ULTRASONICS – POWER MEASUREMENT – HIGH INTENSITY THERAPEUTIC ULTRASOUND HITU TRANSDUCERS AND SYSTEMS 1 Scope This International Standard • establishes general principles relevant to HI
General
The radiation force balance includes a target linked to a balance, where an ultrasonic beam is directed either vertically or horizontally The balance measures the radiation force exerted by the ultrasonic beam, allowing for the determination of incident ultrasonic power based on the difference in force with and without the ultrasonic radiation Calibration of the balance is achieved using small precision weights of known mass.
The target shall be chosen so as to closely approach one of the two extreme cases, i.e perfect absorber or perfect reflector
To calculate the acoustic incident power \( P_i \) from an ultrasonic transducer for a plane incident wave, one must use the radiation force component \( F \) acting on the target in the direction of propagation, applying either Equation 1 or Equation 2 as suitable.
The equation for pressure intensity is given by \$ P_i = \frac{cF}{2 \cos 2 \theta} \$, where \$ c \$ represents the speed of sound in the fluid, specifically water, and \$ \theta \$ denotes the angle between the direction of the incident wave's propagation and the normal to the reflecting surface.
The direction of the incident wave refers to the orientation of the field axis, interpreted in a global context rather than a local one.
The relationship between radiation force and incident power is fundamentally influenced by assumptions regarding the radiated field and its interaction with the target and measurement tank For non-plane waves, such as convergent or divergent waves, or those generated by multiple simultaneous sources, it is essential to establish the accurate relationship between radiation force and incident power Additionally, it is important to estimate the uncertainty in the incident power caused by the non-plane characteristics of the field.
In certain situations, the forces exerted on a target by acoustic streaming can be substantial when compared to the radiation force To accurately assess the magnitude of the radiation force in these instances, it is essential to implement corrective measures, which may involve applying a theoretical correction or utilizing a streaming foil positioned near the target Additional guidance is provided in Annex E Furthermore, it is important to estimate the uncertainty in the incident power resulting from streaming forces.
NOTE 2 The appropriate formulae for certain simple idealised transducer configurations are given in Annex C
To ensure accurate measurement of incident power, the transducer must be operated in a manner that reflects its intended clinical application, such as using continuous wave or the standard clinical pulsing sequence, as long as it aligns with the time response of the balance.
To prevent damage to the target or transducer, it is essential to explore alternative pulsing sequences This investigation will focus on how varying thermal loads impact the power output of the transducer.
Further background information about the requirements in the remainder of Clause 6 can be found in Annex A of IEC 61161:2013.
Requirements for equipment
Target type
The use of an absorbing target is recommended The use of a conical reflecting target is not recommended in general but may be necessary in some situations
The target shall have known acoustic properties, these being relevant to the details of the relation between ultrasonic power and radiation force (See also A.5.2 of IEC 61161:2013)
An absorbing target shall have:
• an amplitude reflection factor of less than 5 %;
• an acoustic energy absorption within the target of at least 98 %
For measurements on a collimated transducer, an absorbing target should be orientated at a small angle to the axis of symmetry of the transducer to minimise coherent reflections
To minimize the risk of permanent thermal and mechanical damage from ultrasound exposure, it is essential to select appropriate absorbing materials and target designs Any temporary variations in the amplitude reflection factor or acoustic energy absorption must ensure that the overall measured power is affected by less than 2%; otherwise, a correction is necessary.
A reflecting target shall have an amplitude reflection factor greater than 99 %
When utilizing ultrasound technology, it is essential to account for the potential reflection of ultrasound energy back to the transducer from the target Additionally, selecting the target's shape should align with the geometry of the transducer for optimal results.
A conical reflecting target is generally unsuitable for measurements in convergent or divergent fields, particularly for convergent transducers, multi-element transducers, or when ka < 17.4, unless specific transducer geometry necessitates its use If the use of a conical reflecting target is essential due to the transducer's shape, it is important to estimate the expected relationship between incident power and radiation force, and to include the associated uncertainty in section 6.4.2.
NOTE 1 The exact meaning of the quantity a depends on circumstances For practical transducers, this is the effective transducer radius in accordance with the particular definition in the field of application In model calculations using a piston approach, it is the geometrical piston radius.
