Journal of Neuroscience Methods 92 (1999) 123–135

Fast scanning and efficient photodetection in a simple two-photonmicroscope

Y.P. Tan a,1, I. Llano a, A. Hopt b, F. Wurriehausen b, E. Neher b,*a Cellular Neurobiology Group, Max-Planck-Institut for Biophysical Chemistry, D-37077 Gottingen, Germany

b Department of Membrane Biophysics, Max-Planck-Institut for Biophysical Chemistry, D-37077 Gottingen, Germany

Received 22 February 1999; received in revised form 23 June 1999; accepted 1 July 1999

Abstract

Two-photon laser scan microscopy carries many advantages for work on brain slices and bulk tissue. However, it has very lowsignal levels compared to conventional fluorescence microscopy. This is disadvantageous in fast imaging applications when photonshot noise is limiting. Working on brain slices with excitation powers of 8–10 mW at the specimen plane, the resting signal fromcerebellar Purkinje cell somas loaded with 10 mM Oregon Green 488 BAPTA-1 averaged 4 detected photons/ms; axons ofinterneurons loaded with 200 mM of this indicator yielded about 1 photon/ms. To obtain satisfactory images at high timeresolution, long pixel dwell times are required and data collection should be restricted to as few pixels as necessary. Furthermore,a large proportion of total measurement time (duty cycle) should be available for data collection. We therefore developed amethod for scanning small regions of interest with line repetition rates two to four times higher than conventional ones and a dutycycle of 70%. We also compared the performance of several photodetectors and found the optimum choice to depend strongly onthe photon flux during a given application. For fluxes smaller than 5 photons/ms, the photon counting avalanche photodiodeshows the best signal to noise ratio. At larger fluxes, photomultipliers or intensified photodiodes are superior. © 1999 ElsevierScience B.V. All rights reserved.

Keywords: Calcium signaling; Fluorescence; Non-linear optics; Photodetection; Scanning

www.elsevier.com/locate/jneumeth

1. Introduction

Two-photon excitation of fluorescence (Goppert-Mayer, 1931; Kaiser and Garrett, 1961) was suggestedas a method of particular interest for the study ofbiological material in the scanning optical microscopeas early as 1978 (Sheppard and Kompfner, 1978). Itwas introduced experimentally into laser scan mi-croscopy by Denk et al. (1990), who pointed out itsvarious advantages over conventional methods. Theseinclude larger penetration depth into scattering tissueand less photodamage. Meanwhile, numerous applica-tions on brain slices (Denk et al., 1995a; Yuste andDenk, 1995; Svoboda et al., 1996, 1997, 1999; Denkand Svoboda, 1997; Koster and Sakmann, 1998) andon developing embryos (Potter et al., 1996) have docu-

mented these advantages. Nevertheless the method suf-fers from relatively low signal level, which isparticularly severe for fast imaging applications wherephoton shot noise is limiting. Part of the reason for lowsignal level results from basic physical principles. Someof the advantages of two-photon microscopy (TPM)result from the square law of fluorescence excitationwhich holds only at excitation energies and fluorescencelevels substantially below fluorescence saturation. Com-bined with present technology, which employs femto-second laser pulses at :80 MHz repetition rate forexcitation, this restriction limits the photon flux thatcan be obtained from a given dye molecule to 8×106

per second (at about one photon every ten pulses;higher excitation rates would prevent the desired squarelaw dependence). In contrast, single-photon excitationis only limited by fluorescence saturation, which occursat typically 5×108 photons/s. In addition, the appear-ance of non-linear photodamage (Konig et al., 1997) in

* Corresponding author.1 Permanent address: Bogazici University, Istanbul, Turkey.

0165-0270/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.PII: S 0 1 6 5 -0270 (99 )00103 -X

Y.P. Tan et al. / Journal of Neuroscience Methods 92 (1999) 123–135124

biological tissue further restricts the tolerable excitationto levels substantially lower than this theoreticalmaximum.

For practical applications this means that the pho-tons generated should be used as efficiently as possibleand scanning should be restricted to as few pixels aspossible (without spending a substantial proportion oftime for turnaround and flyback of the laser beam). Acommonly used solution to this problem is the line scanor contour scan (Bullen et al., 1997). For many applica-tions, however, information restricted to a single line isnot sufficient to characterize the processes under study.Another solution is multifocal imaging (Straub andHell, 1998; Verveer et al., 1998). This, however, doesnot allow to utilize scattered photons, which is a disad-vantage in brain slice work. We therefore developed atechnique for scanning small patches (regions of interestof typically 20-50 pixels) within times smaller than 10ms using standard galvanometric mirror scanners. Thismethod anticipates high frequency attenuations andphase shifts of the mirror movement to produce mirrordeflections which are linear over 70–80% of the dutycycle for scan speeds close to the roll-off frequency ofthe scanner.

