low light source

8/14/2019 Low Light Source

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LOW LIGHT SIGNAL MEASUREMENTS

TREVOR DOLINAJEC

PARTNER: YOUNG PYO HOUNG

Abstract: The power output of a low light source, in particular a red LED, was measuredfrom across a room in the presence of myriad noise types. The measurement was made pos-sible by the use of a lock-in amplifier in combination with an optical chopper which turnedthe DC signal of the LED into an oscillating signal at a known frequency. The chopper spunat a frequency of 750Hz and a large time constant was chosen for the Lock-In. This allowedfor the minimization of many types of noise. The experimental measurement made for theamount of power received from the LED was 0.542nW and the theoretical value was 1.51nW.

Introduction: This type of low light experiment has applications in astronomy. If, forexample, a pulsar can be observed through a telescope then theoretically a photodiode couldbe used along with a preamp and a fast Fourier transform spectrum analyzer or a lock-inamplifier to identify the frequency of pulsation. This process can obviously be difficult dueto the small magnitude of the signal. Knowledge of noise sources and appropriate filteringcan help with this identification. Using a lock-in amplifier with the reference frequency seton internal can allow for precise identification of the signal frequency through scanning fre-quencies. This method was used in this experiment to determine the frequency at which heLED was being chopped by the optical chopper. The method proved successful in identifying

the frequency of the flickering LED at a distance of 5.8m. In this sense the experiment isa simulation of pulsar investigation and as such a frequency of 750Hz was chosen for thechopper which is a frequency just above the maximum frequency that pulsars pulsate. Usingthe lock-in amplifier to scan for the frequency of interest works best if a relatively low timeconstant and slope is used so that the lock-in is responsive (more on this in the Apparatusand Procedure section). Low time constants and slopes, however, result in mote noise (seenext paragraph) thus once a frequency is determined another procedure is used to determinethe power output of the light source (LED in the experiments case) as accurately as possi-ble. This procedure involves choosing a higher time constant and slope and using the lock-ininterface program on the computer to collect data automatically over the long time spansnecessary for large time constants and over multiple consecutive runs. In this experiment

the experimental power output and the theoretical power output of the LED were only offby a factor of two which probably says more about the method of approximation used in thetheoretical value than the accuracy of the experiment.

In the exploration of low light signals noise is a very large factor. Relevant forms of noiseare 1f noise, Johnson noise, microphonic noise, 60/120Hz noise, shot noise and instrument

input noise (more on specifics of these noise forms is found in the Theory section). Johnsonnoise, shot noise and instrument input noise can and often are measured in units of A

Hz

Date: 9/20/09.1


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2 TREVOR DOLINAJEC PARTNER: YOUNG PYO HOUNG

where Hz is the bandwidth f. This allows us to express these noise values independent ofbandwidth. When working with a fixed bandwidth, however, these noise forms can be mea-sured in Amps. In particular, the photodiode in this experiment sourced 530A of currentas a result of the LED. The Johnson, shot and preamp instrument input noise were 305 f A

Hz,

876 f AHz

and 600 f AHz

respectively while the bandwidth concerned was the Equivalent Noise

Bandwidth (ENBW) of the lock-in amplifier. The ENBW had an inverse relationship tothe slope (measured in dB/oct) and time constant of the lock-in amplifier (more on this inthe Apparatus and Procedure section). At the highest slope of 24dB/oct the ENBW was5/(64T) where T was the time constant. These numbers and calculations are indicativeof the importance of choosing an appropriate time constant on the lock-in amplifier. Forexample, if a time constant of 300s was chosen then these three noise sources alone wouldalmost completely obscure the LED signal. In this experiment a appropriately large timeconstant of 30s was chosen. The lock-in amplifier also had instrument input noise of 6 nV

Hzso

the time constant of 30s was also appropriate in regards to that noise. Capacitive couplingnoise of 60/120Hz was avoided by avoiding multiples of these frequencies and thus the noisesharmonics while 1f noise was avoided by choosing a rotational frequency of the chopper that

was well out of the low frequency range where 1f

noise dominates.

