EEfficient wide-field FLIM
Adam J. Bowman , Brannon B. Klopfer , Thomas Juffmann , and Mark A. Kasevich June 13, 2019
Nanosecond temporal resolution enables new methods for wide-field imaging like time-of-flight,gated detection, and fluorescence lifetime. The optical efficiency of existing approaches, how-ever, presents challenges for low-light applications common to fluorescence microscopy andsingle-molecule imaging. We demonstrate the use of Pockels cells for wide-field image gatingwith nanosecond temporal resolution and high photon collection efficiency. Two temporalframes are obtained by combining a Pockels cell with a pair of polarizing beam-splitters. Weshow multi-label fluorescence lifetime imaging microscopy (FLIM), single-molecule lifetimespectroscopy, and fast single-frame FLIM at the camera frame rate with − times higherthroughput than single photon counting. Finally, we demonstrate a space-to-time image multi-plexer using a re-imaging optical cavity with a tilted mirror to extend the Pockels cell techniqueto multiple temporal frames. These methods enable nanosecond imaging with standard opticalsystems and sensors, opening a new temporal dimension for low-light microscopy. Existing sensors for wide-field nanosecond imagingsacrifice performance to gain temporal resolution,failing to compete with scientific CMOS and electron-multiplying CCD sensors in low-signal applications.A variety of detectors currently access the nanosec-ond regime. Gated optical intensifiers (GOIs) basedon microchannel plates allow for sub-nanosecond gat-ing in a single image frame, and segmented GOIs canacquire multiple frames when combined with imagesplitting. Gating into n frames in this way limitsoverall collection efficiency to < /n , and perfor-mance is further limited by photocathode quantumefficiency, MCP pixel density, excess noise, and lat-eral electron drift. Streak camera techniques havealso been demonstrated for wide-field imaging, butthey also require a photocathode conversion step andadditional high-loss encoding.
5, 6
Silicon photodiodeavalanche detector (SPAD) arrays are an emergingsolid-state approach, but they are currently limitedto sparse fill factors and high dark currents.
3, 7, 8
The limitations of current nanosecond imagingtechniques are particularly manifest in fluorescence Physics Department, Stanford University, 382 ViaPueblo Mall, Stanford, California 94305, USA Faculty of Physics, University of Vienna, A-1090 Vienna,Austria Department of Structural and Computational Biology, MaxF. Perutz Laboratories, University of Vienna, A-1030 Vienna,Austria. Correspondence and requests for materials should beaddressed to A.B. (email: [email protected]) lifetime imaging microscopy (FLIM). Fluorescencelifetime is a sensitive probe of local fluorophore envi-ronment and can be used to report factors like pH,polarity, ion concentration, FRET quenching, andviscosity. As lifetime imaging is insensitive to ex-citation intensity noise, labelling density, and sam-ple photobleaching, it is attractive for many appli-cations. FLIM typically relies on confocal scanningcombined with time-correlated single photon count-ing (TC-SPC) detectors.
9, 10
The throughput of TC-SPC is limited by the detector’s maximum count rate(typically 1-100 MHz), and confocal microscopy re-lies on high excitation intensities that can cause non-linear photodamage to biological samples.
11, 12
Fre-quency domain wide-field approaches are a promisingalternative, but they currently require demodulationwith either a GOI or high-noise modulated camerachip.
