We present a high-speed photon counter for use with two-photon microscopy. Counting pulses of photocurrent, as opposed to analog integration, maximizes the signal-to-noise ratio so long as the uncertainty in the count does not exceed the gain-noise of the photodetector. Our system extends this improvement through an estimate of the count that corrects for the censored period after detection of an emission event. The same system can be rapidly reconfigured in software for fluorescence lifetime imaging, which we illustrate by distinguishing between two spectrally similar fluorophores in an in vivo model of microstroke.
- fluorescence imaging microscopy
- photon pile up
two-photon laser scanning microscopy (TPLSM) (Denk and Svoboda 1997; Denk et al. 1990, 1995; Helmchen and Denk 2005; Yasuda et al. 2006) involves the periodic excitation of molecules by hundred-femtosecond laser pulses, followed by the emission of fluorescent light before the arrival of the next pulse. Despite the relatively large number of photons in each excitation pulse, roughly 100 million at the focus of the objective for nonsaturating intensities, the average number of fluorescence photons that are detected is typically of order one or less (Neher and Hopt 2001; Tsai and Kleinfeld 2009). Thus it is imperative to optimize all aspects of TPLSM, from ensuring that the excitation beam is free from temporal and spatial aberrations (Cui 2011; Field et al. 2010b; Ji et al., 2010; Rueckel et al. 2006; Tsai et al. 2007) to the collection and detection of as many of the emitted photons as possible (Engelbrecht et al. 2008).
All measurements of light contain shot noise, which reflects the discrete nature of photons and limits the signal-to-noise ratio (SNR) for a pixel with an average count of N photons to . Ideally, the photodetection process will not add to this noise. Photomultiplier tubes (PMTs) are universally used to convert the arrival of a photon into a pulse of current, which is then amplified, filtered or integrated, and digitized to generate a pattern of the intensity of fluorescent emission as a function of the position of the focus of the excitation beam. This pattern forms the optically sectioned planar image reported with TPLSM (Denk et al. 1990). Photomultiplier tubes offer a unique combination of good quantum efficiency, high conversion gain, high speed, and linearity of the output current with incident intensity. However, the serial amplification of photocurrents along the dynode chain in a PMT results in a variation in the amplitude of the individual output pulses (Zworykin et al. 1936) that multiplies the variance of the shot effect (Shockley and Pierce 1938). The exact value of this additional noise depends on details of the PMT but is typically 20–70%.
Photon counting is commonly used as a means to circumvent variation in the intensity of the output pulses from the PMT. This technique is based on the assumption that current pulses that exceed a threshold amplitude are the result of photoelectrons generated by absorption of a single photon at the cathode of the PMT, as opposed to a thermally generated electrons. Photon counting devices employ a discriminator to convert analog pulses from the PMT into digital pulses, which are then summed. Since each photon will result in exactly one count, this eliminates a source of variability in the detection process.
Photon counting is preferred so long as the rate of emitted photons is low, so that each emitted photon is counted before a second photon arrives. Although the chance of two photons arriving at the PMT at exactly the same instance is nil, dispersion of the electron current in the PMT, the capacitance of cables, and the response time of amplifiers leads to a photocurrent pulse with a width of one to a few nanoseconds. This creates a censored period after a photon arrives that briefly blocks the counting of subsequent photons. Uncertainty in the number of uncounted events constitutes a source of variability. This uncertainty is negligible when the rate of fluorescent emission is low but will exceed the variability associated with the amplitude of the photocurrent pulses when the rate of emission is high. The best SNR is thus obtained by switching from photon counting to analog integration when the dominant noise source changes from analog variability to uncertainty in the count. However, algorithms to estimate the number of missed counts, as well as to identify the exact count at which the switch from counting to analog detection should occur, do not appear in past literature.
In this report we describe a reconfigurable photon counting system that achieves a resolution of 3.2 ns between successive pulses with a temporal accuracy of 1.5 ns per photon. It is used in conjunction with a maximum likelihood estimate of the number of censored pulses as a means to increase the dynamic range of counting. At the core of the system is a high-speed complex programmable logic device (CPLD) that operates together with commercially available components to transfer pulses to a master computer at the typical 0.5- to 2.5-MHz rates of pixel acquisition. Although photon counting has been previously utilized for TPLSM (Amir et al. 2007; Benninger et al. 2008; Buehler et al. 2005; Field et al. 2010b; Sheetz et al. 2008; Vucinić and Sejnowski 2007), previous systems did not transfer the measured counts at these clock rates. Furthermore, the flexibility of our counter allows it to be rapidly reconfigured for fluorescent lifetime imaging (FLIM) (Berezin and Achilefu 2010; Harvey et al. 2008; Konig et al. 1996; Pepperkok et al. 1999; Yasuda et al. 2006) and potentially other modes of nonlinear imaging.