Apparatus and Procedure: This experiment primarily used a SR830 Lock-In Ampli-fier, SR760 Fast Fourier Transform (FFT) Spectrum Anayzer, SR570 Low-Noise CurrentPreamplifier and SR540 Optical Chopper as well as a PIN-10DP Photodiode, MV5753 redLED, 12V/50W lamp, DS345 Synthesized Function Generator, HP 3465A Multimeter anda Remote Control Box to run the Optical Chopper the lamp and the LED as well as allowus to check the voltage across the resistor in the LED circuit from ease of our lab station.

The FFT Spectrum Analyzer uses a fast method of Fourier transform to take signaldata in the time domain and transform it to data in the frequency domain. This methodallows for real-time Fourier transforms but the digital aspect of the FFT analyzer meansthat resolution of the transform is span dependent. Connecting the Function Generator tothe FFT Analyzer and setting up a 400Hz sine wave shows that the FFT analyzer reads afrequency of 398.44Hz when set at a span of 1.56kHz and a frequency of 400.391 at a spanof 780Hz.The FFT does, however, clearly display the harmonics of the 400Hz wave comingout of the Function Generator which shows that the Function Generator is not perfect andthat the FFT is indeed a very precise instrument.

The Lock-In Amplifier works by using the fact that the product of two sine waves is zerounless the frequencies are exactly the same. In other words, the Lock-In gives a DC outputthat is proportional to the frequency that matches the reference frequency by multiplying allcomponents of the input signal by the reference signal simultaneously. The Lock-In displaysthe input signal in Vrms not Vpkpk. Although the Lock-In does not exactly display Vrms;for example, if a function generators creates a square wave with an amplitude of 1V theLock-In does not display 1Vrms but rather 0.9141Vrms. This is because the Lock-In actuallydisplays the amplitude of the fundamental Fourier component of the reference frequency.The sensitivity setting on the Lock-In should always be set greater than the Vrms of theinput signal to avoid overload.

A important feature on the Lock-In Amplifier is the time constant setting. By usingthe Lock-In Interface Program and a signal from a function generator it can be shown that


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LOW LIGHT SIGNAL MEASUREMENTS 3

if the amplitude of the signal is suddenly and drastically changed, say two orders of magni-tude, that by counting the bins and noting the sample rate the time for the signal amplitudereading on the Lock-In to settle down can be calculated. This settle down time is directlyrelated to the slope setting and the time constant setting of the Lock-In. If the slope isset at 18dB/oct then the wait time for the signal to settle down is 9T where T is the time

constant; 9 seconds for a 1 second time constant for example. The four slope setting on theLock-In basically correspond to 1 through 4 pole type filters. The following table from theuser manual of the Lock-In amplifier shows the relationship between slope and wait time.The table also shows the relationship between slope and Equivalent Noise Bandwidth asdescribed in the introduction.

The time constant clearly determines the ENBW (more on ENBW in the Theory section).The Low-Noise Current Preamplifier basically converts the current signal from the pho-

todiode to a voltage signal that then feeds into the The preamp sensitivity setting was usedto maximize the voltage going into the Lock-In amp while not exceeding the operationalguideline of having a source impedance greater than (sensitivity)1. Given that the PIN-10DP photodiode had an impedance of approximately 177.8k this allowed a sensitivityof 1A/V although in practice 10A/V was used so that the Lock-In would not overload.The Preamp effectively multiplied the incoming current by (sensitivity)1. For example, ifthe photodiode produced 2.4A of current then the preamp would produce approximately2.4mV if the sensitivity was set to 100A/V.

In the LED measurement experiment the chopper speed was set at 750Hz. This ratewas measured by connecting the frequency out cable from the chopper control to the Lock-Inamplifier and setting the reference frequency to external. The tuning of the frequency wasdone using the Remote Control Box. The chopper did not maintain a precise frequency butthe Lock-In adjusted accordingly (the variance was about 1.3Hz). The frequency of 750Hzwas chosen because it was not a multiple of 60/120Hz noise nor was it low enough to be inthe frequency range dominated by 1

fnoise. A cone was attached around the photodiode to

prevent the Lock-In amplifier from unexpectedly overloading. The basic set up is shown inthe following schematic.


