CHAPTER 3

MAKING MEASUREMENTS

When using a new piece of apparatus, try to perform a preliminary experiment in which a basic measurement is made. This will increase familiarity with the equipment and confidence that it is giving a reliable result. For example, with a multimeter, the (electric) potential difference of an AA battery could be measured, expecting the outcome of around 1.5 V. Alteratively measure the resistance of a known resistor. A preliminary experiment should also allow a check to be made that the equipment is working correctly, that it has a suitable range and precision for the experiment and allow an estimate to be made of the uncertainty or error in the measurements.

This section focuses on a range of measuring devices which may be encountered, explaining how they are used and sometimes the underlying physics. Care should always be taken when reading analogue or pointer style meters and scales to avoid parallax errors. These arise when the eyes are not directly above the scale meaning the pointer may line up with an incorrect mark on the scale. Taking large numbers of decimal places from digital meters should also be avoided unless it is known the meter has been calibrated to this resolution and that the result is genuinely meaningful.

The International System of Units is abbreviated SI from the French, Le Système International d’unités. It gives a set of seven base units in which all units can be expressed: see Table 3.1. For example the Newton is equivalent to the kgms⁻² and the Joule is equivalent to kgm²s⁻².

Table 3.1: The SI units

Table 3.2: The SI prefixes

Prefixes are used to show multiples and submultiples of SI units. Table 3.2 shows a list of values.

Figure 3.1: A Vernier Scale. The top is the main scale and the bottom in the traveling scale. The left panel shows a reading of 0.0 mm; The middle panel shows a reading of 0.1 mm; The right panel shows a reading of 0.6 mm.

Vernier calipers (usually with a resolution of 0.01 mm) are used to measure very small distances, such as the thickness of a wire, precisely. Achieving an accurate reading with Vernier calipers is dependent on the skill of the operator. The object must always be clamped squarely between the jaws of the calipers which must be forced into contact with the object to be measured. As both the object and the calipers are slightly elastic, if too much force is applied and the object squashed the calipers will under-read. Conversely, if not enough force is used the calipers will over-read.

A Vernier scale is two adjoining traveling scales with slightly different spacings. The main scale, for example, has divisions every 1 mm. The lower scale has divisions every 0.9 mm. So 10 divisions on the lower scale take 9 mm. This means the tenth division on the lower scale lines up exactly with 9 divisions on the main scale. This can be seen in the left panel of Figure 3.1.

As the lower scale is moved by 0.1 mm, the first division on the lower scale will line up with the first division on the main scale. This is shown in the middle panel of Figure 3.1. The right panel of Figure 3.1 shows a reading of 0.6 mm.

Figure 3.2: A digital calipers measuring; Left: the diameter of a wire and Right: the inside diameter of a pipe.

For objects larger than 1 mm, the number of millimeters on the main scale immediately to the left of the zero mark on the traveling scale must be added to the reading from the traveling scale.

Digital calipers are becoming more and more common as a replacement for Vernier calipers as they are easier and quicker to use. The jaws are closed and the reading is zeroed, usually by pressing the “zero” button. The object to be measured can then be held in the jaws and the distance read from the display. Figure 3.2 shows a digital calipers being used to measure a thin wire (0.68 mm) and the inside diameter of a cylindrical pipe (13.95 mm).

Micrometers use a screw to convert a small linear distance moved into a large rotation which can be read from a scale. A Vernier style scale is also sometimes incorporated to increase the precision of the micrometer. The screw is usually fitted with a ratchet mechanism which allows objects to clamped with a consistent and appropriate force which reduces error due to the elastic nature of the object and the micrometer.

Figure 3.3: A micrometer measuring a: 5.21 mm and b: 3.76 mm

To make a measurement with a micrometer an object is positioned between the jaws. The ratchet screw is turned until it clicks indicating the object is correctly pressed between the jaws. A reading of the lowest half millimeter is taken from the fixed stem of the micrometer. The alignment of the rotating barrel of the micrometer with the axial line on the stem provides an extra decimal place to the reading. For example Figure 3.3a shows the micrometer displaying 5.21 mm and Figure 3.3b shows the micrometer displaying 3.76 mm.

For Figure 3.3a:

Stem Reading	5.00 mm
Barrel Reading	0.21 mm
Total	5.21 mm

For Figure 3.3b:

Stem Reading	3.50 mm
Barrel Reading	0.26 mm
Total	3.76 mm

Digital balances provide an indirect method for finding the mass of an object. Balances which measure to many mass ranges and precisions are available and it should always be ensured that the balance used is appropriate for the measurement needed. For example: it would not be appropriate to use a 0–2 kg balance which reads to the nearest 1 g to try to measure 100 mg of metal, neither is it appropriate to check the mass of a 1 kg standard mass with a 0 - 500 g balance which reads to the nearest 1mg.

Balances involve the use of one or more pressure sensors which produce an electrical output dependent upon the force acting on them. This electrical output has been calibrated by the manufacturer as corresponding to a particular force. This force is then converted to a mass by dividing by an average value for the acceleration due to gravity. According to the latest data from the NASA Grace mission the acceleration due to gravity varies around the Earth by at least 0.001 ms⁻². Thus quoting masses to more than 4 significant figures is inappropriate on balances not calibrated for use in a specific location, although this may not be true for mass differences.

The balance should be positioned directly on a flat surface: ensure there are no wires or other objects under the balance. When making measurements on a table, desk or worksurface ensure that no one touches, leans or sits on the surface as this can sometimes significantly alter the reading on the scale. It is useful to perform a quick experiment to see the significance of this. Some balances have a cover to prevent draughts (possibly from people walking past or convection currents from heating or air conditioning) affecting the results: this should be placed down and closed when any readings are taken.

To take a measurement first ensure that the scale pan is clean and free from loose material and the balance reads zero. If not the “Tare” or “Zero” button should be pressed. If a container is used often to hold powder which is being measured out, this can be placed on the balance before it is zeroed. Finally add the object to be measured to the scale pan and take a reading.

Ammeters measure the current flowing in a circuit. Current is the rate of flow of charge. They are placed in series with the component through which the current is to be measured. To cause the minimum (or no) change to the behavior of the rest of the circuit an ideal ammeter will allow current to flow through with no resistance. In practice ammeters have a very low resistance, which is assumed to be small compared to the circuit being measured. To picture this more clearly consider the equation for the total resistance of resistors in series:

It is required that R_T is as close as possible to the resistance, R of the component. This can be achieved by making R_ammeter as small as possible.

Voltmeters measure the (electric) potential difference (sometimes called the voltage drop) across a component or between two points in a circuit: this is the difference in energy per coulomb of charge. They are placed in parallel with the component across which the (electric) potential difference is to be measured. To cause the minimum (or no) change to the behavior of the rest of the circuit an ideal voltmeter will have an infinite resistance and allow no current to flow through it. In practice, voltmeters have a very high resistance, which is assumed to be large compared to the circuit being measured. To picture this more clearly consider the equation for the total resistance of resistors in parallel:

Table 3.3: Resistor color codes

It is required that R_T is as close as possible to the resistance, R of the component. This can be achieved by making R_voltmeter as large as possible.

Resistors typically have 4 colored lines indicating the size of the resistance. Table 3.3 indicates how to find the resistance.

Frequently ammeters and voltmeters used in the lab will actually be part of a multimeter device. Multimeters are versatile devices capable of making measurements of variables such as current, (electric) potential difference in both AC and DC circuits and resistance. Figure 3.4 shows two typical multimeters. The round dial in the center selects which variable the meter measures as well as the maximum reading measurable in that range. The Ω symbol indicates a resistance measurement, the A symbol indicates an ammeter and the V symbol indicates a voltmeter. The symbol of a solid line above a dashed line indicates DC and the sin wave symbol indicates AC. The setting 20 µA indicates that the maximum reading measurable will be 20 µA and the reading given will be in units of µA. The setting 200 kΩ indicates that the maximum reading measurable will be 200 kΩ and the reading will be given in units of kΩ.

Figure 3.4: Two different multimeters.

Two wires must be connected to the front of the multimeter: one to the black common point and the other to a red point corresponding with the variable being measured.

To measure a resistance using only two connections the multimeter generates a known constant current which it passes through the component or circuit connected to the meter. It then acts as a voltmeter and measures the potential difference across the component. The simple calculation of R = V/I gives the resistance.

The usual method of attaching two wires to a component/sample of material to measure its resistance involves passing current and measuring the (electric) potential difference through the same wires. This has the disadvantage of measuring the sum of the component/sample resistance, contact resistance and the resistance of the measurement wires. In some cases where the component/sample resistance is much higher than the lead resistance this is acceptable as the additional resistance only forms a very small part of the measurement. In the case of samples with resistance O(mΩ) an alternative method must be found especially if the measurement wires have a high resistance (perhaps due to their narrow diameter to reduce the heat load on a cryogenic experiment).

Figure 3.5: Simple diagram of a four-wire method of measuring the sample resistance. R1, R2, R3, and R4 are resistances which represent the contact and lead resistances.

