Background of the invention Technical field

The invention relates to measurement of gas using tuneable laser spectrometers. More specifically it relates to measurement of noise levels to evaluate signal integrity that again can be used to verify validity of measurement values as well as instrument integrity.

Background of the invention

Instrumentation based on tuneable laser spectroscopy has been quite common in many industries for process control, emissions monitoring and for safety

applications. Different approaches have been used for the measurement techniques like direct absorption or wavelength modulation spectroscopy, the latter normally meaning a sort of harmonic detection.

Different scan frequencies for direct absorption methods could lead to varying anomalies in the signal due to non-gas signal sources like varying dust loads in cross-stack measurement and different atmospheric effects leading to signal intensity fluctuations like scintillations, turbulence, mirage, flames, fog, rain and snow in open path measurement. Typically higher scan frequencies in the instruments will lead to less influence of at least these natural effects in open air.

Instruments based on wavelength modulation spectroscopy like second harmonic detection is less susceptible to influence from the effects that could be present in open air due to the higher signal frequency that is a result of the harmonic detection technique. However, when measuring in ducts and stacks with a high gas velocity and varying dust loads, variations in the light intensity could also for these cases lead to deviations in the measured values. There are also cases where the signal intensity is low with no influence due to unusual external modulation of the signal where the low signal intensity just leads to a low signal to noise ratio. For instruments used as detectors of toxic or explosive gases it could lead to false alarms if for instance signal fluctuations due to snow is detected as an absorption line and thus as emission of a toxic gas.

Prior art

US patent application publication US 2006/0044562 A1 , "Gas Monitor", describes concepts for gas monitors and in particular gas monitors based on direct absorption spectroscopy. Academic publication "Gasmonitoring in the process industry using diode laser spectroscopy", Linnerud et.al. , Appl. Phys. B 67, 297-305 (1998) describes several aspects of gas monitoring based on second harmonic laser spectroscopy.

Examples of prior art are the LaserGas II HF Open Path and LaserGas III HF Open Path monitors of the current assignee. The HF open path monitors could be used for detection of hydrogen fluoride gas in petrochemical plants or in primary aluminium smelters. The LaserGas II monitor is based on wavelength modulation spectroscopy or second harmonics while the LaserGas III monitor is based on direct absorption technology. LaserGas II and III are products based on current and available technology for which the method of the present invention could be applied in the future versions.

One example of how the current tuning of a laser could be done in the prior art is shown in figure 5. The figure shows direct absorption spectroscopy and shows 3 cycles of laser ramp scans. The laser is scanned by a current ramp scan (1000) where the laser will scan a wavelength interval comprising absorption features of at least one gas to be measured. The current ramp scan is followed by a dark reference time interval (1 100) where the laser current is turned off. The dark reference time interval (1 100) is followed by a stable time interval (1 150) where the laser current is stable, but close to the start level and the objective with the stable time interval (1 150) is to stabilise the laser after the dark reference time interval (1 100) where the laser current is off. Disclosure of the invention Problems to be solved by the invention

The main objective with the present invention is to measure and detect noise on signals from spectrometers based on tuneable laser spectroscopy. In particular it is an objective to detect noise from external factors like scintillations, turbulence, mirage, flames, fog, rain and snow and give a warning or error signal from the spectrometer when such noise could lead to false alarms or severe deviations in instrument readings.

It is an additional objective to detect influence from varying dust load if these could lead to wrong reading and/or false alarms. Yet another objective is to detect low signal to noise levels whenever present. Yet another objective is to increase averaging time of the signal before calculation of a concentration or other parameter so that the signal to noise ratio can be improved traded off against the time response.

A general objective of the invention is to solve problems with solutions according to state of the art.

Means for solving the problems

The objectives are achieved according to the invention by a method for

measurement of noise level in signals from gas analysers using tuneable laser spectroscopy as defined in the preamble of claim 1 , having the features of the characterizing portion of claim 1 .

Summary of the invention

The basic concept of the invention is intermittently or regularly to measure noise by stopping the laser modulation for a short time such that the laser wavelength is constant (not scanned) and so that the signal should also be constant since no spectroscopic features are scanned. The laser must still be on and emit light when the laser wavelength is constant. This normally means that the laser is operating above the lasing threshold. This is shown in figure 1 . The signal variations in the received laser light will then be measured while laser modulation is off (1200, 2000). If no signal variations are measured everything should then be fine. However, if we are in an open path application and in open air and we find that we have significant changes in signal level when it should be close to constant it is likely that we are disturbed by either rain or snow.

