FK8010: Physical Measuring Techniques.
Part 1: Introduction and simple measurements Overview • History of measurements - theory of science fundamentals • Different types of measurement errors - automatic measurements •Stochastic variables, some statistics, probability densities, correlations, covariance matrixes, estimators, optimal estimators , etc., [Monte Carlo technique]
History and philosophy • Measurement history • Measurement standards • Theory of science • Falsifications (Popper) •The hypothetic-deductive method •Kuhn’s research programs
Topics Observation and measurement • Observations • Measurements • Classifications • The experiment • Sensitivity • Static measurements • Trigger methods • Human sensory systems
Reliability • Measurement reliability • Systematical errors • Statistical or random errors • Hysteresis and drifts • Automatic measurements
FK8010: Physical Measuring Techniques.
Measurement history Measurements of weight, size, distance and time were used very early in the history of our civilization. (caveat) To make a measurement you need a reference to compare with • Body parts were used as reference thumb (inch), foot, yard, fathom etc (caveat) OK for one person and similar for persons of the same general size • Nearly invariant relations were fixed i.e. 12 inches to a foot, 3 feet to yard (caveat) If you need better precision, you must use more invariant references (measuring rods, standard weights) • You also need to develop methods and tools for comparisons
“Judgment of the Dead”, from the Temple of Deir-el-Bahari, Egypt, c1025 BC
The oldest known weight measure, the talent, was used in Mesopotamia 3000 BC. It corresponded to between 25 and 50 kilo, depending on when and where.
FK8010: Physical Measuring Techniques. Show me the money • Measurement were used to simplify transactions were goods and services were exchanged Taxations require measurements • Important to record and measure agricultural areas. Surveying was developed by the Babylonians Length and weight (stones) references from 3000 BC were found in Babylonian excavations. In the Indus valley high precision references allowing reliable measurements down to the mm level were used around 2000 BC • Good references necessary when building large buildings and monuments. • The Egyptians used cubits (6-9 hands = 24-36 fingers)
• Grains of wheat were used as weight units Barleycorn • Grains could also be used to determine volume • Increasing demands for measurement quality.
• Archimedes introduced measurements of composite entities, such as density
• Measuring precision and accuracy must balance manufacturing precision, which in turn determines the construction complexity that can be achieved
FK8010: Physical Measuring Techniques.
Measurement standards
Increasing standardisation
Increasing precision
• The existence of reliable measurement standards promoted trade and commerce It was therefore necessary that the state could guarantee the accuracy of the references • Imperial standards in Rome 12 uncia (inch 2.46 cm) = 1 pes (0.2957 m) 5 pedes = 1 passus double step 125 passus = 1 stadium 1000 passus = 1 mille (1480m) • When the empire dissolved the standards could no longer be maintained leading to a proliferation of measurement units during the medieval period In 1800 there were 112 different alns in Germany • Charlemagne’s foot, “pied du roi”, was a French standard for over 1000 years • Standardization of the yard in England during the 13th century (Edward I) • The metre standard was formally defined in 1793 by Napoleon 1/10000000 of the distance between pole and the equator • Weight, volume and liquid volume, decimal system John Wilkins (1668) • Standardization in Sweden 1665 – Stiernhielm • Metre system introduced 1881 • Rail roads required national time standards
FK8010: Physical Measuring Techniques.
