Exp-8-Speed of Light.doc (TJR) Physics Department, University of Windsor 64-311 Laboratory Experiment 8 The Speed of Light Introduction Galileo was right. Light did not travel instantaneously as his contemporaries thought and so he set out to measure it with the aid of some shuttered oil lamps and a trustworthy assistant on a distant hill. Although he did not succeed, he concluded that light was exceedingly fast. Experiments since then have improved steadily and the accepted value is 299 792 458 ms -1, i.e. about 3 x 10 8 ms -1. This is a staggering number in the world of cars and rockets. It is unfortunate that we get too used to it in the world of physics. This experiment is more concerned with technique than with observing a complex process (after all, the only required equation is v = d/t.) Its aim is to introduce the student to the application of fast timing electronics to measure the speed of light by the time-of-flight method. You will also gain a good deal of experience with single photon counting using a photomultiplier. Experiment Figure 1. Multi-mirrored apparatus for measuring the speed of light. 1
Figure 1 depicts the apparatus used for the measurement. A simple pulsing circuit (Ciholas and Wilt, 1987) is used to produce a sharply peaked 30 ns wide pulse of red light from a light emitting diode (LED). A short focal length lens is used to collimate the beam. The beam is directed between the mirrors as shown and into a photomultiplier. There is a shutter and a red filter in front of the photomultiplier. For alignment of the beam, the pulser can be switched to the continuous mode. There is an output on the pulser labeled start. The output from the photomultiplier and its preamp is labeled stop. These signals will be used to start and stop an electronic timer known as a Timeto-Amplitude Converter (TAC). The electronics used to process the pulses are shown in Figure 2. The electronics units are standard Nuclear Instrumentation Modules (NIM) which fit in a NIM bin. It is important to understand that NIM's were developed to handle electronic pulses, both analog and digital. There are two standard logic pulses used in counting and timing measurements. The NIM standard positive logic is defined as follows: Logic 1 +3 to +12 V, i.e. +5 V; Logic 0-2 to -1.5 V, i.e. 0 V and the pulse width is typically 0.5 μs. The standard input impedance is 1000 Ω. Count rates up to 20 MHz can be measured with NIM positive logic. NIM s also have a fast negative logic which is defined as follows for a 50 Ω termination: Logic 1-12 to -36 ma, i.e. -500 mv on 50Ω ; Logic 0-4 to + 20 ma, i.e. 0 mv These negative pulses are usually very short, although the width is not important. The risetime (actually a fall time) is important and is about 2 ns. It is this very fast leading edge of the negative going logic pulse that is used for triggering in fast timing applications. (NIM's also use ECL and TTL logic, but that is not important here.) Returning to the electronics, a fast negative NIM logic pulse is produced by the LED flasher when it is turned on. This triggers the start on the TAC. Light from the LED makes multiple passes between the mirrors and eventually reaches the photomultiplier. Each single photon of light produces a single pulse of electrons at the output of the photomultiplier. Each pulse is about 10 ns wide and can reach up to -50 mv into a 50 Ω load. This is too feeble for standard NIM fast logic, so the output from the photomultiplier is connected to a pre-amp and then to a fast amplifier. Fast Amplifier Fast Discriminator Counter +ve Out In Out In From Photomultiplier -ve Out Pulse Height Analyser From LED Pulser Nanosecond Delay Stop TAC Start Figure 2. Signal processing electronics. 2
The pulses from the fast amplifier are sufficient for NIM negative logic, but if you were to observe them on an oscilloscope you would see that they vary widely in height from several mv to several volts. The smaller pulses arise from thermionic emission of electrons from the dynodes in the photomultiplier. These pulses are referred to as dark counts since they are always present in absolute darkness. It will not be necessary (or desirable) to count those. Since dark counts are mostly small pulses, a discriminator can be used to remove them. Setting the proper threshold involves a close examination of the pulse height distribution. A fast discriminator receives analog pulses, and produces a slow positive and fast negative NIM logic pulses if the input analog pulse has a magnitude higher than the threshold voltage. The threshold is set by the front panel 10-turn potentiometer. The fast logic pulse is connected to the stop input of the TAC, and the slow logic to a counter. The TAC produces a 3 μs wide pulse whose height is determined by the time difference between the start and stop pulses. The output amplitude ranges from 0 to + 10 V. The conversion scale of the output is set by two front panel rotary switches. Use 100 ns or 200 ns scale for the purposes of this experiment (i.e. 0 to + 10 V represents 0 to 200 ns). Now that the timing information is contained in the height of a pulse, this information must somehow be recorded. There are several ways of doing this, but one of the most convenient is the Pulse Height Analyzer (PHA). The PHA is essentially a fast digitizer with many counters. It converts the pulse height into a number. That number becomes the address of a counter. The value in that specific counter is then increased by one. The contents of all the counters can be