Target diameter
The target diameter must be sufficiently large to capture at least 98% of the ultrasound energy that reaches the measurement plane, with the necessary calculations for determining the required diameter provided in Annex B.
NOTE Other methods may be used to determine the minimum target diameter for an individual transducer design: for instance, modelling or hydrophone measurements.
Balance / force measuring system
The radiation force balance can either be a gravimetric balance with a vertical beam orientation or a force feedback design with a horizontal beam When calibrated against mass units, it is essential for the manufacturer or user to ensure accurate conversion of balance readings to force values.
NOTE Calibration of set-ups with horizontal beam orientation may be carried out using an appropriate balance arm attachment, or by calibration against sources of known acoustic power
The balance used shall have sufficient resolution for the magnitude of the ultrasonic power to be measured (See A.5.4 of IEC 61161:2013)
System tank
To ensure accurate measurements, a measuring vessel with an absorbing lining must be utilized when a reflecting target is present, limiting returning reflections to no more than 2% of the total measured power.
Target support structures
In static-force balances, it is essential to design the structural members that support the target and transmit the radiation force across the air-water interface to minimize the impact of surface tension and buoyancy variations due to water level changes, ensuring these effects remain below 2% of the total measured power.
Transducer positioning
The ultrasonic transducer mount must ensure stable and consistent positioning of the transducer relative to the target, maintaining that variations in overall measured power remain within 2%.
Anti-streaming foils
To ensure accurate measurements, the target must either be equipped with an anti-streaming foil to prevent acoustic streaming in the water path, or the measurement process, including data acquisition and analysis, must be conducted to limit the impact of streaming forces to no more than 2% of the total measured power; if this threshold is exceeded, a correction must be implemented.
To ensure optimal performance, an anti-streaming foil must be placed near the target and should not be aligned parallel to the ultrasonic transducer's surface It is essential to measure its transmission coefficient and apply a correction if its impact exceeds a specified threshold.
2 % of the overall measured power
NOTE In practice a tilt angle of 5° to 10° has been found to be adequate.
Transducer coupling
The ultrasonic transducer must be connected to the measurement device in a way that ensures the effect on the total measured power remains below 2% If this threshold is exceeded, a correction must be implemented, as outlined in A.5.9 of IEC 61161:2013.
Calibration and stability
The force measuring part of the radiation force balance shall be calibrated by the use of small weights of known mass
The sensitivity of the radiation force balance to ultrasonic power will be monitored using an ultrasonic source with a known output power This sensitivity will be tested annually, or more often if there are signs of changes in the balance's sensitivity to ultrasonic power.
NOTE The sensitivity to ultrasonic power may change due to degradation of the target material caused, for instance, by thermal or cavitation damage.
Requirements for measuring conditions
Lateral target position
The lateral position of the target during measurement shall be constant and reproducible to an extent that related changes in overall measured power do not exceed 2 %.
Transducer/target separation
The distance between the ultrasonic transducer surface and the target, including any foil used, must be accurately known and consistently reproducible This ensures that any variations in the overall measured power remain within a maximum limit of 2%.
Water
When using a radiation force balance, the liquid used for the measurements shall be water
For output powers exceeding 1 W, it is essential to use only degassed water, following a defined process as outlined in IEC 62781 The water must be adequately degassed to prevent visible bubble formation in the water path or on the transducer and target surfaces Any measurements taken in the presence of air bubbles must be disregarded Ideally, the total amount of dissolved gas in the water should be minimized.
< 2 mg/l during all measurements, and may need to be lower in some cases
The use of degassed water is also recommended for determining output powers below 1 W
Bubbles may form on surfaces in gassy water if the temperature of the water increases
Ultrasound can induce bubble formation even at power levels below 1 W, particularly when the beam area is small Therefore, it is essential to inspect for bubbles on the transducer and target surfaces before, during, and after each measurement.
NOTE 1 The gas level required to prevent bubble formation will depend on many factors including acoustic working frequency and maximum negative pressure in the water path Changing or fluctuating radiation force may indicate the formation of bubbles
NOTE 2 Chemical degassing methods which remove only one or a few gas components (eg the use of Na 2 SO 3 ) are not generally sufficient for HITU measurements Provided more general methods of degassing are used, monitoring of the oxygen content is simple to do and provides information about the effectiveness of the degassing and the extent of subsequent regassing
NOTE 3 Filtration of the water can be helpful to avoid or reduce cavitation by removing particulate matter which can act as cavitation nuclei.
