1. Introduction

In this paper we present a calibration method for a photon counting system capable of distinguishing up to three simultaneous photon events. The system is based on three parallel discriminators that are to be set at different levels corresponding to typical pulse heights of one to three detected photons. Discriminator level optimization for single-photon counting is well known [1 and others], but in order to count random multi-photon events correctly, multiple discrimination levels must be optimized. This is especially important when these random signal fluctuations are large as compared to the average of the signal.

We have previously presented a microfluorometer instrument for bioaffinity assays based on two-photon excitation of fluorescence and observation of individual suspended microparticles [2–4]. The work that we present now, although general in applicability, is aimed for further optimization and improvement of the previously presented instrument. In our system nanosecond laser pulses are used for two-photon excitation of fluorescence. Because of the high peak power of the laser the probability of detecting multi-photon events can sometimes become high during observation of individual microparticles. Therefore conventional photon counting with one discriminator level cannot be used without compromising the working range of the instrument. On the other hand, most measurements are performed under conditions where single-photon counting provides the optimum signal to background ratio. Due to this photon counting character of the measurement, a novel type of photomultiplier tube, channel photomultiplier (CPM) was chosen as the photodetector. CPM has high gain and excellent narrow response for single photoelectrons making it a good choice for single-photon counting [5]. Other advantages are its compact size and reasonable price. Unfortunately, its multi-photon resolution is rather poor. Despite of the poor multi-photon resolution, our results show that it can be used as a multi-photon fluorescence detector in cases where the gain variation of individual pulses can compensated by integration of signals. This assumption holds when the multi-photon signals distributed randomly in time are distributed in signal around a common mean.

2. Calibration method

The basic idea of the calibration method bases on the use of a pulsed light source. The short pulses of light are directed both to a coincidence photodiode and the photomultiplier to be calibrated. A strong attenuation of light is required for the photomultiplier tube. In our case the attenuation is achieved via indirect detection of the laser pulses: the laser is used for two-photon excitation of fluorescence, which is detected using the photomultiplier tube–i.e., the calibration is performed directly in our instrument. There is a linear dependency between the number of photons incident on the photocathode and the generated photoelectrons. Therefore we assume that the photoelectrons emitted from the photocathode follow Poisson statistics. The probability P(n) for the photomultiplier to detect a pulse of n photoelectrons is thus

where µ is the mean number of photoelectrons emitted from the photocathode.

The value of µ can be estimated by using a priori information that a part of the excitation light pulses do not lead to detection of any photons. Assuming that the total number of detected single- and multi-photon pulses during a measurement is N_C1 (as detected using one discriminator with level set optimally for single-photons), and N_L laser pulses are registered at the same time, the probability of not detecting any photons is

The mean number of photoelectrons per pulse is obtained from (1) and (2):

The total number of photons during the measurement time N_L µ and the estimated numbers of single- and multi-photoelectron events N_L P(n) can now be calculated.

As the next step, discriminator levels are adjusted for detection of multi-photon pulses. As discriminator 1 detects all photoevents, discriminator 2 should detect events of two or more photoelectrons N_C2, discriminator 3 detects events of three or more photoelectrons N_C3 and so on. The measurement can be repeated and the levels adjusted until registered and estimated event numbers match, i.e. N_Cj≈N̂_cj, where the estimates (denoted with ^) are

In the case of three comparators, assuming that the events involving 4 or more photoelectrons is small,

3. Experimental setup

The measurement system shown in Fig. 1 is a variation of the setup reported in publications [2–4]. A passively Q-switched, diode-pumped microchip laser (FIRN IRLH-1062-Q-sw-TO-3) producing ~3 ns pulses at 50 kHz is used as a light-source for two-photon excited fluorescence. The beam is focused with an objective lens (Leica C-Plan 40x/0.5L), into a sample cuvette containing fluorescent Rhodamine B solution. The fluorescence excited in the focus is collected through the same objective lens, filtered with a 550–600 nm bandpass filter (UAB Standa, Vilnius, Lithuania) and finally detected with a channel photomultiplier (CPM) of type C952P (PerkinElmer Optoelectronics GmbH, Heimann Opto, Wiesbaden, Germany). A photodiode (SFH 213FA, Infineon Technologies, Munich, Germany) operates as a laser pulse detector.

 

Fig. 1. Block diagram of the measurement set-up optical components.

