Equivalent Wavelength Calibration Device and Method for Ultra-Fast Pulse Laser Interference System

Abstract

An equivalent wavelength calibration device and method for an ultrafast pulsed laser interference system, comprising: a light source component, an interference optical path component, and a signal acquisition and processing component arranged in sequence, wherein: the signal acquisition and processing component receives two interference light signals from the interference optical path, converts the interference light signals into voltage signals for processing, obtains the phase difference between the signal light and the reference light, and calculates the equivalent wavelength of the pulsed laser interference in combination with the displacement information of the nano-positioner. The present invention improves the effectiveness of the pulsed laser equivalent wavelength and the measurement accuracy of the ultrafast pulsed laser interference vibration measurement system by at least one order of magnitude.

Description

Technical Field

[0001] The present invention relates to a technology in the field of laser vibration measurement and ranging, and specifically relates to an equivalent wavelength calibration, measurement device and method for an optical interference vibration measurement system based on an ultrafast pulsed laser. Background Art

[0002] The laser measurement technology for micro-amplitude vibration is a non-destructive measurement technology developed based on the optical interference phenomenon and the modulation effect of a vibrating object on a laser beam. This technology generally judges the displacement of a measurement point by detecting the phase difference between a reference light wave and a measurement light wave in an interference optical path. If an ideal monochromatic light is used for measurement, the relationship between displacement and phase difference is: d = φ·λ / (4π), where: d is the displacement of the measurement point, φ is the phase difference, and λ is the wavelength of the monochromatic light.

[0003] Continuous-wave laser interference vibration measurement and ultrafast pulsed laser interference vibration measurement are two micro-amplitude vibration laser measurement technologies. In practical applications, the light source is generally idealized as a monochromatic light for processing, and the corresponding wavelength is called the equivalent wavelength. Among them, the former generally uses the output wavelength of a continuous-wave laser as the equivalent wavelength. Since the continuous-wave laser spectrum is extremely narrow and the energy is concentrated, such an equivalent processing effect is very good, so the measurement result accuracy is extremely high, and the typical accuracy value is less than 10 ppm. However, the response frequency of the optoelectronic sensor used in this technology must be higher than the vibration frequency to be measured. When receiving high-frequency optical signals above 1 GHz, the noise increases, making this technology unable to effectively measure high-frequency vibrations. The latter can convert high-frequency signals into lower-frequency optoelectronic signals for measurement by means of high-frequency vibration sampling, so it is not restricted by the high-frequency noise of the optoelectronic sensor. The existing ultrafast pulsed laser interference vibration measurement technology generally calculates with the energy peak wavelength as the equivalent wavelength. However, the pulse laser light source actually used has a wide spectrum and dispersed energy, and the energy peak wavelength cannot well represent the optical characteristics of the pulsed light. If the energy peak wavelength is simply used as the equivalent wavelength to calculate the vibration displacement, the error can exceed 1000 ppm, resulting in a serious restriction on its measurement accuracy, which is much lower than the accuracy of the continuous-wave laser interference vibration measurement technology. Summary of the Invention

[0004] In view of the above deficiencies of the prior art, the present invention proposes an equivalent wavelength calibration device and method for an ultrafast pulsed laser interference system, which improves the effectiveness of the pulsed laser equivalent wavelength and the measurement accuracy of the ultrafast pulsed laser interference vibration measurement system by at least one order of magnitude.

[0005] The present invention is realized through the following technical solutions:

[0006] The present invention relates to an equivalent wavelength calibration device for an ultrafast pulsed laser interference system, comprising: a light source component, an interference optical path component, and a signal acquisition and processing component arranged in sequence, wherein: the signal acquisition and processing component receives two interference light signals from the interference optical path, converts the interference light signals into voltage signals for processing, obtains the phase difference between the signal light and the reference light, and calculates the equivalent wavelength of the pulsed laser interference in combination with the displacement information of the nano-positioner.

[0007] The light source component includes: an ultrafast pulsed laser light source and a first linear polarizer, wherein: the first linear polarizer is located on the optical path of the ultrafast pulsed laser light source and is used to modulate the laser emitted by the ultrafast pulsed laser light source into linearly polarized light.