Resistance can be measured by using the four wire method (Figure 3.5) where four wires are separately attached to the sample. Two are used to pass current through the sample and a further two are used to measure the (electric) potential difference across the sample. The source current flows through R1, the sample and R2 and because no current flows through R3 and R4 the (electric) potential difference measured by the voltmeter is just that across the sample.

Figure 3.6: Simple four-wire mounting configuration of a sample to measure resistance along in the direction of the current flow.

Figure 3.6 shows a contact configuration which can be used to measure the resistance of a sample of conductive material. The current is passed through the sample via the two surfaces at each end and the (electric) potential difference is measured over a distance l between the other two contacts. The voltage contacts should be far away from the current contacts to ensure the current flow is uniform and parallel between the voltage contacts. The current contacts should cover the whole of the end surfaces to ensure a uniform flow.

When making electrical measurements in which the resistance of the sample might change, a constant current source is needed. This is not trivial to construct as a cell, battery, or normal power supply all have internal resistance. Recalling that:

where I is the current, ∈ is the EMF of the power source, R is the external resistance and r is the internal resistance of the power source. If R changes, but ∈ and r remain constant then the current in the circuit changes. R and I have a non linear relationship which makes calculation of R given V and I very difficult.

An ideal current source should output the same current regardless of the resistance of the sample or the leads. A number of different methods of generating constant current can be used.

The most straight forward method is to use a variable resistor R_series in series with the sample. An AC or DC supply can be connected to this. Alternatively, if a lock-in amplifier is used they have an internal oscillator which outputs an AC EMF in the range 0 – 5 V. Typically resistors between R_series=1 kΩ and 10 kΩ can be connected to the lock-in amplifier front panel oscillator output and to the sample as shown on the left in Figure 3.7. It is easily seen that the current flowing through the sample is given by:

R_series >> R_sample otherwise as the sample resistance changes for any reason (perhaps due to a change of temperature) the current going through the sample will also change leading to ambiguous results. The value of R_series used is limited by the fact that most lock-in amplifiers can only output 5 V; when a larger R is used, the current becomes very small. Currents need to be sufficiently large to produce a high quality signal above any background noise as well as sufficiently low so that no self heating is detectable in measurements.

An alternative method is to use the (electric) potential difference controlled current source circuit as shown on the right in Figure 3.7. For an op-amp with the non-inverting(+) input connected to ground, the (electric) potential difference between the inverting(-) input and ground is also zero. An ideal op-amp has an infinite input impedance so draws no current from its input circuit implying the sum of the currents (Kirchoff’s First Law) at point A should be zero:

Where V_in is the (electric) potential difference from the lock-in oscillator output; R_i and R_f are the values of the resistors and V_B is the (electric) potential difference between point B and ground. Summing the currents going through the sample gives:

Figure 3.7: Left panel shows a circuit layout of a resistor (typically Rseries = 1 kΩ to 10 kΩ) used as a constant current source. It is connected in series with the sample and the oscillator output on a lock-in amplifier. Right panel shows a circuit diagram of a (electric) potential difference controlled constant current source. The op-amp used is an Linear Technology LTC1150CN8#PBF (RS order number 5455629).

Combining Equations 3.5 and 3.6 gives I_sample which is independent of the sample resistance and is proportional to V_in.

The lock-in oscillator output is connected to V_in and the sample current contacts are those attached to the op-amp output. The current in the sample is given by Equation 3.7.

A final method of generating a constant current is to use a dedicated off the shelf constant current source such as a Keithley 6221 AC and DC current source. This has two current output leads which are connected to the sample.

At a very simplistic level this can be thought of as a voltmeter. It accurately measures very small AC signals by using phase-sensitive detection to extract the signal from an often huge background that would otherwise obscure the signal.

The sample is excited by an AC current at fixed frequency, ω_r, and the lock-in detects the response of the sample at the same frequency along with any background noise, ∑_f V _{f ,sig} Sin(ω_f t + θ _{f ,sig}). It uses a phase sensitive multiplier to multiply this by a self generated reference signal at the same frequency as the current V_L sin(ω_r t + θ _ref).

For each component frequency, ω_f, that is detected this output is two AC signals, one at the difference frequency ω_r−ω_f and the other at the sum frequency ω_r+ω_f, which are then passed through a low pass filter. In the general case for ω_r and ω_f there is no signal from the low pass filter as both signals are AC and are filtered out. If ω_r=ω_f then part of the signal is no longer AC, but DC and proportional to the signal amplitude . This gives the X output of the lock-in. The Y output is obtained by using a second phase sensitive detector to multiply the detected signal by the reference frequency shifted by 90^° which gives an output .

Changing the offset of the reference frequency, θ_ref, alters “the phase” (θ_sig − θ_ref) of the measurement. For a pure resistor in an AC circuit the voltage response is exactly in phase with the current so the phase should be set to zero (θ_sig − θ_ref = 0) meaning that the X (“in phase”) output of the lock-in gives the measured signal (cos(0)=1) and the Y (“out of phase”) output is zero (sin(0)=0). For an inductor the current lags the voltage by 90^° and for a capacitor the current lead the voltage by 90^° thus both these will show up on the Y (“out of phase”) output.

The frequency of the excitation current, ω_r, can be altered on the lock-in. Typically it would be in the region 50–100 Hz: but taking care to avoid the mains electricity frequency (50 Hz in UK and 60 Hz in USA) and its harmonics (factors or multiples).

Figure 3.8 shows the front panel of a Stanford Research Systems (SRS) 830 lock-in amplifier. Usually BNC cables would be connected to the “A” and “B” inputs in the bottom left of the front panel and to the “SIN OUT” or “REF IN” BNC connectors at the bottom right of the front panel.

First, a frequency must be selected for the lockin amplifier to use. The right hand display shows the frequency when the “Freq” button is pressed. It can be adjusted by rotating the dial on the right of the front panel. Often the internal frequency generator is used which outputs a sine wave via the “SIN OUT” connector. This is then used within the circuit - for example see Section 3.12 on constant current sources. If the internal frequency generator is used, the amplitude can be displayed by pressing the “Amp” button and can be changed by rotating the dial.

The frequency can also be selected by supplying a sine wave or squarewave to the “REF IN” input. The “Source” button can be pressed to switch between the “REF IN” signal and the internal frequency. When the lock-in amplifier has not identified a signal to lock on to the “UNLOCK” light is illuminated.

Figure 3.8: The front panel of a Stanford Research Systems (SRS) 830 lock-in amplifier.

The left display (channel 1) would usually be set to show the “X” input which is the in phase component of the signal. The right display (channel 2) would then be set to show the “Y” input which is the out of phase component of the signal. The parameter displayed can be changed by pressing the “Display” button.

The sensitivity panel displays the maximum (electric) potential difference which can be measured in the present range. The range can be changed by using the arrow keys to cycle through the available sensitivities/ranges. Underneath the X and Y display there is a red “bar graph”. This gives a visual representation of size of the signal in proportion to the present range. The range does not change automatically and so needs to be adjusted as the signal amplitude changes.

The time constant setting gives the characteristic time period over which the outputs are averaged. A long time constant can be used to smooth out very noisy signals, but this will increase the response time.

To measure the true signal from a sample the phase should be set correctly. The right hand display shows the phase when the “Phase” button is pressed. For a resistance measurement, as a first approximation, assume the sample is purely resistive and the experimental equipment is sufficiently well designed that it doesn’t cause large capacitive or inductive signals. The phase of the measurement can be set using the “Phase” button on the “Auto” panel of the lock-in. This sets the phase such that the Y output is zero. In most cases this is a perfectly adequate assumption to make. In some cases such as when the sample contacts are not of optimal quality the phase of the measurement needs to be set to account for the phase shift of the true resistive component of the signal. Firstly, the normal measurement circuit shown in the left panel of Figure 3.9 is modified to include a series resistor, approximately of the same resistance as the sample giving the circuit in the right panel of Figure 3.9. The (electric) potential difference across this resistor is then measured with the lock-in. In the ideal case this is a pure resistor so the auto-phase button is pressed to set the phase such that the out-of-phase component, Y, is zero, the phase is then kept at this value when the circuit is then returned to the original configuration for the experiment.

Figure 3.9: Left panel shows the circuit setup for a normal 4-wire measurement configuration. Right panel shows the circuit setup when setting the phase. Current is passed though the sample and a series resistor, R. The (electric) potential difference drop is measured across only the resistor.

There are a number of possible sources of noise/error which might affect electrical measurements such as external electromagnetic fields, ground loops, capacitive coupling, self-inductive effects and inductive cross-talk between wires.

The total impedance of a circuit is given by the sum

where R is the resistance, X_C is the reactance due to the capacitive voltage component with a phase which lags the current by π/2 and X_L is the reactance due to the inductive voltage component which leads the current by π/2. This means that the Y output on the lock-in amplifier contains all the (electric) potential differences of capacitive and inductive origin and is dependent on the frequency of the excitation current ω_r and the X output contains just the resistive component and is independent of frequency. Clearly the resistive, capacitive and inductive components can also be temperature dependent.

The effect of external fields can be reduced by shielding as much of the wiring as possible. This takes the form of a grounded fine woven metal braid and/or metal foil surrounding a set of wires and is built into cables used to connect experimental equipment. Static electromagnetic waves are unable to penetrate a volume of space entirely surrounded by a conducting shield and oscillating electromagnetic waves undergo an exponential decay through the shield [7].