We also made an effort to develop criteria for choos-ing an optimal photodetector for a given application.To this end we defined and measured an ‘apparentquantum efficiency’ (AQE) as a figure of merit for adetector system in a given application. Measurement ofthe AQE is based on the signal to noise ratio for auniform photon flux. Our definition of the AQE resultsin a value of 100% for an ideal photon counter; theAQE can reach a maximum value equal to the quantumefficiency of the given detector, but it is usually lowerthan that due to noise sources in addition to the photonshot noise. We find that for very low photon fluxes andpixel dwell times of 10 ms the photon countingavalanche photodiode is the best photodetectorpresently available. It reaches an AQE equal to its ratedvalue of quantum efficiency (:50%) for photon fluxesof about 1 photon/ms (or 0.5 detected photons/ms).AQE values, however, drop both at lower fluxes (due todark counts) and at higher ones (due to dead time ofthe counting device). Thus, at fluxes higher than 5photons/ms, photomultiplier tubes (PMTs), intensifiedphotodiodes (IPDs) and intensified cameras are better.For fluxes higher than 50 photons/ms (outside the rangeof TPM) CCDs may be an option. It should be notedthat, in the framework of this analysis, simple photo-diodes, which reach quantum efficiencies of 80%,are superior to all other devices at very high photonfluxes. But with present technology of photocurrentrecording, this will only occur at fluxes \10 000 pho-tons/ms due to noise in the current measurement. Someof this work was published in abstract form (Neher etal., 1997).

2. Methods and results

2.1. The laser scan microscope: principle of scanneroperation

The aim of our scanning scheme is to scan short(about one-tenth of the field of view) lines at highrepetition rates, wasting little time for turnaround orflyback of the beam. A limitation in this respect is theinertia of the scanning system, which sets an upper limitto the angular acceleration of the mirrors. Anotherlimitation is the bandwidth of the scanner controller,which together with the galvanometer and positionsensor forms a feedback loop with a characteristicroll-off frequency. If the mirrors are operated close orslightly above the roll-off frequency, the response of thesystem is distorted and an appreciable fraction of timehas to be spent to revert the scan direction. In such asituation, substantial time will be spent for flyback, ifstandard sawtooth (or ramp) waveforms are used forline deflection. Higher line frequencies will be obtainedif waveforms close to triangular ones are employed,using both directions of mirror movement for datacollection. In both cases the mirror movement will notfollow exactly the command signal supplied to the scancontroller input and it will display distortions and timelags if repetition rates are comparable to the roll-offfrequency of the system. In the following we discuss astrategy for selecting optimum waveforms for the de-sired mirror movement in such a situation, and presenta method to calculate frequency- and phase-correctedcommand signals, which, when applied to the input ofthe controller, will result in the targeted mirrormovement.

2.2. Selecting optimum scan wa6eforms for the linedeflection

The frequency response of scanning systems dropsvery rapidly above the roll-off frequency ( fc) such thatbasically no deflection (above noise) can be obtainedbeyond 5fc. The aim, therefore, must be to define aperiodic waveform for the line deflection which doesnot require frequency components \5fc. For the fol-lowing it will be assumed (for simplicity) that thefundamental frequency of the mirror movement isabout equal to fc, such that we are limited to fiveharmonics. As argued above, highest line frequenciescan be obtained for triangular waveforms, using bothforward and backward movements as lines. For suchwaveforms, which are inversion symmetric around zerocrossings and maxima, the second and fourth harmonicis zero, such that we are left with the problem ofselecting the best values for the relative amplitudes ofthe third and fifth harmonic. Phases for such wave-forms are zero, if the zero crossing is chosen as the time

Y.P. Tan et al. / Journal of Neuroscience Methods 92 (1999) 123–135 125

origin. An obvious choice would be to use the coeffi-cients of a Fourier expansion of a triangular waveformas amplitudes. However, examination of such a wave(Fig. 1A) shows that it has substantial deviations fromlinearity over most of the range. We therefore used aleast square fit routine (using IGOR-PRO, Wavemet-rics, Lake Oswego, USA) to minimize the deviationsfrom linearity, i.e. from y=x/(p/2) of the function:

y=y0+ %n

6=1

a6 sin 6 ·x (1)

in the range −aBxBa. For a=0.78 ·p/2 (i.e. a78% duty cycle) and n=5, we obtain a3/a1= −0.086and a5/a1=0.017 (a2 and a4=0). This curve is plottedin Fig. 1B, together with the deviation from y=x/(p/2), the latter at ten times expanded scale. It is seen thatdeviations from linearity within the specified range of

x-values are very small (0.33% compared to 1.4% inFig. 1A, when maximum deviation from linearity isrelated to the specified y-range, i.e. 4a/p). If the samecalculation is done for a=0.9·p/2, the usable scanrange extends to about 90% of the cycle. However, thedeviations within the scan range are again larger (:0.66%). Thus, depending on requirements, a compro-mise has to be found between width of the duty cycleand the deviation from linearity within it. For this itshould also be considered that a lower value for theduty cycle requires less angular acceleration duringturnaround. This has the advantage, in practice, thatlarger amplitudes are allowed.

For some of our fastest scans ( f0\ fc) we had torestrict ourselves to the fundamental frequency and thethird harmonic. In that case a duty cycle of 75%requires a3/a1= −0.073, resulting in deviations fromlinearity of about 0.7%. For slower scans, more compo-nents can be used.

A similar approach can be used to generate ramp- orsawtooth-like waveforms. When the linear portion iscentered around t=0, all phase values are zero in suchscans and amplitudes and deviations from linearity areobtained, as given in Table 1.

2.3. A wa6eform for fast line ad6ance

Advancing lines can be accelerated by using a stepfunction with an overshooting rising phase. This proce-dure is very similar to the ‘supercharging’ technique,employed by Armstrong and Chow (1987) for obtainingfast step deflections in voltage clamping. We obtainedbest results (by trial and error) when using a waveformfor the command signal at the y-scanner input whichactually employed both an overshoot and an immedi-ately following undershoot before it settled to the newposition. Amplitudes and durations of the over- andundershoot varied considerably between scanners. Fora particular one, they were 100% and 44% with dura-tions of 60 and 40 ms, respectively. Given the delay inthe electronics of the scanner controller (General Scan-ning 120 GTD), the overshoot could already be ini-tiated about 60 ms before the end of the previous scanline. Settling times (10–90% of full deflections) of 100ms could be reached.