[0008] The interference optical path component includes: a polarization beam splitter prism, a first quarter-wave plate, a first mirror, a second quarter-wave plate, a second mirror, a nano-positioner, a non-polarizing beam splitter prism, a second linear polarizer, a third quarter-wave plate, and a third linear polarizer, wherein: the polarization beam splitter prism is arranged on the optical path of the first linear polarizer in the light source component, divides the pulsed beam into a first reflected light as the reference light and a first transmitted light as the signal light, the first quarter-wave plate is arranged on the reference light optical path for modulating the reference light incident from the polarization beam splitter prism and the reference light reflected back from the first mirror, the first mirror is arranged on the optical path of the first quarter-wave plate for reflecting the reference light incident from the first quarter-wave plate along the original optical path, the second quarter-wave plate is arranged on the signal light optical path for modulating the signal light incident from the polarization beam splitter prism and the signal light reflected back from the second mirror; the second mirror is located on the optical path of the second quarter-wave plate and is arranged on the nano-positioner for reflecting the signal light incident from the second quarter-wave plate along the original optical path, the polarization angles of the reference light and the signal light are perpendicular to each other after passing through the polarization beam splitter prism for the second time, and enter the non-polarizing beam splitter prism along the same optical path, the movable direction of the nano-positioner is parallel to the signal light optical path, the non-polarizing beam splitter prism is arranged on the common optical path of the signal light and the reference light emitted by the polarization beam splitter prism for dividing the signal light and the reference light into a second reflected light and a second transmitted light; the second linear polarizer is arranged on the optical path of the second reflected light incident from the non-polarizing beam splitter prism for causing the reference light component and the signal light component contained in the second reflected light to interfere, the third quarter-wave plate is arranged on the optical path of the second transmitted light incident from the non-polarizing beam splitter prism for delaying the phase of the signal light component in the second transmitted light by 90°; the third linear polarizer is arranged on the optical path of the second transmitted light incident from the third quarter-wave plate for causing the reference light component and the signal light component contained in the second transmitted light to interfere.

[0009] The reference light and the signal light have an adjustable optical path difference of 2ΔL, where: ΔL is the displacement of the nano-positioning stage. After passing through the non-polarizing beam splitter, each of the two beams of light is divided into two beams of equal light intensity. Among them, the reflected light forms interference light after passing through the second polarizer. The interference light is composed of two pulsed lights with equal intensity but different phases. When the reference light part E r1 =∈(t)·e i[ωt+θ(t)] , where: there is an optical path difference of 2ΔL between the signal light component and the reference light, so the time delay between the two is τ = 2ΔL / c, where: c is the speed of light. Then the signal light equation E s1 =∈(t + τ)·e i[ω(t+τ)+θ(t+τ)] ; The intensity of the interference light received by the first photodetector is: E1 = |E r1 +E s1 | = ∈ 2 (t)+∈ 2 (t + τ)+2∈(t)∈(t + τ)cos(ωτ + θ(t + τ)-θ(t)); After filtering the DC part, the intensity is updated to E1(AC) = 2∈(t)∈(t + τ)cos(ωτ + θ(t + τ)-θ(t)); The second transmitted light passing through the non-polarizing beam splitter first passes through the third quarter-wave plate, so that the phase of the signal light component lags behind that of the reference light component by π / 2; Then the reference light part E r2 =∈(t)·e i[ωt+θ(t)] , the signal light part E s2 =∈(t + τ)·e i [ω(t+τ)+θ(t+τ)-π / 2] , The intensity of the interference light received by the second photodetector after filtering the DC part is E2(AC) = 2∈(t)∈(t + τ)sin(ωτ + θ(t + τ)-θ(t)). The phase difference φ(τ) between the signal light and the reference light is calculated as φ(τ) = arctan(E2(AC) / E1(AC)). By adjusting the nano-positioner, the optical path difference can be continuously changed to obtain a series of ΔL i values and the corresponding phase difference values φ i , from which the corresponding equivalent wavelength can be obtained

[0010] The installation angle of the polarization beam splitter prism makes the light intensities of the first reference light and the second signal light approximately equal.

[0011] The optical axis of the first quarter-wave plate forms an angle of 45° with the polarization direction of the reference light.

[0012] The optical axis of the second quarter-wave plate forms an angle of 45° with the polarization direction of the signal light.

[0013] The installation angle of the non-polarizing beam splitter prism makes the light intensities of the second reflected light and the second transmitted light approximately equal.