All cable shielding and grounds of equipment should be connected together to a single grounding point. Alternatively the cable shielding is sometimes broken in a certain place to isolate two true ground points from each other. If great care is not taken over this then there may be more than one grounding point in the circuit. An (electric) potential difference can arise between these points which can cause large noise currents to flow and adversely affect the quality of the measured signal significantly.

Inductive cross-talk is noise resulting from the mutual inductance of two or more closed circuits with paths located near each other i.e. the changing magnetic field created by an alternating current in one circuit creates spurious signals in a neighboring circuit according to Faraday’s law V=dϕ/dt. Figure 3.10 shows an arrangement of wires that are subject to cross-talk. In the left wire a current I with frequency ω_r flows. The current creates a magnetic field at distance r from the wire at time t given by

Figure 3.10: Inductive cross-talk between wires in two closed circuits carrying AC signals.

The other two wires are part of a neighboring circuit and situated parallel to the first wire a distance of r₁ and r₂ away. The separation of these two wires (r₂−r₁) continues for length l. Ampere’s law can be used to show the magnetic flux induced through this area of the circuit is

Using Faraday’s law shows the (electric) potential difference this causes is proportional to ω_r and ln r₂/r₁

To minimize EMFs induced in this way the frequency of the AC current is kept low and the loop area between wires is kept to a minimum by twisting both wires of a circuit together creating twisted pairs. Another important reason to keep loop areas to a minimum arises when measurements in a magnetic field are considered. Any current carrying loop of wire in a magnetic field will be subject to a torque (T=IAB) proportional to the current I, the loop area A and the magnetic field B. As the current is AC, this will cause the loop to vibrate and induce an EMF at the same frequency, ω_r as the current. The best way to minimize this is to securely stick/tie down all wires especially those which are very thin and light.

Lock-in amplifiers use a differential amplifier whose ideal output is proportional to the (electric) potential difference between its inputs i.e. the (electric) potential difference across the sample V=Gain × (V₊ – V_–). A real amplifier also has an output component proportional to the actual (electric) potential differences . This additional component is the common-mode (electric) potential difference. When the (electric) potential difference measured by the lock-in is very small this common-mode leak (electric) potential difference can adversely affect the results. The best way to minimize the common-mode (electric) potential difference is to balance the resistance of each wire in the circuit with its pair.

A signal generator produces a time varying EMF output. The frequency is selected by choosing a range using the range dial and then setting the frequency dial. The amplitude of the wave can be increased or decreased using the amplitude/volume control. The format of the wave can be chosen from a sinusoid, a square wave, a triangular/saw tooth wave or the TTL output. Figure 3.11 shows an example of a signal generator.

The TTL (Transistor-Transistor Logic) output provides a standard signal between 0 V and 5 V. A TTL output signal is defined as “low” when between 0 V and 0.4 V with respect to the ground terminal, and “high” when between 2.4 V and 5 V. A TTL input signal is defined as “low” when between 0 V and 0.8 V with respect to the ground terminal, and “high” when between 2 V and 5 V. These signal are used to pass timing or triggering signals between different pieces of equipment such as signal generators and oscilloscopes or current sources and lock-in amplifiers.

Figure 3.11: A signal generator.

Oscilloscopes are enormously useful pieces of equipment in the laboratory provided their operation is understood. Figure 3.12 shows the front panel of an analogue or CRT oscilloscope and Figure 3.13 shows the front panel of a digital oscilloscope. The screen on an oscilloscope can be loosely thought of as a graph. It is usually marked with a graticule scale of large squares with length 1cm, as well as smaller sub divisions. The horizontal axis is usually the time and the vertical axis is the electric potential difference.

There are two inputs for BNC cables: Channel 1 (CH1) and Channel 2 (CH2). BNC cables provide a firm connection which does not break when pulled. The metal cap on the wire must be pushed towards the instrument and twisted counterclockwise (clockwise) to disconnect (connect) the cable. Cables are usually coaxial which means they have a core down which the signal travels. This is surrounded by an insulating wrapper and then anther conducting wrapper which may be foil or braid and acts as an electrical shield. Finally this is surrounded by another insulating sheet.

Figure 3.12: An CRT oscilloscope.

The following list gives a brief description about the function and use of common oscilloscope buttons.

•“CH1 Volts/Div” and “CH2 Volts/Div” also sometimes called the “Vertical Gain”. There is one dial per channel, which controls the vertical amplitude of the waveform. The settings are usually given in terms of Volts per cm. So decreasing the Volts per cm, increases the gain and the amplitude of the waveform on the screen. The vertical gain is normally set so that the waveform fills the screen from top to bottom without going off the screen. There are three common sources of confusion in checking amplitude measurements are as expected.

•AC (electric) potential differences are usually discussed in terms of RMS (root mean square) values. Oscilloscopes display peak values which are √2 = 1.41 times larger than RMS values.

•Sometimes there are calibration controls in the center of the Volts/Div and timebase dials. These should be in a normal position indicated by a “locking” felt at the dial is rotated.

•Sometimes special probes are used on an oscilloscope which scale the signal by a factor of 10 or 100. This will be printed on the probes attached to the CH1 and CH2 inputs.

•Some oscilloscopes have a button to magnify the x and/or y axis by a factor of 10 independently of the volts/div or timebase controls.

•Vertical Position This controls the vertical position of the waveform on the screen. When no signal is present the trace on the screen is usually adjusted so that it sits on a convenient graticule marking on the screen so that amplitudes above and below zero can be easily measured. When taking amplitude measurements it is sometimes convenient to adjust the vertical position to line up the peak and trough of the waveform with the graticule lines.

•Timebase The timebase or SEC/DIV dial controls the speed at which the screen is scanned. The settings are usually given in terms of the number of seconds per cm. The frequency of the waveform can be calculated from this by taking one divided by the time period for one wavelength. For example if the time base setting is 0.01 seconds/cm and one complete wavelength takes 5 cm, the period is 0.05 seconds and the frequency is 1/0.05 = 20 Hz. Similar to the vertical gain, the timebase is set so that the waveform fills the screen with a small number of periods from right to left.

•Horizontal Position This is similar to the vertical position control, but changes the horizontal position. This can be adjusted when taking time measurements so that the waveform lines up well with the graticule lines.

•Autoset Some modern oscilloscopes have an autoset button. When this is pressed, the CH1 gain, CH2 gain and the timebase are automatically set to appropriate values. This is an especially useful feature to have as it saves a great to deal of wasted time when oscilloscope settings are unfamiliar or the frequency/magnitude of the signal is unknown.

•Trigger The trigger setting controls the point at which the waveform begins to appear on the left hand side of the screen. Each time the waveform reaches the right hand side of the screen the oscilloscope will pause and wait until a certain condition is met before starting again at the left hand side of the screen. For periodic functions this provides a synchronised waveform which does not drift across the screen and it enables randomly occurring pulses to be displayed easily. The trigger level control sets the (electric) potential difference which the input has to reach before the display of the waveform is restarted. Other trigger related buttons can control when the trigger is based on channel 1 or channel 2 or whether it is based upon the rising or falling edge of the waveform. The trigger can also be set to external. This triggers the oscilloscope based upon a pulse from an external source such as the TTL output from a signal generator or lock-in amplifier.

•Mode There are usually a series of buttons or a dial which sets what is displayed on the screen (in Figure 3.12 they are down the right hand side of the screen). This allows a choice between displaying only channel 1 (CH1), only channel 2 (CH2), both channel 1 and 2 at the same time (DUAL), the sum on channel 1 and channel 2 (ADD). The XY mode displays the CH1 input as the x coordinate and the CH2 input as the Y coordinate. If two different AC signals (at frequencies f₁ and f₂) are connected to CH1 and CH2 when the oscilloscope is in XY mode, interesting patterns called Lissajous figures appear when f₂ = nf₁.

•Coupling The GND/DC/AC buttons for CH1 and CH2 alter the coupling between the signal input and the input to the amplifier. The DC setting means that the input is connected directly to the amplifier. The AC setting means that a capacitor is connected between the input and the amplifier so that DC (electric) potential differences are blocked. The GND setting means that the amplifier input is connected to the ground (0 V) which allows a check of the position of 0 V on the display. The DC position should be appropriate in most cases.

•Measurements More modern, digital oscilloscopes have horizontal and vertical cursors or bars which can be displayed on the screen. Usually the button is labeled “Measure”. The cursors can be moved and the screen displays the (electric) potential difference between the horizonal cursors and the time period between the vertical cursors. It is also possible to get the oscilloscope to calculate and display the period, frequency and amplitude of the signals.

To begin using an oscilloscope first find and operate the power button on the front panel. It is then usual for a power LED to turn on and perhaps a number of other LEDs. If nothing happens, check for an additional power switch on the back of the oscilloscope and that the mains lead is properly connected and that the mains is turned on.

Wait for the beam to be displayed. An analogue oscilloscope may take a moment or two to turn on and a digital one will take longer as the software starts up. If the trace is not displayed on the screen then check the trigger level dial is set to the center and the horizontal and vertical position controls are set to the center.