Water contact
Before conducting measurements, it is essential to eliminate all air bubbles from the active faces Once the measurements are finished, a thorough inspection of the active faces must be performed, and any measurements will be deemed invalid if air bubbles are detected.
Environmental conditions
The measuring device must include thermal isolation, or the measurement process, including data acquisition, should be conducted to ensure that thermal drift and other disturbances do not impact the overall measured power by more than 2%.
The measuring device shall be protected against environmental vibrations and air flow such that they cause no more than a 2 % effect on the overall measured power.
Thermal drifts
To assess the thermal effects caused by absorbed sound energy in an absorbing target, it is essential to record the measured signal before and after the ultrasonic transducer is activated and deactivated, focusing on changes in expansion and buoyancy.
Measurement uncertainty
General
An estimation of the overall measurement uncertainty or accuracy assessment shall be determined individually for each set-up used This assessment should include the following elements
The uncertainty shall be assessed using the ISO Guide98-3 [5].
Non-planar ultrasound field
The uncertainty in the incident power, arising from the non-plane nature of the field, will be estimated In the absence of a more accurate estimate, this uncertainty is considered to be 50% of the difference between the calculated incident power.
Annex C) and the value which would result from applying the plane-wave Equations 1 or 2 as appropriate.
Balance system with target suspension
The balance system shall be checked or calibrated using small weights of known mass with the whole system prepared for radiation force measurements, the target being suspended in water
The calibration procedure will be conducted multiple times with each weight to assess the random variation in results An estimate of uncertainty for the balance calibration factor will be calculated based on the calibration outcomes and the mass uncertainty of the utilized weights.
The results of these checks should be filed in order to enable a judgement of the long-term stability of the balance calibration factor.
Linearity and resolution of the balance system
The linearity of the balance system shall be checked at least every six months as follows
To ensure accurate measurements, at least three weights of varying masses must be used within the balance's output range, as outlined in section 6.4.3 The relationship between the balance readout and input mass can be illustrated in a graph, as shown in Figure 1 Ideally, the plotted points should form a straight line beginning at the origin Any deviations from this linearity will necessitate the calculation of an additional uncertainty contribution.
Weights under 10 mg are challenging to manage, so balance linearity can be assessed using an ultrasonic transducer with defined characteristics By varying the voltage amplitude, different levels of radiation force can be generated In this context, the ultrasonic output power of the transducer is plotted on the x-axis of Figure 1, with its associated uncertainty considered.
The limited resolution of the balance leads to a power uncertainty contribution that needs to be taken into account in the uncertainty analysis.
Extrapolation to the moment of switching the ultrasonic
To determine the radiation force value using an electronic balance, the output signal is recorded over time and then extrapolated to the moment the ultrasonic transducer is activated or deactivated This extrapolation introduces uncertainty, primarily influenced by the scatter in the balance output signal, which is related to the signal-to-noise ratio.
The uncertainty of the extrapolation result shall be estimated by means of standard mathematical procedures in utilizing the regression algorithm.
Target imperfections
The influence of the target imperfections shall be estimated using a plane-wave approach such as described in A.7.5 of IEC 61161:2013
An uncertainty estimate for changes in target properties will be based on stability investigations conducted with a source of known acoustic power The findings from these assessments should be documented to evaluate the long-term stability of sensitivity to acoustic power.
Reflecting target geometry
The influence of the reflecting target geometry shall be estimated and incorporated into the overall system uncertainty.
Lateral absorbers in the case of reflecting target
The imperfections of the lateral absorbers shall be estimated and incorporated into the overall system uncertainty.
Target misalignment
The influence of target misalignment shall be estimated and incorporated into the overall system uncertainty.
Ultrasonic transducer misalignment
The influence of ultrasonic transducer misalignment shall be estimated and incorporated into the overall system uncertainty (See A.7.9 of IEC 61161:2013)
Water temperature
The uncertainty caused by water temperature shall be estimated and incorporated into the overall system uncertainty (See A.7.10 of IEC 61161:2013)
Ultrasonic attenuation and acoustic streaming
The uncertainty caused by ultrasonic attenuation and acoustic streaming shall be estimated and incorporated into the overall system uncertainty (See A.7.11 of IEC 61161:2013)
Foil properties
When utilizing a coupling or shielding foil in radiation force measurements, it is essential to consider the transmission loss of the foil, whether measured or estimated Additionally, the potential impact of reflected waves on the ultrasonic transducer must be evaluated Each of these factors contributes to the overall system uncertainty and should be assessed individually.