Given the disadvantages of existing wide-field and TC-SPC approaches, FLIM especially callsfor the development of new, efficient imaging strate-gies to extend its utility for bio-imaging.Here we demonstrate ultrafast imaging techniques– compatible with standard cameras – that have noinherent loss or dead time, allowing access to sub-frame rate sample dynamics at timescales as fast asnanosecond fluorescent lifetimes. First, we show anall-photon wide-field imaging system based simply ona pair of polarizing beam-splitters (PBS) and a Pock-1 a r X i v : . [ phy s i c s . op ti c s ] J un igure 1: Wide-field efficient ultrafast imaging with a Pockels cell (a) Schematic of two temporal bin wide-fieldimaging for a single pixel fluorescence decay. Fluorescence emission is first polarized, a time dependent retardance (stepfunction illustrated) is applied by the PC, and polarizations are split again before the sensor. Two pairs of outputs correspondto integrated intensity before (1, 3) and after (2, 4) a step function gate is applied in the illustration. Other modulationsV(t) may be applied beyond a simple step function as described in the text. Equal optical path lengths are used in practice.(b) Gating efficiency ( I π − I ) is calculated for a 30 mm KD*P Pockels cell as a function of incident angle from conscopicinterference patterns, demonstrating high efficiency gating for wide-field imaging within 6 mrad half-acceptance angle. els cell (PC). This can be used to create two tem-poral bins or to modulate images on any timescale– from nanoseconds to milliseconds. We use thisto demonstrate efficient wide-field FLIM of a multi-labelled sample, single molecules, and a biologicalbenchmark. Second, we demonstrate the use of a re-imaging optical cavity as a time-to-space converterto enable n -frame ultrafast imaging when combinedwith a Pockels cell gate. Our approach is photonefficient and retains the sensitivity and image qual-ity of scientific cameras, making it widely compatibleand potentially inexpensive. The ability to performsingle-frame FLIM without gating loss is a particu-larly unique advantage, as it enables dynamic FLIMwithout the loss, noise, and potential motion and in-tensity artifacts of other approaches. Results
Gating with two temporal bins.
Light from animaging system is polarized with a beam-splitter, andthe image associated with each polarization is alignedto propagate through different locations in a wide-aperture PC, as shown in Figure 1. The PC pro-vides an electric field-dependent retardance betweenthe input light’s polarization components, mappingthe temporal signature of the applied field onto thepolarization state of the imaging beams. A second PBS after the PC again splits the separated imagingbeams, giving four image frames on the camera. Theresulting images now encode temporal information,as shown in Figure 1. To illustrate our method, weconsider a step function voltage pulse applied at de-lay time t d with respect to a short ( ∼ ns) excitationpulse. The step function with edge at t d creates pairsof output images corresponding to integrated signalbefore and after t d .In practice, we implement this configuration witheither a Gaussian gating pulse at t d or a step gatewith few nanosecond rise time as described in the fol-lowing examples. In fact, arbitrary V(t) may be ap-plied to the PC for specific applications (see Discus-sion). Note that a gating pulse can be applied eitheras a single shot measurement or over repeated eventsintegrated in one camera frame. Fluorescence lifetimemay be recovered by either varying the gate delay t d to directly measure the fluorescence decay (see multi-label FLIM below) or by single-frame ratios of gatedand ungated channel intensities (see single-moleculeFLIM below). In cases where the PC aperture is lim-ited, two separate PC crystals may be used insteadof using different areas of the same crystal. Separategates can be applied to each PC to create four timebins. Imaging through Pockels cells.
Standard PCs2se thick (30-50 mm) potassium dideuterium phos-phate (KD*P) crystals with longitudinal field. Thesegive high extinction ratios and are ubiquitous for Q-switching and phase modulation applications. Off-axis rays experience different birefringent phase shiftsthan those on-axis, limiting the numerical aperture(NA) of the crystal for wide-field imaging. In an im-age plane, the PC half angular acceptance α limitsthe NA of collection optics to M α for small angles,where M is magnification. In a diffraction plane (orinfinity corrected space), the field of view (FOV) isinstead limited to 2 tan( α ) f obj where f obj is the imag-ing objective focal length. For example, we foundthat a 10 µ m FOV is achieved with a 1.4 NA micro-scope objective ( f obj = 1.8 mm) and 40 mm thicklongitudinal KD*P PC crystal in the infinity space( α ∼ Further, periodic drive avoids excit-ing piezoelectric resonances and is compatible withfrequency-domain FLIM at high excitation rates.To assess gating efficiency, the impact of off-axisbirefringence was simulated through the Muller ma-trix formalism to arrive at a conscopic interference(isogyre) pattern, as viewed through crossed polar-izers. Subtracting the transmitted intensity pattern I at zero voltage ( V ) from that at the half-wavevoltage ( V π ) gives the gating efficiency ( I π − I ),where the useful NA of the PC is set by the region ofhigh gating efficiency at lower angles [Figure 1(b)].The PC is treated as a linear homogeneous retarderwith off-axis retardance determined by a coordinatetransformation of the crystal axes (SupplementaryNote 1). Angular acceptance may be improvedby making the crystal thinner, with a 3 mm crystalincreasing α to ∼
20 mrad, effectively removing NAand FOV restrictions. Here we show results using athick commercial PC (Figures 2, 3, and 5) and a cus-tom 3 mm KD*P PC (Figure 4). Further, completecancellation of off-axis birefringence may be obtainedby combining the negative uniaxial ( n e < n o ) KD*Pcrystal with a positive uniaxial ( n e > n o ) staticcompensating crystal (e.g. MgF ).
