It is important to realise that the amount of information we can collect is always finite. The example of kitchen scales has introduced us to the limiting effects of clipping, noise, and response time. It doesn't matter how clever we are, these problems occur in all physical systems since they are consequences of the way the real world works. To see some of the other problems which arise when we're collecting information, consider the system in figure 1.2. This diagram represents a diffraction grating being used to measure the power/frequency spectrum produced by a light source.
The system is intended to provide us with information about how bright the light source is at various light wavelengths. It relies upon the reflection properties of a surface made with a series of parallel ridges called a Reflection Grating. For an ordinary plane mirror, the angle of reflection equals the angle of incidence. For a grating, the angle of reflection also depends upon the wavelength of the light and the details of the grooved surface pattern. Hence the arrangement shown acts as a sort of adjustable filter. Only those light wavelengths which reflect at the appropriate angle will make their way through the output slit onto the detector.
As with the kitchen scales, the system provides an indirect way to measure the light's spectrum. We use the angle of the diffraction grating to tell us the wavelength being observed. The voltage displayed on the meter indicates the light power falling on the detector. To discover the light's spectrum we slowly rotate the grating (or move the output lens/slit/detector) and note how the voltmeter reading varies with the grating angle. To convert these angles and voltages into wavelengths and light powers we then need to know the Sensitivity of the detector/amplifier system and the angles at which various wavelengths would be reflected by the grating – i.e. the system must be calibrated.
In most cases the instrument will be supplied with appropriate display scales. The voltmeter will have a dial marked in units of light power, not volts. The grating angle display will be marked in wavelengths, not degrees. These scales will have been produced by a calibration process. If the measurements we're making are important it will probably be sensible to check the calibration by making some measurements of our own on a ‘known’ light source.
As with the kitchen balance, our ability to measure small changes in the light level will be limited by random noise — in this case random movements of the electrons in the measurement system and fluctuations in the rate at which photons strike the detector. The accuracy of the power measurement will depend upon the ratio of the light power level hitting the detector to the random noise. We could increase the light level and improve the precision of the power measurement by widening the slits and allowing more light through. However, this would have the disadvantage of allowing light reflected over a wider range of angles to reach the detector. Since the angle of reflection depends upon the light wavelength this means we are allowing through a wider range of wavelengths.
In fact, looking at the system we can see that it always allows through a range of wavelengths. Unless the slits are narrowed down to nothing (cutting off all the light!) it will always allow light reflected over some range of angles, 
(and hence having a range of wavelengths, 
) to get through. As a result there is an unavoidable ‘trade off’ between the instrument's power sensitivity and its frequency Resolution or ability to distinguish variations in power confined to a narrow frequency interval. This kind of trade off is very common in information collection systems. It stems from basic properties of the physical world and means that the amount of information we can collect is always finite — i.e. we can never make perfect measurements with absolute accuracy or precision or certainty.
Summary
You should now know that information is collected by Instruments which perform some kind of Measurement. That measurement systems usually give an Indirect indication of the measured quantity and that all measurements are Comparisons which have to be Calibrated in some way. The amount of information we can collect is always finite, limited by the effects of Noise, Saturation (or Overload), and Response Time. That many information gathering techniques involve a Trade-Off between various quantities — for example, between the Resolution of a wavelength measurement and the Sensitivity of a related power measurement. That these limitations arise from the properties of the physical world, not poor instrument design.
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University of St. Andrews, St Andrews, Fife KY16 9SS, Scotland.