2.4. Frequency and phase compensation of the linedeflection

Eq. (1) together with the coefficients (Table 1) de-scribe the target wave for the x-mirror movement (linedeflection). In practice, a command signal was appliedto the input of the scanner controller, which anticipatesthe frequency-dependent attenuation An(v) and 8n(v)of the scan system, where v is the angular frequency ofthe periodic waveform:

Fig. 1. Optimal scan waveforms for the line deflection (A, solid line).Fourier approximation to a triangular waveform (dotted line, onlyone half cycle is displayed). The stippled line is ten times thedeviation between the two curves. (B) Similar to A; however, Fouriercoefficients are calculated to minimize the deviation in the interval91.2.

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Table 1Fourier coefficients for exemplar waveforms

Wave Range of a2/a1 a3/a1 a4/a1 a5/a1 a6/a1 a7/a1 Duty cyclea (%) Linearityb (%)linearitydescription

Two compo- 0.70 −0.073 75nents, trian-gular

−0.287 +0.062Three compo- 58 0.4nents, ramp

Narrow 0 −0.086Three compo- 0 0.017 78 0.33Wide 0 −0.1 0 0.0283nents, trian- 90 0.66

gularNarrow −0.355 0.129 −0.037 0.0064 59 0.1Five compo-Wide −0.394 0.172 −0.0658 0.0177nents, ramp 70 0.2

Four compo- Narrow 0 −0.0923 0 0.0221 0 −0.0052 78 0.1Widenents, trian- 0 −0.103 0 0.0313 0 −0.012 88 0.4

gularNarrow −0.3966 0.177 −0.0738 0.0259 −0.0068 0.001 62 0.01Seven compo-Wide −0.428 0.218 −0.11 0.0504 −0.019nents, ramp 0.005 72 0.07

−0.429Widec 0.22 −0.112 0.0522 −0.02 0.006 74 0.06

a See text for explanation.b See text for explanation.c Coefficients were further optimized by introducing weights in the fitting routine, which emphasize points at the edge of the specified range.

x(t)=Y0 %n

r=1

a6A6

sin(6 ·v0t−86) (2)

We determined the coefficients An and 8n by aniterative procedure, in which we applied the desirednumber of cycles according to Eq. (2) to the scannerand sampled the resulting sensor signal. The latter wasthen Fourier analyzed, starting with the second or thirdcycle (to allow for settling of the movement) and theresulting Fourier coefficients a %n were compared with thevalues a6 as given in Table 1 (after proper scaling).Values for An were then adjusted by linear scaling.Phases, obtained in the Fourier analysis, were used foran additive correction of 8n. Initial guesses for An and8n were obtained by applying a small signal for whichan rose linearly with n and analyzing the resultingsensor signal.

If the total amplitude of the scan signal was suffi-ciently small, the iterative improvement of the signalconverged after three to five cycles. If too large deflec-tions or too high scan frequencies were requested,non-linearities of the scanning system prevented conver-gence. The sensor signal for a triangular wave afterconvergence is displayed in Fig. 2 together with thedesired waveform and the command signal, which wasapplied to the scan controller. It is seen that after aninitial settling period the mirror movement followsclosely the desired waveform, both with respect toamplitude and with respect to phase. The sensor signal,however, may have a small phase lag with respect to theactual mirror movement. Therefore, a software optionwas provided to introduce a compensating time shift inthe command signal. In practice, this parameter wasdetermined by scanning fluorescent beads with triangu-

lar waveforms and minimizing small shifts betweenalternating lines in the image.

2.5. Two-photon excitation path

Fig. 3 presents a schematic of the optical path. Theexcitation light for two photon imaging was providedby a Ti–sapphire laser (Tsunami Spectra Physics,Mountain View, CA, USA), which was pumped by afrequency doubled Nd:YVO4 laser (Millennia, TsunamiSpectra Physics). This all solid-state configurationavoids the excessive amounts of cooling water require-ments associated with argon lasers albeit of slightlyhigher powers. At a repetition rate of 82 MHz withpulses of 70 fs duration, the laser provides around 700mW of average output power at 820 nm when pumpedwith a power of 5 W.

A small fraction of the beam was reflected from amicroscope cover slip for diagnostic purposes as ex-plained below. An electronically controlled shutter(Melles Griot) was placed on the laser path to block thebeam when it was not required. Neutral density filters,up to 3.0 OD units (New Focus, Santa Clara, CA,USA) were used to reduce beam intensity in steps of 0.1OD units. Working with cerebellar slices the beamintensity was typically reduced tenfold to yield �8–10mW of average power onto the specimen plane. Intypical whole-cell recordings from neuronal cells inbrain slices, we find that this intensity level allows up to1000 scans without causing any detectable changes inthe cell’s electrical properties or in the peak and timecourse of depolarization-induced intracellular Ca2+

rises.

