Instrument Characteristics

1. Instrument Characteristics • Scientific Instrument: • A device for making a measurement. • Measurement: • An action intended to assign a number as the value of a physical quantity in stated units.

2. The function of a scientific instrument, therefore, is primarily to convert the quantitative aspect of some natural phenomenon into a series of recognizable coincidences in time and space. • No instrument will perfectly indicate the “true” quantitative aspect of the phenomenon.

3. Therefore, no statement of the result of a measurement is complete unless it includes an estimate (necessarily in statistical terms) of the probable magnitude of the uncertainty. The uncertainty is the interval within which the true value of a quantity can be expected to lie with a stated probability.

4. Characteristics of Instruments • Static Performance Characteristics: • A measure of how well a sensors observed output reflects the input at one particular time. (After the sensor has ceased changing in response to the input.) • Dynamic Performance Characteristics: • A measure of how well a sensor responds to changing input over time.

5. Static Characteristic Determinations • All input variables other than the primary one should be minimized and quantified as much as possible so the user may know what change in the sensor response was due to the primary input. • Typically, the instrument is placed in a controlled environment chamber, allowed to come to steady state and the “read.” This is done over a range of input values..

6. The better the secondary inputs are understood, the better the response of the instrument to the primary input and the instruments measurement ability can be understood.

7. Input-Outpud Diagram

8. Static Performance Characteristics • True Value • An ideal value which could be known only if all the causes of error were eliminated (never knowable). • The value which is assumed to characterize a quantity in the conditions which exit at the moment the quantity is observed.

9. Correction • The value added to the result of a measurement to allow for any known errors.

10. Accuracy • Degree to which the response of a sensor conforms to the true environment. The closeness to the truth. • Expression of how close are the limits between which the “true value” exists. • The accuracy of a sensor depends upon the degree and speed of reaction between the sensor and its environment. • Sensor Accuracy • Instrument or System Accuracy

11. Accuracy • Sensor Accuracy • How well the sensor itself responds and conforms to the true environment. • Instrument or System Accuracy • How well the instrument, including the mechanisms, electronics, optical, chemical, mechanical devices respond and indicate the quantitative value of the true environment.

12. Error • Difference between the result of a measurement and the “true value.” • Systematic error: (can correct for) • Either: • Remains constant. • Varies in a known manner. Input/Output Curve

13. Random Error • Varies in an unpredictable manner in magnitude or sign. (cannot correct for) • Spurious (outlier) Errors: • In a series of measurements, the errors may be normally distributed. Outliers fall outside of the normal distribution. • Human error • It is legitimate to discard them

14. Precision • Closeness of agreement between independent measurements of a single quantity obtained by applying a stated measurement procedure several times under prescribed conditions. • Accuracy has to do with closeness to the true value. • Precision has only to do with closeness together of measured values, whether they are accurate or not.

15. Repeatability • Closeness of agreement when random errors are present. • Measurement of the same value determined under the same conditions: • Same environmental conditions • Same observer • Same instrument • Same location • Same technique • Short interval of time between measurements

16. Time interval is short enough for real differences to be unable to develop. • A subset of Precision.

17. Stability/Reproducibility • A measure of how well an instrument maintains it I/O characteristics. • The closeness of agreement between measurements of the same value of a quantity under different conditions. • Different observer • Different location • Long time interval

18. Resolution • Smallest change in a physical variable which will cause a variation in the response of a measuring system. In some fields of measurement it is synonymous with discrimination.

19. Representativeness • The degree to which the value indicated by the instrument portrays the environment in the spatial and time region of the environment desired. • E.g.; How well do values of temperature, pressure and rainfall at a point source (automatic weather station site) represent the mass of air that those values are supposed to represent? • Pressure - fairly well, • Temperature - less well • Rainfall - least of all

20. Sensitivity • The degree to which the instrument responds to changes in the environment. • The slope of the I/O curve. • If the slope changes with time, the instrument is displaying sensitivity (scale factor) drift.