All data were obtained with a custom-built two-photon microscope, as described previously (Tsai and Kleinfeld 2009), and a tunable Ti:Al2O3 pulsed laser (Mira 900; Coherent) that operated at 75.5 MHz. We used ×20, 1.0 numeric aperture (NA) (Zeiss) and ×40, 0.8 NA (Olympus) dipping objectives. The microscope was controlled with MPScope 2.0 software (Nguyen et al. 2006, 2009), which synchronized data acquisition, both analog and digital, with bidirectional scanning of galvanometric mirrors.
Signal acquisition begins with a PMT (H7422-40; Hamamatsu) that converts photons into brief current pulses with a conversion gain of ∼3 × 105. For imaging by analog integration, the PMT output is switched (ZSWA-4-30DR; Mini-Circuits) to a current-to-voltage converter and a direct current-coupled amplifier, both with a 0.3-μs time constant, low-pass filtered with a 3-pole Bessel filter (model 3202; Kronhn-Hite) set so that the −3-dB cutoff frequency of the filter, denoted fc, is equal to , where fpixel is the frequency of the pixel clock (Tan et al. 1999), and then digitized by an analog-to-digital board (PCI-6110; National Instruments), where it is sampled at the pixel clock rate (Fig. 1).
For imaging by photon counting, the output of the PMT is directed through a high-speed alternating current-coupled amplifier (ZPUL-30P; Mini-Circuits), and the signal is converted to a transistor-to-transistor logic (TTL) pulse with a discriminator, either a commercial device (PRL-350TTL; Pulse Research Lab) or one of local design (Fig. S1 in Supplementary Information on Firmware and Hardware). (Supplemental material for this article is available online at the Journal of Neurophysiology website.) The threshold is set above the thermal voltage noise and typically at 0.2 times the measure height of the current pulse. All lines are terminated at 50 Ω. The TTL pulses are counted using a custom photon counting board, implemented with a CPLD (ispMach LC4256V; Lattice). The counts are read from the board at the pixel clock rate by a digital interface board (DIO-32HS, National Instruments) on a Windows-based computer. The firmware for the CPLD is written in ispLevel Classic (Lattice Semiconductor) and is flashed to the CPLD board through a standard parallel port interface. The CPLD implements a high-speed dual ripple counter (Fig. S2 in Supplementary Information on Firmware and Hardware), in which the active counter alternates at each imaging pixel. This allows time for the counters to settle before being read by the computer interface board, which inputs 32 bits in parallel from the CPLD counters at the pixel clock rate.
For FLIM, a timing signal from the laser excitation pulse must be passed to the CPLD counting board. We split a small portion of the pulsed laser excitation light onto a high-speed photodiode (DET10A; Thor Labs). This signal is amplified (ZJL-4G+; Mini-Circuits) and divided by a passive coupling device (ZFDC-10-5; Mini-Circuits). The larger portion of the signal is piped to a discriminator, where it is converted to a TTL logic level signal, while the weaker signal is directed to an oscilloscope to monitor the mode-locking of the excitation laser. Fluorescence lifetime data for each pixel are acquired by sequentially enabling a series of six separate counters on the CPLD device. These counters are gated so that the first counter is enabled for 0–1.5 ns after the initial laser excitation pulse, the second counter is enabled for 1.5–3 ns after the laser excitation pulse, and so forth. The end result is a six-bin histogram of arrival times for fluorescence photons from which the exponential decay time of the fluorophore, τ, can be calculated. The implementation of multiple counters for FLIM, acquisition of specific number of counts per pixel clock, and simultaneous data acquisition by two or more PMTs is detailed in Supplementary Information on Firmware and Hardware and Figs. S2–S4.
The timing signal for the laser excitation pulse must be aligned to coincide with the start of the fluorescence excitation. We thus delay the signal from the excitation pulse to maximize fluorescence counts acquired in the first time bin. A coarse delay line, with a resolution of 1.5 ns, is implemented in the firmware of the CPLD (Fig. S3A in Supplementary Information on Firmware and Hardware). A fine-grained delay is achieved with a custom analog delay line that was constructed by switching among 12 lengths of impedance-matched (50 Ω) wire that incremented the delay from 0 to 1.65 ns in increments of 0.15 ns.