A first aspect of the invention is a method for measurement of noise level in signals from gas analysers using tuneable laser spectroscopy. The method comprises the following steps:

- pointing a tuneable laser through a gas volume adapted to contain at least one gas to be measured,

- receiving light having passed through the gas volume from the laser on a light sensitive detector,

- acquiring a light detector signal from the detector,

- scanning the laser in a first wavelength interval comprising at least one spectral feature of the at least one gas to be measured,

- intermittently scanning the laser wavelength for an intermittent time interval in a second wavelength interval where there are no spectral features,

- acquiring the detector signal during the intermittent time interval, and

- determining a noise level based on the light detector signal acquired during the intermittent time interval. Preferably the method can be using a direct absorption measurement technique or a wavelength modulation spectroscopy or a harmonic detection measurement technique.

Preferably, the laser can be scanned in continuous scans over the first wavelength interval comprising at least one spectral feature of the at least one gas to be measured and thereafter over the second wavelength interval where there are no spectral features, and measuring the noise level based on the detector signal acquired during scanning the interval with no spectral features. The laser wavelength can be scanned in continuous scans over the first wavelength interval and directly thereafter over the second wavelength interval.

Further, the laser wavelength can preferably be scanned continuously only in the first wavelength interval comprising the at least one spectral feature of the at least one gas to be measured, and intermittently be scanned in the second wavelength interval where there are no spectral features, and where the noise level is measured based on the detector signal acquired during the intermittent time interval where the laser is scanned in the second wavelength interval where there are no spectral features. The laser wavelength can be scanned repeatedly only in the first wavelength interval, and intermittently in the second wavelength interval.

The laser wavelength can preferably not only be scanned in the second wavelength interval where there are no spectral features, but also the laser scanning can be stopped so that the laser wavelength is kept stable within the second wavelength interval where there are no spectral features.

Further, a time delay can preferably be inserted after the laser has been scanned into the second wavelength interval where there are no spectral features to allow the laser wavelength to stabilise, and the noise level can be measured based on the detector signal acquired during the part of the intermittent time interval that is after the inserted time delay. The step for determining the noise level can be based on the peak to peak value of the acquired detector signal, or on the standard deviation or the variance of the light detector signal.

The step for determining the noise level can be based on the information content of the light detector signal, information content constituting either frequency

components, curve shapes or patterns, a score function generating a score as a function of information content that could lead to high noise, the score from the score function indicating the noise level. The measurement of the noise level can preferably be used to raise a warning or error signal indication if the measured noise level is above a user defined or predefined threshold to improve the overall instrument reliability.

The method can preferably comprise performing a gas measurement comprising the following steps:

- calculating a concentration of the at least one gas to be measured from the light detector signal from the detector acquired in the first wavelength interval , and

- using the noise level to increase the averaging time of the gas measurement if the measured noise level is above a user defined or predefined threshold to improve the overall signal to noise ratio of the gas measurement. The time interval for measurement of noise level can preferably be included only once for a user defined or predefined time interval, or once for a user defined or predefined number of laser scans to reduce actual time not used for measurement of gas.

The method can comprise performing a gas measurement comprising the following steps:

- calculating a concentration of the at least one gas to be measured from the light detector signal from the detector acquired in the first wavelength interval, and - using the noise level to calculate a confidence interval of the gas measurement.

Brief description of the drawings

Note that figures are not to scale and effects illustrated can be simplified or exaggerated to easier explain the concepts.

Figure 1 shows two cycles of one possible implementation of the method according to the present invention. In figure 1 the laser current is shown as function of time for two cycles or scans for a direct absorption implementation. The ramp scan (1000) of the laser is intended to scan the laser wavelength across the spectral features to be registered. The following zero-setting of the laser current (1 100) is used to get a zero signal reference and a flat laser current level (1200) then follows. After a short time the laser has stabilised and this is indicated on the selected part (2000) of the flat laser current level (1200).

