1. Measurement Characteristics Meelis Sildoja

2. 26.04.2006 2Measurement Characteristics - Meelis Sildoja, MRI Introduction  Measurement is the experimental process of acquiring any quantitative information. When doing a measurement, we compare the measurable quantity – measurand - with another same type of quantity. This other quantity is called measurement unit  Measurand – a physical quantity, property, or condition which is measured

3. 26.04.2006 3Measurement Characteristics - Meelis Sildoja, MRI Measurements  Can be divided into direct or indirect measurements  Direct measurement – measured quantity is registered directly from the instruments display.  Measuring voltage vith voltmeter  Measuring length with ruler  Indirect measurement – result is calculated (using formula) from the values obtained from direct measurements  Finding work done by current:  U – voltmeter  I – ammeter  t – clock  A=U * I * t

4. 26.04.2006 4Measurement Characteristics - Meelis Sildoja, MRI Classification of physical quantites  Can be divided for quantities which value  is determined uniquely and does not depend on the zero level  mass  can only be determined as a reference to some fixed zero level  potential energy (zero level can be ground floor or 3d floor and result depends on that)  Time  but time interval and change in potential energy belong to the upper class

5. 26.04.2006 5Measurement Characteristics - Meelis Sildoja, MRI Measurements main equation  The value of the measured quantity can be expressed as  where [Y] is the measurement unit and y is the number, which shows how many times the measurable quantity differs from the unit

6. 26.04.2006 6Measurement Characteristics - Meelis Sildoja, MRI What is instrument  Instrument is a device that transforms a physical variable of interest (the measurand ) into a form that is suitable for recording (the measurement)  An example is ruler  the measurand is the length of some object  the measurement is the number of units (meters, inches, etc.) that represent the length  In order for the measurement to have consistent meaning, it is necessary to employ a standard system of units

7. 26.04.2006 7Measurement Characteristics - Meelis Sildoja, MRI Simple Instrument Model  The key functional element of the instrument model is the sensor, which has the function of converting the physical variable input into a signal variable output  Due to the property that signal variables can be manipulated in a transmission system, such as an electrical or mechanical circuit, they can be transmitted to a remote output or recording device  In electrical circuits, voltage is a common signal variable Measurement Physical Process Display Physical Measurement Variable Signal Variable SENSOR XSM Measurand

8. 26.04.2006 8Measurement Characteristics - Meelis Sildoja, MRI Simple Instrument Model Common physical variablesTypical signal variables Force Voltage Length Current Temperature Displacement – spring of newtonmeter Acceleration Light – change in intensity Velocity Pressure Frequency Capacity Resistance Time …

9. 26.04.2006 9Measurement Characteristics - Meelis Sildoja, MRI Simple Instrument Model  If the signal from Sensor output is small, it is needed to be amplified. In many cases it is also necessary for the instrument to provide a digital signal output for connection with a computer- based data acquisition systems. Physical Process Output Physical Measurement Variable Analog Signal Variable SENSOR XS Measurand AMPLIFIER A/D Converter Digital Signal Variable Computer Memory Analog Signal Variable

10. 26.04.2006 10Measurement Characteristics - Meelis Sildoja, MRI Sensors  Sensor - the part of a measurement system that responds directly to the physical variable being measured  Sensors can be categorized into two broad classes  Passive sensors  Active sensors

11. 26.04.2006 11Measurement Characteristics - Meelis Sildoja, MRI Passive Sensors  Passive sensors do not add energy as part of the measurement process, but may remove energy in their operation, ie energy is converted to measurable quantity  One example of a passive sensor is a thermocouple, which converts a physical temperature into a voltage signal

12. 26.04.2006 12Measurement Characteristics - Meelis Sildoja, MRI Active Sensors  Active sensors add energy to the measurement environment as part of the measurement process  An example of an active sensor is a radar or sonar, where actively out-sended radio (radar) or acoustic (sonar) waves reflect off of some object and thus measures its range from the sensor Arecibo Observatory in Puerto Rico Besides being most powerful radio telescopes and the largest single unit telescope in the world, it is also a radar  probably the world biggest active sensor though