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On three separate nights three runs were made. On all three runs the Low-Noise Pream-plifier was set to a sensitivity of 10A/V and the Lock-In Amplifier sensitivity was set to50V. Also a 30s time constant and slope of 25dB/oct was used on all three runs. The onlysetting that was changed from the first to the second and third runs was the Gain Mode onthe preamp was changed from High BW to Low Noise (the results of this change our outline

in Results and Conclusions). The Filter Type was set to none on the preamp for all threeruns. Each run consisted of seven runs as set in the Lock-In Interface Program.

Theory and Supporting Data: One of the predominate theoretical concepts in this labwas the idea of maximizing the time constant so as to minimize noise that was dependenton bandwidth. When considering time constants in general, however, there is more at playthan simply minimizing noise. For example, if a signals amplitude was varying with time alarge time constant would be detrimental to recovering the signal because it would averageout the signal. The following graph shows that a time constant of 100ms does not keep upwith toggling the amplitude of the signal between 2Vpkpk and 1Vpkpk. The sample rate

was 128Hz.

This graph shows data using a slope of 6dB/oct which has the shortest of the wait timesbut we clearly see that the Lock-In does not have time to get back to 0.707Vrms or down to0.354Vrms. A time constant of 10ms allows for much more accurate data in this case. Theamplitude of the triangle wave created by the chopper and the LED, however, was quiteconstant so this consideration did not have to be made in that experiment. Choosing a timeconstant T such that T1 is significantly larger than the reference frequency can also createvery inaccurate data.

The theory behind noise is also a major part of this experiment. There is not much tosay about 1f noise that the name doesnt say. It is only relatively strong at low frequencies

due to its simple mathematical definition and it diverges at zero. Its ubiquitous and there isno universal theory to explain it. Capacitive coupling noise is arguable more complex. In thisexperiment frequencies above kHz were unexplored thus the only relevant capacitive couplingnoise is that of 60/120Hz and harmonics. It can be shown (see Calculations (i)) that theminimum stray capacitance needed to induce a 1mVrms voltage across a 1M resistor from a120Vrms power line with f=60Hz is 0.02pF. This is small necessary capacitance to producea relatively high voltage, especially when one considers that one foot of RG/58 coaxial cablehas 33pF of capacitance. Perhaps this explains the large magnitudes of 60/120Hz noise inmany experiments. The following graph shows the spectrum of a unshielded cable attached to


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the FFT analyzer and laying on the table. We can see 1f

noise to the far left and a large peak

at 60Hz. We can also see many harmonics of 60/120Hz noise. Some are larger than others,such as 180Hz which is second only to the fundamental. The harmonics gradually decrease inmagnitude with higher frequencies until they are essentially lost among miscellaneous noise.

The harmonics on the fundamental of 60Hz noise exist because 60Hz noise is not perfectly60Hz and the Fourier transform exposes its components. It is unfortunate that the verticalscale of this graph is dBV so for clarity the 60Hz peak has an amplitude of 14mV rms. Whena much shorter cable was used the amplitude of the 60Hz peak fell drastically to 125Vrms.When the full length cable is hanging rather than laying the 60Hz peak is at 580Vrms.When the cable is coiled inside of the shielding tube the peak drops to 395Vrms and whenthat shielding is grounded the peak drops further to 180Vrms. The following graph showsthe grounded and shielded case.

The horizontal range is much shorter on this graph than the last but we can make out theattenuation of our the noise peaks. The peak at 75Hz was from the computer monitor andwould completely disappear when the monitor was turned off. Interestingly, this graph doesnot represent the greatest attenuation of the 60Hz peak. When the cable was coiled butnot in the shielding the 60Hz peak was the lowest of all at 90Vrms. This suggests that theshielding was acting more as an antenna than shielding. The theory behind coiling is thatwhen coiled the cable has inductance across the output and thus acts as a High-Pass filter.