Y.P. Tan et al. / Journal of Neuroscience Methods 92 (1999) 123–135 127

The beam expansion/compression unit, built usingtwo 10× objectives (Achrostigmat, Zeiss, Goettingen,Germany), had a dual purpose. A 100-mm pinholeplaced at the focal plane of the first objective served asa spatial filter to provide an optically cleaner beam.This pinhole removed the high frequency components,which might have been introduced by dust particleseither in air or on optical surfaces. The second objec-tive, which was mounted on a micrometric drive, al-

lowed some adjustment of the beam shape in order tocompensate for the chromatic aberrations when a lownoise cooled CCD (Imago T.I.L.L. Photonics, Planegg,Germany) camera was used as the imaging device (seebelow). In that case differences in the focal width of theobjective between excitation and detection wavelengthsled to serious degradation of the image quality. Makingthe beam slightly convergent and underfilling the objec-tive’s back pupil allowed the compensation of up to 4mm of chromatic aberration in the Z-direction (Keller,1995). This, however, resulted in changes in the focusspot size. The beam was then directed to the scan headof the microscope (Axioplan 2, Zeiss). The galvanome-ters (G120DT) and the Minisax drive electronics (Gen-eral Scanning MA, USA) were mounted within thescanhead. A dichroic mirror (KP600, Zeiss) was used toreflect the beam down through the microscope optics.In most of the experiments, a Zeiss achroplan 63× , 0.9NA water immersion objective was used.

2.6. Fluorescence emission path

Care was taken so that fluorescence emission fol-lowed the simplest possible optical path, with the mini-mal amount of optical components between theobjective and the detector. The fluorescence emissionwas directed to one of the three detectors by placing amirror into the emission path. The optical path to theavalanche photodiode (APD; type SPCM-AQ-231 pho-ton counting module; EG&G, USA) and to the pris-matically enhanced photomultiplier (PEPMT; ThornEMI Model 9658A, UK) contained 1-mm thick BG39(Schott) filters to block any laser reflections from theglass surfaces. The PEPMT and the APD weremounted on the epi-ports of the microscope. ThePEPMT was mounted with a spacing of 30 cm from theintermediary image plane, in order to blur the image onthe photocathode, and thus reduce the effect of photo-cathode irregularities. The 40× long working distanceobjective (LD Achroplan NA 0.6, Zeiss) and the APD(with 500-mm diameter sensitive area) were preposi-tioned with respect to each other by the use of three-di-mensional manipulators such that the photodiode’sactive area was centered in the focus of the objective.The objective was then cemented to the APD mountand the back pupil of the objective was placed in theintermediary image plane on the epi-luminescence portof the microscope. This configuration allowed the ob-servation of an area corresponding to a diameter of 55mm in the specimen plane.

For detection with a low noise cooled CCD camera,the standard fluorescence excitation port of the micro-scope was used. The relay optics and an inner dichroicmirror turret for selection of the appropriate excitation/roll-off wavelengths were manufactured locally and re-placed the optics provided by the manufacturer.

Fig. 2. Signals for a fast scan. (A) An approximation to a triangularwaveform with just two Fourier components (a3/a1= −0.073) whichis the waveform designated as ‘two components, triangular’ in Table1. The fundamental frequency of the waveform is 2 kHz, resulting infour scan lines per millisecond. (B) The command signal, calculatedaccording to Eq. (2), as applied to the input of the scan controller.(C) The sensor signal, as measured at the scan controller output.

Y.P. Tan et al. / Journal of Neuroscience Methods 92 (1999) 123–135128

Fig. 3. Schematics of the optical path. See text for details.

Fluorescence emission emanating either from the exci-tation by the Ti–sapphire laser or by the monochro-matic light beam (polychrome-II, T.I.L.L. Photonics)coupled through a locally added excitation port, couldbe diverted to the camera by the use of the appropriatedichroic mirror selected from the front turret.

2.7. Beam diagnostics

The two-photon advantage factor, z, is found todepend on tp

−1, the width of the pulse at half maximalintensity (reviewed in Denk et al., 1995b). It is thereforecrucial to measure and monitor the pulse width of thelaser beam. The use of a commercial autocorrelator iscumbersome and is not well suited to monitor pulsewidth throughout a long lasting experiment. Therefore,a more flexible and cheaper method was implemented.

Approximately 4% of the laser beam was reflectedfrom a coverslip into the entrance slit of a monochro-mator (Model 7/748 UV, Jobin-Yvon, France), whoseexit slit was replaced by a cheap CCD camera (TV-CCD200 Monacor, Bremen, Germany). The 70-fspulses typically generated by our system are spreadover 13 nm (see Denk et al., 1995b) and the camera isplaced such that the dispersion from one end of theCCD chip to the other end corresponded approxi-mately to twice this value, i.e. 26 nm. This set-upallowed us to measure the center wavelength (cw) andto monitor the bandwidth of the pulse during an exper-iment (Fig. 4A1). The image of the pulse gave a roughestimate of its bandwidth without having to measure itby the time-consuming autocorrelation technique. Fur-thermore a simple glimpse to the monitor screen al-

lowed detection of any tendency of the laser to go outof mode-locking, which appeared initially as the shift ofthe center frequency to shorter wavelengths, the ap-pearance of a cw component (Fig. 4A2) followed bycomplete loss of pulsing (Fig. 4A3). It is worth notinghere that the cw component does have a bandwidth ofapproximately 0.1 nm (Fig. 4B3). Therefore, it waspossible to detect a cw component smaller than 1%,which might break in due to excessive pump power orincorrect setting of the intracavity dispersion adjust-ment prisms.

Although the Ti–sapphire laser is quite stable andwill remain mode-locked for a long time, air drafts orchanges in the room temperature were found to have aprofound effect on the laser’s stability. It was found outthat the aforementioned way of beam diagnosis wasmore useful than many commercially available tools.