22, 23
Such acrystal fully compensates for off-axis rays at V and further improves the NA at V π (KD*P becomes Figure 2: Multi-label FLIM (a) Direct measurement offluorescence decays obtained by sweeping gate delay time t d for Orange (O, 4.9 ns), Red (R, 3.4 ns), Nile Red (NR, ∼ τ are given. The measured Gaussian instrumentresponse function (IRF) is plotted in black. (b) Intensity imageof a three-label wide-field sample of Orange, Nile Red, andInfrared beads (labels strongly overlap spatially) (c) Lifetimeimage reveals spatial distribution of the labels. Lifetime ismeasured by fitting the decay traces at each pixel (scale bars10 µ m). biaxial with applied field, preventing full high voltagecompensation). Supplementary Figure 1 comparesthe effect of off-axis birefringence for thick, thin, andcompensated KD*P crystals. Multi-label FLIM.
The two bin method has nointrinsic gating loss and allows for imaging ontoany sensor. Fluorescence lifetime imaging is thusan ideal demonstration for the technique, wherethe PC gating pulse is applied after delay t d fromthe fluorescence excitation. Lifetime may then bedetermined by either varying the delay time t d overmultiple frames (as used here) or by taking thesingle-frame ratio of pre- and post-gate intensities(following section). In Figure 2 we image a mixtureof three labels having different lifetimes measuredindividually to be 3.1 ns (2 µ m Nile Red Invitrogenbeads), 4.9 ns (0.1 µ m Orange Invitrogen beads –background), and 2.3 ns (0.1 µ m Infrared Invitrogen3igure 3: Wide-field FLIM of Alexa Fluor 532 molecules (a) Gated channel intensity (b) Ungated channel intensity(scale bar 1 µ m). (c) Measured lifetimes are plotted along with total brightness for the numbered, diffraction limited regionswith SE error bars indicated (see Methods). The majority of these spots are single-molecule emitters as demonstrated by theirphotobleaching and blinking dynamics (Supplementary Figures 4 and 5). Source data are provided as a Source Data file. beads – formed into crystals). For this data, thePC was located in the image plane, allowing forwide-field FLIM of bright samples at 0.1 NA and 20xmagnification with 100 micron FOV. The sample isexcited by laser pulses with duration 1 ns at 532 nmand 5 kHz repetition rate. The fluorescence signal re-sults from the convolution of the decay function withthe laser’s Gaussian excitation pulse with FWHMpulse width ∼ . σ e . The commercial PC used inFigure 2 applies a Gaussian gate function g ( t − t d )in our experiment with a pulse width of 2 . t d , the convolution of thefluorescence with the gating function is measured: f ( t, τ, σ e ) ∗ g ( t − t d ) . Temporal information such asfluorescence lifetime may be calculated by directlyfitting the measured convolution. Note that theconvolution of excitation and gating functions in thiscase gives a Gaussian instrument response function(IRF) with σ IRF = (cid:113) σ e + σ g , measured directlyin Figure 2(a). The fitting approach samples thefluorescence decay at more time points and can beadvantageous for brightly labeled samples comparedto a two-bin measurement . This could be used tomore effectively measure multi-exponential decaysfor instance. Wide-field FLIM of single molecules.