Figure 2 is similar to figure 1 , but adapted to wavelength modulation spectroscopy and second harmonic detection. A dark reference time slot (1 100) where the laser is off is present between scans. The laser ramp (1000) where the absorption line is scanned comes in front of the dark reference (1 100). The dark reference (1 100) is followed by a stable region (1200) where the laser current is constant with exception of the sine wave modulation. The last region (2000) of the constant laser current region (1200) is where the noise measurements should be done.

Figure 3 shows the correspondence of the laser current / on the left Y-axis and the wavelength (lambda) on the right Y-axis. An absorption line is indicated to the right and a region (4100) where the absorption line is present is matching the laser ramp (1000). The region (4200) with no absorption line matches the region (1200) with constant laser current and this is when the noise data should be recorded.

Figure 4 shows a similar scenario as figure 3, but for an alternative modulation where the laser constantly is scanned or modulated around the absorption line and where the detected signal normally is at harmonics. Normal measurement mode (3000) matches the region with absorption line (4100) in the wavelength domain. From time to time when the instrument checks the noise level, the laser settings will be changed to another region (3200) where no absorption lines will be scanned and this matches region (4200) in the wavelength domain.

Figure 5 shows a standard approach with a laser ramp scan (1000) and a dark reference check (1 100) with the laser off and a short laser stabilisation period (1 150) after the dark reference check. Thereafter a new scan (1000) is performed. Figure 5 is included to serve as a reference example to the prior art and how the laser current tuning could be done.

Description of reference signs

Ref number Description

1000 Normal part of laser ramp scan where laser is scanned across

an absorption line

1 100 Dark reference time slot where laser is off

1 150 Part of laser ramp where the laser current is constant to stabilise the laser after the dark reference time slot (1 100). Used in prior art.

1200 Part of laser ramp where laser current is constant

2000 Part of laser ramp where laser current is constant and laser

wavelength is stable and where noise measurements should be acquired

3000 Alternative modulation normal measurement

3200 Alternative modulation noise measurement

4100 Wavelength interval where gas absorption line(s) are present

4200 Wavelength interval where no gas absorption lines should be

present Detailed description of the invention

Various aspects of the disclosure are described more fully hereinafter with reference to the accompanying drawings. This disclosure may, however, be embodied in many different forms and should not be construed as limited to any specific structure or function presented throughout this disclosure. Rather, these aspects are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. Based on the teachings herein one skilled in the art should appreciate that the scope of the disclosure is intended to cover any aspect of the disclosure disclosed herein, whether implemented independently of or combined with any other aspect of the disclosure. For example, an apparatus may be implemented or a method may be practiced using any number of the aspects set forth herein. In addition, the scope of the disclosure is intended to cover such an apparatus or method which is practiced using other structure, functionality, or structure and functionality in addition to or other than the various aspects of the disclosure set forth herein. It should be understood that any aspect of the disclosure disclosed herein may be embodied by one or more elements of a claim.

The invention will be further described in connection with exemplary embodiments which are schematically shown in the drawings.

An embodiment of the method according to the present invention for a direct absorption measurement type is as follows:

A tuneable laser is pointed through a target gas onto a light sensitive detector. The laser is temperature regulated to operate close to one or more absorption lines to be scanned by the laser. The laser current is then ramped (1000) so that the wavelength of the laser changes and scans across the absorption lines in question. The signal on the detector is continuously acquired and stored during all parts of the operation for each cycle or scan. After the ramp (1000) follows an optional dark reference period (1 100) where the laser current is turned off. After the dark reference follows a stable time interval (1200) where the laser current is constant. The laser wavelength will be stable a certain time after the stable section (1200) has started. This is indicated by the region (2000) where the noise measurement will take place. When the laser current is in the stable section (1200, 2000) the laser is on and emitting light and the laser is normally above the lasing threshold. The data acquired during the ramp (1000) will be used for normal calculations of gas concentrations and the wavelength will be in a first wavelength interval (4100) while data acquired during stable time interval (2000) will be used for noise measurement and the wavelength will be in a second wavelength interval (4200). The data acquired during the second wavelength interval (4200) is intended to be variations in the received laser light on the detector. It is possible to operate the laser in more than one wavelength interval comprising spectral features of at the least one gas to be measured. In cases where it is desired to scan over two or more spectral features located in two or more