Finite target size
The effect on uncertainty of the finite target size shall be determined and included in the overall system uncertainty (See A.7.13 of IEC 61161:2013)
Environmental influences
The uncertainties caused by environmental vibrations, air flow or temperature variations shall be estimated and incorporated into the overall system uncertainty (See A.7.16 of
Excitation voltage measurement
The measurement of the excitation voltage applied to the ultrasonic transducer is crucial for accurate ultrasonic power measurement Therefore, it is essential to estimate the measurement uncertainty of this voltage and include it in the overall system uncertainty.
Ultrasonic transducer temperature
When comparing ultrasonic power values at various temperatures, it is essential to assess the relationship between power and temperature, ensuring that this influence is considered Refer to A.7.18 of IEC 61161:2013 for further guidance.
Nonlinearity
This article evaluates the potential impact of nonlinearities on overall system uncertainty, focusing on several key factors: the linearity of the balance system and target suspension, nonlinear effects from inadequately degassed water, ultrasonic attenuation, acoustic streaming, and the theoretical relationships of radiation force.
Other sources
Periodic checks are essential to ensure that the overall uncertainty, as outlined in sections 6.4.2 to 6.4.18, remains unaffected by other sources of random scatter For further details, refer to A.7.21 of IEC 61161:2013.
Calculation of output power
To determine the output power, it is essential to calculate it from the incident power while considering the impacts of attenuation, nonlinear loss, and acoustic streaming in the water path between the transducer and the target.
The output power to incident power ratio is influenced by factors such as distance, frequency, and target geometry, and in cases of nonlinear propagation, it also depends on the drive voltage For additional details, refer to Annex E.
To verify linearity, one can use small weights of known mass, where the input quantity is the mass of these weights Alternatively, if linearity is assessed through the radiation force generated by an ultrasonic transducer with defined characteristics, the input quantity becomes the ultrasonic output power of the transducer.
Figure 1 – Linearity check: balance readout as a function of the input quantity
General
The expansion method [6], [7] relies on measuring the change in buoyancy of an expansion target caused by thermal expansion of a liquid inside a target suspended in a water bath
The change in volume is directly proportional to the absorbed energy, assuming no energy loss occurs to the surrounding medium through thermal conduction or convection, and remains unaffected by the focusing or angle of incidence.
The expansion balance features a target linked to a balance that responds to vertical forces An ultrasonic beam is aimed at the entry window of the expansion target, allowing for the measurement of buoyancy changes by the balance.
When using a vertically acting gravimetric balance, it is beneficial to position the transducer to face either vertically up or down This orientation allows for the simultaneous measurement of radiation force alongside the expansion measurement.
The time-averaged incident power shall be determined using Equation 3:
B is the change in the buoyancy force, and t 0 is the duration of insonation
In certain situations, the forces exerted on a target by acoustic streaming can be substantial when compared to changes in buoyancy To accurately assess the extent of buoyancy changes in these instances, it is essential to implement corrective measures, which may involve applying a theoretical correction or utilizing a streaming foil positioned near the target For further details, refer to Annex E.
The uncertainty in the incident power due to streaming forces shall be estimated
The incident power should be measured with the transducer driven in a way similar to its intended clinical use (e.g continuous-wave or with the usual clinical pulsing sequence)
NOTE 2 It is not generally necessary to use a different pulsing sequence to avoid damage or to maintain compatibility with the time response of the balance
Further background information about the requirements in the remainder of Clause 7 can be found in Annex A of IEC 61161:2013.
Requirements for equipment
Target type
An example expansion target is described in Annex D
The expansion target is a container filled with a liquid that absorbs ultrasound and expands when heated It features an entry window that is nearly transparent to ultrasound within the desired frequency range, while the rest of the container is designed to minimize heat transfer to and from the absorbing liquid This target is suitable for immersion in a water bath and includes a mechanism for attachment to a balance The entry window can be oriented vertically, horizontally, or in any other convenient position.