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A block diagram of the electronics of the system is shown in Fig. 2. An adjustable high-voltage source C30N (EMCO High Voltage Corporation, Sutter Creek, CA, USA) is used for generating the operating voltage for the CPM. Detector output is connected to a charge-sensitive amplifier producing unipolar pulses of 8 µs duration. The speed of the electronics is optimized for <100 kHz laser pulse rate. Three comparators (DSC1-DSC3) of type LH1712 (Linear Technology, Milpitas, CA, USA) are used as pulse discriminators. Delayed output of laser pulse detector (PD) is controlling the latch (hold) input of the comparators. The latch is activated at the peak of the unipolar pulse and held for 2 µs. During that time a counter (CNT123) on a CPLD (XC9572, Xilinx Inc., San Jose, CA, USA) is incremented once for each ‘high’ state of DSC1-DSC3. Three additional counters (CNT1, CNT2 and CNTL) are implemented on the CPLD for counting of DSC1 and DSC2 signals and laser pulses, respectively. Counter values are regularly fetched by a digital signal processor (DSP) on ADSP21061 EZ-KIT Lite DSP board (Analog Devices, Norwood, MA, USA).

 

Fig. 2. Block diagram of the measurement electronics set-up.

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The single and multi-photon responses of the CPM were measured with PCA II multichannel scaler (Canberra Industries, Meridien, CT, USA), Fig. 3. Rhodamine B solved in ethanol at concentrations of 100 nM, 1 µM and 2.5 µM were used as samples yielding different numbers of fluorescence photons per excitation. In order to utilize fully the input voltage range of the PCA II card the output of the charge-sensitive amplifier was further amplified by 2.5x using AM502 differential amplifier (Tektronix, Beaverton, OR, USA). Voltage calibration of the system was performed with TGA 1230 signal generator (Thurlby Thandar Instruments Ltd., Huntingdon, U.K.) replacing the charge-sensitive amplifier.

In order to test the linearity of single or multi photon counting approach a series of Rhodamine B solutions ranging from 0.1 nM to 5 µM was measured, Fig. 4. The integration time was 10 s. Prior to the measurement the comparator levels were adjusted according to the procedure described above using 500 nM Rhodamine B solution as a sample. Reference voltages of DSC1-DSC3 were determined to be correct at 50 mV, 290 mV and 430 mV, respectively.

4. Results and discussion

The normalized single and multi-photon responses of the CPM are shown in Fig. 3. At the lowest dye concentration (100 nM) almost all pulses were caused by single photoelectrons, since µ≈0.09. In that case the photoelectron distribution was narrow and well separated from noise background, and it was straightforward to set the discrimination voltage of DSC1. Higher concentrations resulted in wider photoelectron distribution and higher pulses, in average. Multiple peaks that would correspond to multi-photoelectron pulses were not observed. Consequently, it is not possible to register individual multi-photon events with good accuracy with this type of detector.

 

Fig. 3. Measured photoelectron distribution from different concentrations of Rhodamine B solution.

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Figure 4 shows the response curves of the system with Rhodamine B solutions in several concentrations, using one and three discriminators. Using one discriminator it is possible to calculate the photoelectron rates from Eq. (3) multiplied by the laser pulse rate. However, this method cannot be used if the light intensity is fluctuating during the integration time, as in our measurement system. In that case the use of multiple discriminators results in improvement in linearity emphasized in measurements of high concentration (>500 nM) samples. The 25% deviation from the linear response occurs at 25 kCPS and 75 kCPS using one and three discriminators, respectively. The improvement would be even more significant if the CPM gain did not drop as a result of charge distribution inside the tube, at high photoelectron rates. At all concentrations, the large gain variation from pulse to pulse of the CPM is well compensated by the 10 s integration time.

 

Fig. 4. Measured fluorescence photon count rates (CPS) from Rhodamine B solutions. The signal has been measured using a single comparator (sphere) and three comparators (square).

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In the previous version of our instrument analog mode detection has been used instead of photon counting [4]. Analog mode detection is sensitive to small signal baseline variations. It also requires rather complicated electronics, particularly in systems operating at high speed and having several detection channels. On the other hand, photon counting using multi-level discrimination is tolerant to small baseline variations below the discrimination levels. Pulse counters and other digital circuitry can be implemented on a programmable logic chip (FPGA or CPLD), which simplifies the electronics considerably. The calibration of the discriminator levels is straightforward and simple. It can be performed automatically online, for example, by using low fluorescence yield sample solution. Along with the other benefits of photon counting the presented system has proven to be the method of choice in our application areas.