Sound card based digital correlation detection of weak photoelectrical signals

Transcription

1 INSTITUTE OF PHYSICS PUBLISHING Eur. J. Phys. 26 (25) EUROPEAN JOURNAL OF PHYSICS doi:.88/43-87/26/5/6 Sound card based digital correlation detection of weak photoelectrical signals Guang-Hui Tang and Jiang-Cheng Wang Department of Physics, Normal College of Shihezi University, Xinjiang 8323, People s Republic of China jcwang5@63.com Received 4 March 25, in final form 8 May 25 Published 8 July 25 Online at stacks.iop.org/ejp/26/835 Abstract A simple and low-cost digital correlation method is proposed to investigate weak photoelectrical signals, using a high-speed photodiode as detector, which is directly connected to a programmably triggered sound card analogueto-digital converter and a personal computer. Two testing experiments, autocorrelation detection of weak flickering signals from a computer monitor under background of noisy outdoor stray light and cross-correlation measurement of the surface velocity of a motional tape, are performed, showing that the results are reliable and the method is easy to implement.. Introduction The correlation method is a technique to investigate weak signals against a noisy background. Through correlation calculation of the unknown signal, the useful signal is enhanced while the background noise is suppressed. Due to its importance and effectiveness, the correlation method has been introduced in college physics education for many years and also been widely applied in technology. One of the applications is to detect weak photoelectrical signals in optical spectroscopy measurements [, 2]. In general, to implement such technique, dedicated hardware or a software correlator is required most of the time, which consequently increases the experimental costs and difficulties, especially for researching applications to examine a dynamic process in microseconds to nanoseconds. However, for some relatively slow processes, i.e. the time scale is milliseconds or submilliseconds, such as correlation velocimetry [3 5], and microscopic photon correlation spectroscopy on living cells [6], it is possible to use an inexpensive and slower correlator to analyse such slow signals. As we know, a sound card is a very common component in a computer. It is also an economic and yet precise analogue-to-digital converter with the general sampling rate as high 43-87/5/5835+7$3. c 25 IOP Publishing Ltd Printed in the UK 835

2 836 G-H Tang and J-C Wang as 44.k. With the support of software, the computer sound card can be used as a digital data acquisition system for mid- and low-frequency signals [7, 8], which meets the need of investigation of the above-mentioned relatively slow signal. A photodiode is a kind of optical sensor frequently applied in photoelectrical signal inspections. As illuminated, due to the photovoltaic effect, there is a voltage across the PN junction in the photodiode. This voltage changes linearly with the illumination light intensity. At present, a photodiode is very sensitive, has high speed and is inexpensive. In this paper, we propose a simple and low-cost digital correlation method to detect weak photoelectrical signals. The method needs a sound card, photodiode and personal computer. To show the feasibility of the method, we perform two experiments: autocorrelation detection of weak flickering signals from a computer CRT (cathode-ray tube) monitor and cross-correlation measurement of the surface velocity of a motional tape. 2. Theory Correlation detection theory can be found in many textbooks. To simplify, given two signals f (t), f 2 (t) consisting of useful signals s (t), s 2 (t) and noise n (t), n 2 (t), where t is the time. f (t) = s (t) + n (t) () f 2 (t) = s 2 (t) + n 2 (t). (2) The cross-correlation function (CCF) of f (t) and f 2 (t) is defined as T R f f 2 (t) = lim f (τ)f 2 (τ + t)dτ. (3) Therefore, R f f 2 = R s s 2 + R s n 2 + R n s 2 + R n n 2, where R s s 2 is the CCF of s (t) and s 2 (t); R s n 2 and R n s 2 are the CCF of s (t), n 2 (t) and n (t), s 2 (t), respectively; R n n 2 is the CCF of n (t) and n 2 (t). Because of randomness of noise, the correlations of R s n 2, R n s 2 and R n n 2 are close to zero; hence R f f 2 R s s 2. Only the useful signal is enhanced and the distraction of noise is well restrained. The power spectra of useful signals can be obtained through Fourier transformation of the correlation function, To calculate R f f 2 in a digital way, we have R s s 2 (j t) = N j s (i t)s 2 (i t + j t) (4) N where j =,, 2, 3,...,k (k N). t is the sampling time, N is the total number of samples. According to sampling theory, in order to undistortedly digitalize an analogue signal, the sampling frequency should be at least twice that of the sampled signal. Furthermore, due to the digitalizing process, there is a technological temporal delay between the correlation function and the original signal. The delay depends on the equipment s sampling rate and calculation ability. Nowadays correlators can make the delay very small and reconstruct the original signal almost in real time. However, for a relatively slower correlator, the delay is significant and has to be considered if the time dependence is concerned. In practice, we often use a normalized CCF, ˆR s s 2 = R s s 2 / R s s R s2 s 2 / N j N N ˆR s s 2 (j t) = s (i t)s 2 (i t + j t) s (i t)s (i t) s 2 (i t)s 2 (i t). (5)