When selecting the size and shape of the target for the transducer measurement, it is crucial to ensure that the target's length meets the specifications outlined in section 7.2.1.3 for the relevant frequency Additionally, it is important to consider the energy that escapes through the target's sidewalls to ensure compliance with the same section.
NOTE A cylindrical target with an entry window on one end is often convenient, but any other geometry may be used and may be necessary for certain transducer configurations
The characteristic acoustic impedance of the liquid shall be between 1,33 × 10 6 kg/m 2 s and
1,63 × 10 6 kg/m 2 s The expansion ratio of the liquid shall be known and shall be constant to within 2 % over the temperature range 10 °C to 60 °C
NOTE 1 This range of acoustic impedance results in an amplitude reflection coefficient of less than 5% consistent with the requirement of 6.2.1.2 for radiation force measurement
NOTE 2 Annex D gives an example of a liquid which meets these requirements
An expansion target shall absorb at least 98 % of the energy incident on the entry window, otherwise a correction shall be applied
To minimize the risk of permanent thermal and mechanical damage from ultrasound exposure, it is essential to select appropriate absorbing materials and target designs Any temporary variations in the amplitude reflection factor or acoustic energy absorption must ensure that the overall measured power is affected by less than 2%; otherwise, a correction is necessary.
The entry window must exhibit an energy reflection factor of less than 2% within the specified frequency range To reduce coherent reflections during measurements on a collimated transducer, the entry window should be positioned at a slight angle relative to the transducer's axis of symmetry.
The expansion target must either have thermal insulation or the measurement process, including data acquisition and analysis, should be conducted to ensure that thermal losses from the absorbing liquid to the water tank or other internal components do not exceed 2% of the overall measured power; otherwise, a correction must be applied.
Heating of the absorbing liquid near the entry membrane increases with frequency, becoming significant at frequencies above 3 MHz This necessitates corrections for heat loss during and after the insonation period.
Entry window diameter
The entry window must be sufficiently large to capture at least 98% of the ultrasound energy directed at the measurement plane For calculating the necessary target diameter, refer to the formulae provided in Annex B, which are specifically applicable to radiation force measurement.
Balance / force measuring system
The balance shall be sensitive to forces in the vertical direction and shall have sufficient resolution for the change in buoyancy to be measured
NOTE A longer insonation period will result in a larger change in buoyancy and smaller uncertainty due to balance resolution However the uncertainty due to thermal losses and extrapolation may increase.
System tank
Since an expansion target is absorbing, it is not necessary to use an absorbing lining for the measuring vessel.
Target support structures
In static-force balances, it is essential to design the structural members that support the target and extend through the air-water interface to minimize the impact of surface tension and buoyancy variations due to water level changes, ensuring these effects remain below 2% of the total measured power.
Transducer positioning
The ultrasonic transducer mount must ensure stable and consistent positioning of the transducer relative to the target, maintaining that variations in overall measured power remain within 2%.
Anti-streaming foils
To ensure accurate measurements, the expansion target must either be equipped with an anti-streaming foil to prevent acoustic streaming in the water path or the measurement process, including data acquisition and analysis, must be designed to minimize the impact of streaming forces to an acceptable level.
2 % effect on the overall measured power, otherwise a correction shall be applied
To ensure optimal performance, an anti-streaming foil must be placed near the target and should not be aligned parallel to the ultrasonic transducer's surface It is essential to know its transmission coefficient through measurement, and a correction should be implemented if its impact exceeds a specified threshold.
2 % of the overall measured power
NOTE In practice a tilt angle of 5 ° to 10 ° has been found to be adequate.
Transducer coupling
The ultrasonic transducer shall be coupled to the measurement device such that the impact on the overall measured power is less than 2 %, otherwise a correction shall be applied.
Calibration
The expansion balance shall be calibrated as a force measuring device by the use of small weights of known mass
Buoyancy sensitivity must be assessed annually using either a collimated ultrasonic source with a known output power (ka>30) or an internal electric heating element with a specified heat output This evaluation should occur more frequently if there are signs of changes in balance sensitivity to ultrasonic power or if the properties of the absorbing liquid may alter over time due to factors such as water uptake, oxygenation, or microbial growth.
NOTE 1 The output power of a collimated source with ka>30 can be measured with uncertainties of less than 5% using a radiation force target
NOTE 2 More information about determining the buoyancy sensitivity can be found in D.3 and in [6] and [7].