The average intensity of the laser beam was con-stantly monitored with a slow, calibrated photodiodeusing a small fraction of the beam split with anothercoverslip. With these two provisions it was possible torun the experiment for up to 6 h, mostly limited by thehealth of the biological sample.

To measure the group velocity dispersion (GVD)introduced by the glass of the microscope optics, aMichelson-type interferometer as depicted in Fig. 5Awas constructed. The interferometer could be insertedinto or taken out of the optical path by placing mirrorsmounted on precision flipping kinematic mounts (Flip-per, New Focus, Santa Clara, CA, USA). When theinterferometer was included in the optical path, thebeam was split into two by the use of a beamsplitter.The relative time delay in one of the arms was varied by

Y.P. Tan et al. / Journal of Neuroscience Methods 92 (1999) 123–135 129

changing the position of the mirror glued onto a PCspeaker coil and its periodic motion was controlled bya function generator. For coarse distance adjustmentone of the mirrors was mounted on a micrometer stage.The two beams were initially combined at the backpupil of the objective, and the position of the movablemirror was adjusted until the autocorrelation was ob-served. The second order autocorrelation function wasobserved as the variation of two photon fluorescenceintensity as a function of position of the mirror. Fluo-resbrite beads (Polysciences Warrington, PA, USA)were used at the specimen plane as the source of thesecond order fluorescence emission. As depicted in Fig.5B, the pulse broadening introduced by the microscopeoptics resulted in a pulsewidth of 150 fs at the specimenplane. We considered it was unnecessary to implementthe negative GVD compensation techniques in ouroptical path (Fork et al., 1987). The second orderautocorrelation function from these measurements devi-ated from the expected 8:1 ratio (Diels et al., 1985).This was due to the non-equal distribution of the lightintensities in the two arms of the interferometer. Onemight argue that the glass contents of the two opticalpaths are not equal and, therefore, call for the four-mir-ror, two-beam splitter version of an interferometer (seeDiels et al., 1985; Brakenhoff et al., 1995). We believethat this is an unnecessary complication and the sim-plest form of a Michelson interferometer is quite satis-factory for measuring pulse width at the specimenplane.

At various stages of our experiments, it was neces-sary to observe the shape or the position of the laserbeam at the back pupil of the objective. For thispurpose one of the faces of an isosceles right angleprism was frosted by rubbing it with coarse grit car-borundum. The prism was mounted on the micro-scope’s revolver with the frosted face placed at aposition equivalent to that of the objective’s back-pupil.The total internal reflection from the hypotenuse facerotated the beam by 90°, providing a convenient way ofobserving the back-pupil through the non frosted face.The frosted surface being a diffuser, the shape of thelaser beam could be safely observed even at full powerby this simple technique.

2.8. Mechanical stage

In order to optimize the stability and repeatability ofthe scans, care was taken to choose non-moving opticalparts throughout. As the system was designed with thepossibility of double patch clamping which demandshigh levels of mechanical stability, a computer-con-trolled mechanical stage was constructed. The motionon the three axes was commanded with a C-842 four-axis motor controller module (Physik Instrumente,Waldbronn, Germany). This card implemented the PID(proportional integral derivative) control algorithms inhardware, providing smooth acceleration and decelera-tion, essential when moving the stage with a cell alreadyin patch-clamp configuration. Once the optimal PID

Fig. 4. Monitoring mode locking. Different modes of operation of the laser. (A1) The mode-locked configuration. The interference fringes are theresult of spatial sampling by the CCD of the beam dispersed by a grating. (A2) The appearance of a cw component on a laser with a tendencyto get out of mode-locking. (A3) Pure cw mode of operation. (B1, B2, B3) The intensity profiles across a line drawn through the center of theimages.

Y.P. Tan et al. / Journal of Neuroscience Methods 92 (1999) 123–135130

Fig. 5. Interferometric pulse width measurement. (A) A relatively simple Michelson interferometer could be integrated into the system by movingtwo flipping mirrors (FLM) out of the optical path. Mirror MM, which was glued on a speaker coil, could be moved back and forth �400 mmby applying a sinusoidal wave from a frequency generator. KP600, dichroic mirror; BS, beam splitter. (B) The second order autocorrelationfunction, measured as the fluorescence of the fluoresbrite bead by the PMT with a Gaussian fitted to the envelope of the autocorrelation trace.See text for details.Fig. 7. (A) Plot of the apparent quantum efficiency (AQE) of three photodetectors as a function of photon flux. A 10 mM fluorescein solution wasexcited at different powers (l=840 nm) and the emitted light was collected at 10-ms sample interval by one of the three detectors. APD, avalanchephotodiode; PMT, prismatically enhanced photomultiplier; CCD, IMAGO cooled charge-coupled device camera. The photon flux for a givensample and excitation power was determined as described in the text. AQE is plotted against the number of photons/ms impinging on the detector(one-tenth of the number given by Eq. (8)). The lines on the right indicate the QE for the PMT and the CCD at maximum photon flux. (B)Comparison of the signals obtained with the APD (left image) and the PMT (right image) from the axon of a cerebellar basket cell loaded viaa patch pipette with the Ca2+ sensitive indicator Oregon Green BAPTA-1 (OG1; 200 mM). The excitation power and scan parameters were thesame for both images. The pseudo-color scale corresponds to 0–2.3 MHz for the APD image; 0–400 mV for the PMT image.

parameters were found, movement of the stage wasnever the cause of the loss of a cell. A M525.22 (PI)linear positioning stage was used for the Z movement;this stage carried an XY cross table. For the XYmovement, linear positioning stages from Micos(Umkirch, Germany) were chosen for their double,crossed, cylindrical bearings, and these proved to be very

reliable on the long run. The controller card was drivenby a joystick interfaced by routines written in LabViewG language. This allowed us to move the specimensmoothly and to display the coordinates of the cells inreal time, a very useful feature especially for returning toa specific cell or a specific position. The repeatability ofthe system was estimated to be better than 1 mm.