In vivo physiology.
Our subjects were C57Bl6 mice and green fluorescent protein-expressing inhibitory interneuron (GIN) mice that ranged in mass from 20 to 30 g. All procedures were performed in anesthetized animals. Anesthesia was induced with 4% (vol/vol) isoflurane in 30% oxygen and 70% nitrous oxide and was maintained with 1–2% (vol/vol) isoflurane. The care and experimental manipulation of our mice were reviewed and approved by the Institutional Animal Care and Use Committee at the University of California at San Diego.
In the GIN animals, a craniotomy was performed to generate a cranial window with the dura left intact (Helmchen and Kleinfeld 2008; Holtmaat et al. 2009). Individual neurons were imaged as described (Drew et al. 2010). The C57Bl6 mice were used to form occlusions to single penetrating arterioles, as described previously (Blinder et al. 2010; Nishimura et al. 2007), with some modifications for mice. The pial vasculature was imaged through a thinned skull preparation reinforced with a glass coverslip (Drew et al. 2010). The vasculature was labeled by injecting 50 μl of 2.5% (wt/vol) Texas red-dextran (70 kDa; Invitrogen) in phosphate-buffered saline (PBS) through the infraorbital vein. Targeted photothrombosis was initiated by illuminating a target vessel with focused 530-nm laser light immediately following the injection of 50 μl of 1.25% (wt/vol) rose Bengal in PBS, also administered through the infraorbital vein. After confirmation of single vessel occlusion, the mice were allowed to survive for 2 days before reimaging. The vasculature was relabeled with another injection of Texas red-dextran. The nuclei of dying, membrane-disrupted cells were labeled by a single intraperitoneal injection of 1 mg/kg propidium iodide in PBS, as described previously (Unal Cevik and Dalkara 2003).
Mice were injected with a fatal dose of pentobarbital and transcardially perfused with PBS followed by 4% (wt/vol) paraformaldehyde in PBS. The brains were removed and cryoprotected in 30% (wt/vol) sucrose overnight. The forebrain was cryosectioned coronally at a thickness of 50 μm, and immunohistochemistry was performed on free-floating sections. Tissues were stained with primary antibodies for microtubule-associated protein-2 (MAP-2; no. AB5622, Chemicon) and secondary anti-rabbit Alexa 488 antibodies. Images were obtained using a Fluoview 1000 confocal microscope with an oil-immersion ×63 objective.
At low signal intensities, the average fluorescence that follows each laser pulse will contain, on average, significantly less than one photon. The signal must be integrated across multiple pulses, and the background electronic noise from the PMT, as well as from associated analog electronics, will reduce the ability to distinguish image features from the background. As an example, we used in vivo TPLSM (Svoboda et al. 1997) to image neurons in parietal cortex of mice that express green fluorescent protein in somatostatin-positive inhibitory cells (Bozza et al. 2004). The same field was imaged, using the same rate for the pixel clock, with our photon counting scheme (Fig. 2A) and with traditional analog integration (Fig. 2B). In general, the lower noise in the counting image reveals processes and details that are not seen in the analog images (n = 5 fields). A histogram of the counts and normalized intensity shows a clearly perceptible hump in the digital count (star in Fig. 2C), consistent with a non-Poisson distribution of the signal photons.
The scaling of excess noise with analog integration versus photon counting was directly tested by obtaining equivalent images of a sample, fluorescein-labeled cellulose that had a broad spatial distribution of emission intensities (Fig. 2, D and E). The mean count per pixel is βr, where r is the number of laser pulses in the period of the pixel clock, i.e., r ≡ fpulses/fpixel ∼ 100, and β is the measured number of emissions per laser pulse (Table 1). The variance for the photon counting data, denoted σ2, scales identically with the mean count per pixel, i.e., σ2 = βr. In contrast, the analog signal showed excess variance compared with the Poisson limit (Fig. 2F). The data were well described by the phenomenological fit of σ2 = (1 + η)βr, with η = 0.57 for our conditions.
Correction to the photon count and variance.
We analyzed the effect of near-simultaneous arrival of multiple photons, or photon pileup (Coates 1968), that can occur when the lifetime of the fluorophore is comparable to the time resolution of the detection electronics. This is the typical case with genetically expressible indicators and most biologically relevant organic dyes, but not for quantum dots (Berezin and Achilefu 2010; Shaner et al. 2005). At modest to high imaging intensities, a single laser excitation pulse can result in two or more signal photons arriving at the PMT within the pulse-pair resolution of a single channel of the photon counter, denoted Δ, where Δ = 3.2 ns for our system. Thus pairs or n-tuples of photons are counted as a single event, because all but the first photon are censored for a period Δ. This phenomenon leads to the loss of information as to the exact number signal photons per laser excitation pulse.
