, humidity, and barometric pressure data is as follows:

[0031] Use the VISA module of the LABVIEW software to read the serial port data and intercept it byte by byte in sequence.

[0032] Preferably, the module M3 includes: When calculating the refractive index, first calculate the partial pressure of saturated water vapor, and then use the Edlén formula to calculate the refractive index of air;

[0033] The Edlén formula is:

[0034]

[0035] If the volume fraction of CO 2 in the air is not 0.0003, then the refractive index needs to be corrected, and the correction formula is as follows:

[0036] (n - 1) x =[1 + 0.540(x - 0.0003)](n - 1) s

[0037] Among them, (n - 1) x is the difference between the corrected refractive index and 1; (n - 1) s is the difference between the refractive index before correction and 1; x is the volume fraction of CO 2 ; σ is the wave number in vacuum, unit: μm -1 , p is the pressure, unit: Pa; t 90 is the temperature, unit: °C; f is the partial pressure of water vapor, unit: Pa; (n - 1) tp represents the difference between the intermediate refractive index after introducing pressure and temperature and 1; n tpf represents the final refractive index value; n tp represents the intermediate refractive index after introducing pressure and temperature.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. The present invention uses a high-precision digital sensor to obtain the values of air pressure, temperature, and humidity, and processes them using LABVIEW software to obtain a relatively accurate value of the air refractive index. Compared with the traditional direct measurement method, the present invention does not require complex optical instruments, has a simple structure, and the accuracy is controllable.

[0040] 2. The digital sensor adopted by the present invention reduces the complexity of the system and greatly reduces various errors introduced by the signal conditioning circuit. The use of LABVIEW brings great convenience to data acquisition, data processing, and display of measurement results, embodying the idea of "virtual instrument".

[0041] 3. Although the present invention calculates the air refractive index by collecting air pressure, temperature, and humidity data, these data can be used for altitude measurement, dew point calculation, etc. with almost no modification. Therefore, the system has a certain universality in application.

[0042] Other beneficial effects of the present invention will be described in the specific implementation manner through the introduction of specific technical features and technical solutions. Those skilled in the art should be able to understand the beneficial technical effects brought by the said technical features and technical solutions through these introductions. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] By reading the following detailed description of non-limiting embodiments with reference to the accompanying drawings, other features, objects, and advantages of the present invention will become more apparent:

[0044] Figure 1 is the flowchart of the method of the present invention;

[0045] Figure 2 is the structural diagram of the refractive index measurement system;

[0046] Figure 3 is the serial communication interface circuit. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0047] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that those of ordinary skill in the art can make several changes and improvements without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0048] An embodiment of the present invention provides an air refractive index measurement method. This method uses high-precision digital, temperature, and humidity sensor chips, combines with LABVIEW software to complete data acquisition and processing, and finally realizes the display of the refractive index measurement result. The use of digital high-precision sensors and LABVIEW software simplifies the system structure and can ensure the measurement efficiency and accuracy. Refer to Figure 1 As shown, the method specifically includes:

[0049] Step S1: Use a temperature and humidity sensor and a barometric pressure sensor to collect ambient temperature data, humidity data, and barometric pressure data, and package them into a data packet for transmission to the test computer.

[0050] For the collection of temperature data and humidity data, a sensor that can measure temperature and humidity simultaneously is used; a single-chip microcomputer is used for control, and serial communication is adopted. First, the sensor is reset, and then the sensor is configured as the temperature and humidity measurement mode and starts measurement. After the measurement is completed, wait for the "measurement completion signal" to be established and then read the measurement data.

[0051] For barometric pressure data collection, an absolute atmospheric pressure sensor is used. A single-chip microcomputer is used for control, and serial communication is adopted. First, the sensor is reset, and then the sensor is configured as the high-precision mode and measured. After the measurement is completed, wait for the "measurement completion signal" to be established and then read the measurement data.

[0052] The specific method for packaging and transmitting temperature, humidity, and barometric pressure data to the test computer is: The computer sends a "can transmit" command to the single-chip microcomputer. After receiving it, the single-chip microcomputer sequentially transmits the temperature, humidity, and barometric pressure data stored in its internal memory, and each data is represented in floating-point type.

[0053] Step S2: The test computer receives the data packet and separates the temperature data, humidity data, and barometric pressure data. The specific method is: Use the VISA module of LABVIEW software to read the serial port data and intercept it byte by byte in sequence.