Next connect the signal via the BNC connector on the front panel to at least one channel. The coupling should be set to DC in most cases and the mode set to either CH1, CH2, or DUAL depending on where the input signal(s) are connected. Set the vertical gain and timebase dials to an appropriate setting so that the waveform occupies a large part of the screen. If no signal appears, try pressing the autoset button if the oscilloscope has one otherwise the BNC cables and any other cables should be checked. If there appears to be poor connection, then the cables should be swapped for a different set. If this fails the oscilloscope could be connected to a signal generator which is known to be working.

Figure 3.13: A digital oscilloscope.

Finally the trigger should be set to one of the channels with a signal and the level control can be adjusted along with the rising or falling edge selection so that the best waveform is displayed.

Light gates are very useful for measuring time, speed/velocity and acceleration of moving objects. To simplify and improve the flow of the language, in this section it will be assumed the object is a toy car. Of course, in reality it may be any other suitable moving object. It is vital to point out that light gates are timers. The only measurement they make is the time for which a light beam (usually infrared) is broken. Further processing and thoughtful setup is required to find the velocity and acceleration using either one or two light gates. Often, the light gate control box or computer will do much of the processing, but will initially need to be programmed with a number of distance measurements.

Usually a small, vertical piece of card of known length would be fixed to the top of the car. The velocity of the car at a given point is found by placing the light gate at the point and dividing the length of the card by the time taken for the card to travel through the light gate. If a piece of card is not used, it must be clear the exact length of the car which is breaking the light beam.

In this case a piece of card is not necessary and the method may be more suitable where card can not easily be used. The two light gates are setup a known short distance apart. The light gates are setup to measure the time between the gates, so that the timer is started as the car travels through gate A and is stopped when the car travels through gate B. The velocity is found by dividing the distance between the light gates by the measured time. This gives an average velocity over the distance between the two light gates and is similar to how average speed checks on roadways in the US work.

Two velocity measurements taken a known time apart are needed. Each of these can be taken in a similar way to the measurement of the velocity with one light gate. The average acceleration of the car between the two light gates is found by diving the difference in the two velocity measurements by the duration of time between them.

To measure the acceleration with just one light gate, two velocity measurements are still needed. These can be taken using a “U” shaped card. The first velocity is measured using the first card to break the beam and the second velocity is measured using the second card to break the beam. Here it is important to measure the width of each of the vertical sections of the “U”. The acceleration is calculated in a similar way by diving the difference in the two velocities by the duration of time between them.

PASCO Scientific produce a range of interface boxes to connect a measurement devices to a computer for data logging. One example of this is the Science Workshop 500 Interface see: Figure 3.14. This box connects to the mains via a transformer and to the computer via a USB to serial converter. A large selection of sensors are available such as: photogate, ultra sound motion sensor, (electric) potential difference, temperature, pressure, and force. These are connected to digital or analogue channels inputs on the interface.

Specially designed “PASCO DataStudio” software is used to record the data into the computer and is available for Mac and Windows, although it has now been superseded by “PASCO Capstone”.

Plug in the USB wire between the interface box and the computer. Select “File, New Activity”. Then pick “Create Experiment”. The interface should be detected and an “Experiment Setup” window should appear. Plug the sensor into the interface box. Select the correct sensor from the list by double clicking on it: see Figure 3.15. For example, choose the photogate from the “Science Workshop Digital Sensors” drop down. Select the measurement required, for example “Velocity in Gate, Ch1”.

Figure 3.14: A PASCO Science WorkShop 500 Interface box connected to a photogate.

Choose the method required for the display by clicking and dragging a display type from the “Displays” panel at the bottom left to the measurement in the “Data” panel at the top left. For example, choose “Digits”.

To record data, press the “Start” button in the menu bar at the top of the screen. The “Digits” display will update each time the light beam is interrupted. Data taking can be stopped using the “Stop” button. See Figure 3.16.

Alternatively, setup an ultrasound motion sensor to measure position and select a “Graph” from the “Displays” panel. Use the “Motion Sensor” tab in the “Experiment Setup” window to calibrate the sensor. Position the sensor a “Standard Distance” from a large solid surface such as a wall, floor, or a large book. Then press the “Set Sensor Distance = Standard Distance” button. Record the data by using the “Start” button as before. See Figure 3.17.

Figure 3.15: Choosing a sensor in PASCO DataStudio.

A table of values can be saved by dragging the “Table” option from the “Displays” panel up to the “Data” panel even after the data has been recorded. The data can be saved for use later or in other software by choosing “Export Data” from the “File” menu.

Data Harvest QAdvanced dataloggers give reliable datalogging which is quick and easy to setup, see Figure 3.18. They can be used in either a standalone mode or when connected to a computer. When connected by a USB cable to a (Windows) computer the “Data Harvest EasySense” software can be used to record, graph, and save data. With a sensor connected to one of the inputs on the datalogger, when the program opens choose “EasyLog” and then press the “Start/Stop” button. Live data will be displayed on the graph. See Figure 3.19. Alternatively, in a stand alone mode, the results are displayed on the built in screen or recorded and saved to the datalogger.

Figure 3.16: Using PASCO DataStudio to measure the velocity in a photogate.

Figure 3.17: Using PASCO DataStudio to produce a distance time graph.

Figure 3.18: A Data Harvest QAdvanced Datalogger with a Light Level probe connected to input 1.

Figure 3.19: A screen shot of the Data Harvest EasySense software showing a graph of Light Level against time.

For example to setup a velocity measurement using a single light gate, connect the light gate to the input labeled A. Press any button to turn the device on. The arrow buttons can be used to navigate through different menu options. Navigate to “Time & Motion” and press the green arrow button. Navigate to “Speed” and press the green arrow button. Navigate to “Speed at A” and press the green arrow button. Choose the “1 Interrupt card” option and press the green arrow button. Finally navigate to the length of the interrupt card being used and press the green button. The datalogger will display the latest speed as well as an average speed.

To use a Light Level probe, connect this to input 1. Navigate to “Meter” and press the green arrow button. The display will show a reading updated a few times per second.

Use the red square button to go back to the previous menu. Navigate to “Logging” and press the green arrow. Use the arrow keys set a “Duration” and “Interval” for the measurements and choose a start time. Logged data is saved to the datalogger, this can be downloaded to the “Data Harvest EasySense” software on the computer for graphing or analysis. When the program starts, choose “Remote” and then “Retrieve Remote”. Select the data to collect from the datalogger and click the “Retrieve” button. The data is now displayed as a graph on the computer: see Figure 3.19.

There are a number of pressure gauges which may be met. Each is based upon a different mechanical or electrical way of detecting pressure and is sometimes only suitable for certain pressure ranges or a certain resolution. A table of different pressure units was given in Section 2.5.1.

A basic pressure gauge can be made using a “U” shaped tube which is half full of a liquid (such as water or mercury). One side of the U tube is connected to a known reference pressure P₁ such as atmospheric pressure or a vacuum and the other is connected to the pressure region to be measured P₂. The difference in liquid level, h, between the two sides of the “U” tube is related to the pressure difference:

where g is the acceleration due to gravity and ρ is the density of the liquid.

Mechanical gauges measure pressure by monitoring an element which flexes or bends due to a pressure difference across it. The element which may be a Bourdon tube, a diaphragm or another similar device which causes a pointer to move against a calibrated scale. A Bourdon tube is a flattened tube which tries to regain its circular cross section when it is pressurized. This effect can be amplified sufficiently to turn a pointer by forming the tube into a “C” shape or a coil. A diaphragm is a flexible membrane which separates areas of different pressures. The change in position of the membrane is reproducible, related to the pressure difference across the membrane and can be used to move a pointer.

The mechanical gauges may be read electronically by linking the Bourdon tube to a piezoelectric strain gauge or the diaphragm to a capacitance sensor.

A Pirani gauge is a common electronic gauge useful for measuring pressures between 0.1 Pa and 1000 Pa. It consists of a metal wire which is heated by a current flowing through it. Thermal equilibrium of the wire is achieved due to a cooling effect of the gas surrounding the wire. If the gas pressure decreases there will be fewer collisions of gas molecules with the wire meaning its temperature will increase. The increase in temperature of the wire causes its resistance to increase. Measurements of the current flowing through the wire and the electric potential difference across the wire are used to find its resistance. A calibration table or mechanism is then used to convert the resistance of the wire in to pressure.

Ionization pressure gauges are more sensitive and measure pressures in the range 10⁻⁸ Pa to 10⁻¹Pa. Free electrons are generated which ionize gas molecules. These gas molecules are attracted to an oppositely charged electrode. The small current between the positive and negative electrodes is proportional to the rate of ionization. Lower density (therefore lower pressure) gases produce less ions and so the current is linked to the pressure. However, the number of ions produced can be dependent on the gas so a good calibration for the appropriate gas is necessary. There are two subtypes: hot cathode gauges and cold cathode gauges. Hot cathode gauges use a heated filament to produce electrons via a process called thermionic emission. The most common of these is called a Bayard-Alpert gauge. A cold cathode gauge produces electrons by high EMF discharge. The most common of these are called a Penning gauge or an Inverted Magnetron.