13. 26.04.2006 13Measurement Characteristics - Meelis Sildoja, MRI Sensor Fusion (uniting of sensors)  Sensor fusion - in this case, two or more sensors are used to observe the environment and their output signals are combined in some manner (typically in a processor) to provide a single enhanced measurement Physical Process SENSOR 1 X1X1 SENSOR FUSION Instruments SENSOR 2 SENSOR 3 X3X3 X2X2 S1S1 S2S2 S3S3 Examples: 1. Sensor output relation to the ambient temp is taken account during the measurements 2. Image synthesis where radar, optical, and infrared images can be combined into a single enhanced image

14. 26.04.2006 14Measurement Characteristics - Meelis Sildoja, MRI Operational Modes of Instrumentation I (Null instrument)  Null Instrument - A measuring device that balances the measurand against a known value, thus achieving a null condition. Two inputs are essential to the null instrument. Null measurement devices usually consist of 1. automatic or manual feedback system that allows the comparison of known standard value, 2. an iterative balancing operation using some type of comparator 3. and a null deflection at parity

15. 26.04.2006 15Measurement Characteristics - Meelis Sildoja, MRI Null instrument  Advantages:  Minimizes measurement loading errors (i.e. alter the value of the measured signal ). Effective when the measurand is a very small value.  minimizes interaction between the measuring system and the measurand, by balancing the unknown input against a known standard input  Achieving perfect parity (zero condition) is limited only by the state of the art of the circuit or scheme being employed  Disatvantages:  Slow - an iterative balancing operation requires more time to execute than simply measuring sensor input. Not suitable for fast measurements i.e. only for static measurements

16. 26.04.2006 16Measurement Characteristics - Meelis Sildoja, MRI Null instrument - example  An equal arm balance scale with manual balance feedback  Potetntiometer AB is the potentiometer wire with resistance R 1. The EMF of a standard DC source is  volts. The rheostat resistance is R. If the null point is obtained at point C, then the EMF of  and  1 are equal

17. 26.04.2006 17Measurement Characteristics - Meelis Sildoja, MRI Operational Modes of Instrumentation II (Deflection instrument)  Deflection instrument - a measuring device whose output deflects (deviates) proportional to the magnitude of the measurand  Deflection instruments are the most common measuring instruments  Advantages:  high dynamic response i.e. can be used for fast measurements  can be designed for either static or dynamic measurements or both  Disadvantages:  by deriving its energy from the measurand, the act of measurement will influence the measurand and change the value of the variable being measured. This change is called a loading error.

18. 26.04.2006 18Measurement Characteristics - Meelis Sildoja, MRI Deflection isnstrument - example Spring scale as a deflection instrument. Scale has to be calibrated.

19. 26.04.2006 19Measurement Characteristics - Meelis Sildoja, MRI Flow chart of a deflection instrument  Examples of signal conditioning are to multiply the deflection signal by some scaler magnitude, such as in amplification or filtering, or to transform the signal by some arithmetic function The logic flow chart for a deflection instrument is straightforward (e.g.multiplication of deflection signal due to amplification )

20. 26.04.2006 20Measurement Characteristics - Meelis Sildoja, MRI Analog and Digital Sensors  Analog sensors - provide a signal that is continuous in both its magnitude and its temporal (time) or spatial (space) content  Digital sensors - provide a signal that is a direct digital representation of the measurand. Digital sensors are basically binary (“on” or “off ”) devices. Essentially, a digital signal exists at only discrete values of time (or space)

21. 26.04.2006 21Measurement Characteristics - Meelis Sildoja, MRI Analog sensor  The defining word for analog is “continuous” i.e. if a sensor provides a continuous output signal that is directly proportional to the input signal, then it is analog Thermocouple as an analog sensor