displayed in histogram. Repeating this process over and over again produces a pulse height distribution of the TAC output which, in turn, is measure of the distribution of flight times for photons between the LED and photomultiplier. Procedure i.) Operating the photomultiplier and pulse amplifiers. Plug all the NIM units into the NIM rack (Ensure the NIM Bin is powered off while inserting or removing NIM modules.) Set up the LED pulser, photomultiplier (RCA 1P21) and mirrors on the track. The LED pulser operates at 2.5 khz. Connect the pre-amp (ORTEC Model 9301D) directly to the photomultiplier output with a BNC coupling. Power for the pre-amp is supplied at the rear panel of the fast amplifier. Making sure that the power is off and that the SHUTTER IS CLOSED (i.e. the pushing rod is down ), connect the high voltage to the photomultiplier (it has an SHV jack). Connect the output of the pre-amp to channel 1 of an oscilloscope with a 50 Ω termination. Set the vertical scale to 100 mv per division, and the sweep speed to 10 ns per division. Set the trigger mode to auto, the source to channel 1, and the slope to negative. You should see a flat trace. Now turn on the voltage to the photomultiplier. You should see sharp negative going pulses displayed on the oscilloscope with amplitudes ranging from 0 to -50 mv. If you do not see the pulses, adjust the trigger level on the oscilloscope until you do. Even then, the traces will be very faint - why? (You may have to shut off the lights in the room to see the oscilloscope display.) These pulses are the dark counts from the photomultiplier cathode and dynodes. Make a sketch of what you see. The preamp has a gain of 10 tends to lengthen the actual photomultiplier pulses as well. The fast amplifier is an ORTEC Model 474 Timing Filter Amplifier (TFA). Plug the photomultiplier output into the TFA input. Set the Integrate and Differentiate controls to out (i.e. off ). Set the toggle switch to invert. Plug the output of the preamplifier into the oscilloscope using 50 Ω termination. Switch the slope to positive and observe the pulses. Set the coarse gain on the TFA 3
to x20, with the fine gain no higher than 5 ; the pulse heights should then range from 0 to under +5.0 V. The gain of the TFA is the product of both the coarse and fine gain adjust knobs. (The TFA begins clipping the pulses at +5 V, that is its limit of amplification.) Sketch the TFA output. The pulses from the photomultiplier are never the same size. As mentioned earlier, the smallest pulses arise from random thermionic emission from the dynodes. It would be useful to know the way the pulse heights are distributed in order to set the discriminator at a threshold which would ignore most of the small pulses but still acknowledge the larger pulses which would come from the genuine signal. That is the subject of the next section. ii.) Pulse height analysis of the photomultiplier dark counts. Setting the discriminator level. The fast discriminator is an ORTEC Model 551 timing Single Channel Analyzer (SCA). The SCA does a lot more than function as a discriminator described earlier. In addition to adjusting a lower level threshold, an upper level threshold can be adjusted so that the SCA produces an output only if the pulse height is between the lower and upper levels. (That is the function of a single channel analyzer.) One can also set the toggle switch to the window mode, and in that case, the SCA produces an output if the input pulse is between the setting of the lower level, and the sum of the lower level plus the width of the window set by the upper knob. You will use the SCA first in the window mode to examine the pulse height distribution of the TFA output. This will enable you to determine the proper setting of an optimum discrimination threshold to eliminate the many smaller pulses due to dark counts. Set the 10-turn knob marked delay to its lowest point. Set the delay toggle switch to 0.1-1.1 μs (This refers to the amount of time taken for the SCA to produce an output once the threshold has been crossed.) Set the toggle switch to the right of that to WIN, as this puts the SCA in the window mode. The lower level 10-turn knob has a range from 0 to 10.0 volts. Adjust it to 100 mv. The upper level or window 10-turn knob has a range from 0 to 10.0 volts. Set it to 100 mv. The SCA will now produce a slow and fast logic output when the pulse height on the input is between 100 and 200 mv. Plug the output from the TFA into the SCA input. Plug the SCA positive output into the counter positive input (Mechtronics Model 719). The counter should be in the repeat mode, with a counting time of 1 second. Switch the gate time to 1, the multiplier to 10, and the time to 0.1 sec. Press start. The counter will count for 1 second, stop, hold the value momentarily (set by the hold time ), reset itself, and start all over again. The count rate will vary, and may be as high as 5000 cps (counts per second) or Hz. If it is higher, then there could be a light leak. Check by shutting off the room lights. (It does not matter if there is, as long as it is small (below 5000cps). Record the count rate with the SCA lower level at 100 mv. Then record the count rate with the SCA lower level at 200 mv. Be sure the count time is long enough (~10s) to get good statistics, i.e., at least over 1000 counts. Continue incrementing the lower level in 100 mv steps, and recording the count at each interval, until you reach 5.0 V. As you increase the lower level, the count rate will drop dramatically. Do not