Requirements for measuring conditions
Lateral target position
The lateral position of the target during measurement shall be stable and reproducible to an extent that related changes in overall measured power do not exceed 2 %.
Transducer/Target separation
The distance between the ultrasonic transducer surface and the target, including any foil used, must be accurately known and consistently reproducible to ensure that variations in the overall measured power remain within 2%.
Water
The liquid used for the measurements shall be water
For output powers exceeding 1 W, it is essential to use degassed water, following the procedures outlined in IEC 62781 The water must be adequately degassed to prevent visible bubble formation in the water path or on the transducer and target surfaces Any measurements taken in the presence of air bubbles must be disregarded It is preferable that the total amount of dissolved gas in the water is minimized.
< 2 mg/l during all measurements, and may need to be lower in some cases
The use of degassed water is also recommended for determining output powers below 1 W
Bubbles may form on surfaces in gassy water if the temperature of the water increases
Ultrasound can induce bubble formation, even at power levels below 1 W if the beam area is sufficiently small Therefore, it is essential to inspect for bubbles on both the transducer and target surfaces before, during, and after each measurement.
NOTE 1 The gas level required to prevent bubble formation will depend on many factors including acoustic working frequency and maximum negative pressure in the water path Changing or fluctuating radiation force may indicate the formation of bubbles
NOTE 2 Chemical degassing methods which remove only one or a few gas components (e.g the use of Na 2 SO 3 ) are not generally sufficient for HITU measurements Provided more general methods of degassing are used, monitoring of the oxygen content is simple to do and provides information about the effectiveness of the degassing and the extent of subsequent regassing
NOTE 3 Filtration of the water can be helpful to avoid or reduce cavitation by removing particulate matter which can act as cavitation nuclei.
Water contact
Before starting the measurements, all air bubbles shall be removed from the active faces
After measurements are completed, the active faces shall again be inspected, and the measurements shall be discarded if any air bubbles are found.
Environmental conditions
The measuring device must include thermal isolation, or the measurement process, including data acquisition, should be conducted to ensure that thermal drift and other disturbances do not impact the overall measured power by more than 2%.
The measuring device shall be protected against environmental vibrations and air flow such that they cause no more than a 2 % effect on the overall measured power.
Thermal drifts
To assess the thermal effects caused by energy transfer between the target and the surrounding water, the weight of the target will be measured before and after activating and deactivating the ultrasonic transducer.
Measurement uncertainty
General
An estimation of the overall measurement uncertainty or accuracy assessment shall be determined individually for each set-up used This assessment should include the contributions described in 7.4.2 to 7.4.15
The uncertainty shall be assessed using the ISO Guide [5].
Buoyancy sensitivity
The uncertainty in the buoyancy sensitivity shall be evaluated The factors contributing to the uncertainty in buoyancy sensitivity will depend on the method for determining the sensitivity.
Non-planar ultrasound field
The expansion method does not rely on any plane-wave assumptions so there is no uncertainty contribution due to any non-plane nature of the ultrasound field.
Balance system including target suspension
The balance system shall be checked or calibrated using small weights of known mass with the whole system prepared for use, including with the target suspended in water
The calibration procedure will be conducted multiple times with each weight to assess the random variation in results An estimate of the uncertainty for the balance calibration factor will be calculated based on the calibration outcomes and the mass uncertainty of the utilized weights.
The results of these checks should be filed in order to enable a judgement of the long-term stability of the balance calibration factor.
Linearity and resolution of the balance system
The linearity of the balance system shall be checked at least every six months as follows
To ensure accurate measurements, at least three weights of varying masses must be used within the balance's output range, as outlined in section 7.4.4 The relationship between the balance readout and input mass can be illustrated in a graph, as shown in Figure 1 Ideally, the plotted points should form a straight line beginning at the origin Any deviations from this linearity will necessitate the calculation of an additional uncertainty contribution.
Weights under 10 mg are challenging to manage, so balance linearity can be assessed using an ultrasonic transducer with defined characteristics By varying the voltage amplitude, different levels of buoyancy change can be produced In this context, the ultrasonic output power of the transducer is plotted on the abscissa of Figure 1, and it is essential to consider its uncertainty.
The limited resolution of the balance leads to a power uncertainty contribution that needs to be taken into account in the uncertainty analysis.