There are a board range of methods for measuring temperature in the laboratory. The chosen method will be different depending on the temperature range to be measured, the accuracy and precision required and the conditions under which the measurement must be taken. Temperature can be measured in Kelvin (K), Celsius (^°C) or Fahrenheit (^°F). Temperatures can be converted from one scale to another using:

Mercury and Alcohol Thermometers

A glass column is attached to a small reservoir or bulb at one end. This is filled with a liquid whose volume depends significantly on temperature. The two most common liquids are mercury and alcohol. Mercury thermometers are becoming rarer as government rules try to reduce the amount of mercury in the environment and as of 2012 their sale to (although not use by) the public is prohibited. Mercury thermometers have been replaced by colored chemical thermometers. As the liquids increase in temperature their volume increases and they expand up the glass column.

Mercury thermometers are limited by the temperature range in which mercury is a liquid (−39^°C up to 357^°C). Similarly ethanol thermometers only work when ethanol is a liquid between −114^°C and 78^°C. To enable mercury free thermometers to be used above 78^°C other chemicals can be used such as isoamyl acetate, toluene, or kerosene which have higher boiling points.

IR Thermometers

An infrared thermometer infers the temperature of an object from the thermal radiation it emits. By knowing the amount of infrared radiation emitted by the object and its emissivity, the object’s temperature can be determined.

A black body is an idealized object which absorbs all incident electromagnetic radiation no matter what the angle of incidence or frequency. A black body emits electromagnetic radiation, of intensity, I, where I(f,T), is the amount of energy per unit surface area per unit time per unit solid angle emitted at a frequency, f, by a black body at temperature T. This is Planck’s Law:

where c, is the speed of light, h is Planck’s constant and k, is the Boltzmann constant. Integrating this over solid angle and all frequencies gives the Stefan-Boltzmann Law:

where P is the total power radiated by the object, A is the surface area of the object, ε is the emissivity of the object (ε = 1 for a perfect black body and ε < 1 for all other objects), σ is the Stephan-Boltazman constant which is 2π⁵k⁴ /15c²h³ = 5.67 ×10^{− 8} Wm ⁻² K^–4 and T is the temperature of the object. This means that the amount of emitted radiation is determined by only the temperature of the object.

Infrared thermometers are useful as they can make non-contact measurements in environments where other thermometers would not work or would be difficult to implement such as in a vacuum, at very high temperatures, in electromagnetic fields or where access is difficult. Sometimes they have a built in laser spot used to aim the thermometer indicating approximately from where the emitted radiation is being measured.

A infrared thermometer may give an inaccurate reading when it is not correctly aimed, when the emissivity is only given an approximate value for a particular surface/object or if stray radiation is picked up from nearby objects (usually at a higher temperature).

Thermocouples

Any conductor which is subjected to a thermal gradient (between the temperature of a sample and known reference temperature) will generate a small (electric) potential difference across its ends. This is known as the thermoelectric effect or Seebeck effect. It can be measured using a voltmeter.

In order to form a complete circuit to measure this (electric) potential difference a further conductor must be connected to the sample end of the first conductor. This further conductor will be subjected to the same temperature gradient which will develop its own (electric) potential difference which will oppose and exactly cancel the original (electric) potential difference. However, the magnitude of the effect depends on the metal from which each conductor is made. Thus, using two dissimilar metals results in a small, but measurable, net (electric) potential difference. The measured (electric) potential difference increases with temperature, and is typically between 1 and 70 µV/^°C.

Since the (electric) potential difference is generated along the portion of the length of the two dissimilar metals that is subjected to a temperature gradient and both lengths of dissimilar metals experience the same temperature gradient, the end result is a measurement of the difference in temperature between the thermocouple junction and the known reference temperature.

Thermocouples can be purchased according to standard specifications denoted by letters. Different types are best suited for different applications. They are usually selected on the basis of the temperature range, sensitivity needed, how inert the metals are in the measurement environment and sensitivity to magnetic fields.

Table 3.4: Thermocouples, Compositions, Temperature Ranges, and Sensitivities.

Table 3.4 gives the properties of some common thermocouples: K is the most commonly used, and E is not affected magnetic.

A range of methods have been developed to allow measurement of low temperatures. Each method has associated advantages and disadvantages. It is likely that one or more of these methods will be met but the one in use will depend upon the experimental requirements and environment.

Gas Thermometry

With this method it is difficult to obtain a high accuracy due to the corrections needed for inaccuracies such as the volume of connecting tubing, contraction of the bulb, and pressure corrections due to non-ideality of the gas. The pressure measurements become more accurate when diaphragms are used to separate the gas in the bulb and gas in the pressure gauge. Electronics can then be used to detect the movement in the diaphragm. This method also has the advantages that it is unaffected by magnetic fields and that it is easy to measure differential temperatures. Typically 3-He or 4-He gas would be used since they have a very low boiling point.

Resistance Thermometry

Resistance thermometry depends upon the variation of resistance with temperature. This method is much easier than the gas thermometry to perform and is reliable down to a lower temperature. A good material would have a (relatively) linear dependence of resistance on temperature, be easily obtainable in high purity, chemically inert and with a stable resistance. Metals such as platinum (Pt) are suitable. The possible resolution when using Pt decreases below about 10 K so materials such as Rhodium Iron (RhFe) are more useful. RhFe also has the advantage that is has a large and positive temperature coefficient below 30 K. Another useful material is Arsenic (As) doped Germanium (Ge). Thin Film Resistors using certain materials are prone to the effect of magnetic fields whereas carbon-glass thermometers are only slightly affected by a magnetic field. Thick film resistors using Ruthenium Oxide (RuO₂) have also been used due to their low cost, ease of use, ease of lowering their temperature due to a low heat capacity and the possibility of predicting their low temperature resistance from that at room temperature.

Electronic Thermometry

Electronic thermometry has a wide temperature range, a higher sensitivity compared to other methods, simpler operation and a more linear V verses T characteristic than most resistance thermometers. Silicone (Si) junctions make the most stable and reproducible thermometers, but they have high magnetic field dependence. A Gadolinium-Aluminium-Arsenic (GaAlAs) semiconductor has a much reduced dependence on magnetic field. They are inexpensive, but electrical noise limits currents to above 10 µA so heat dissipation becomes a problem at very low temperatures. Carbon and Germanium based semiconductors show a significant hysteresis effect when cooled again after being allowed to reach room temperature.

Thermocouples

Low temperatures can also successfully be measured using thermocouples. Stable, temperature sensitive alloys with a strongly temperature dependent magnetic moment must be used eg. those of Cu or Au. Great care is needed to get an accuracy of less than 1 % especially at low temperatures since the thermocouples become much less sensitive as the temperature drops.

Capacitance Thermometry

Capacitance thermometers, primarily using SiO₂-OH, have been successfully developed and have become popular due to their insensitivity to magnetic fields. The readings are stable and have a constant sensitivity right down to just above 0 K. However, after they are cycled to room temperature they show a significant hysteresis and drift effects.

Calibration

Thermometers operating at low temperatures can be calibrated in a number of ways. The first is by extrapolation of an existing scale down to lower temperatures. The second, is by direct measurement of a few known points such as in liquid helium (4.2 K), liquid nitrogen (77 K) and ice water (273 K). Mathematics can be used to interpolate temperatures between these. Alternatively a comparison with a primary (previously calibrated) thermometer can be made.

These methods can fail due to unknown additional temperature dependence at lower temperatures or due to unexpected and therefore uncorrectable systematic errors.

High temperatures can be measured without contact using an infrared thermometer. Resistance thermometry may also be appropriate for contact measurements in a similar way as they are used at low temperatures. Platinum is particularly appropriate due to a linear and well defined resistance, its resistance to oxidation or other degradation in the high temperature environment and its relatively high melting point. A further method in common use is the thermocouple.

A PID controller is able to change and hold a parameter at a particular value called the setpoint. It consists of a control loop mechanism with feedback and is usually realized in an electronic circuit. It is commonly found in temperature controllers where a temperature can be set, monitored using a thermometer and increased using heater. Cooling usually occurs due to heat transfer to the surrounding.

A PID controller is named after its three correcting terms: the proportional, integral and derivative. These are summed to calculate the output of the PID controller. Defining x(t) as the controller output (which in the case of a temperature controller may be applied to the heater), the PID algorithm is:

where P is the proportional gain constant, I is the integral gain constant, D is the derivative gain constant, e is the error (the difference between the set point and the present value), t is the time and τ is the variable of integration.

The proportional term produces an output value that is proportional to the current error. The proportional output is found by multiplying the error by the proportional gain constant, P. A high proportional gain results in a large change in the output, x(t) for a given change in the error. A small proportional gain results in a small change to the output for the same change in error making the controller less responsive or less sensitive.

The integral term produces an output value that is proportional to both the magnitude of the error and the duration of the error. It is the sum of the instantaneous error over time and gives the accumulated offset that should have been corrected previously. The accumulated error is multiplied by the integral gain constant I to give the integral output. The integral term accelerates the movement of the process towards the setpoint. However, since the integral term responds to accumulated errors from the past, it can cause the present value to overshoot the setpoint value.