Y.P. Tan et al. / Journal of Neuroscience Methods 92 (1999) 123–135 131

2.9. Scan control electronics, data acquisition andanalysis

Waveforms as described in the section above werecalculated in IGOR-Pro and connected to the X- andY-inputs of the scanner control circuit, after DA con-version on two channels of an ITC-16 laboratory inter-face (Instrutech Corp., Port Washington, NY, USA),using ‘Pulse Control’ software modules, provided byDr. R. Bookman, University of Miami.

During the course of this work we used two differenttypes of scan controllers, both driving general scanning,G120 DT galvanometric scanners: An AMP2 (LoboElectronic, Aalen, Germany) and a Minisax (GeneralScanning Inc., Watertown, MA, USA) unit. The twotypes of controllers gave comparable results, with theexception that the Minisax drivers, at a given fre-quency, allowed larger scan amplitudes before signs ofamplifier saturation (lack of convergence; distortions inthe recorded waveforms) became apparent. It was pos-sible to drive galvanometers up to fundamental fre-quencies of 2 kHz. The line deflection signal was eithertriangular, where both directions of the scan were usedfor data acquisition (up to 4 lines/ms) or had a saw-tooth shape where only one direction was used for datasampling. Either of the signals was expressed as aFourier series including components up to the fifthharmonic (see above). Once the calibration and com-pensation parameters had been determined for a givenscan pattern according to the procedure describedabove, the waveforms for driving the scanners werestored on disc and used for periods of weeks. They wereupdated after all major changes in the optical path orthe mechanical set-up of the microscope. Provisionswere made to rotate the scans to an arbitrary degree, togenerate line scans, or to compress images (zooming) inorder to increase the effective pixel dwell time.

The sensor signals provided by the scan controller (orelse fluorescence signals) were preamplified, filtered anddigitized on the ITC-16 interface at 10-ms sample inter-vals, using Igor Pro and Pulse Control. Signals fromthe APD (see below) were linearized, as suggested bythe manufacturer, to correct for the dead time of thedevice. A minimal set of analysis routines was imple-mented to display the images on line. To generateimages, the parts outside the linear scan range, includ-ing the data corresponding to turnaround points, werestripped from the continuously acquired data. Fig. 6illustrates the images constructed from two types ofscans of a cerebellar basket cell axon loaded with theCa2+ sensitive indicator Oregon Green BAPTA-1(OG1). In one of them an area of 8.25×4.75 mm2 (19lines) was scanned in less than 10 ms.

Most of the analysis was performed off-line. Typicalanalysis routines consisted of the measurement of inten-sities of regions of interest (ROIs), and the calculation

of DF/F0 ratios with provision of subtracting back-ground intensities from the selected areas of the image(example in Fig. 6C). In the cases where DF/F0 imageswere generated (DF is the difference between thefluorescence intensity at any given time and the pres-timulus intensity F0; see Fig. 6B3), the images weremedian-filtered to smooth out the noise inherent todivisions with integers close to zero (Llano et al., 1997).

2.10. Analysis of photodetector performance

We compared the performance of several types ofphotodetectors, including a type SPCM-AQ-231(EG&G Optoelectronics, Vandreuil, Canada) photon-counting APD, a Thorn Emi, type 9658A photomulti-plier tube (PMT), a cooled CCD camera (Imago CCD,TILL photonics) and several types of photodiodes. Inorder to handle all these signals (except for the camerasignals) with one type of data acquisition system wehad to reconvert the digital counting pulses provided bythe APD to analog signals, such that they could besampled, as described above. This was done simply bylow pass filtering of the pulse stream. Since the noise ofthe recording, under all conditions, was dominated byphoton shot noise this did not lead to deterioration ofthe signal to noise ratio. In order for the noise, aftersuch conversion, to be identical to that of a counter setto a counting window of length T (equivalent to asample interval of T) the analog signal had to befiltered with a −3 db frequency of (Hopt, 1998):

fc=1T

·'ln2

p(3)

This equation holds for a Gaussian and also for ahigher order Bessel filter. The criterion constitutes asmall amount of oversampling with respect to theNyquist criterion.

For a quantitative measurement of fluorescence, wefirst calibrated our APD in terms of its quantum effi-ciency. For these measurements, we counted photonpulses, using a PM 6671 counter (Phillips, Eindhoven,The Netherlands). Light from a green light emittingdiode was filtered with a 540/30 (center wavelength/halfwidth) bandpass and the light intensity P was mea-sured at a distance of 4.3 cm with a type 13PDH001(Melles Griot) power meter. The photon flux was calcu-lated according to f=P ·l/ (hc) where l is the wave-length of 547 nm, h is Planck’s constant and c is thespeed of light. Subsequently the power meter was re-placed by the APD, and the measured counting ratecompared to the expected rate, based on f and the lightsensitive area of the APD. This resulted in a value h ofthe quantum efficiency of 64%, which was later usedduring measurements on the microscope for convertingcount rates into photon fluxes. When required (forcounting rates above 1 MHz) a dead time correction

Y.P. Tan et al. / Journal of Neuroscience Methods 92 (1999) 123–135132

Fig

.6.