21. Zero Effect / Bias • The amount of displacement of the output from zero when the input is zero. • May require re-calibration of the instrument.

22. Zero Drift • The amount of change of zero bias with time.

24. Range • The maximum and minimum values the instrument can indicate. Also used to refer to the maximum and minimum values for which the instrument remains within its stated accuracy.

25. Span • The difference between the maximum and minimum values. • This usually refers to the values which lie within the stated accuracy of the instrument. • The instrument may respond to values outside these maximum and minimum values but its accuracy decreases beyond stated accuracy.

26. Linearity • The degree to which the I/O curve approaches a straight line. • It is customary to express this measure in terms of the maximum deviation from the reference line divided by the full scale range. • For most instruments, it is desired that they be linear. There is less expense involved to show the instrument output from the sensor input if the input to output relationship is constant.

27. Non-linearity can be important for some instruments. • A dew point hygrometer, which responds non-linearly to humidity, is also highly sensitive in the low humidity range but decreasingly so in the higher hujidity range. Its low humidity sensitivity makes it very suitable for upper-air soundings of humidity.

29. Hysteresis • The difference in output (indicated value) when an input value is approached first with increasing, then with decreasing values, vice versa.

30. Threshold • Smallest measurable input to start / stop indicating as a sensed parameter increases from or decreases toward zero.

32. Dead Band • The range through which the input varies without initiating a response (or indication) from the instrument.

34. Traceability • The property of the result of a measurement or the value of a standard whereby it can be related to stated references, usually national and/or international standards through an unbroken chain of comparisons all having stated uncertainties.

35. Uncertainty • The interval within which the true value of a quantity can be expected to lie with a stated probability. • The uncertainty of a measurement generally consists of several components which may be grouped into two categories according to the method used to estimate the numerical values: • Those uncertainties which may be evaluated by statistical methods.

36. Those uncertainties which may be evaluated by other means: • Previous measured data, • Experience with the sensor, • General knowledge of the behavior of relevant materials and instruments, • Manufacturer’s specifications, • Calibration reports and uncertainties assigned to reference date in handbooks.

37. Upon examining the various static response characteristics, it is evident that not all are of equal significance or importance. An instrument must be chosen that has values of those properties suitable for a particular scientific use. • Hysteresis, drift, threshold, and dead-band are more serious errors which are generally difficult or unable to be corrected.

38. Dynamic Performance Characteristics • Involves evaluating the instruments output astime changes and the element which is being measured changes.

39. Evaluation is by use of differential equations; as above: • Where, x(t) = Output (response) function, the dependent variable. • xI = Input (forcing) function; the final atmospheric value to which the sensor is trying to respond. It is a constant value. • T = Time, the independent variable. • l = Time constant, the system dynamic performance parameter.

40. Rearranging

41. Integrating • Where, • x0 = Temperature output at time = 0 • x = Temperature output at time = t. • xI = Value attempting to reach; final temp.

42. Integrating between the limits gives:

43. If t = l • Thus, when elapsed time, (t), equals the timeresponse of the instrument, (l), then the amount of change that yet needs to occur, (x - xI), is equal to 37% of the total change, (x0 - xI); Or, 63% of the change has occurred when t = l.

45. Time Response • The time elapsed between the signal input and that signal output which is 63% of the amount of change that must occur to indicate the true value.

46. Time Response for liquid thermometers • Varies with • Air Density • Wind velocity

48. Standardization of Instruments • Standard Unit - • A quantity agreed upon to have a value of one by which other units can be measured or expressed. • Standard Procedure - • A method of reproduction of a unit of measurement making use either of fixed values of certain properties of bodies or of physical constants.

49. Standard Instrument - • A measuring device intended to define, to represent physically, to conserve or to reproduce the unit of measurement of a quantity. • Used to calibrate other instruments. • Collective Standard - • A group of instruments which together provide the standard of measurement

50. Primary Standard - • A standard which has the highest qualities in a given field. From its measurement, the closest value to the “true value” can be obtained. • Secondary Standard - • Its value is determined by comparison with a primary standard.