[0014] The optical axis of the second linear polarizer is located on the angular bisector of the included angle between the polarization directions of the reference light and the signal light in the second reflected light.

[0015] The fast axis of the third quarter-wave plate should coincide with the polarization direction of the reference light component in the second transmitted light.

[0016] The optical axis of the third linear polarizer is located on the angular bisector of the included angle between the polarization directions of the reference light and the signal light in the second transmitted light.

[0017] The signal acquisition and processing component includes: a first photodetector and a second photodetector for receiving two interfering lights incident from the second linear polarizer and the third linear polarizer and converting them into voltage signals, a data acquisition module for collecting the voltage signals output by the first photodetector and the second photodetector, and a calculation module for further processing and calculating the voltage signals collected by the data acquisition module and obtaining equivalent wavelength data. Among them: the output ends of the first photodetector and the second photodetector are connected to the input end of the data acquisition module, and the output end of the data acquisition module is connected to the calculation module.

[0018] The present invention relates to a calibration method for the equivalent wavelength of an ultrafast pulsed laser interference system based on the above system, including the following steps:

[0019] Step 1) Assemble the above system, adjust the installation position of the nano-positioner so that the point where the optical path difference between the reference light and the signal light is zero is included within the travel range of the nano-positioner.

[0020] Step 2) Adjust the position of the second reflecting mirror mounted thereon back and forth through the nano-positioner, and observe the change in the signal strength in the first photodetector. The point where the signal is the strongest is the position point where the optical path difference is zero, denoted as the displacement zero point.

[0021] Step 3) Make the nano-positioner step from the above displacement zero point to the end point of the travel at one end and then move in the reverse direction to the end point of the travel at the other end, and record the position (ΔL i ) and the corresponding phase difference φ i at this time, and calculate the equivalent wavelength values corresponding to each optical path difference interval and find their average value Among them: N is the number of measurement intervals, and this average value is the equivalent wavelength value. Repeat this process multiple times to obtain the standard deviation of the equivalent wavelength, that is, the uncertainty or measurement accuracy of the measurement.

[0022] Technical effects

[0023] The present invention as a whole solves the defect of low measurement accuracy in the existing ultrafast pulsed laser interference technology.

[0024] Compared with the prior art, the present invention can accurately measure the interference equivalent wavelength value of an ultrafast pulsed laser source through a nano-positioner combined with an interference optical path. The error is reduced by at least 10 times compared with the nominal wavelength, greatly improving the accuracy of the equivalent wavelength value. In addition, based on this device, only by replacing the mirror on the nano-positioner with the resonant device to be measured and slightly adjusting the intensities of the reference light and the signal light, the measurement can be directly implemented, further ensuring the effectiveness of the equivalent wavelength after calibration, thereby greatly improving the measurement accuracy of the ultrafast pulsed laser interference vibration measurement system. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 is a schematic structural diagram and an optical path diagram of the system of the present invention;

[0026] Figure 2 is a flowchart of the method of the present invention;

[0027] Figure 3 is a test result diagram of the optical path difference varying with time in the embodiment;

[0028] Figure 4 is a test result diagram of the phase difference varying with time in the embodiment;

[0029] Figure 5 is a calculation result diagram of the equivalent wavelength in the embodiment;

[0030] In the figure: 1 ultrafast pulsed laser source, 2 first polarizer, 3 first mirror, 4 first quarter-wave plate, 5 polarization beam splitter, 6 second quarter-wave plate, 7 second mirror, 8 nano-positioner, 9 first photodetector, 10 second polarizer, 11 non-polarizing beam splitter, 12 third quarter-wave plate, 13 third polarizer, 14 second photodetector, 15 data acquisition module, 16 calculation module. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0031] As Figure 1 shown, this embodiment relates to an equivalent wavelength calibration device for an ultrafast pulsed laser interference system, including: a light source assembly, an interference optical path assembly, and a signal acquisition and processing assembly arranged in sequence.

[0032] The light source assembly includes: an ultrafast pulsed laser source 1 and a first linear polarizer 2. Among them: the spectral range of the ultrafast pulsed laser source 1 is from 760 nm to 810 nm, the peak wavelength is 783.67 nm, the repetition frequency is 50 MHz, the pulse width is 120 fs, and the optical axis of the linear polarizer 2 forms an angle of 45° with the horizontal direction. The beam emitted from the ultrafast pulsed laser source 1 is modulated into linearly polarized light at the corresponding angle after passing through the linear polarizer 2.