Microphonic noise can be caused by shaking in a cable that either has voltage throughit or a cable hanging. A hanging cable when shaken produces low frequency humps thatcan approach the magnitude of the 60Hz noise peak. The humps are only noticeable up toabout 60Hz. If shaking of a cable is estimated to cause a certain change in capacitance than


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microphonic noise in a cable with voltage across it can be estimated quantitatively. If, forexample one is to shake one meter of RG/58 coaxial cable at a frequency of 10Hz with 1Vacross it and 33pF/ft of capacitance leading into a scope with 1M impedance, then givenan estimated change of capacitance of 1pF there would result 10V of microphonic noise(see Calculations (ii)). Microphonic noise can be minimized by having shorter cables that

are less likely to vibrate or shake or even by having stiffer wires.Shot noise is yet another form of ambient noise and the first of the three bandwidthdependent noises mentioned in this section. Like Johnson noise and Instrument noise shotnoise can be measured in A

Hz. Shot noise occurs when current flows through electronic

devises such as diodes. Shot noise is basically given by the standard deviation of the currentover a given bandwidth. More precisely the formula for shot noise is Inoise(rms)=

2qIf.

Where q is the electron charge of 1.61019 Coulomb and f is the ENBW. For example,the photodiode used in this experiment had a measured current during standard operationof approximately 2.4A thus the shot noise of the photodiode at a given frequency would be8.76 1013 A

Hz. As mentioned before, the larger the time constant the smaller the ENBW,

i.e the smaller the f and hence the smaller amount of noise.

Johnson noise is similar to shot noise in many ways, but instead of being associated withthe current flow it is associated with thermal activity. Johnson noise is the root mean squareof the voltage across a resistor. Specifically, Johnson is given by V=

4kTf R where k is

the Boltzmann constant and T is the temperature. Johnson nose can also be described as a

current as I=

4kTfR . Thus Johnson noise can be given in units of

VHz

or AHz

. The PIN-

10DP photodiode had a resistance of 177.8l so its Johnson noise was 54.2 nVHz

or 305 f AHz

.

If we were looking at a current source we would want high impedance according to the aboveequation and if we were looking at a voltage source we would want low impedance accordingto the appropriate equation above. In the case of our photodiode we are looking at it as acurrent source. The reason that we look at the photodiode as a current source and not a

voltage source is because the PN junction behavior of the photodiode is such that voltage asa function of incoming power is nonlinear whereas current as a function of incoming poweris linear.

In order to experimentally confirm the theoretical values for Johnson noise discussedabove an experiment was performed with 10K and 100K resistors attached to the Lock-Inamplifier via a short stiff cable used in order to minimize microphonic noise. The Lock-Inwas set to low noise with a slope of 24dB/oct. The Lock-In Interface Program was used andthe number of runs was set at seven and the BEST CHOICE sampling mode was chosen.The internal reference frequency on the Lock-In was set to 500Hz, chosen because its notso low as to be dominated by 1f noise or possible microphonic noise and because it is not

a multiple of 60/120Hz noise. With these settings one run each was conducted using time

constant of 30ms, 100ms, 300ms, 1s and 3s for each resistor. The analyzed data outputtedby the Interface Program contained a column of seven values (one for each run) that repre-sented the RMS of the voltages in the first column. This value, of course, represented theJohnson noise. For each time constant for each resistor these seven values were averaged.This averaged value was generally off by about

2 from the theoretical value. The reason

that the experimental value was seemingly off by a factor of

2 was because the Interfaceprogram when calculating the values in the < dR2 >1/2 column took the RMS of Johnsonnoise which is essentially already an RMS value. Thus, in the following comparison of the


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two vales, the experimental numbers are always multiplied by a factor of

2 to match themto the theoretical numbers. The Lock-In amplifier also had instrumental noise of its own so inorder to compare the theoretical Johnson noise to the experimental Johnson noise of the re-

sistors the following concept is helpful: (Total Theoretical Noise) =

(VJ,theo)2 + 6nV

5

64T.

The following two graphs show all the experimental values of noise compared with the totaltheoretical noise values.

We can see that to about a factor of two the experimental and theoretical values agree.However, the results appear to be more inaccurate for the 10k then for the 100k for somereason. Also, the 3s time constant produces odd results experimentally for both the 10k and100k resistors. This may be do to some sort of ambient behavior at 3s intervals that is beingpicked by the cable holding the resistor as if it was an antenna.