Curve-fitting and extrapolation
An electronic balance records output signals over time, necessitating curve-fitting and extrapolation to account for buoyancy changes and thermal drift This process introduces uncertainty, primarily influenced by the scatter in the balance output signal, known as the signal-to-noise ratio To estimate the uncertainty of the results, standard mathematical procedures using a regression algorithm are employed.
Water temperature
The uncertainty caused by water temperature shall be estimated and incorporated into the overall system uncertainty.
Ultrasonic attenuation and acoustic streaming
The uncertainty caused by ultrasonic attenuation and acoustic streaming shall be estimated and incorporated into the overall system uncertainty
Attenuation generally causes uncertainty in the output power measured through buoyancy changes, while the incident power remains unaffected In contrast, acoustic streaming can introduce uncertainty in both incident and output power To estimate the uncertainty from acoustic streaming, one can place a streaming foil near the target and compare the results obtained with and without the foil.
Foil properties
When using a coupling or shielding foil in measurements, it is essential to consider the transmission loss of the foil and the potential impact of reflected waves on the ultrasonic transducer Each of these effects should be individually evaluated and included in the overall system uncertainty assessment.
Finite target size
The effect on uncertainty of the finite target size shall be determined and included in the overall system uncertainty.
Environmental influences
The uncertainties caused by environmental vibrations, air flow or temperature variations shall be estimated and incorporated into the overall system uncertainty.
Excitation voltage measurement
The measurement of the excitation voltage applied to the ultrasonic transducer is crucial for accurate ultrasonic power measurement It is essential to estimate the measurement uncertainty of this voltage and include it in the overall system uncertainty.
Ultrasonic transducer temperature
To compare ultrasonic power values measured at various temperatures, it is essential to examine the relationship between power and temperature, ensuring that this influence is considered in the analysis.
Nonlinearity
The assessment of nonlinearities will evaluate their potential impact on overall system uncertainty, focusing on the linearity of the balance system and target suspension, nonlinear effects from inadequately degassed water, ultrasonic attenuation and acoustic streaming, and increased heat loss from the target due to elevated heating of the absorbing liquid near the entry window.
Other sources
Checks should be performed periodically to determine whether the overall uncertainty as specified in 7.4.2 to 7.4.14 using the above guidelines is not influenced by any other sources of random scatter.
Calculation of output power
To determine the output power, it is essential to calculate it from the incident power while considering the impacts of attenuation, nonlinear loss, and acoustic streaming in the water path between the transducer and the target.
The output power to incident power ratio is influenced by factors such as distance, frequency, and target geometry, and in cases of nonlinear propagation, it also depends on the drive voltage For additional details, refer to Annex E.
Electrical impedance
The electrical impedance of an ultrasonic transducer is frequency dependent and complex
Impedance is usually measured with an impedance analyser and can be expressed in terms of real and imaginary components or as magnitude and phase The data can be provided at a specific frequency or displayed in tables or graphs across a range of frequencies.
To accurately measure electrical impedance, the ultrasonic transducer must be submerged in water, with acoustic reflections minimized through the use of acoustic absorbers It is essential to verify the impact of these reflections on impedance values by adjusting the position of the transducer or absorbers within the water tank over several wavelengths Additionally, the frequency and specific location in the electrical circuit where the impedance measurement is taken should be clearly indicated, such as at the end of a designated length of cable.
The impedance of a transducer can vary with temperature, making it sensitive to the electrical power applied and the duration of excitation due to self-heating effects.
Radiation conductance
The radiation conductance of an ultrasonic transducer varies with frequency and is typically estimated from the output power and the square of the r.m.s drive voltage measured at a specific point in the electrical circuit This data is often provided at a designated frequency but can also be displayed in tables or graphs across a range of frequencies Additionally, it is applicable to multi-element transducers when all elements are driven with the same voltage in a configuration that mimics its intended clinical application.
To determine the radiation conductance, it is essential to measure the r.m.s drive voltage simultaneously and under the same excitation conditions as the output power assessment The frequency and specific location in the electrical circuit for the r.m.s drive voltage measurement must be clearly indicated, such as at the end of a designated cable length It is important to note that the drive voltage may not be sinusoidal, and the r.m.s drive voltage is frequently not equal to 0.707 times the voltage amplitude.