The derivative term produces an output value that is proportional to the slope of the error over time. Is is found by multiplying the rate of change of error with time by the derivative gain constant, D. The derivative term slows the rate of change of the controller output. Derivative control is used to reduce the magnitude of the overshoot produced by the integral component. However, the derivative term slows the response of the controller. Also, differentiation of a signal amplifies noise and thus this term in the controller is highly sensitive to noise in the error term.

In order for a system to reach its setpoint quickly the PID values must be adjusted until their optimum value is found. This can be done manually: the I and D values are set to zero. The P value is increased until the present value oscillates. P should then be set to half the value which caused the oscillation. The present value will then overshoot the setpoint. The I value can then be increased from zero until the offset is corrected in a reasonable time. Finally the D value can be increased so that any instability in the system is corrected in a reasonable time.

Table 3.5: Effect of changing PID values.

Table 3.5 gives the effect of changing one of the PID constants independently: An alternative to setting the PID gain constants manually is to follow one of a number of pre-defined algorithms for setting them such as the Ziegler–Nichols method [8]. As before the I and D gain constants are set to zero. The P gain constant is increased until it reaches the ultimate gain P_U at which the output of the loop oscillates with a constant amplitude. The values of P_U and T_U (where T_U is the time period of oscillation) are used to set the values of the PID gain constants using the relationships shown in Table 3.6 [9].

A vital part of any Physics Laboratory has been a book of physical constants and material properties. It has allowed physicists to look up quantities they need for data analysis or to check the accuracy of values they have measured. The standard book is Kaye and Laby Tables of Physical and Chemical Constants. This can be purchased as a printed book, but is also now freely available online at http://www.kayelaby.npl.co.uk/. This book and website give a wealth of information on a wide range of topics. Naming only three as examples: nuclear decay chains for every radio active isotope, the pressure dependence of the boiling point of organic compounds and the velocity of sound in a range of gases.

Table 3.6: Relationships for setting PID values.

3.24.1 Optical Microscopes

Optical microscopes can be a valuable tool for enlarging small samples. The wavelength of visible light is in the range 400 nm–700 nm, so distances smaller than this can not be resolved by an optical microscope, no matter how good the quality.

To view samples under an optical microscope a good light source is needed to illuminate the sample. Typically optical microscopes fall into two categories. Most common are transmission microscopes, which illuminate a sample primarily from beneath and rely on light transmitted through the sample. More useful in physics is a reflection microscope which usually have larger lenses to allow the collection of more light. They rely on the sample being brightly lit from above and collect light reflected from the sample.

Most microscopes will have position adjustable eyepieces which should be set to suit the user. Both the eyepiece and objective lens will have distinct magnifications, the total magnification is given by their product. Better quality microscopes will have a range of different magnifications to choose from selecting the appropriate objective lens.

As well as the limit imposed by the wavelength of light, optical microscopes suffer from various aberations which reduce the quality of the images. Chromatic aberations occur when light of different colors (different wavelengths) is not focused at the same point. This is due to an effect called dispersion of the lens which arises because the lens has a decreasing refractive index for increasing wavelengths of light. Figure 3.20 illustrates the effect of a chromatic aberation. Chromatic aberation produces fringes of color along boundaries between light and dark parts of the image. A simple method of reducing chromatic aberation is to make the focal length as long as possible or use monochromatic (a single wavelength) of light. More modern methods involve the use of low dispersion glass or the production of achromatic lenses using layers of materials with different dispersions.

Figure 3.20: Illustration of chromatic aberation of a lens. Red light (the dashed line) is refracted less than blue light (the dotted line).

Spherical aberations result from the use of spherical lenses. These are cheaper and easier to produce than aspherical lenses. Light which strikes the lens further from the center is refracted too much compared to light which strikes the lens nearer the center. Figure 3.21 illustrates the effect of spherical aberations. Spherical aberation can be reduced by making aspherical lenses or by combining a number of spherical lenses.

Figure 3.21: Illustration of spherical aberation of a lens.

Astigmatism occurs when light rays which propagate in two perpendicular planes have different foci. They typically arise as an artifact of the manufacturing process.

To observe distances smaller than the limit of an optical microscope electrons can be used as they have a shorter wavelength: typically 3.4 pm for 120 kV electrons. Samples must be electrically conductive. Insulating samples are first covered with a thin film of metal such as gold.

Electrons are usually created by thermionic emission and then accelerated by passing through a high potential difference. The higher the potential difference, the higher the energy and the smaller the wavelength of the electrons, meaning smaller features can be resolved.

The lenses in a transmission electron microscope (TEM) are made using electromagnets. Glass lenses would not work as electrons do not penetrate far into matter (hence very thin samples are needed to observe the diffracted beam). Permanent magnets would be equally useless because the image could not be focused. Electromagnets allow the lens currents to be varied and so allow the image to be focused onto a screen. A vacuum is needed inside the column of the microscope because electrons would collide with air molecules rapidly destroying the beam.

When the electron beam hits the sample some electrons are scattered and some are transmitted. If the transmitted beam is selected using the correct size aperture a bright field image is formed. An aperture is usually a platinum metal disk with a hole in the center placed in the path of the electrons. Since the scattered electrons are stopped by the objective aperture the amount of scattering determines the contrast in the bright field image. Where many electrons are scattered the image will look dark, where few are scattered the image will be lighter. A dark field image is formed when the scattered beam is selected using an aperture designed to block the direct beam. An advantage of dark field images is the much higher contrast which can be obtained, although a large electron flux is needed which may damage the sample.

Figure 3.22: Left: Electron diffraction pattern from Gold. Right: A dark field image of islands of Gold.

Alternatively a scanning electron microscope (SEM), scanning tunnelling microscope (STM) or atomic force microscope (AFM) may be used. It is unlikely these microscopes will be encountered in the undergraduate laboratory, however it is still useful to have a brief overview of their operation. It should be noted that images taken with any of these microscopes are often given false colors. Since many of the features imaged are less than 400 nm (the wavelength of violet light) they can’t actually have a color in the traditional sense as they are not capable of reflecting visible light.

A scanning electron microscope (SEM) works in a similar way to a TEM except a narrow focused beam of electrons is scanned across the surface of the sample producing a image with a large depth of field giving a three dimensional appearance and a resolution down to about 1 nm. As with a transmission electron microscope, traditional SEM require samples to be placed in a high vacuum and be electrically conductive.

There are a range of methods of making measurements: transmitted electrons can be monitored or back scattered (reflected) electrons can be collected which allows areas with different chemical compositions to be identified as elements with high atomic numbers back scatter electrons more than elements with low atomic numbers. Alternatively characteristic X-rays can be detected, they are emitted when the electron beam removes an electron from the inner shell of an atom. This causes a higher energy electron to drop down to take the place of the ejected electron, releasing energy in the form of an X-ray. Characteristic X-rays are used to identify elements present and their relative proportions in the sample. Acceleration and scintillation based detection of secondary electrons allowed the development of an environmental scanning electron microscope which allows insulating samples to be imaged in low pressure gas or water vapor. Secondary electrons are those removed from the 1s (or k) orbital in atoms in the sample by inelastic scattering with electrons from the electron beam.

A scanning tunneling microscope (STM) can give a resolution of around 0.1 nm and a depth resolution of 0.01 nm. This is sufficient to image and even move individual atoms. Little sample preparation is needed: the STM works in vacuum, air or liquid over a wide range of temperatures. A very sharp conducting tip is positioned above the sample and scanned across the surface to build up the image pixel by pixel. A potential difference (or bias voltage) is applied between the sample and the tip which allows electrons to quantum mechanically tunnel between them. The resulting tunneling current can be measured and used to produce an image of the hight/relief of the sample. The challenge with STM is to have a very clean sample surface, the tip needs to be very sharp with just a single atom at the tip and there needs to be very good vibration suppression in the equipment and the building.

An atomic force microscope (AFM), similar to the STM, also has a sharp tip which is scanned across the surface of a sample. However with an AFM the tip is on the end of a cantilever. As the tip is brought close to the surface of the sample forces between the tip and the surface cause the cantilever to deflect a small amount. This is typically measured using a laser which is reflected from the top surface of the cantilever. This “optical lever’ allows a much bigger deflection to occur in the laser which can more easily be measured. Usually there is a feedback mechanism which adjusts the height of the sample to avoid the tip colliding with the surface. Images produced with an AFM give a three dimensional view of the surface of the sample. The sample needs no special treatment and can be imaged at room temperature in either air or liquid.

A spectroscope or spectrometer takes light from an object and splits it into its component colors/energies. Typically light will be brought to a focus on a slit at the entrance to the spectroscope. Light which passes through the slit falls onto a mirror which collimates the light i.e. makes the light rays parallel. This light is then directed to a diffraction grating. The angle at which the intensity minima and maxima of the interference/diffraction pattern occur depends on the wavelength of the light. The result is that the incident light is spread out. If white light entered the spectroscope the spectrum would be a rainbow pattern. If a sodium lamp is used, this only emits two specific wavelengths of orange light so there would be an emission spectrum showing two narrow orange lines against a dark background. A camera may be used to image the resulting spectrum and measurements may be taken to identify the wavelength of the emission or absorption lines.