3 Sound card correlation detection 837 When f (t) = f 2 (t) = f(t) = s(t) + n(t), we have the autocorrelation function (ACF) of signal f(t),r ff R ss ; from equation (5), the normalized ACF becomes / N j N ˆR ff (j t) = ˆR ss (j t) = s(i t)s(i t + j t) s(i t)s(i t). (6) Supposing signal s(t) is a periodic signal with period T,s(t) = s(t + T), its ACF is R ss (t) = lim s(τ)s(τ + t)dτ = lim s(τ + T)s(τ + t + T)dτ = R ss (t + T). Therefore the ACF of s(t) is also a periodic function with the same period. This can be used to measure the frequency of a weak periodical signal. Supposing signal f 2 (t) = f (t ), i.e. f (t) is f 2 (t) with a delay time, R f f 2 (t) = lim f (τ)f 2 (τ + t)dτ = lim f (τ)f (τ + t ) dτ. When t =, R f f 2 goes to its maximum. This principle is frequently used in the non-contact measurement of surface velocity [3 5]. As reflection or transmission light from a certain area of a motional surface goes through two optical sensors a distance L apart, the CCF of the two photoelectrical signals gives a peak. The time corresponding to the peak is the passing time and the velocity of the surface then is determined by L/. Therefore, one of the systemic measurement errors is mainly caused by the passing time measuring error, i.e., the systemic sampling time. In practice, the distance between the two sensors should be small enough to obtain better correlation, and the motional surface should be free of shaking and vibration to avoid uncorrelated signals. 3. Experiment According to the principle described above, the main experimental problem is how to acquire digitalized sample data as time and calculate the correlation function programmably. The basic experimental set-up includes a photodiode; a computer equipped with a sound card and corresponding software. In the experiment, we choose a sensitive, high-speed FDS Si photodiode (Thorlabs, Inc., spectral response 35 nm, rise time ns) as the light intensity sensor. Since we are mainly concerned with the change of the light intensity, the effects of different light wavelengths on the photodiode do not alter the frequency of a periodically changing light intensity and hence are not considered. The maximum photovoltaic voltage is about.3 V as measured using white light. For simplicity, to avoid disturbance of low-frequency radiation by a power supply, instead of using an input matching circuit, we use coaxial cables to directly connect the photodiodes to the line-in port of the sound card. This sound card data acquisition system is triggered by a Matlab program. There are many commercial or free download software programs to support this, such as sound card spectrum analyser, oscilloscope, signal analyser toolkit, etc (e.g. [7, 8]). Here we use Matlab version 6.5, a software platform that has been applied extensively in technology and engineering. It has many application toolboxes. One of them is a data acquisition toolbox. It offers an example to apply a computer sound card as an analogue-to-digital converter to acquire digitalized sample data. On this software platform, we write a small simple program to trigger the sound card to collect digitalized light intensity data from the photodiode and calculate its correlation function according to equations (5) and (6). Figure shows the experimental set-up of the autocorrelation detection of weak flickering signals from a computer monitor. First, we put the photodiode into a black box and trigger