NOTE 1 The r.m.s drive voltage is used (rather than, for instance, peak-to-peak drive voltage) because its value is less affected by distortion of the applied electrical signal
The radiation conductance can vary with temperature, making it sensitive to the electrical power of the transducer and the duration of its excitation due to self-heating effects.
NOTE 3 The radiation conductance is not the same as the real part of the radiation admittance of the ultrasonic transducer or transducer element
NOTE 4 This estimate of relative conversion is affected by electrical losses due to impedance mismatch and cables, and acoustical losses due to backing materials and lens losses.
Efficiency
The acoustic efficiency of an ultrasonic transducer is determined through both electrical and acoustic measurements, typically provided at a specific frequency or across a range of frequencies This measurement is particularly useful for multi-element transducers when all elements are driven in a manner consistent with their intended clinical application, such as continuous wave or standard clinical pulsing sequences To obtain the acoustic efficiency value, the time-average value is calculated using the formula: \$\eta = \frac{P_{el}}{P}\$ (4).
P el is the time average transducer electrical power
For accurate electrical measurements, it is essential to maintain the ultrasonic transducer in the same position and environment as used for measuring output power Additionally, the specific frequency and location within the electrical circuit where the transducer's electrical power is measured must be clearly specified.
(for instance as being at the end of a specified length of cable)
Both powers must be measured using a transducer operated in a manner that reflects its intended clinical application, utilizing drive waveforms such as continuous wave or standard clinical pulsing sequences.
The efficiency of the transducer can vary with temperature, making it sensitive to the electrical power applied and the duration of excitation due to self-heating effects.
Electrical power measurement systems are often designed for specific resistance loads, but the impedance of ultrasonic transducers typically varies from these specifications Therefore, it is crucial to select a method for determining the electrical power of the transducer that aligns with its unique impedance characteristics.
Efficiency in ultrasonic transducers and HITU systems can be defined in various ways, each serving different purposes These alternative definitions are explored in detail.
The measurement of recoil force on a transducer for HITU equipment has been proposed, although the current standard lacks specific guidance or requirements Future amendments may introduce detailed instructions or criteria.
Conventional calorimetry can be utilized to measure power for HITU equipment, although the current standard does not provide specific guidance or requirements Future amendments may introduce detailed instructions or criteria.
Power measurement can be conducted using planar scanning with hydrophones for HITU equipment Currently, the standard lacks specific guidance or requirements, but future amendments may introduce these details Readers are encouraged to stay informed for updates.
The assessment formula (Equation B.1) determines the minimum target radius \( b \) necessary to achieve a radiation force that is at least 98% of that produced by an infinitely large target, ensuring an error of less than 2% [10] This equation is applicable to an absorbing circular target within the field of a continuously vibrating, baffled circular plane piston ultrasonic transducer of radius \( a \) in a non-absorbing medium However, it is important to note that the formula may not be suitable for measurements based on buoyancy changes, so users should evaluate its appropriateness for their specific applications.
In ultrasonic measurements, the distance \( z \) between the target and the transducer is crucial, with the wavelength \( \lambda \) of the ultrasonic wave in the medium playing a significant role The circular wavenumber is defined as \( k = \frac{2\pi}{\lambda} \), and the normalized distance between the target and the transducer is expressed as \( s = \frac{z\lambda}{a^2} \).
Equation (B.1) can be rearranged to solve for s, providing the maximum normalized distance between the target and the ultrasonic transducer for a specified target radius b The effects of absorption and acoustic streaming are analyzed independently.
By way of precaution, b should never be reduced below 1,5a, even if this were possible in accordance with the above equation
The formulas mentioned are primarily designed for absorbing targets, but they can also help determine the suitability of a reflecting target when using a diverging beam In this context, \( b \) represents the radius of the largest cross-section of the target, which, for a convex-conical reflector, corresponds to the base of the cone Meanwhile, \( z \) denotes the distance from the transducer to that cross-section.
The assessment procedure for determining the minimum radius \( r \) of an absorbing circular target differs from the method outlined in B.1 The key criterion is that the radiation force must be at least 98% of the radiation force that would be present if the target had an infinite cross-sectional area.
For a spherically curved transducer, the focal length and target distance should be measured from the "bottom of the bowl." To obtain the values of d and z, it is necessary to subtract the depth of the bowl from these measurements.