[0033] The described interference optical path component includes: a polarization beam splitter prism 5, a first quarter-wave plate 4, a first mirror 3, a second quarter-wave plate 6, a second mirror 7, a nano-positioner 8, an unpolarized beam splitter prism 11, a second linear polarizer 10, a third quarter-wave plate 12, and a third linear polarizer 13, where: The nano-positioner 8 has a single-direction degree of freedom, a displacement resolution of 0.01 nm, and its displacement can be adjusted by a controller. A second mirror 7 is installed on it, and the displacement direction is parallel to the signal light optical path. The beam incident from the linear polarizer 2 is divided into two linearly polarized light beams with polarization directions of 90° and 0° respectively after passing through the polarization beam splitter prism 5, which are used as the reference light and the signal light respectively. The fast axes of the first quarter-wave plate 4 and the second quarter-wave plate 6 form an angle of 45° with the horizontal direction. The reference light and the signal light are modulated into circularly polarized light after passing through them respectively. The installation angles of the first mirror and the second mirror are such that the reference light and the signal light are both reflected along the original optical path. After passing through the first quarter-wave plate 4 and the second quarter-wave plate 6 for the second time respectively, they are modulated into linearly polarized light. At this time, the polarization direction of the reference light becomes 0°, and the signal light becomes 90°. The signal light and the reference light enter the polarization beam splitter prism 5 for the second time and exit along the same optical path, and then enter the unpolarized beam splitter prism 11 and are respectively divided into two beams. Subsequently, a part enters the second linear polarizer 10 to generate interference, and the other part enters the third quarter-wave plate 12 and then enters the third linear polarizer 13 to generate interference. The optical axis angles of the second linear polarizer 10 and the third linear polarizer 13 are both 45°, and the fast axis direction of the third quarter-wave plate is 0°.

[0034] The described nano-positioner 8 includes: a clamping component, a piezoelectric motion component, and a closed-loop control circuit, where: The clamping component is installed on the piezoelectric motion component and is connected to the second mirror 7. The closed-loop control circuit controls the motion of the clamping component through a piezoelectric control component.

[0035] The described signal receiving and processing component includes: a first photodetector 9, a second photodetector 14, a data acquisition module 15, and a calculation module 16, where: The two interference light beams respectively enter the first photodetector 9 and the second photodetector 14, and are converted into voltage signals. After entering the data acquisition module 15, they are converted into digital signals and enter the calculation module 16 for calculation.

[0036] The described calculation module 16 includes: a piezoelectric motion component control unit, an optical path difference calculation unit, and an effective wavelength calculation unit, where: The piezoelectric motion component control unit is connected to the nano-positioner 8 and transmits motion instructions and reads positions. The optical path difference calculation unit calculates and determines the optical path difference range and zero point and is connected to the piezoelectric motion component control unit for transmitting motion range instructions. The effective wavelength calculation unit combines the position information of the nano-positioner 8 and the voltage information of the data acquisition module 15 and calculates the interference effective wavelength.

[0037] The calibration method for the equivalent wavelength of the ultrafast pulsed laser interference system based on the above system in this embodiment includes the following steps:

[0038] 1. Install each component according to the above requirements, and adjust the nano-positioner to the zero point of the optical path difference.

[0039] 2. Make the nano-positioner move reciprocally, record the displacement value (ΔL) of the positioning stage every certain distance and calculate the phase difference data φ(τ), Figure 3 is the variation of the optical path difference (2ΔL) with time, Figure 4 is the variation of the phase difference with time.

[0040] 3. Near the zero point of the optical path difference, calculate according to the formula and take the average within the above range to obtain the equivalent wavelength.

[0041] After specific actual experiments, adjust the time interval between the two interfering laser pulses within the range of + / - 5 fs (i.e., the optical path difference is + / - about 1.49 μm). After repeating 16 times, the average value of the measured equivalent wavelength is 780.03 nm, and the standard deviation of repeating 16 times is 0.29 nm, which is 3.64 nm different from the peak wavelength 783.67 nm of the laser used in the embodiment, as Figure 5 shown. In this embodiment, if the peak wavelength 783.67 nm of the laser is used as the effective wavelength according to the conventional method in the past, the error is 3.64 nm / 780.03 nm = 4666 ppm, while after using this method, the uncertainty is equal to or less than 0.29 nm / 780.03 nm = 372 ppm, greatly improving the accuracy and effectiveness of the measurement.