Measurement standards Old Swedish measurement units before the introduction of the metre system in 1881
Length units before 1881
Surface units before 1881
Verklinje Verktum Qvarter Aln Famn Gammal mil
= 2.061 mm = 24.74 mm = 14.85 cm = 59.38 cm = 1.781 m = 10.69 km
Engelsk tum
= 25.40 mm
Decimallinje Decimaltum Föt Stång Ref
= 2.969 mm = 29.69 mm = 29.69 cm = 2.969 m = 29.69 m
Qvadratverktum Qvadrataln Qvadratfamn Kappland Tunnland
= 6.122 cm2 = 35.26 dm2 = 3.173 m2 = 154.3 m2 = 4936 m2
Qvadratdecimallinje = 8.815 mm2 Qvadratdecimaltum = 8.815 cm2 Qvadratföt = 8.815 dm2 Qvadratstång = 8.815 m2 Qvadratref = 881.5 m2
= 12 =6 =4 =3 = 6000
verklinjer verktum qvarter alnar famnar
= 576 =9 =9 = 32
qvadratverktum qvadrattalnar qvadratfamn kappland
FK8010: Physical Measuring Techniques. Volume units before 1881
Weight units before 1881
Pharmacy weights before 1870
Jumfru Qvarter Kubikaln Kubikfamn Kubikecimallinje Kubikecimaltum Kubikföt Kubikstång Kanna Våt tunna Torr tunna Kol tunna
= 8.179 cm3 = 327.1 cm3 = 209.4 dm3 = 5.653 m3 = 26.17 mm3 = 26.17 cm3 = 26.17 dm3 = 26.17 m3 = 2.167 dm3 = 125.6 dm3 = 146.6 dm3 = 164.9 dm3
Qvintin Lod Skålpund Lispund Skeppund
= 3.321 g = 13.28 g = 425.1 g = 8.515 kg = 170 kg
=4 = 32 = 20 = 20
qvintin lod skålpund lispund
Kom Ort Skålpund Centner Nyläst
= 26.17 mg = 26.17 g = 2.167 g = 125.6 kg = 146.6 kg
= 100 = 100 = 100 = 100
kom ort skålpund centner
Gran Skrupel Drakma Uns Liber
= 61.84 g = 1.2371 g = 3.7112 g = 29.6899 g = 356.2796 g
= 20 =3 =8 = 12
= 40 = 64 = 27
jumfrur qvarter kubikalnar
gran skrupel drakma uns
FK8010: Physical Measuring Techniques.
The MKSA system
The 7 basic units:
2 supplementary units
19 derived units with own names:
Length Mass Time Electric current Temperature Light intensity Substance amount Angle Solid angle Frequency Force Pressure Energy, work Power Charge Electrical potential, voltage Capacitance Resistance Conductance Magnetic flux Magnetic flux density Inductance Celsius temperature Light flux Luminance Activity (radioactive) Absorbed dose (ionizing rad.) Dose equivalent (ionizing rad.)
meter, m kilogram, kg second, s ampere, A kelvin, K candela, Cd mole, mol radian, rad steradian, sr hertz, Hz newton, N pascal, Pa joule, J watt, W coulomb, volt, V farad, F ohm, W siemens, S weber, Wb tesla T henry, H Celsius, oC lumen, lm lux, lx becquerel, Bq gray, G sievert, sv
physics definition kilogram, prototype physics definition physics definition physics definition physics definition physics definition geometric definition geometric definition s-1 kg.m.s-1 N.m-2 N.m J.s-1 A.s W.A-1 C.V-1 V.A-1 A.V-1 V.s-1 Wb.m-2 Wb.m-2 K cd.sr lm.m-2 s-1 J.kg-1
FK8010: Physical Measuring Techniques.
The theory of science Aristotle's theory of science was used until the renaissance Simple observations (but no experiments) & reasoning knowledge However, it was successful in explaining many phenomena.
Inductionism was introduced during the 17th century by Francis Bacon Here knowledge was derived from experience via observations The observations must be general and without preconceived assumptions From observations one can draw conclusions
The principle of induction allows generalizations from a large number of observations. Problems/Fundamental questions: •When do you have a sufficient number of observations •When are all special observation situations covered •How do you make observations without preconceived assumptions
FK8010: Physical Measuring Techniques.
Falsifications (Karl Popper) •A theory cannot be verified by induction - only falsified by observations or experiments
Falsified theories must be replaced •Trivial hypotheses (ad hoc) explaining the falsification as caused by an exception in the specific case, not useful •A new hypothesis should present new predictions that can be falsified. Increased predictive power. •Progress is thus made via trial and error.
Problems with the falsification method: •Observations rely on assumptions (theories) that may be wrong •If a hypothesis is falsified by an observation (experiment) it may be that it is the observation that is false, not the hypothesis •Experimental results are seldom absolute but are mostly given as confidence intervals
FK8010: Physical Measuring Techniques.
The hypothetic-deductive method The falsification method is also called the hypothetic-deductive method H-D asserts hypothesis which are tested against reality A hypothesis can be regarded as a temporal truth, valid as long as it agrees with observations
Hypothesis 2
Hypothesis 1
Range: H1 H2 Increasing the empirical base H2
H1+H2
Unifying theories
H3>H1+H2
H1
H2
FK8010: Physical Measuring Techniques.