Y.P. Tan et al. / Journal of Neuroscience Methods 92 (1999) 123–135 133

was applied to the count rate as specified by the manu-facturer. The validity of this correction was verified bymeasuring light fluxes with a series of calibrated neutraldensity filters. This showed that the corrected countrate was linear for light intensities between 10 kHz and10 MHz (or 0.006–5.7 pW), apart from a constant darkcount of 1.5 kHz.

2.11. The apparent quantum efficiency

For comparing the performance of different photode-tectors under a variety of experimental conditions wemeasured the signal to noise ratio while imaging uni-form fluorescence emanating from a fluorescein solu-tion (10 mM). We derived a figure of merit of a givendetector, which we call the ‘apparent quantum effi-ciency’ (AQE) according to the following rationale. Fora photon counting detector with quantum efficiency h,the mean number of counts n during a time interval Twill be given by:

n=hN( +ND (4)

where N( is the number of photons hitting the detec-tor and ND is the number of dark counts. The variancesn

2 in the number of counts will also be hN( +ND.Therefore, the following identity holds:

(n−ND)2

sn2N( =

h

1+ (ND/hN( )(5)

The left side of this equation involves ratios ofmeasurable quantities (background corrected mean,variance and photon flux) and the expression on theright will be equal to h for ND=0. In the presence ofdark counts (extra noise) it will be smaller than h. Wecall this quantity the apparent quantum efficiency h

(with respect to noise performance), because a noiselessphoton counter with h= h would provide the samesignal to noise ratio.

For an analog detector, such as a photomultiplier, anequivalent equation can be readily derived:

h (y)2

sy2N( 5

h

Z [1+ (ND/hN( )](6)

with

y=q(N( −ND) (7)

Here y is the digitized, background corrected analogsignal, q is the mean contribution of a single detectedphoton to it, and Z is an extra noise factor (Hopt,1998). This factor reflects the amplitude distribution ofthe quantal events. It is 1 for the photon counting APDand the CCD and approximately 1.4 for a PMT (Jones,1971). The equals sign holds when the read-out noise isnegligible. When the photocurrent or analog PMT sig-nal is digitized with a standard AD converter, a filtercriterion as specified above (Eq. (3)) has to be used fora correct evaluation of h. All noise sources in excess ofshot noise, such as read-out noise or some dispersion inthe amplitude distribution of photon generated pulses(Z\1), tend to decrease h.

For the photodetectors under consideration we eval-uated variance and mean value of the fluorescencesignal which was sampled by the ITC-16 (see above)while scanning homogeneous regions of interest at vari-ous illumination intensities and plotted s2 versus mean.It is expected that the slope of such a plot is equal toqZ. For this analysis it is important to use the filtercriterion, given above, which, for 10-ms sample interval,requires a filter setting (−3 dB point) of 47 kHz. Also,in the case of the APD signal, the amplitude had to berestricted to the linear range of the device. From theslopes of such plots we obtained q-values for the vari-ous photodetectors, using Z-values as specified above.The number of detected photoelectrons was obtainedby dividing the mean dark count corrected signal by thequantity q, derived from the slope value. The photoncount, measured this way, agrees within 10% with thevalue obtained by directly counting the output of theAPD. Given the quantum efficiency of the APD (64%)we converted the count rates to photon fluxes. Using 10mM fluorescein and an excitation wavelength of 840nm, we obtained a flux of 1.13×106 photons/s for 1.16mW of excitation power, as measured in the focalplane. By variation of the excitation power, we confi-rmed the square law of two-photon fluorescence excita-tion. Thus, for a given measurement, we calculated N( ,the mean number of photons reaching the detector in a10-ms measuring window as:

N( =11.3� P

1.16×10−3

�2

(8)

Fig. 6. Illustration of single scan images obtained with two different scan protocols from the axon of a cerebellar basket cell loaded via a patchpipette with the Ca2+ sensitive indicator OG1 (200 mM). The scan in A covers 26×31 mm2 in 195 ms, with an effective pixel size of 250 nm. Thistype of scan was used to select a region of the axon suitable for the study of Cai-dependent signals with fast scanning. The two upper panels inB show pseudocolor images of the fluorescence measured in a small subfield of this axon with scans of 8.25×4.75 mm2 (9.9 ms scan time; effectivepixel size of 250 nm) at rest (B1) and at the peak of the response to a 50-ms depolarizing pulse to 0 mV (B2). The scan was rotated 135° withrespect to the large field scan shown in A. B3 shows the DF/F0 image at the peak of the Cai rise. (C) Plot of the temporal evolution of the relativechanges in fluorescence for a region in the branching point, whose position is given by the square drawn in B3. The arrow marks the onset ofthe depolarizing pulse.

Y.P. Tan et al. / Journal of Neuroscience Methods 92 (1999) 123–135134

Fig. 8. Scans of a portion of a CA3 pyramidal cell dendrite, loaded via a patch pipette with 200 mM OG1. Each image is the average of 32 scanstaken at the same focal plane. The effective pixel size was decreased from 250 nm in A to 125 nm in B and 62.5 nm in C. The experimentalpreparation was an organotypic hippocampal culture, kindly provided by Dr B.H. Gaehwiler.

where P is the power in watts measured in the focalplane after replacing the fluorescein solution by thepower meter. Performing measurements with differentphotodetectors under a variety of illumination condi-tions, we calculated h from Eqs. (5) and (6) and plottedit versus N( (see Fig. 7A).