[0054] Step S3: Calculate and display the air refractive index based on the separated temperature data, humidity data, and barometric pressure data.

[0055] When calculating the refractive index, first calculate the saturated water vapor partial pressure, then use the Edlén formula to calculate the air refractive index, and correct the carbon dioxide formula in it to 0.00045.

[0056] Among them, the Edlén formula is:

[0057]

[0058] If CO in the air 2If the volume fraction is not 0.0003, the refractive index needs to be corrected, and the correction formula is as follows:

[0059] (n - 1) x =[1 + 0.540(x - 0.0003)](n - 1) s

[0060] Where, (n - 1) x is the difference between the corrected refractive index and 1; (n - 1) s is the difference between the refractive index before correction and 1; x is the volume fraction of CO 2 ; σ is the wave number in vacuum, unit: μm -1 , p is the pressure, unit is Pa; t 90 is the temperature, unit °C; f is the partial pressure of water vapor, unit Pa; (n - 1) tp represents the difference between the intermediate refractive index after introducing pressure and temperature and 1; n tpf represents the final refractive index value; n tp represents the intermediate refractive index after introducing pressure and temperature.

[0061] The present invention also provides an air refractive index measurement system, and the air refractive index measurement system can be realized by executing the process steps of the air refractive index measurement method, that is, those skilled in the art can understand the air refractive index measurement method as a preferred embodiment of the air refractive index measurement system. Referring to Figure 2 as shown, the devices in this system include: a barometric pressure sensor, a temperature and humidity sensor, an MCU, a computer, and a result display. The barometric pressure sensor and the temperature and humidity sensor complete the collection of barometric pressure, temperature, and humidity data. The MCU realizes communication and control of the sensors through the bus respectively, obtains the collected data, and finally transmits the collected data to the computer. The computer realizes the processing of the collected data, the calculation of the refractive index, and the display of the result. The specific content of this measurement system includes:

[0062] Module M1: Use the temperature and humidity sensor and the barometric pressure sensor to collect ambient temperature data, humidity data, and barometric pressure data, and pack them into data packets and transmit them to the test computer.

[0063] Among them, for the collection of temperature data and humidity data, a sensor that can measure temperature and humidity simultaneously is used; a single-chip microcomputer is used for control, and serial communication is used. First, the sensor is reset, and then the sensor is configured as the temperature and humidity measurement mode and starts to measure. After the measurement is completed, wait for the "measurement completion signal" to be established and then read the measurement data.

[0064] For air pressure data acquisition, an absolute atmospheric pressure sensor is used. A single-chip microcomputer is used for control, and a serial interface is used for communication. First, the sensor is reset, and then the sensor is configured into a high-precision mode and measurement is carried out. After the measurement is completed, wait for the "measurement completion signal" to be established and then read the measurement data.

[0065] The specific method for packing and transmitting temperature, humidity, and air pressure data to the test computer is as follows: The computer sends a "can transmit" command to the single-chip microcomputer. After receiving it, the single-chip microcomputer sequentially transmits the temperature, humidity, and air pressure data stored in it, and each data is represented in floating-point type.

[0066] Module M2: The test computer receives the data packet and separates the temperature data, humidity data, and air pressure data. The specific method is as follows: Use the VISA module of LABVIEW software to read the serial port data and intercept it byte by byte in sequence.

[0067] Module M3: Calculate and display the air refractive index based on the separated temperature data, humidity data, and air pressure data.

[0068] When calculating the refractive index, first calculate the partial pressure of saturated water vapor, and then use the Edlén formula to calculate the air refractive index, and correct the carbon dioxide formula in it to 0.00045.

[0069] Among them, the Edlén formula is:

[0070]

[0071] If the volume fraction of CO 2 in the air is not 0.0003, the refractive index needs to be corrected, and the correction formula is as follows:

[0072] (n - 1) x =[1 + 0.540(x - 0.0003)](n - 1) s

[0073] Among them, (n - 1) x is the difference between the corrected refractive index and 1; (n - 1) s is the difference between the refractive index before correction and 1; x is the volume fraction of CO 2 ; σ is the wave number in vacuum, unit: μm -1 , p is the pressure, unit is Pa; t 90 is the temperature, unit °C; f is the partial pressure of water vapor, unit Pa; (n - 1) tp represents the difference between the intermediate refractive index after introducing pressure and temperature and 1; n tpf represents the final refractive index value; n tp represents the intermediate refractive index after introducing pressure and temperature.