Kuhn’s research programs Thus falsifications are seldom absolute •Statistically based falsifications may tell you that the hypothesis is false e.g. with 95% probability In that case one falsification will not be sufficient to disprove a theory •A paradigm contains relevant laws of nature, how they are interpreted and all the concepts required to manipulate them.
Prescience
normal science increasing number of falsifications
crisis, revolution new paradigms
paradigm shift
FK8010: Physical Measuring Techniques.
Observations Are the source of knowledge in all empirical sciences. The observational conditions must be carefully specified to make the observations reproducible. The problem is sometimes to know what conditions to record
The observations may be: •Quantitative •Qualitative •Qualitative and quantitative
Measurements Classifications Event counting
FK8010: Physical Measuring Techniques.
Measurements There is no way to predict the exact result of a measurement because there are always factors beyond our control that will affect the result However there are ways to predict how a result can vary •One way is to study how the uncertain factors vary and analyze how they affect the result •Another way is to make many measurements and find out how the result varies Statistically, measurement results are stochastic variables •Stochastic or random variables do not have one fixed value •They have a range of values that may occur with different probabilities •Stochastic variables x are defined by their range and a probability function P defined on this range
f(x)=P(x RX R3 R2 R1
Um=0 -->
ZX R2
1 jC3 R1 1 jC3 R3
U Zx
FK8010: Physical Measuring Techniques.
Trigger methods In order to process large amounts of data produced in modern physics experiments, it is often necessary to use loose selection criteria during data acquisition that only select events are likely to be of the desired type.
•This selection process is called a trigger. An ideal trigger eliminates all uninteresting events, i.e. it makes an efficient data reduction, without losing the real events.
Since a real trigger seldom completely succeeds in removing the background and the trigger efficiency is seldom 100%, some real events will escape the trigger. Such a limitation can be accepted if the effects are known and understood so that the results can be corrected accordingly.
FK8010: Physical Measuring Techniques.
Human sensory systems
•Receptor •Peripheral treatment of data •Nerve transmission •Analysis – synthesis •Feed-back – active peripheral processing •Reflexes •Specific and general emotional processes •Conscious processes
FK8010: Physical Measuring Techniques.
Measurement reliability
Mistakes and failures, systematic errors, statistical errors
Mistakes • The human factor • The more measurements, the more manual recordings the larger the probability of a mistake
Failures • During time critical experiments it is important to quickly isolate, identify and repair the instrument failure to resume the measurement • Measure more than necessary – create redundancy • Check consistency
FK8010: Physical Measuring Techniques.
Systematical errors Depends on limitations and errors in the assumed model of the measurement process • Large systematical errors = poor accuracy • Systematical errors can be reduced by calibrations The chain of calibrations that connects an instrument with the definition of the measuring unit is called the traceability chain of the measurement If the measuring process is linear it is in principle enough to adjust 0 and make sure one point is calibrated
If the measurement is nonlinear it is necessary to calibrate several points
Systematical errors typically appear • via instrumentation errors, • via external influences or • via the influence of the measurement process on the object itself
FK8010: Physical Measuring Techniques.
Statistical or random errors •The size of these errors are related to the precision. Identify the fluctuating parameters. •Repeat and form averages Reduced statistical errors and increased precision
Precision and accuracy are not necessarily connected
But they may be
FK8010: Physical Measuring Techniques.
Hysteresis and drifts
Hysteresis means that the actual value depends on how it was reached
• The hysteresis may be due to magnetic or mechanical effects (play)
Drifts are temporal instabilities in the equipment
• Often thermal causes to instability Wait until stable • The measuring time is often correlated with the achieved accuracy
FK8010: Physical Measuring Techniques.
Automatic measurements Control unit
Addressing Standardizing Protocol Intrument bus
Storage unit
Presentation unit
Measuring instruments Sensor Detectors
Actuators Object Environmental control
The solution to many measurement problems: use automatic measuring systems • Automatic readings and records reduces mistakes • Self diagnostics flags faulty performance in the system.
• Many calibrations reduce systematical errors. • The statistical errors can be reduced by more acquiring measurement data than what is practically possible with manual methods • The measurements can be made faster thus reducing drifts • The measurements can be made in such a way that hysteresis is avoided.