[0042] The above method for measuring and calibrating the effective wavelength of ultrafast pulsed laser interference does not directly use the peak wavelength of the ultrafast pulsed laser as the effective wavelength of interference for calculation, but uses a nano-positioning stage with feedback control to calibrate the autocorrelation and interference effective wavelength of the ultrafast pulsed laser. Compared with the prior art, this method greatly improves the measurement accuracy of ultrafast pulsed laser interference. As described in the above embodiment, the measurement accuracy is improved by at least one order of magnitude.

[0043] Those skilled in the art can make local adjustments to the above specific implementation in different ways without departing from the principles and purposes of the present invention. The protection scope of the present invention is subject to the claims and is not limited by the above specific implementation. All implementation solutions within its scope are subject to the constraints of the present invention.

Claims

1. An equivalent wavelength calibration device for an ultrafast pulsed laser interference system, characterized in that, Comprising: A light source component, an interference optical path component, and a signal acquisition and processing component arranged in sequence, where: The signal acquisition and processing component receives two interference light signals from the interference optical path, converts the interference light signals into voltage signals for processing, obtains the phase difference between the signal light and the reference light, and calculates the equivalent wavelength of pulsed laser interference in combination with the displacement information of the nano-positioner; The interference optical path component includes: a polarization beam splitter prism, a first quarter-wave plate, a first mirror, a second quarter-wave plate, a second mirror, a nano-positioner, a non-polarizing beam splitter prism, a second linear polarizer, a third quarter-wave plate, and a third linear polarizer, where: The polarization beam splitter prism is arranged on the optical path of the first linear polarizer in the light source component, divides the pulsed light beam into a first reflected light as the reference light and a first transmitted light as the signal light, the first quarter-wave plate is arranged on the reference light optical path for modulating the reference light incident from the polarization beam splitter prism and the reference light reflected back from the first mirror, the first mirror is arranged on the optical path of the first quarter-wave plate for reflecting the reference light incident from the first quarter-wave plate along the original optical path, the second quarter-wave plate is arranged on the signal light optical path for modulating the signal light incident from the polarization beam splitter prism and the signal light reflected back from the second mirror; The second mirror is located on the optical path of the second quarter-wave plate and is arranged on the nano-positioner for reflecting the signal light incident from the second quarter-wave plate along the original optical path, the polarization angles of the reference light and the signal light are perpendicular to each other after passing through the polarization beam splitter prism for the second time, and enter the non-polarizing beam splitter prism along the same optical path, the movable direction of the nano-positioner is parallel to the signal light optical path, the non-polarizing beam splitter prism is arranged on the common optical path of the signal light and the reference light emitted from the polarization beam splitter prism for dividing the signal light and the reference light into a second reflected light and a second transmitted light; The second linear polarizer is arranged on the optical path of the second reflected light incident from the non-polarizing beam splitter prism for causing the reference light component and the signal light component contained in the second reflected light to interfere, the third quarter-wave plate is arranged on the optical path of the second transmitted light incident from the non-polarizing beam splitter prism for delaying the phase of the signal light component in the second transmitted light by 90°; The third linear polarizer is arranged on the optical path of the second transmitted light incident from the third quarter-wave plate for causing the reference light component and the signal light component contained in the second transmitted light to interfere; The reference light and the signal light have an adjustable optical path difference of 2ΔL, where: ΔL is the displacement of the nano-positioning stage; after passing through the non-polarizing beam splitter, the two beams of light are each divided into two beams of equal light intensity. Among them, the reflected light forms interference light after passing through the second polarizer. The interference light is composed of two pulsed lights with equal intensity but different phases. When the reference light part E r1 =∈(t)·e i [ωt+θ(t)] , where: there is an optical path difference of 2ΔL between the signal light component and the reference light, so the time delay between the two is τ = 2ΔL / c, where: c is the speed of light. Then the signal light equation E s1 =∈(t + τ)·e i[ω(t+τ)+θ(t+τ)] ; The intensity of the interference light received by the first photodetector is: E1 = |E r1 +E s1 | = ∈ 2 (t)+∈ 2 (t + τ)+2∈(t)∈(t + τ)cos(ωτ + θ(t + τ)-θ(t)); After filtering out the DC part, the intensity is updated to E1(AC) = 2∈(t)∈(t + τ)cos(ωτ + θ(t + τ)-θ(t)); The second transmitted light passing through the non-polarizing beam splitter first passes through the third quarter-wave plate, so that the phase of the signal light component lags behind the reference light component by π / 2; Then the reference light part E r2 =∈(t)·e i[ωt+θ(t)] , the signal light part E s2 =∈(t + τ)·e i [ω(t+τ)+θ(t+τ)-π / 2] , the intensity of the interference light received by the second photodetector after filtering out the DC part is E2(AC) = 2∈(t)∈(t + τ)sin(ωτ + θ(t + τ)-θ(t)). Calculate the phase difference φ(τ) between the signal light and the reference light as φ(τ) = arctan(E2(AC) / E1(AC)). By adjusting the nano-positioner, the optical path difference can be continuously changed to obtain a series of ΔL i values and the corresponding phase difference values φ i , equivalent wavelength 2. The equivalent wavelength calibration device of the ultrafast pulsed laser interference system according to claim 1, characterized in that, The light source component includes: an ultrafast pulsed laser light source and a first linear polarizer, where: The first linear polarizer is located on the optical path of the ultrafast pulsed laser light source for modulating the laser emitted from the ultrafast pulsed laser light source into linearly polarized light.