It is seen that the APD reaches an apparent quantumefficiency of about 50% for photon fluxes between 105

and 106 s−1. This is close to the directly measuredquantum efficiency of 64%. h drops both for smallerphoton fluxes (due to the extra noise of dark counts)and for larger fluxes (due to saturation of the APD). Itshould be noted that dead-time corrected readings wereused for calculating sy

2 and y in the case of the APD.The PMT reaches h-values close to its specified quan-

tum efficiency (29%) for fluxes larger than 3×106 s−1.At lower fluxes its performance is degraded due to itsrelatively high dark count (0.3×106 s−1) under theconditions of operation in our microscope. The perfor-mance of the CCD is severely compromised at the lowphoton fluxes used here by its readout noise corre-sponding to approximately 16 photoelectrons (rms-value). It does, however, reach h-values close to 20%for fluxes of 108 s−1 and higher.

The analysis shows that the choice of the best detec-tor, in terms of the achievable signal to noise ratio, verymuch depends on the photon flux under study. Forfluxes lower than 5×106 photons/s, which is obtainedfor a 10 mM fluorescein solution at about 2.5 mW ofexcitation power in the focal plane, as measured usinga 63× , 0.9 NA water immersion objective, the APD isthe photodetector of choice. For larger fluxes, photo-multipliers are superior. It should be noted that thenumbers given refer to a measurement interval (or pixeldwell time) of 10 ms. Effects of read-out noise, whichare very limiting for the CCD, will be less severe forlonger pixel dwell times.

As mentioned above, our experience using this sys-tem for the study of intracellular Ca2+ dynamics in

neurons of brain slices, indicates that maintaining theexcitation power at the specimen plane below 10 mW(with l=840 nm) significantly improves the survival ofthe preparation. For this excitation power, the averagephoton fluxes obtained from the center of cerebellarPurkinje cell somas loaded via patch pipettes with 10mM OG1, at resting Ca2+, levels, ranged from 2.4 to 7MHz (mean9S.E.M.: 4.190.53 MHz (10 cells)). Simi-lar photon fluxes are reached in the soma rim of inCs-loaded cells, following a 50-ms depolarization to 0mV. In axons of cerebellar interneurons, after 20–30min of whole-cell recording with pipettes containing200 mM OG1, basal photon fluxes averaged 1.390.13MHz (20 cells; see example in Fig. 6). As shown in Fig.7B, the low signal levels in the axonal structures requirethe highest AQE provided by the APD.

An analysis of apparent quantum efficiency, as pre-sented here, is quite labor intensive, because it requiresabsolute calibration of a photodetector, and measure-ment of the slopes in a s2 versus mean plot (forcalculating N( ). It should be noted, however, that twodetectors can be readily compared in this approach bymeasuring the signal to noise ratios (SNR) with each ofthe detectors on a region of a uniform fluorescence withidentical illumination conditions. If SNR2 and SNR1

are the SNRs of detector 2 and 1, respectively, SNR2/SNR1 will be equal to h2/h1, and will be a good relativemeasure of performance under the given conditions.

3. Discussion

We have described the construction and operationalperformance of a two-photon fluorescence scanningmicroscope built from commercially available compo-nents. As the main interest was the measurement ofCa2+ dynamics in small patches, we have developedalgorithms that allowed us to scan at the maximumpermissible rate. The 250-nm effective pixel size used in

Y.P. Tan et al. / Journal of Neuroscience Methods 92 (1999) 123–135 135

such scans, allowed us to visualize small structures likespines on the CA3 pyramidal cells (Fig. 8). The effec-tive pixel size could be reduced by an arbitrary amountto have an electronic zoom effect as exemplified in Fig.8B,C.

Most of the two-photon scanning systems are basedon coupling a pulsed laser into a standard confocalmicroscope. This approach has the advantage of requir-ing a minimum of installation effort and allows the useof commercially developed, user-friendly software rightaway. The main disadvantages are the non-accessibilityof the software, and the necessity to use a very compli-cated optical path for the excitation and the descanningof the fluorescence through the same optics. In most ofthe commercial systems, line-scan mode is used as thesolution to the study of fast processes, but it is mostlyrestricted to either the X- or the Y-axis.

The strength of the system described here lies in thefact that it was designed with two-photon fluorescencein mind: The excitation and emission paths are opti-cally very simple, the system employs a standard labo-ratory interface for beam deflection and dataacquisition, and the scanning software is fully accessibleto the experimenter. Very small areas can be scanned atabout 100 Hz, and scan patterns can be oriented ratherthan orienting the biological sample. Imaging at thosehigh rates, however, is severely limited by the relativelylow quantal content of two-photon excitation at biolog-ically permissive excitation levels. Therefore, an APDwith its 50% apparent quantum efficiency was imple-mented as the detector of choice.

Acknowledgements

We thank Dr R. Uhl for his help in some of theoptical problems and Dr R. Bookman, University ofMiami, for the ‘Pulse Control’ software and detailedadvice on its use. We acknowledge the mechanicalexpertise of R. Schurkotter and his group at the centralfine mechanic workshop. We acknowledge the help ofZeiss (Germany) in providing us with a prototype ofthe scanhead. This work was partially financed by theBehrens-Weise Stiftung and by grants from theDeutsche Forschung Gemeinschaft (SFB406) and fromthe European Community (No. ERBFMRXCT-980236).

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