The last significant theoretical concept in this experiment is the approximation methodsused to determine theoretically the amount of power emitted by the LED which would bereceived by the PIN-10DP photodiode. Firstly, the circuit containing the LED was analyzed.This circuit consisted of a 5V power supply, a 150 resistor and the LED itself. The voltage

across the resistor was measured at 1.4024V and thus the current was calculated at 9.34mA.Since the voltage across the LED was 5V-Vresistor the power output of the LED can be cal-culated as WLED =VI=33.6mW. This number, however, represents the total power outputnot that which is discernible as visible light. To calculate the power output of the LED asred light the standard eyeball curve along with the specifications of the LED were used. TheLED according to its specifications sheet has a dominant wavelength of 635nm so using thecurve this corresponds to 175lumens/watt. The LED has a millicandela rating of 15mcd. Toconvert these candela to lumens we multiplied by 4. Then to convert lumens to watts weused the curve and divided by 175 to get a power output of 1.07mW in terms of red light.This value is appropriately small compared to the 33.6mW total power output. The portionof this power that hits the photodiode across the room is given by the integral

P=

photodiodessurface

I(r) dA.

I(r) can be approximated as Ccos2()

r2.

Completing the integral gives us C=3P

2.

This integral works out this way because we are only interested in the hemisphere with thephotodiode o the z axis. Using the power we calculated using the standard eyeball curve


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we get a value for C of 511W. Using a small angle approximation and the location of thephotodiode on the z axis we can estimate the Pphotodiode as I( = 0, r)Area of Photodiode.The specification of the photodiode tells us that the area of the diode is 1cm 2. Thus thepower received by the photodiode from the LED can be estimated at 1.51nW. This is theso-called theoretical value that is compare with the measured value.

Results and Conclusions: While conducting the experiment to determine the poweroutput of the LED using the set up described in Apparatus and Procedure we found that ifthe preamp was set on High BW then the signal from the LED was indiscernible on the FFTbut when the preamp was set on Low Noise or Low Drift the signal was visible on the FFT.That is to say, there was a small peak of magnitude 13.2 V that was significantly largerthan surrounding noise at the frequency of approximately 750Hz which was the frequencythe chopper was set at.

Three data runs were done to measuring the power output of the LED. The first wasdone using the High BW gain mode. No filter, input offset or bias was used on the Low

Noise Preamplifier. The preamp was set to a sensitivity of 10A/V as it was it on on allthree runs. On all three runs the Lock-In was set on a slope of 24dB, time constant 30s andsensitivity of 50V. The average voltage given by the Lock-In on this first run was 13.1 V.Using Low Noise gain on the second and third run resulted in average voltages of 13.2 Vand 13.3V. Its worth noticing that changing from High BW to Low Noise had little effecton the amplitude of the signal but a large effect on the spectrum as seen on the FFT.

The time constant of 30s was used to minimize Johnson, shot and instrumental noise. Alarger time constant could have been used but the greater time necessary for data collectionmay have not been worth the slight loss in noise. Using our theoretical knowledge of noisewe would expect about 15.6pV of instrumental noise from the Lock-In and the Preamp hadapproximately 156pV of instrumental noise. Likewise, we would expect about 8.27nV of

Johnson noise and 252pV of shot noise (assuming we can use the impedance of the photodi-ode to calculate voltage shot noise). This noises sum to 9.18nV of noise whereas the Lock-InInterface Program reads a RMS of the voltage around 19-28nV. The unexplained noise likelycomes from using the impedance of the photodiode for calculating Johnson and Shot noiseas registered by the Lock-In. Microphonic noise could have been present considering thelong cable leading from the PIN-10DP photodiode to the Preamp but this noise like 1

fwould

have had a much lower frequency than the 750Hz.Using the voltage values given by the Lock-In and the theory described above the ex-

perimental power picked up by the photodiode from the LED was 0.754nW as compared tothe theoretical wattage of 1.51nW using the specifications of the LED and the the approx-imation methods described above. This values are within a factor of two from each other

but this does not necessarily say that the experiment was inaccurate in its measurements.In fact, since the cos2() approximation is an over approximation it is to be expected thatthe theoretical values are larger than the experimental. What we can conclude is that thepower measurements are quite accurate and that this accuracy was made possible by theLock-In amplifier in conjunction with the chopper and that our use of a large time constantminimized some of the most troublesome noise.


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low light source

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