22. 26.04.2006 22Measurement Characteristics - Meelis Sildoja, MRI Digital sensor  A common representation of digital signal is the discrete sampled signal, which represents a sensor output in a form that is discrete both in time or space and in magnitude. A rotating shaft with a revolution counter. Each revolution generates a spike. In this example, the continuous rotation of the shaft is analog but the revolution count is digital. The amplitude of the voltage spike is set to activate the counter and is not related to the shaft rotational speed. Data can be sent either in serial or parallel format

23. 26.04.2006 23Measurement Characteristics - Meelis Sildoja, MRI Analog Readout Instruments  An analog readout instrument provides an output indication that is continuous and directly analogous to the behavior of the measurand  For example  deflection of a pointer or an ink trace on a graduated scale  the intensity of a light beam or a sound wave

24. 26.04.2006 24Measurement Characteristics - Meelis Sildoja, MRI Digital Readout Instruments  A digital readout instrument provides an output indication that is discrete  Many digital devices combine features of an analog sensor with a digital readout or, in general, convert an analog signal to a discrete signal. In such situations, an analog to digital converter (ADC) is required. HP3458A digital multimeter, most widely used device in MRI HP3458A digital multimeter, most widely used device in MRI

25. 26.04.2006 25Measurement Characteristics - Meelis Sildoja, MRI Input Impedance  In the ideal case, the act of measurement should not alter the value of the measured signal. Any such alteration is a loading error  Loading errors can be minimized by impedance matching of the source with the measuring instrument – reduce the power needed for measurement  The power loss through the measuring instrument  where Z(  ) is the input impedance of the measuring instrument, and E(V) is the source voltage potential being measured  To minimize the power loss, the input impedance should be large

26. 26.04.2006 26Measurement Characteristics - Meelis Sildoja, MRI Input impedance - connecting instruments  The potential actually sensed by device 2 will be  The difference between the actual potential E 1 and the measured potential E 2 is a loading error. High input impedance Z 2 relative to Z 1 minimizes this error.  A general rule is for the input impedance to be at least 100 times the source impedance to reduce the loading error to 1%. An equivalent circuit is formed by applying a measuring instrument (device 2) to the output terminals of an instrument (device 1).

27. 26.04.2006 27Measurement Characteristics - Meelis Sildoja, MRI Calibration  Calibration is the relationship between the physical measurement variable (input) and the signal variable (output) for a specific sensor  Calibration curve – graph that characterizes sensor or instrument response to a physical input  Sensitivity of the device is determined by the slope of the calibration curve.  Dynamic range - the difference between the smallest and largest physical inputs that can reliably be measured by an instrument  Saturation - increasing the physical input value to the level where there is no change in output signal dynamic range Saturation region Calibration curve example.

28. 26.04.2006 28Measurement Characteristics - Meelis Sildoja, MRI Error types and sources Systematic errors (bias) – measured values have similar deviation from correct value Random errors (noise)– measured values deviate randomly around mean value. Noise describes the precison of measurements Random error (precision) Systematic error (bias)

29. 26.04.2006 29Measurement Characteristics - Meelis Sildoja, MRI Correct terms  Measurement is described by its discrimination, its precision, and its accuracy  These are too often used interchangeably, but they cover different concepts:  Discrimination - the smallest increment that can be discerned. Term resolution is used as a synonym, but according to the “book", it is now officially decleared as incorrect!  Precision - the spread of values obtained during the measurements. Two terms that should be used here are:  repeatability - variation for a set of measurements made in a very short period  reproducibility – same concept, but for measurements made over a long period  Accuracy - is the closeness of a measurement to the value defined to be the true value

30. 26.04.2006 30Measurement Characteristics - Meelis Sildoja, MRI Discrimination, precision and accuracy thickness of the hole decides the discrimination Better accuracy i.e. Mean value closer to bullseye Better precision i.e. better repeatability Two sets of arrow shots fired into a target to understand the measurement concepts of discrimination, precision, and accuracy