[0074] Next, a more specific description of the present invention will be given.

[0075] An air refractive index measurement system provided by the present invention, as Figure 2 shown in the structure, the MCU controls the barometric pressure sensor and the temperature and humidity sensor to complete data acquisition and temporary storage. After all data is acquired, it is transmitted to the computer through the serial port. Programming is performed on the computer to calculate the air refractive index and display it.

[0076] The barometric pressure sensor uses the SCP1000D01 digital barometric pressure sensor of VTI Corporation in Finland. The temperature and humidity sensor uses the SHT11 series digital temperature and humidity sensor of Sensirion Corporation in Switzerland. The MCU selects the AT89S52 single-chip microcomputer of Atmel Corporation. Communication between the MCU and the computer uses the RS232 protocol, as shown in the appendix Figure 3 shown.

[0077] On the computer, LABVIEW uses the VI of VISA READ to read data and separate the barometric pressure, temperature, and relative humidity values. In the Edlén formula, the three parameters for calculating the air refractive index are barometric pressure, humidity, and the partial pressure of water vapor. Therefore, it is necessary to calculate the value of the partial pressure of water vapor through the temperature and relative humidity.

[0078] The Hyland-Wexler formula is selected to calculate the saturated water vapor partial pressure. After calculation, the result of this formula is relatively close to the experimental value. The partial pressure of water vapor at this humidity is obtained by multiplying the partial pressure of saturated water vapor by the relative humidity.

[0079] After obtaining the barometric pressure, temperature, and partial pressure of water vapor, the air refractive index can be calculated through the Edlén formula. The Edlén formula is:

[0080]

[0081] If the volume fraction of CO 2 in the air is not 0.0003, the refractive index needs to be corrected. The correction formula is as follows:

[0082] (n - 1) x = [1 + 0.540(x - 0.0003)](n - 1) s

[0083] Among them, (n - 1) x is the difference between the corrected refractive index and 1; (n - 1) s is the difference between the refractive index before correction and 1; x is the volume fraction of CO 2 ; σ is the wave number in vacuum, unit: μm -1, p is the pressure, with the unit of Pa; t 90 is the temperature (adopting the ITS-90 standard), with the unit of °C; f is the partial pressure of water vapor, with the unit of Pa; (n - 1) tp represents the difference between the intermediate refractive index after introducing the pressure and temperature and 1; n tpf represents the final refractive index value; n tp represents the intermediate refractive index after introducing the pressure and temperature.

[0084] When designing the program, according to the recent CO 2 measurement value, its volume fraction is set to 0.00045.

[0085] The embodiment of the present invention provides a method and system for measuring the refractive index of air. By using high-precision digital, temperature, and humidity sensor chips, combined with LABVIEW software, data acquisition, processing are completed, and finally the display of the refractive index measurement result is realized. The use of digital high-precision sensors and LABVIEW software simplifies the system structure and can ensure the measurement efficiency and accuracy. The rapid measurement of the refractive index of air is realized, which can be used in fields such as precision measurement, laser communication, and optical remote sensing.

[0086] Those skilled in the art know that in addition to implementing the system and its various devices, modules, and units provided by the present invention in the form of pure computer-readable program code, the method steps can be logically programmed to enable the system and its various devices, modules, and units provided by the present invention to be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers, etc. to achieve the same functions. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be regarded as the structure within the hardware component; the devices, modules, and units for implementing various functions can also be regarded as both software modules for implementing the method and the structure within the hardware component.

[0087] The specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. Without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A method for measuring the refractive index of air, characterized in that: include: Step S1: using a temperature and humidity sensor and an air pressure sensor to collect ambient temperature data, humidity data and air pressure data, and packaging them into data packets to be transmitted to a test computer; Step S2: The test computer receives the data packet and separates the temperature data, humidity data and air pressure data; Step S3: Calculate and display the air refractive index based on the separated temperature data, humidity data and air pressure data.