wavelength intervals (4100) which are separated so long apart that it is not possible to scan over the two or more wavelength intervals using one continuous laser current ramp scan (1000), the laser settings will be changed between the scan of the different wavelength intervals comprising spectral features of the at least one gas to be measured. The current tuning range of tuneable lasers is limited. By "laser setting" it is here meant the settings of the laser that makes it operate in the desired wavelength region and the temperature of the laser is normally the most important setting which sets the laser wavelength close to the wavelength intervals to be scanned during the laser current ramp scan (1000). As an example to illustrate the case gas A has spectral features in a wavelength interval AA and gas B has spectral features in wavelength interval BB. Wavelength interval CC does not contain any spectral features. The wavelength distance between interval AA and BB is so long that it is not possible to scan the laser in one laser current scan (1000) while interval CC is adjacent to BB. CC is at a longer wavelength than BB which is at a longer wavelength than AA. The procedure will then be to set the laser temperature or settings so that the laser wavelength is close to the shortest wavelength of interval AA, then scan the laser current with the ramp (1000), then adjust the laser

temperature or settings again so that the laser wavelength is close to the shortest wavelength of interval BB and then scan the laser using a ramp through region BB and then into CC. Intervals AA and BB will constitute examples of the "first wavelength interval" while interval CC be an example of the "second wavelength interval". The order in which the different intervals are located in wavelength will depend on the actual gas or gases to be measured and where regions without spectral features are available in the proximity of selected wavelength intervals and the above example is just an illustration.

Another embodiment of the method is with wavelength modulation spectroscopy and one example of this is second harmonic detection (figure 2) where a sine wave modulation will be added to the current that scans the laser (1000, 1 100, 1200). For the noise signal measurement method to work in this implementation it is important that no absorption lines are present close to the laser wavelength corresponding to the stable current level (1200) which wavelength wise will be in the second wavelength interval (4200). There must be sufficient clearance so that the sine wave modulation on top of the basic signal (1000, 1 100, 1200) does not scan the wavelength into regions where absorption features are present as this could lead to detector signals that could be interpreted as noise.

Also for direct absorption methods it is important that the laser wavelength is a certain distance from absorption features so that noise in the laser wavelength, laser driver etc. does not modulate the laser so that part of an absorption feature will be scanned and generate a false noise signal. The correct wavelength interval is the second wavelength interval (4200).

The method of the present invention is not limited to the laser scan scheme presented in figure 1 . The dark reference feature (1 100) can be skipped so that the laser current goes from the ramp (1000) directly to the stable time interval (1200).

It is also possible to run the ramp (1000) in the opposite direction from a high current to a lower current and the stable level (1200) could optionally correspond to the highest laser scan current.

Any laser scan configuration can be used for the noise measurement method according to this invention as long as it has a time interval where the laser current is stable and that this interval is sufficiently long to allow the laser wavelength also to stabilise before the noise measurement starts. For methods applied on any kind of harmonic detection an additional requirement is that there must not be any spectral features in the second wavelength interval (4200) which is around the wavelength corresponding to the laser current of the stable region (1200). It is important that these spectral features cannot be reached by the additional sine wave modulation.

To increase the time where actual gas measurement is being done it is possible to do the noise measurement at certain time intervals or after a certain ramp scan counts either set fixed from the factory or to be user selectable. It could also be automatically adjustable based on previous noise readings so that when little noise has been present, the interval between noise measurements will increase. It could also be configured so that the noise is checked if the instrument is set in a mode where it will give an alarm based on the current instrument reading. It is also possible to be most of the time in a normal mode where only a wavelength interval around the absorption line is scanned and at certain time intervals start a noise measurement procedure comprising the steps of adjusting the laser drive parameter so that the wavelength are in an interval with no spectral features and then acquire detector data that will be analysed for noise using the selected means. This is illustrated in figure 4. This will as in the section above also lead to actual measurement a larger part of the time. When the noise data has been acquired and typically is present in an array of numbers the data will be analysed. Ideally the measured data from the time interval (2000) should describe a constant level. However, some noise will always be present, but high levels normally indicate some deviations from the normal case. The noise measured in the time interval (2000) can be analysed or calculated using all methods capable of giving an indication of the actual noise level. One first and simple method is to calculate the peak to peak noise i.e., max signal - min