31. 26.04.2006 31Measurement Characteristics - Meelis Sildoja, MRI Systematic error sources  If measurements are made at temperature other than the sensor was calibrated it introduces systematic error. If systematic error source is known, it can be corrected for by the use of compensation methods  Aging of the components will change the sensor response and hence the calibration  Damage or abuse of the sensor can also change the calibration  Invasiveness - the measurement process itself changes the intended measurand. This is key concern in many measurement problems.  Reading measurements by human observer – common error source is parallax i.e. reading dial from non- normal angle  NB! Interaction between measurand and measurement device is always present

32. 26.04.2006 32Measurement Characteristics - Meelis Sildoja, MRI Invasivness - example  Reducing invasivness  to use high impedance electronic devices to measure voltage  Extreme invasiveness  large warm thermometer to measure the temperature of a small volume of cold fluid

33. 26.04.2006 33Measurement Characteristics - Meelis Sildoja, MRI Periodical calibration  In order to prevent systematic errors, sensors should be periodically recalibrated

34. 26.04.2006 34Measurement Characteristics - Meelis Sildoja, MRI Physical Process Environmental Noise SENSOR X AMPLIFIER N1N1 Sensor Noise N2N2 Random error sources  An example for N 1 would be background noise received by a microphone  An example of N 2 would be thermal noise within a sensitive transducer, such as an infrared sensor  A common example of N 3 is 50 Hz interference from the electric power grid Transmission Noise N3N3  The noise will be amplified along with the signal as it passes through the amplifier  Noise is presented as signal to noise ratio (SNR).  SNR(dB)=10*log(Psignal/Pnoise )

35. 26.04.2006 35Measurement Characteristics - Meelis Sildoja, MRI Random noise  What if P signal < P noise ?  If some identifying characteristics of that signal are known and sufficient signal processing power is available, then the signal can be interpreted.  Example of such signal processing is the human ability to hear a voice in a loud noise environment

36. 26.04.2006 36Measurement Characteristics - Meelis Sildoja, MRI Estimating the measurement accuracy  Error is defined as the difference between the measured value and the true value of the measurand  E =(measured) - (true)  where  E = the measurement error  (measured) = the value obtained by a measurement  (true) = the true value of the measurand  Error can almost not be ever known, becuse we don’t know the (true) value, error can only be estimated.

37. 26.04.2006 37Measurement Characteristics - Meelis Sildoja, MRI What is uncertainty?  Uncertainty of measurement is a parameter that describes the distribution of the (thinkable) measured values  The word ‘uncertainty’ expresses the boubt to the exactness of the result of the measurement  Measurement result is the measurement value with its uncertainty

38. 26.04.2006 38Measurement Characteristics - Meelis Sildoja, MRI Classification of uncertainties  Standard uncertainty – uncertainty of a measurement expressed as a standard deviation  Standard uncertainty consists of many components which are divided into two categories  type A uncertainty which is estimated using statistical methods  u A (x), where x denotes the measured value for which the uncertainty is given  type B uncertainty which is estimated using means other than statistical analysis  u B (x)  Combined standard uncertainty -  Expanded uncertainty – Where k is the coverage factor, typically in range 2-3

39. 26.04.2006 39Measurement Characteristics - Meelis Sildoja, MRI How to estimate uncertainties?  Type A – when taking multiple values the distribution of these values corresponds to normal or Gaussian distribution  Where the  x describes the broadness of the curve and its square is called variance   standard deviation     variance

40. 26.04.2006 40Measurement Characteristics - Meelis Sildoja, MRI How to estimate uncertainties II?  Standard deviation  Where x t is the true value  Since we don’t know the true value, we use  Where is the mean value and s x experimental standard deviation  and

41. 26.04.2006 41Measurement Characteristics - Meelis Sildoja, MRI How to estimate uncertainties III?  If you take e.g. 100 measurements and divide them to 10 series each consisting 10 values and then calculate the mean to each series, you can show that the Stdev of the mean of the series is related to the Stdev of one series as follows  Number n under the square-root, is the number of measurements in one series