3.26.1 Plugs, Sockets and Connectors

Table 3.7 gives images of a wide range of connectors which might be frequently used in the laboratory. It is does not constitute a complete list: even for a type of connector which is listed there may be other sizes or shapes of connector not shown. These images may be helpful in identifying unknown connectors.

Name	Male (Plugs)	Female (Sockets)
Mains
Mains
Mains
3 Phase Mains
VGA
DVI
S-Video
Composite
HDMI
3.5mm Audio
USB Type A
USB Type B
mini USB
USB 3
miniUSB 3
FireWire (IEEE1394)
mini FireWire
BNC
9pin Serial (RS-232)
25pin Serial (RS-232)
Parallel
Parallel
GPIB (IEEE488)
PS-2
Ethernet (RJ45)
Modem (RJ11)

Table 3.7: Common plugs and sockets.

This section provides a brief tutorial on setting up Delphi, LabView and MATLAB to record experimental data. It is likely that any computer used in the undergraduate laboratory will already be setup. However this section aims to give an overview of what is going on “behind the scenes” and provide a starting point for setting a computer at a later point in time.

Instruments can communicate with a computer via a number of different connection interfaces. This simply involves connecting a cable from the instrument to a computer. Old interfaces include parallel and serial ports, but a more modern method is by USB. Frequently on modern computers serial ports are becoming obsolete — although they can often be purchased on separate PCI cards or as a USB adapter.

More specialist scientific equipment often connects via ethernet (standard network cables) or GPIB (which requires a special adapter card inserted inside a computer or a USB converter).

To use a GPIB interface a GPIB PCI card (perhaps manufactured by Measurement Computing) needs to be installed into a standard Windows PC and the drivers correctly setup. A GPIB cable is run from the back of the card on the PC to the first instrument. Up to 14 further instruments can be connected in a daisy chain with a single cable linking an instrument to the previous one. Each instrument requires a unique address which is set in the configuration options on the instrument itself. (Addresses can be chosen regardless of where the instrument is located in the chain and also of which other address are chosen provided each is unique). The card driver installation on a Windows computer creates a shortcut called CBCONF32 in the Start Menu. This program is used to link the GPIB address of the instrument to a short text handle which is used to refer to the instrument in the program code. Any other settings required can be configured using this program too, although the defaults are sufficient for most instruments.

Delphi

The Delphi programing environment needs to be installed on the PC. Each instrument requires specific text commands sent over the GPIB bus in order to respond with the required data. These sometimes complex commands can be written out once in Delphi in an interface unit specific to that instrument. Each Delphi program that is then written uses these interface units to communicate with instruments. A standard interface unit (called gpib) is also required in order for the Delphi program to communicate with the GPIB card in the computer. All the steps described in the this section need only be performed once. After this is all setup it provides a simple and rapid method to write new programs.

As an example consider reading the X output from a SR830 lock-in amplifier. A simple interface unit would be as follows below. The unit name (DCSTAN830) is given at the top, then there are two main sections “interface” and “implementation”. The interface section contains definitions of class properties, global variables and all procedures contained in the unit. The first line of the implementation section contains a list of other units from which code is referenced rather than duplicated. The code at the very end encapsulated with a “begin” and “end” statement creates the class and sets a text handle which corresponds to the text handle linked to the correct GPIB address set earlier in the CBCONF32 program. There are two procedures also in the implementation section, the first initialises the instrument and the second “GetVolts” sends a message over the GPIB interface (“SNAP?1,2,3,4”) and waits for the response to come back before interpreting it and saving part of it as the variable x. These messages and the form of the response are detailed for each instrument in its manual.

unit DCSTAN830;

interface

type TLIA= Class

ieeehdl:integer;

ieeestr:String;

x:real;

Procedure Initialise;Procedure GetVolts;end;

var LIA:array[1..4] of TLIA;

implementation

uses dieeecb,dmisc,sysutils,gpib;

Procedure TLIA.Initialise;begin

ieeeHdl:=InitDevice(ieeeStr);

ibclr(ieeeHdl);

writeieee(ieeeHdl,’OUTX1’);

writeieee(ieeeHdl,’*CLS’);

end;

Procedure TLIA.GetVolts;var s:string;begin

writeieee(ieeeHdl,’SNAP?1,2,3,4’);

readieee(ieeeHdl,s);

x:=s2r(copy(s,1,pos(‘,’,s)-1));

end;

begin LIA[1]:=TLIA.Create;

LIA[1].ieeeStr:=’SR830’;

end.

As well as the interface unit the actual program is needed - the simple one shown below sets a label on the Delphi form to show the lock-in X value when a button is pressed. At the top in the “uses” section the name of the interface unit (DCSTAN830) has been added: this automatically includes the code from the file above to save it being typed out again. The “FormCreate” function is run automatically when the program is opened and runs the instrument initialisation procedure. The “Button1Click” function is run when the button on the form is clicked. This first runs the “GetVolts” procedure to get the value from the instrument and then sets the label caption to be the value returned and saved to the variable x.

unit Unit1;

interface

uses

Windows, Messages, SysUtils, Variants, Classes,

Graphics,

Controls, Forms,

Dialogs, StdCtrls, dcstan830, dmisc;

type

TForm1 = class(TForm)

Button1: TButton;

Label1: TLabel;

procedure Button1Click(Sender: TObject);

private

Private declarations

public

Public declarations

end;

var

Form1: TForm1;

implementation

$R *.dfm

procedure TForm1.Button1Click(Sender: TObject);

begin

lia[1].getvolts;

label1.caption:=r2s(lia[1].x,13,-1);

end;

procedure TForm1.FormCreate(Sender: TObject);

begin

Lia[1].initialise;

end;

end.

This example can be extended to include all the instrument functions that are required. In practice the programs are run on a timed loop which reads the value on the instrument approximately every one second and records this to a data file or plots it to a live graph.

In order, save the data to a file it needs to be assigned a handle using Assign File(handlename,filename); It is then opened in append mode to add a line to the file or rewrite mode to over-write the current contents. append(handlename); or rewrite(handlename); The line is then written using writeln(handlename, “Text”,_tb,VariableName); where each element is separated with a comma, text is written in quote marks, variable values are written by including the variable name and a tab is written with “_tb”. The file is then closed using closefile(handlename); The “handlename” variable needs to be declared as a textfile and the “filename” variable declared as a string.

MATLAB

MATLAB can be used in a similar way to record data and plot graphs. The Instrument Control Toolbox must be installed. It comes with a comprehensive manual explaining how to communicate and control instruments via GPIB and Serial interfaces.

As a brief illustrative example, the following code snippet shows one of a number of methods data can be captured from an instrument connected via a GPIB interface. Here the data is stored in the variable “data1”.

% Create a GPIB object.

obj1 = instrfind(‘Type’, ‘gpib’, ‘BoardIndex’, 7, ‘PrimaryAddress’, 10, ‘Tag’, “);

%Create the GPIB object if it does not exist

%otherwise use the object that was found.

if isempty(obj1)

obj1 = gpib(‘ni’, 7, 10);

else

fclose(obj1);

obj1 = obj1(1)

end

% Connect to instrument object, obj1. fopen(obj1);

% Communicating with instrument object, obj1. data1 = query(obj1, ’SNAP?1,2,3,4’);

% Disconnect from instrument object, obj1.fclose(obj1);

%Clean up all objects.

delete(obj1);

LabVIEW

LabVIEW software gives a graphical point and click interface which allows acquisition and processing of data and data logging. It also has the ability to make decisions based on the measurements and control equipment. LabVIEW programs can be run on Windows, Mac and Linux.

A LabVIEW program is called a VI. When LabVIEW is started, from the “Create Project’ window select the “Blank VI” template: see Figure 3.23. This brings up two windows: one shows the “block diagram” where the code is developed and the other shows the “front panel” which is where the user interface can be customized to include graphs and buttons: see Figure 3.24.

In the “block diagram” window, pictogram components can be wired together to create a program. Each block has inputs and outputs just like a function in a traditional programming language. When a component executes it produces data which passes down the wire to the next block. The movement of data determines the order in which the components are executed in the program.

Figure 3.23: Creating a new VI in LabVIEW.

The component from which the measurement is to be made needs to be connected to the computer. A common way is via GPIB interface or via a USB system such as a National Instruments compact DAQ or an equivalent system made by Stanford Research Systems or another supplier. For example, to setup and read from the GPIB bus, right click in the “block diagram” window and find the “express” palette, then choose “input” and the “Instr Assist” button. Place the “Instrument I/O Assistant” onto the block diagram. Right click on it and choose the “Instrument I/O Palette”, the “GPIB” and finally the “Read” button. See Figure 3.25. Place the “GPIB Read” component onto the block diagram. Hovering the mouse over the different input and output markers around the edge shows that one is the “address string”. Right click on this and choose “String Palette” and then “String Constant”. Place this on the block diagram and type in the address string for the instrument. The address string must be set to the text handle linked to the correct GPIB address via the CBCONF32 program as discussed in Section 3.26.2. Also set a numerical value which indicates the number of bytes which must be read from the instrument.

Figure 3.24: The LabVIEW program. On the left is the ‘block diagram’ window and on the right is the ‘front panel’ window.