signal=peak to peak. Other methods are, but not limited to, standard deviation, variance, correlation or matching with functions which have signal frequency specifications suitable for the actual noise to be expected. Fast or discrete Fourier transforms might also be used to determine the overall noise level as well as to discriminate between different noise sources based on the frequency range in which the noise components are found. Another embodiment of the method according to the invention is in advance to analyse the information content of the signal from the first wavelength interval (4100), the information content comprising either which frequency components are present in the signal or which curve shapes that could be present in the first wavelength interval (4100) as function of gases to be measured by the gas analyser. With the term «curve shape» or its plural counterpart it is in the following meant signal curves with a shape or alternatively a pattern that is characteristic and that can be recognised either visually by humans or by calculating means according to the present invention. The advance analysis according to this embodiment comprises the steps to vary the concentration of the at least one gas to be measured over the same concentration range as to be expected when the method is executed. Typically the said gas concentration will be varied in a limited number of steps spread over the concentration range. For each step in the concentration range the information content is analysed. The analysis results will be stored for use when the method is executed. The objective with the advance analysis is to find and store information on normal signals when little or no noise is present. Then when the method is executed the noise signal from the second wavelength interval (4200) from a normal noise measurement will be analysed with regards to signal frequency components or curve shapes that could be present in the first wavelength interval (4100) where the gas concentration is measured and this analysis is again based on the stored analysis results from the advance analysis. If for instance the noise contains strong frequency components that also could be strong in a normal signal in the first wavelength interval (4100) when at the at least one gas to measured is present and these strong frequency components are the result of the presence of the at least one gas to be measured, it is likely that the noise will result in a larger error in the gas measurement than a noise signal not containing these frequency components. In the embodiment analysing the curve shapes, a strong correlation between the noise signal and a signal from the first wavelength interval (4100) when the at least one gas to be measured is present, will indicate that the noise could contribute stronger than in a case where the correlation is weaker. However, an opposite curve shape or pattern could possibly also contribute to a gas measurement error and even lead to a reduced measurement value or a negative value. By an "opposite" curve it is here meant a curve that has a negative correlation and that will or could lead to a lower reading of the concentration of the gas to be measured. The frequency components can be calculated from the signal using the direct or discrete Fourier transform (DFT), fast Fourier transform (FFT) or a multiresolution technique like wavelets or any other suitable technique. Strong frequency

components can be found by choosing a certain number of the strongest

components, either strong by themselves or compared to the DC or the lower frequency components. A score function for noise measurement based on frequency components could correlate frequency components from the first wavelength interval (4100) to frequency components from noise measurement in the second wavelength interval (4200). A good match is when the distribution of strength of each frequency component is similar in the noise signal acquired by the detector from the second wavelength interval (4200) as well as in the signal from the first wavelength interval (4100). The score function will give a high score when there is a good match and a low score when the match is less. A high score indicates a high noise level. However, it is possible to design score functions that have a low score with good match and a high score with no or limited match and in such cases the criteria have to be adopted accordingly. To determine similarity between the curve shape of the noise and the signal from the first wavelength interval (4100) different score functions can be used. Score functions based on correlation, template matching, convolution or possibly digital filtering techniques could be applied. If the method in one embodiment uses a score function based on correlation, the score can be higher if there is a higher correlation and if it is a negative correlation you get a negative score. Then the criteria of the presence of high noise is a high score above a predetermined or user selectable threshold or a negative score below a similar predetermined or user selectable threshold. Another embodiment of the method according to the present invention comprises the additional step to calculate the confidence interval of the gas measurement based on the noise measurement. The accuracy of gas measurement based on tuneable laser spectroscopy typically depends on the overall signal to noise ratio of which some of the noise contributions can be measured using the method according to the present invention.

One first embodiment of confidence interval calculation is to send the acquired detector signal from the second wavelength interval (4200) through the gas measurement signal processing algorithms that are designed for calculating a gas concentration from a signal acquired by the detector in the first wavelength interval (4100). The first embodiment of the confidence interval calculation will use the output from the gas concentration performed on the noise signal. This output based on the noise signal will be used together with the gas measurement value from the calculation of the concentration of the at least one gas to be measured. The result including the confidence interval will then be the gas measurement value plus/minus the result from calculating the gas concentration performed on the noise signal. A ratio of the calculated confidence interval can also be used. An optional

implementation of the confidence interval measurement can be based on measuring the peak to peak value of the noise and treat this peak to peak value as a line strength of an absorption line. Then the gas concentration corresponding to the same absorption line strength for the at least one gas to be measured is calculated. This gas concentration which corresponds to the same absorption line strength for the at least one gas to be measured as was measured as peak to peak signal for the noise can then be used as indication of the confidence level.

