Contributed editorial appearing in
Scientific Computing & Instrumentation 17:8, July 2000, pg. 14.
Absolute values do exist. Examples that come to mind include the temperature of absolute zero and hosts of irrational numbers such as pi, the natural logarithm (e), and the square root of 2. However, no one has actually seen one or held it in their hands. Absolute values remain as ideals, archetypes. The difficulty lies in our inability to reach a temperature of absolute zero experimentally or our desire to represent irrational numbers beyond a few million digits. In lieu of the absolute, humans settle for prototypes of the ideal. When performing data acquisition, we estimate the relationship between an observed quantity and the prototype. In order to communicate our findings to others we must agree upon the existence of the prototypes and to their precise value.Assume our data acquisition task is to determine the number of cars in a grocery-store parking lot at a given instance in time. Before the measurement, we must agree upon a prototype of the unit “car”. Do we include pick-ups and mini-vans? Must the cars be parked or can they be in transit? If the parking lot is full, do we include overflow into the lot across the street? As we pore over our system under study, we search for items having high correlation with our prototype and increase the tally as matches are found.
The collection of sanctioned unit prototypes is known as the International System of Units or, from the French, “SI Units”. The prototype for units including length, mass, and time have changed since their inception, but these adjustments result in increased prototype precision. The SI unit prototype of length, the meter (m), originally was one ten-millionth of the length of the meridian passing through Paris from pole to equator. Even given such a large prototype on a human scale, it only differs by 0.2 mm from the modern prototype based on the distance light travels in a vacuum over the interval of 1/299,792,458 of a second. The prototype for mass is a hunk of platinum-irridium alloy defined to be 1 kilogram (kg). Time was formally based on a fraction of the mean solar day, but 1 second (s) is currently defined as 9,192,631,770 periods of the radiation corresponding to a transition in the ground state of cesium-133. As our ability to measure natural phenomena with greater precision increases, prototype complexity increases concomitantly.
Before values obtained from our data acquisition system are useful, we must calibrate the system, i.e. determine its ability to recognize the measurement prototype accurately. Since it is often difficult to have the actual unit prototype on hand, such as constructing our own cesium clock or borrowing the prototype kilogram from France for a few hours, facsimiles of the unit standard, known as calibration standards, are used instead. Documents of certification are delivered with the calibration standard enumerating its pedigree to the actual prototype.
The simplest measurement system for mass is a pair of scales. The unknown mass is placed on one pan and standard masses are added to or removed from the other pan until the scales are brought into balance. Scales reinforce the fact that our data acquisition system is relating the mass of the unknown object to that of the known standards. An absolute measurement is not being performed. Mechanical balances incorporate a permanent set of standard masses and often hide them from view. The ergonomics make the measurement more convenient but do not decrease its dependence on the unit prototype.
Modern data acquisition is most often thought to be exclusively electronic and digital in nature. Two fundamental devices facilitate electronic data acquisition, namely, the differential amplifier and the analog-to-digital converter (ADC). The differential amplifier is analogous in function to the scales used in the determination of mass. As the input voltage (Vin) dips less than a standard reference voltage (Vref), the amplifier output (Vout) becomes increasingly negative. Conversely, Vout increases positively as Vin becomes larger than Vref. When Vin equals Vref, Vout is zero. A voltmeter is constructed when Vout is connected to an analog meter. As in the case of the scales, the two leads from the voltmeter reiterate that the measurement is made relative to a reference value.
An ADC is used to obtain a numerical representation of a voltage. As a number, the value can be stored, transmitted, and used in calculations. An ADC contains a differential amplifier and a digital-to-analog converter (DAC). The voltage to be measured (converted) now serves as the reference voltage (Vref). The voltage generated by the DAC is used as the input voltage (Vin) to the differential amplifier. The output of the DAC is adjusted until it matches the reference voltage and at that condition, the numerical value used to generate the DAC voltage is recorded.
Electronic mass balances use an ADC to measure the amount of electrical current required to suspend the sample in a magnetic field. The amount of current is compared with the values of current required to suspend the calibration masses. In this instance, the calibration masses have been separated temporally, rather than spatially as in the cases of the scales and the mechanical balance. In all three mass-measuring instruments, the use of standard calibration masses is required. Of course, calibration is not limited to mass measurements. Since all instruments make relative measurements, each one requires calibration in order to convey legitimate results to the community. Do you know the date of your last calibration?