2. The method for measuring the refractive index of air according to claim 1, characterized in that: The step S1 includes: the temperature and humidity sensor and the air pressure sensor are controlled by a single chip microcomputer and communicated via a serial interface; First, reset the temperature and humidity sensor and the air pressure sensor, then configure the temperature and humidity sensor to the temperature and humidity measurement mode, configure the air pressure sensor to the high-precision mode and start measuring. After the measurement is completed, wait for the measurement signal to be established before reading the measurement data.

3. The method for measuring the refractive index of air according to claim 1, characterized in that: In step S1, the specific method of packaging and transmitting the temperature data, humidity data and air pressure data to the test computer is: the test computer sends a transmission command to the single-chip microcomputer, and after receiving it, the single-chip microcomputer sequentially transmits the temperature data, humidity data and air pressure data stored inside it, wherein each data is represented by a floating point type.

4. The method for measuring the refractive index of air according to claim 1, characterized in that: In step S2, the test computer receives the data packet, and the specific method of separating the temperature, humidity and air pressure data is: Use the VISA module of LABVIEW software to read serial port data and intercept it byte by byte.

5. The method for measuring the refractive index of air according to claim 1, characterized in that: The step S3 comprises: when calculating the refractive index, firstly calculating the saturated water vapor partial pressure, and then using the Edlén formula to calculate the air refractive index; The Edlén formula is: If the volume fraction of CO2 in the air is not 0.0003, the refractive index needs to be corrected. The correction formula is as follows: (n-1) x =[1+0.540(x-0.0003)](n-1) s Where, (n-1)x is the difference between the corrected refractive index and 1; (n-1)s is the difference between the refractive index before correction and 1; x is the volume fraction of CO2; σ is the wave number in vacuum, unit: μm- 1 , p is pressure, unit is Pa; t 90 is the temperature, unit is ℃; f is the partial pressure of water vapor, unit is Pa; (n-1)tp represents the difference between the intermediate refractive index after the introduction of pressure and temperature and 1; ntpf represents the final refractive index value; ntp represents the intermediate refractive index after the introduction of pressure and temperature.

6. An air refractive index measurement system, characterized in that: include: Module M1: Use temperature and humidity sensors and air pressure sensors to collect ambient temperature data, humidity data and air pressure data, and package them into data packets for transmission to the test computer; Module M2: The test computer receives the data packet and separates the temperature data, humidity data and air pressure data; Module M3: Calculate and display the air refractive index based on the separated temperature data, humidity data and air pressure data.

7. The air refractive index measurement system according to claim 6, characterized in that: The module M1 includes: the temperature and humidity sensor and the air pressure sensor, which are controlled by a single chip microcomputer and communicated via a serial interface; First, reset the temperature and humidity sensor and the air pressure sensor, then configure the temperature and humidity sensor to the temperature and humidity measurement mode, configure the air pressure sensor to the high-precision mode and start measuring. After the measurement is completed, wait for the measurement signal to be established before reading the measurement data.

8. The air refractive index measurement system according to claim 6, characterized in that: In the module M1, the specific method of packaging and transmitting the temperature data, humidity data and air pressure data to the test computer is: the test computer sends a transmission command to the single-chip microcomputer, and after receiving it, the single-chip microcomputer sequentially transmits the temperature data, humidity data and air pressure data stored inside it, wherein each data is represented by a floating point type.

9. The air refractive index measurement system according to claim 6, characterized in that: In the module M2, the test computer receives the data packet and separates the temperature, humidity and air pressure data in the following specific method: Use the VISA module of LABVIEW software to read serial port data and intercept it byte by byte.

10. The air refractive index measurement system according to claim 6, characterized in that: The module M3 includes: when calculating the refractive index, firstly calculating the saturated water vapor partial pressure, and then using the Edlén formula to calculate the air refractive index; The Edlén formula is: If the volume fraction of CO2 in the air is not 0.0003, the refractive index needs to be corrected. The correction formula is as follows: (n-1)x=[1+0.540(x-0.0003)](n-1)s Where, (n-1)x is the difference between the corrected refractive index and 1; (n-1)s is the difference between the refractive index before correction and 1; x is the volume fraction of CO2; σ is the wave number in vacuum, unit: μm- 1 , p is pressure, unit is Pa; t 90 is the temperature, unit is ℃; f is the partial pressure of water vapor, unit is Pa; (n-1)tp represents the difference between the intermediate refractive index after the introduction of pressure and temperature and 1; ntpf represents the final refractive index value; ntp represents the intermediate refractive index after the introduction of pressure and temperature.

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