Other implementations of calculating a confidence interval could comprise empirical values inserted in a look up table where the noise level measured corresponds to an index for the look up table and the entry for the index corresponds to the empirical noise value of a measurement when the noise level measurement is as found. The empirical values can be measured under controlled or partly controlled conditions and processed to fit a method based on look up tables. Another version of the method based on look up tables could comprise values from simulation of different noise types and levels and their resulting corresponding confidence interval ranges.

Another implementation based on wavelength modulation spectroscopy like second harmonic detection, a higher frequency sine wave will be modulated on top of the laser current during all phases of a laser scan cycle. This is shown in figure 2. It is then of utmost importance that stable region (1200) is corresponding to a wavelength region where there are no spectral features that could be scanned by the sine wave on top of the basic curve (1000, 1 100, 1200). Yet another implementation for other scanning or modulation techniques where spectral features are constantly scanned is shown in figure 4. In such a case the laser drive parameters will be temporarily changed so that the laser scans a wavelength region without spectral features. This is in principle similar to the cases shown in figures 1 and 2 except that the techniques for figure 1 and 2 already includes scanning a part of a wavelength interval that is free of spectral features and that the laser wavelength will be kept constant for a while in that wavelength region.

The method according to the invention can be performed using a direct absorption measurement technique often referred to as direct absorption spectroscopy (DAS). In direct absorption spectroscopy the laser is scanned mainly using a laser ramp current or a current resembling a saw tooth shape. This current ramp can be somewhat modified to compensate for laser nonlinearities.

Alternatives to direct absorption techniques comprise different modulation schemes. Even though the ramp of direct absorption techniques could be regarded as modulation of the laser current, laser spectroscopy based on wavelength modulation spectroscopy (WMS) normally comprise additional modulation of the laser. The additional modulation could be in the form of a higher frequency sine wave on top of ramp as an example. Second harmonic detection is one example of a wavelength modulation spectroscopy technique. A first preferred embodiment of the method according to the invention is to scan the laser in a continuous scan comprising a first wavelength interval (4100) where at least one spectral feature of the at least one gas to be measured is present and then directly thereafter continue the laser scan in a second wavelength interval (4200) where there are no spectral features present.

A second preferred embodiment of the method according to the invention is to scan the laser continuously back and forth within the first wavelength interval (4100) and then at user defined or predefined intervals scan the laser in the second wavelength interval (4200) to measure noise. This makes the method according to the invention compatible with scanning or modulation schemes scanning a very narrow first wavelength interval (4100) more or less only containing spectral features.

The method according to the invention also supports to stop the laser scanning so that the laser wavelength is kept stable in the second wavelength interval (4200). For use with direct absorption techniques the laser scanning is just stopped. For wavelength modulation spectroscopy like second harmonic detection the laser ramp scan is stopped, but the added higher frequency sine wave continues so that the mixer system typically used in the analogue signal processing can continue to operate and give signal out.

If the laser scanning or the laser settings have been changed the laser might need some time to stabilise before the noise should be measured. One embodiment of the method according to the invention inserts a time delay just after the laser has been scanned into the second wavelength interval (4200) and waits until this time delay has passed before the measurement of the noise starts.

There are several ways measurement of noise can be done in a method according to the present invention. A first embodiment is based on measuring the difference between the maximum and minimum noise signal measured or the "peak to peak" signal. Alternatively the standard deviation or the variance of the noise signal can be used. However, any method usable to determine the noise signal can be used. A method according to the present invention comprises embodiments that use the result from the noise measurement to raise a warning or an error message whenever the noise level is above a certain threshold or alternatively the averaging time of a gas measurement can be increased from a standard averaging time to a longer averaging time if the noise level is higher than normal.

One additional embodiment of the method according to the present invention scans the laser in the second wavelength interval at user defined or predefined time intervals to use more of the time measuring spectral features in the first wavelength interval to achieve better overall signal to noise ratio of the gas measurement.