increase the counting time, even though the variance will get progressively poorer. Make a histogram of your results. You will have produced a pulse height distribution of the amplified photomultiplier dark counts. From this plot, you can see how the many small pulses drop off nearly exponentially. The optimal discrimination threshold should be set at that value where this exponential curve has just started to level off (see figure 3). The pulse heights from there and upwards are mostly due to electrons emitted by the photocathode. Consequently they are amplified the most, avalanching through all of the dynodes. Now, set the SCA mode toggle switch to INT. This makes the SCA a simple lower level discriminator, or an integral discriminator as it is called because the upper level knob is disabled. Set the lower level to the optimum threshold you found from the pulse height distribution. The count rate on the counter is now for all the pulses that are larger than the threshold. 4
Figure 3. Pulse height distribution of dark counts from a photomultiplier. The arrow indicates the position at which the lower level discriminator should be set. Frequency of Occurance Pulse Height iii.) Operation of the Time-to-Amplitude Converter. Connect the negative output from the SCA to the oscilloscope with a 50 Ω termination. Switch the trigger slope to negative and adjust the vertical scale until you see a short fast negative NIM logic pulse of about -500 mv in amplitude. Make a sketch of the output. Connect the negative out of the SCA to the stop input of the TAC. Plug the LED trigger output into the oscilloscope to view the pulse (50 Ω termination). It should be at least -400 mv in amplitude or it will not trigger the TAC. Plug it into the nanosecond delay unit, with the delay at 120 ns. The delay is in place to compensate for the delay of the stop signal through the electronics. This will enable the use of a smaller time scale on the TAC. Plug the delay output into TAC. The TAC is an ORTEC Model 566 and its operation has already been described. Set the range to 200 μs. The strobe switch should be on internal. View the TAC output on the oscilloscope (50 Ω). You should see nearly square pulses over 3.0 μs wide with amplitudes uniformly displayed from 0 to + 10 V. That is because the LED pulser is starting the TAC every 400μs, and the TAC stops are coming from the random dark counts. So the pulse height distribution of the TAC output is uniform. Again, make a sketch of what you see. The pulse height distribution of the TAC output is the distribution in time of the pulses coming from the photomultiplier. This is the information we will eventually want. We can measure the pulse height distribution in the manner described in the last section, but fortunately, a better method has been devised using a device called a pulse height analyzer. iv.) Operation of the Pulse Height Analyzer (PHA). Plug the TAC output into the direct input of the Nucleus Model 2560 Multi-Channel Analyzer (MCA). (At this point you have finally completed the circuit diagram of figure 2.) The MCA has a display with four controls underneath for brightness, focus, vertical and horizontal adjust. To the immediate right of that is a panel of switches. In the first panel there is a dead time meter, a channel select cursor knob, and a dwell time knob. Set the dwell time knob to PHA. This puts the unit in the pulse height analysis mode needed for the experiment. The two toggle switches below that should be in the ADD and FULL positions. The next panel to the right has a live time knob. It should be in the off position. The three 5
push buttons below that are used to start and stop data acquisition, and erase the contents of the memory. Further to the right is the input for the PHA mode of operation. There is also an amplifier which is not needed for our purposes. Plug the TAC output into the direct input with the toggle switch in the appropriate position. The next and final panel of switches should be set as follows. Counts full scale: 100; Vertical Expand: off; Horizontal Expand: off; Readout Mode: Scope. The 2560 MCA has an 8-bit digitizer. The pulse heights from the TAC will be digitized, and the resulting number will be the address of the counter which will be incremented by one. (If we had selected the subtract mode, the counter at that address would be decrease accordingly). The contents of all 256 counters are displayed on the screen. The contents of each individual counter can be obtained by the cursor on the display, Move the cursor with the channel select cursor. The current counter (called a channel ) address is displayed by the LED readout at the top, along with its contents. Start the MCA by pressing the Analyze button. You should see a twinkling display on the screen as the PHA circuit busily sorts out the pulse heights from the TAC at 2500 times per second, and update the display. Let the MCA accumulate for a few minutes and then stop it. Be sure to familiarize yourself with the controls because you will have to operate it in darkness. Look at the display. Move the cursor from channel to channel, observing the counts in each channel. The counts may be scattered about some average value, or they may be close to zero. In either case, you have seen it before, the Poisson distribution. You also might have noticed that the display has a slope to it, going from higher to lower counts as the channel number increases. The reason for this is as follows. Every time the TAC is stopped by a random dark count, any