4 838 G-H Tang and J-C Wang Outdoor stray light Line-in Sound card A/D Software Monitor Computer ACF Analysis Figure. The experimental set-up for autocorrelation detection of weak flickering signals from a CRT monitor. The photodiode is connected to only one channel of the sound card line-in port. The monitor refresh rate is set as 85 Hz on a Pentium personal computer. Light source (Laser) Transport Tape d Thick glass CCF Analysis Computer Software Micropump motor Line in R & L Sound card A/D Figure 2. The experimental set-up for cross-correlation measurement of surface velocity. A He Ne laser beam is split into two beams by a thick glass. The two laser beams are cm apart. The two photodiodes are connected to the sound card right and left channels. The transport tape is made of semi-transparent tape and driven by a micropump motor. The transportation speed of the tape is.2 ±. m s as measured using a stopwatch. the sound card to see the dark noise level of the system. Because we are using outdoor stray light as background light, the experiment has to be performed during the daytime. We then point the photodiode at a window with an angle that lets both outdoor stray light and the computer monitor s light go into the photodiode. We then turn off the monitor for a moment and trigger the sound card to receive the outdoor stray light signal, the background noise; next, we turn on the monitor and start the program to trigger data acquisition to detect the monitor flickering plus background light intensity and figure out the flickering frequency from ACF calculation. Since the purpose of the experiment is to test the feasibility of the method to detect weak photoelectrical signals, the monitor light goes into the photodiode at an incident angle of about Therefore, most of the light intensity signals are from the outdoor stray light. Figure 2 shows the experimental set-up of the cross-correlation measurement of motional surface velocity. We choose a He Ne laser (wavelength nm, power. mw) as the light source. The experimental subject is a homemade transportation tape using a semi-transparent tape driven by a micropump motor. As indicated in figure 2, two photodiodes are underneath the tape to receive the transmitted light signal. When the tape moves, we first measure the speed of the tape by a stopwatch and then trigger the program to collect the two signals and calculate their CCF to determine the passing time and figure out the velocity. 4. Results and discussion As the photodiode is connected to the sound card and put into a black box, due to environmental electromagnetic radiation, there is a small response voltage loading on the PN junction. When

5 Sound card correlation detection 839 Intensity (Volt) 2 x -4 - (a) ACF..5 (b) Intensity (Volt) 2 x -4 - (c) ACF..5 (d) Figure 3. Autocorrelation detection of CRT monitor refresh rate against a noisy background. In all panels, the sampling rate is 8 s and the total sampling time is s. (a) Background outdoor stray light intensity fluctuates with time. (b) Time-dependent ACF of data in (a). (c) Monitor refresh induced flickering light intensity signal against noisy background outdoor stray light. (d) Time-dependent ACF of data in (c). The Y-axis in (a) and (c) refers to the voltage input into the sound card by the photodiode, which relatively reflects light intensity. Each circle refers to one raw data point ((a) and (c)) or calculated ACF value of each raw data ((b) and (d)). Solid line in (d) is a nonlinear least-squares fitting curve of the data. The fitting model is y = a + b cos(2πf t + c), wheref is just the refresh frequency of the monitor, since ACF does not change the original signal frequency; a, b and c are fitting parameters respectively. no light illuminates the photodiode, the resistance of the PN junction is high, and when the photodiode is illuminated, the resistance is relatively lower. As measured in the experiment, the dark noise level of the system in figure is low. Based on five times s measurements, the peak value of the noise is V; the average noise level is V. As the photodiode points towards the window and a turned-off computer monitor, this voltage becomes lower due to lower PN junction resistance. Based on five times s measurements, the peak value of the background noise is.37 4 V; the average value is V. Figure 3 shows one of the results of the ACF detection of the flickering signal from a monitor. In figure 3(a), we see that original background light intensity signal is as low as 4 V, which belongs to the weak signal. Its ACF in (b) is also low with no regularity. They belong to the noisy signal. In figure 3(c), this signal is very similar to that in figure 3(a), though it is the signal from both monitor and outdoor stray light. The flickering signal of the monitor is totally covered by the noisy background. However, through calculation of the ACF, as figure 3(d) shows, the flickering signal obviously stands out of the noise. To calculate the signal-to-noise ratio (SNR) in figure 3, we take the peak value in figure 3(a) as the noise level and the peak value in figure 3(c) as the signal level, hence the SNR = log (peak of signal/peak of noise) =. db. If we do the same calculation for the peak value in figure 3(b) and the peak value of the enhanced signal in figure 3(d), we have the SNR =.6 db,