3. The equivalent wavelength calibration device of the ultrafast pulsed laser interference system according to claim 1, characterized in that, The installation angle of the polarization beam splitter prism makes the light intensities of the first reference light and the second signal light equal; The optical axis of the first quarter-wave plate forms a 45° angle with the polarization direction of the reference light; The optical axis of the second quarter-wave plate forms a 45° angle with the polarization direction of the signal light; The installation angle of the non-polarizing beam splitter prism makes the light intensities of the second reflected light and the second transmitted light equal; The optical axis of the second linear polarizer is located on the angular bisector of the included angle between the polarization directions of the reference light and the signal light in the second reflected light; The fast axis of the third quarter-wave plate described above should coincide with the polarization direction of the reference light component in the second transmitted light; The optical axis of the third linear polarizer is located on the angular bisector of the included angle between the polarization directions of the reference light and the signal light in the second transmitted light.

4. The equivalent wavelength calibration device of the ultrafast pulsed laser interference system according to claim 1, characterized in that, The signal acquisition and processing component described above includes: a first photodetector and a second photodetector for receiving two interfering lights incident from the second linear polarizer and the third linear polarizer and converting them into voltage signals, a data acquisition module for acquiring the voltage signals output by the first photodetector and the second photodetector, and a calculation module for further processing and calculating the voltage signals collected by the data acquisition module and obtaining equivalent wavelength data, where: the output ends of the first photodetector and the second photodetector are connected to the input end of the data acquisition module, and the output end of the data acquisition module is connected to the calculation module.

5. A calibration method for the equivalent wavelength of an ultrafast pulsed laser interference system based on the equivalent wavelength calibration device according to any one of claims 1 to 4, comprising the following steps: Step 1) Assemble the above system, adjust the installation position of the nano-positioner so that the point where the optical path difference between the reference light and the signal light is zero is included within the travel range of the nano-positioner; Step 2) Adjust the position of the second mirror mounted thereon back and forth through the nano-positioner, and observe the change in the signal strength in the first photodetector. The position point where the signal is the strongest is the position point where the optical path difference is zero, denoted as the displacement zero point; Step 3) The nano-positioner is stepped from the above displacement zero point to the end point of the stroke at one end and then moves in the reverse direction to the end point of the stroke at the other end, and the position (ΔL i ) and the phase difference φ i at this time are recorded, and the equivalent wavelength values corresponding to each optical path difference interval are calculated and its average value is obtained where: N is the number of measurement intervals, and this average value is the equivalent wavelength value. By repeating this process multiple times, the standard deviation of the equivalent wavelength can be obtained, which is also the uncertainty of the measurement or the accuracy of the measurement.

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