How can we estimate the true count, α, from the measured count, β? In principle, there is a monotonic relation between these quantities. However, as an approximation, one can estimate α from the measured distribution of counts with zero, one, two, etc., photons per laser pulse. We consider first the case of using only the number of samples with zero events, i.e., laser pulses that did not lead to a photocurrent, denoted r0. A maximum likelihood estimate (MLE) yields an estimate, denoted α̂, in closed form (Supplementary Information on Count Estimate), i.e., (1) and (2) The value of α̂ for each pixel forms the image, and the ratio α̂/σ forms the MLE of the SNR for that pixel.
An improved MLE for α̂ is formed by including r1, the number of laser pulses that lead to exactly one measured count. This calculation incorporates the possibility that additional photons may have arrived in the censored period and yields an expression for α̂ that must be evaluated numerically (Supplementary Information of Count Estimate). We use the Newton-Raphson method to find the value of α that maximizes the log-likelihood function l(α), where (3) with (4) and (5) The variance is found by numerically computing the second derivative of l(α) with respect to α, evaluated at α = α̂ (Eq. 3) so that (6) Note that the above expressions (Eqs. 1–6) can further include corrections for emissions that fail to occur with the time between laser pulses (Supplementary Information on Count Estimate). These emissions are not lost but can be counted as originating from a subsequent laser pulse.
We applied the above relations to images taken under relatively high laser intensities, for which the average count per laser pulse was well above one for bright regions of the image. We compared the image found with uncorrected counts (Fig. 3A), the image and SNR using the estimate of α̂ at each pixel with just the number of pulses with no detected emission (Fig. 3B1 using Eq. 1 and Fig. 3B2 using Eq. 2), the image and SNR using the estimate of α̂ at each pixel with both the number of pulses with zero and exactly one detected emission (Fig. 3C1 using Eqs. 3–5 and Fig. 3C2 using Eq. 6), and, last, the image obtained with analog detection (Fig. 3, D1 and D2). These data illustrate three keys points. First, the dynamic range of the uncorrected image was compressed compared with the corrected images (cf. A with B1 and C1 in Fig. 3) and compared with the analog image (cf. A with D1 in Fig. 3). This occurs from the systematic loss of counts the high emission rates associated with bright pixels. Second, the SNR increases substantially when both r1 and r0 are used to estimate α̂ for each pixel, compared with just r0 (cf. B2 with C2 in Fig. 3). Last, the SNR when both r1 and r0 are used to estimate α̂ for each pixel approaches that of analog recording at these high light levels, for which there is substantial censoring.
Crossover from photon counting to analog integration.
At lower imaging intensities, photon counting offers an improved SNR compared with analog integration (Figs. 2F and 3E). At high intensities, however, the uncounted photons in the censored region result in additional variance that degrades the SNR of photon counting. There is a “crossover” point, above which analog integration yields a higher SNR for bright pixels and is preferable. In the example of Fig. 3, obtained with relatively high incident intensity, the crossover point is α̂ = 0.8 when only the number count for no emissions is used, but α̂ = 1.5 when both the number of events with zero count and one count are used (Fig. 3E). There is a 0.45 chance of emitting two or more photons per laser pulse at the intensity that corresponds to α̂ = 1.5, clearly demonstrating the utility of our approach to correct for censored counts.
In vivo detection of neuronal cell death using FLIM.
The distribution of time between an excitation pulse and the returned fluorescence photon is a means to determine the lifetime of the fluorophores (de Grauw and Gerritsen 2001; Suhling et al. 2005; Wang et al. 1990). Thus FLIM can be exploited to separate multiple fluorophores with overlapping emission spectra but different fluorescence lifetimes within the same biological sample (Steinkamp et al. 1999). We use FLIM to distinguish between two red emission dyes, Texas-red dextran and propidium iodide, in a model of microstrokes in which single penetrating arterioles are blocked by targeted photoexcitation (Blinder et al. 2010; Nishimura et al. 2007). The single occlusion leads to a cessation of blood flow in a 500-μm-diameter neighborhood of the block and the eventual formation of a cyst. Both dyes are essential to the assessment of neuronal damage. Texas red-dextran enables deeper vascular labeling than related molecules with green emission, such as fluorescein-dextran, and is used to locate the margin of the stroke. Propidium iodide is commonly used as a cell death indicator, because it preferentially stain cells with membranes disrupted by necrosis or apoptosis. Past studies have shown that propidium iodide can be used as a histological assay of cell damage when administered as an intravenous injection (Unal Cevik and Dalkara 2003). We now extend this technique to image cell death in vivo.