6 84 G-H Tang and J-C Wang Intensity (Volt) 5 x x -3 Φ (a) CCF Φ (b) Figure 4. Cross-correlation detection of motional semi-transparent tape surface velocity. The sampling rate is 8 s and the total sampling time is s. (a) The two light signals intensity versus time. (b) The normalized CCF of data in (a). which is one order of magnitude higher. We see that through correlation detection, the SNR is improved significantly and the sensitivity of the system is as high as db. To make the ACF curve smoother, one can increase the sampling time to get more samples and more suppressed noise. We repeated the experiment ten times and we have the monitor flickering frequency 85.3 ±.4 Hz, which is in good agreement with the computer configuration. In addition, we also measured a fluorescence lamp s flickering frequency in the presence of a noisy background and got a very good result that will be published in the future [9]. Figure 4(a) shows raw data from two photodiodes during the CCF detection experiment. As the lines in figure 4(a) indicate, the parts of the two signals after the lines are similar but with a delay time. This time is the passing time. Figure 4(b) gives the CCF of the two raw signals in (a). We clearly see that there is a peak of the CCF. The time corresponding to the peak is the passing time according to the theory previously described. The distance between the two photodiodes divided by the passing time hence calculates the velocity. We also note that the peak value is about.8. We consider that, because of the shake of the moving tape, some uncorrelated signals may enter the photodiodes and decrease the correlation between the two signals. If there is no such shake, the peak value will be around. After ten such measurements, we have the velocity.2 ±.22 m s, which agrees well with the results from stopwatch measurements.2 ±. m s. From these two testing experiments, though the photoelectrical signal from the photodiode is as low as sub-millivolt, the sound card based correlator can still calculate its correlation function and pick out some useful signals from noisy background. The results are accurate and well reproducible. According to the properties of the sound card, the sampling rate ranges from 8 s to 44 s (for some professional sound cards, the sampling rate is as high as 96 s ), and satisfies the digitalization of signal frequency 2 2 Hz (higher for a professional sound card). Since the sampling time can be as low as a few microseconds, therefore, the sound card correlator may detect a dynamic process from seconds to submilliseconds, and is suitable to investigate some previously mentioned relative slow processes. 5. Conclusions In conclusion, with the assistance of the sound card as an analogue-to-digital converter and a photodiode as an optical sensor, simple and low-cost digital correlation detection

7 Sound card correlation detection 84 of weak photoelectrical signals is feasible and easy to implement. The method may be used as a classroom demonstration of correlation detection or a laboratory experiment for undergraduates physics teaching. It may also be applied in scientific research to investigate some relatively slow dynamic processes, i.e. the time scale as millisecond or submillisecond, such as bio-macromolecule fluorescence spectroscopy and dynamic light scattering spectroscopy. Acknowledgment The authors thank Shihezi University for financial support in part. References [] Pecora R 985 Dynamic Laser Scattering (New York: Plenum) [2] Krichevsky O and Bonnet G 22 Fluorescence correlation spectroscopy: the technique and its applications Rep. Prog. Phys [3] Sabater J 98 Laser speed measurement by correlation J. Opt [4] Gogoasa I, Murphy M and Szajman J 996 An extrinsic optical fibre speed sensor based on cross correlation Meas. Sci. Technol [5] Zeitler R 997 Digital correlator for measuring the velocity of solid surfaces IEEE Trans. Instrum. Meas [6] Wang J C 2 Design and testing of a novel microscopic photon correlation spectrometer with higher accuracy J. Opt. A: Pure Appl. Opt [7] Höller P 995 A software oscilloscope for DOS computers with an integrated remote control for a video tape recorder: the assignment of acoustic events to behavioural observations Comput. Methods Programs Biomed [8] Aliga J and Michaeli L 23 Software for metrological characterisation of PC sound cards Comput. Stand. Interfaces [9] Tang G H and Wang J C 25 Correlation detection of fluorescent lamp flicker using a sound card Am. J. Phys. to be published