Then wire the “String Constant” component to the “address string” input on the “GPIB Read” component. The output from the “GPIB Read” component is a string, this must be converted to a number for processing. Right click on the “data” output marker of the “GPIB Read” component and choose “String Palette”, then “String/Number Conversion” and finally “Fract/Exp String to Number”. Place this onto the block diagram and wire it up.

Figure 3.25: Inserting a ‘GPIB Read’ component in LabVIEW.

To set up a chart, right click in the “front panel” window to bring up the “controls” palette choose “Graph Indicators” and then “Waveform Graph”. Place this on the “front panel” window. Now right click on the input to the “Waveform Chart” component and select the “Array Palette” option and then the “Build Array” component. Add this to the block diagram. Now wire the output of the “Fract/Exp String to Number” component into the “Build Array” component and finally into the “Waveform Graph”. See Figure 3.26.

This will only produce a single value. Inserting a “while” loop will run the program continuously until a “stop” button is pressed. Right click in the block diagram window. Choose “Exec Control” and then a “While Loop”. Use the mouse to draw a box around all the components that are required to be inside the while loop. A stop button has also appeared on the “front panel” window. See Figure 3.27. The program can now be run, by pressing the run arrow in the menu bar at the top of either the “block diagram” or “front panel” windows. Live data should appear on the graph.

Figure 3.26: A LabVIEW program which reads data and produces a graph.

LabVIEW programs can be more complex than this if more instruments are used and the data is written to a file using the “Write Measurement File” component from the “Express, Output” palette. Programs for use by many users would normally be compiled as an executable so that changes to the code can’t be made by mistake.

CCD sensors (or digital cameras) are a useful way to capture data in am image format such as from diffraction/interference patterns, emission/absorption spectra and with the correct optics from a microscope. The CCD sensors used may be sensitive to a wide range of wavelengths of electromagnetic radiation such as X-rays, visible or infrared. A computer can then be used to make detailed measurements from the images using special software.

Often the image on the computer screen will need calibrating so that a certain on screen distance (or number of pixels) can be matched up with a certain physical distance in the real world. Typically a ruler or graticule (a very finely spaced series of lines used under an optical microscope) is photographed under the same conditions of magnification and focus as the sample. A special software program can be used to calculate a scale and to make measurements from the image of the sample using the image of the graticule.

Figure 3.27: A LabVIEW program within a ‘while’ loop.

Alternatively, for a small number of measurements, a simple image editing program can be used to measure the number of pixels between two graticule lines. Figure 3.28 shows a photograph of a graticule taken down a microscope. Each small division corrections to 100 µm. If this was measured to be 40 pixels, then each pixel would correspond to 100/40 = 2.5 µm. Distances on the image of the sample could then calculated by measuring the appropriate number of pixels and multiplying by 2.5 µm.

A similar procedure can be followed if images are scanned into a computer. This is perhaps most likely with images taken using traditional film and developed on photographic paper.

Video cameras, camcorders, and slow motion (high frame rate) video cameras can be used to record experimental data. They are particularly useful for measuring the speed of objects which are moving or events which happen too rapidly to be seen with the human eye. The experiment should be setup so that a ruler or scale is in camera shot and in close proximity to the object. Alternatively a resolution calibration must be performed giving a value in units of meters per pixel.

Figure 3.28: Photograph of a graticule using a microscope.

Captured video can be opened in a program such as Apple QuickTime. The video should be played back frame by frame. The position of the object can be read from the ruler or by measuring its position in terms of pixels from a fixed point. When the same measurements are taken from the next frame the velocity can be calculated using:

or

The change in time is obtainable from the software or by calculating one over the number of frames per second.

If using QuickTime, once the video file is opened, choose “Show Movie Inspector” from the “Window” menu. This window has, amongst other details, the “Current Time”. The video can be moved one frame at a time using the right or left arrow keys on the keyboard.

It is frequently very useful to be able to take graphical data published in textbooks or other authors and to be able to replot this in a different way or in conjunction with your data. Research papers only rarely provide tables with the actual data points which make up the graphs, so more creative means must be adopted to extract the data.

A very useful program called Scan It [10] allows a scanned image of a graph to be loaded. Firstly, set the axes by clicking on three well defined points such as the origin, a point on the x axis and a point on the y axis. For each point input the coordinates based on the scale printed on the graph. This is shown in Figure 3.29.

Figure 3.29: Using ScanIt to set the axis.

The program allows the user to either identify points manually or to automatically detect and trace a curve. Both methods produce a table of x and y coordinates which can be exported to a graph drawing program.

Over recent year there has been great interest in using Nintendo Wii games console controllers as data loggers. Wii controllers have a built in 3 axis accelerometer and an infrared camera which can be used to give the distance from a pair of infrared sources. They can communicate with computers via their built in bluetooth radio.

Early work [11],[12] involved a significant amount of computer programming. Dedicated and easy to use “Wiimote” software has now been written [13],[14] to allow the connection of Wii controller with a computer and subsequent collection of data in real time.

The computer must have a Bluetooth radio adapter. Sometimes these are built into computers (especially laptops), but a cheap USB dongle can also be purchased. The more stable and reliable ones tend to be those which use the Microsoft Bluetooth Stack drivers. Once the computer is setup, the Wii controller needs to be paired by pressing buttons 1 and 2 together and initiating the pairing via the computer. If a passcode is requested in Windows it can be left blank or skipped by pressing Alt-S on the computer keyboard.

Once the Wii controller is paired, the Wiimote software can be started. In accelerometer mode, the acceleration can be recorded in the x, y and z axis. It measures in units of g between ± 3g with a resolution of 0.04 g. When the controller is stationary lying flat on the desk, one of the axes will measure 1 g. This can be used to measure the acceleration of a dynamics cart, a pendulum, a mass spring system, a lift, a car or a rotating disk.

The software can also be set in “position sensor” mode. The bar which usually sits on top of the TV is commonly referred to as the “Sensor Bar”. In fact, it does not sense anything, but is two infrared LEDs positioned 20cm apart. These two sources emit infrared light which is detected by the 1024 pixel by 768 pixel infrared camera in the Wii controller. Given the angular fields of view of the camera are 41^° horizontally and 31^° vertically it is possible to find the average angle subtended per pixel as 0.040^°. The software in the Wii is able to measure the number of pixels, n, between the two light sources on its infrared camera and convert this into the angular separation. Since the sources are known to be 20 cm apart, the distance, d, from the WiiMote to the Sensor Bar can be calculated using triangulation:

Photographic film may still be used to take images from electron microscopes, X-ray cameras, or to make holograms. Where even possible, CCDs for these operations are still expensive and sometimes difficult to fit to older equipment which is more likely to be present in undergraduate laboratories. Thus it is useful to know how to develop film and then to produce paper photographs.

The film is usually a piece of plastic with a silver halide (typically a combination of AgBr and AgI) emulsion coating and a protective gelatin layer. When the film is exposed to photons of electromagnetic radiation an electron within the halide ion absorbs the photon, gaining energy. This frees the electron so that it is able to move within the silver halide crystal. After some time, it can become trapped by a defect in the crystal (often a silver sulphide impurity) known as a sensitivity speck. The electron can then combine with a silver ion, forming a silver atom. The silver atom is an additional impurity which traps further electrons, creating further silver atoms.

Once exposed in the experiment, individual film packets should only be opened in a dark room. The dark room may be dimly lit with a colored light compatible with the film (meaning the film has a low sensitivity to that specific color of light) or in complete darkness. Usually the solutions necessary are placed in 4 side by side trays.

The film is first put into a developer solution. The developer is an alkali which which preferentially reacts with the silver deposits. Since it is a reducing agent it converts further Ag⁺ ions into deposits of silver. This enhances the process which was started by the free electrons generated by the electromagnetic radiation.

If the film is left in the developer for too long, then all the silver halide crystals will be converted into silver atoms giving a black film. A brief wash in water can remove all the developer and prevents any further reactions.

The film is then placed into a third solution, the fixer. This is usually an acid solution which removes any silver halide crystals which have not reacted. Finally the film is washed again to remove the fixer which prevents the film turning brown due to the formation of silver sulphide. The films should then by hung up to dry or put through a suitable dryer.

The exact chemicals used for the developer and fixer depends on the film. They should be regularly changed if a large number of films are being developed. The time the film is left in the developer and fixer solutions has a large effect on the final image and will depend on their strength. The correct timings will usually be given, however as a guide consider around 1 minute in the developer, 30 seconds in the first wash, 2 minutes in the fixer, and 2 minutes in the final wash.

To create a paper photograph a second stage of development is required. The developed film is inserted into a slot below the light source on an enlarger. The light shining through the film creates an image on the easel. Once the size and position of the image have been adjusted the light on the enlarger is turned off. A sheet of photographic paper is placed onto the easel. The light source can then be turned on using a timer, exposing the photographic paper to the image. The final stage is to develop the photographic paper in a similar way to the development of the film. The developer solution is usually specific to the paper, but the same two wash baths and fixer bath as for the negative can usually be used.

Always carefully mop up any chemicals which are spilt and clear away all chemicals at the end of each session/day as they can leave residues behind when they evaporate. Chemicals should not be returned to the original bottle as this will cause contamination.