other dark counts after that are ignored. The TAC can only be stopped once, then it begins converting the time interval into a pulse of the appropriate height, sends it out to the MCA, and then resets itself to wait for another start pulse. In this manner, single photon counting with a TAC always lends a bias to stop signals earlier in the time interval. The effect is to skew the pulse height distribution with a negative slope for Poisson pulses (like dark counts) at low count rate, or even an exponential distribution at high count rates. This is called TAC pile-up. To avoid it, work at count rates of about one stop per start, or about 2500 photons per second above the dark count in our case. Switch the conversion on the TAC to 200 ns and start the MCA. Now you should see much fewer updates of the MCA display (less twinkling) why is that? v.) Measuring the speed of light. Make sure the pulser / photomultiplier / mirror assembly is at the far end of the tracks, firmly up against the stops. The reflector assembly is what is slid up and down the tracks. Move it up to the 0 meter mark and align the mirrors so that the light from the LED makes the multiple passes shown in Figure 1. You will have to shut off the room lights at this point. The light should fall centrally on the entrance of the photomultiplier (the shutter is still closed, right?). Now slide the reflector assemble to the 2 meter mark. The LED light should still fall on the photomultiplier entrance. If not, make the necessary optical adjustments. The light should always hit the target regardless of where the reflector is positioned, without any adjustment of the mirrors, for the highest precision. Once all the alignments have been made, place the reflector assembly close to the LED source. Switch the LED to the pulse mode. Are the lights off? Making sure the photomultiplier is still on and ready, slowly open the shutter until you see the count rate begin to climb. Adjust the opening until the count rate is about equal to the pulsing rate of the LED (2500 cps) plus the dark count. Of course, the ambient light created by the various displays and power on lights of the electronics will contribute to the background. You may want to take steps to eliminate these with some black electrical tape. The red filter on the photomultiplier does a lot to attenuate the background light by keeping photons below 650 nm from entering. 6
Press the acquire button on the MCA and before your eyes you will see a display which accurately represents the distribution of flight times of single photons from the LED to the photomultiplier. Allow the data acquisition to continue until the distribution maximum reaches count of 5000 or more. (Why?). You can press the stop button, and start again without any loss of data. The shape of the distribution is the shape of the intensity of light from the LED when it is pulsed. The result is a time-of-flight spectrum. Once you are done, close the shutter, and then turn on the room lights. Use the channel select cursor to record on paper the channel number, and the counts in each channel for the range of channels that cover the shape of the distribution. Erase the display. Move the reflector assembly on the track 0.500 ±0.001m away from the front of the pulser / photomultiplier / mirror rack. Think carefully about your zero reference point, as this will lead to a systematic error. Shut off the light again. Now repeat the procedure as before, recording the count distribution from the MCA on paper. Repeat this for the mirror assembly at 1.000, 1.500, and 2.000 m. In each case the pulse height distributions should be identical, but delayed. The difference between the centers of the pulse height distributions in channels must be converted to a time. vi.) Calibration of the time scale. This can be done with lights on. Plug the output from the LED pulser into a BNC T-piece. From there one branch should go to the TAC start, and the other to the nanosecond delay box. The output from the delay should go to the TAC stop. Set the delay to 60.0 ns. Acquire a time-of-flight spectrum. You should just see a single spike (although it may cover two channels). Now, set the delay to 120.0 ns and without erasing the first, acquire another spectrum. Calculate the distance between the centers of both spikes in channels, and thus the horizontal time scale. Note the direction in which changing the 60 120 ns delay made the peaks move. The origin of the time scale may be to the right, not left, of the peaks! You should plot the distance versus time delay, and calculate the speed of light from a least squares fit of a straight line through the data points. Questions. Describe the operation of a photomultiplier. There are other sources of dark counts in a photomultiplier which we did not take steps to avoid since they are not critical for this experiment. What are they? Account for all the errors in the measurement you made. What are some at the other methods of measuring the velocity of light? Which is the most precise? How does your measurement and uncertainty compare with other time-of-flight experiments in the American Journal of Physics articles? References Bates H.E., Am. J. Phys. 56, 682 (1988) Becchetti F.D., Harvey K.C., Schwartz B.J. and Shapiro M.L, Am. J. Phys. 55, 632 (1987) Ciholas M.E. and Wilt P M, Am. J. Phys. 55, 853 (1987) Deblaquiere J.A., Harvey K.C., Hemann A.K., Am. J. Phys. 59, 443 (1991) EG&G / ORTEC NIM Catalogue/Handbook Hammamatsu Photomultiplier Handbook RCA Photomultiplier Handbook 7