Two-photon imaging based solely on intensity, or counts, yields individually labeled cells and vessels that are indistinguishable on the basis of brightness (Fig. 4A). Imaging based on lifetime clearly distinguishes between the two structures (Fig. 4B), consistent with the 4.1-ns lifetime of Texas red (Brismar et al. 1995) and the 6- to 12-ns lifetime of propidium iodide when bound to DNA (Hanley et al. 2002). The merged counts and lifetime clearly highlights dying cells (red cells; arrowhead in Fig. 4C) and filled microvasculature (blue vessel; arrow in Fig. 4C). Post hoc histological analysis of this region shows that propidium iodide-labeled neurons are most prominent within the border of the microinfarction (Fig. 4D) and that labeled cells appear to be primarily neurons, based on immunohistochemistry with the pan-neuronal marker MAP-2 (Fig. 4E).
Photon counting (Fig. 1) provides a simple way of increasing the SNR of images obtained with two-photon microscopy for low and medium imaging intensities (Fig. 2). At higher intensities, the increased SNR is offset by the arrival of multiple photons per laser pulse. The undercounting inherent in this process results in an additional noise source. Our analysis shows how to correct for undercounting in a manner that essentially doubles the count at which one needs to switch to analog integration (Eqs. 3–6). In fact, the correction for censored counts is sufficiently good to obviate the need for analog detection, even at high emission rates (Fig. 3).
Theoretical analysis of the shot-to-shot variation in output pulses from the PMT predicts that the analog signal should have a multiplicative factor of η = (1 − g−d + 1)/(g − 1) excess noise power over the Poisson limit (Shockley and Pierce 1938), where g is the gain per stage in the PMT at a particular supply voltage and d is the number of stages. For g = 3.5 and d = 9, parameters for the operating point of our PMT in these studies, the theoretical value of η = 0.4 falls short of the observed value of η = 0.6. The reason for this excess is unclear, yet the implication is that photon counting is effective at higher intensities than suggested by theory.
Our system allows for uninterrupted counting at speeds up to 350 MHz with the use of relatively inexpensive commercially available parts. In addition, by creating the electronics around a reprogrammable CPLD core and by locking the counters to the onset of the excitation pulse, we are able to extend the photon counting device to acquire fluorescence lifetime images with 1.5-ns binwidths (Fig. 4). Locking of the counters to the laser pulse is also essential when alternate pulses are used to acquire different modalities, such as switching between focal depth or polarization (Carriles et al. 2009; Field et al. 2010a). Other potentially useful configurations are possible with only a change in firmware, such as gating to isolate the extremely short-lived signals that are generated by second (Campagnola et al. 2001; Moreaux et al. 2000) and third (Débarre et al. 2006; Squier et al. 1998) harmonic process and coherent anti-Stokes Raman scattering (Ly et al. 2007).
Continuing advances in high-speed digital electronics and serial communication suggest that a next-generation photon counting system may make use of a field-programmable gate array with a USB 2.0 serial communication channel, rather than the current CPLD and parallel communication channel. Furthermore, advances in PMT design and high-speed signal conditioning should decrease the censored period below 3 ns.
This work was supported by National Institutes of Health Grants AG029681 (to G. Cauwenberghs), EB003832 (to D. Kleinfeld and J. A. Squier), and OD006831 and RR021907 (to D. Kleinfeld) and National Science Foundation Grant DBI 0455027 (to D. Kleinfeld).
No conflicts of interest, financial or otherwise, are declared by the author(s).
We thank Earl M. Dolnick for involvement in the design of an analog integrator that predated this work, Quoc-Thang Nguyen for coding the first interface of MPScope with the photon counting device, Jing W. Wang for involvement in exploratory experiments, and Philbert S. Tsai for comments on the original manuscript, particularly with regard to the issue of censored counts.
The CPLD interface, as well as a variable time-delay and discriminator circuit, were developed by the University of California at San Diego (UCSD) Physics Electronic Shop. Confocal microscopy made use of the UCSD Cellular and Molecular Medicine Microscopy Shared Facility.
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