For signal-limited applications relying on efficient photon collec-tion or requiring fast acquisition rates, fluorescencelifetime is best determined by the ratio of gated andungated intensity in a single frame. In Figure 3, wedemonstrate wide-field lifetime microscopy of AlexaFluor 532 (Invitrogen) molecules on glass in a 10 x 10 µ m region. The measured lifetimes are consistentwith both the ensemble lifetime of 2.5 ns and thelarge molecular variation seen in similar studies onglass.
24, 25
The PC is used in the infinity space ofthe microscope objective to apply the same Gaussiangating function at t d = 1 . R = (cid:82) g ( t − t d ) f ( t, τ, σ e ) dt (cid:82) f ( t, τ, σ e )[1 − g ( t − t d )] dt = g ∗ f (1 − g ) ∗ f (cid:12)(cid:12)(cid:12)(cid:12) t = t d . (1)To calculate lifetime, this ratio is experimentallydetermined by summing intensity in a region ofinterest around each molecule. This approach allowssingle-molecule lifetime spectroscopy while maintain-ing diffraction limited resolution and efficient photoncollection of ∼ × photons per molecule (15 sexposure time). Figure 3(c) shows the estimatedlifetime and total brightness for each numbereddiffraction-limited emitter along with error-bars forthe lifetime estimation. Estimation is limited byfluorescence background and dark current here. Alow-cost industry CMOS machine vision camera(FLIR) is used for the detector. In this case, theangular acceptance of the PC limits the field of viewto 10 µ m but still allows photon collection at 1.4 NA.Single-molecule lifetime spectroscopy in wide fieldremains challenging with confocal approaches, whereas here it is readily demonstrated with PCgating and an inexpensive, high-noise camera. Fast FLIM with a thin PC.
By using athin PC crystal, these techniques are extended to4igure 4:
Fast FLIM with a thin PC (a) Intensity image of
Convallaria majalis rhizome stained with acridine orange,a standard FLIM benchmark (scale bar 100 µ m). (b) Lifetime image from fitting a timing trace of 100 ms exposures (50 µW excitation). (c) Lifetime image from a single 100 ms acquisition frame. Inset demonstrates the same single frame with 2ms exposure at high excitation intensity (3 mW - high intensity significantly reduced lifetime in this sample, possibly due tophotochemistry). Lifetime images include an intensity mask to show sample structure. ultra-wide fields of view. A 3 mm thick KD*PPockels cell with a 20 mm aperture gates nearlythe entire output of a standard inverted microscopewith an 0.8 NA objective. A 4 . µ m square FOV. Single frameexposures of 100 ms and 2 ms are demonstrated -the latter may be taken at the maximum cameraframe rate, enabling future FLIM studies withdynamic samples. These acquisitions show dramaticthroughput advantage for wide-field acquisition. The100 ms and 2 ms frames are acquired at 2300 × and78 , × the speed of 20 MHz TC-SPC in raw photonthroughput. The single-frame acquisition method isparticularly powerful, as it prevents image motionartifacts (caused by multiple acquisition frames orscanning for example) and allows self-normalizationwithin a single exposure to remove intensity noise.Quantitative lifetimes are easily calculated using thepre-calibrated IRF as described in the prior sections. Gated re-imaging cavities for multi-frameimaging.
Nanosecond imaging with PCs can beextended beyond two temporal bins through theuse of gated re-imaging optical cavities. Larger binnumbers enable increased estimation accuracy formulti-exponential decays, improve lifetime dynamicrange, and also allow efficient single-shot ultrafastimaging. We exploit the round-trip optical delay ofa re-imaging cavity combined with a tilted cavity mirror to provide nanosecond temporal resolution byspatially separating the cavity round trips. Whileimaging with n -frames using GOIs is limited to < /n collection efficiency, this re-imaging cavitytechnique enables efficient photon collection forlow-light or single-photon sensitive applications. Inrelated work, cavities have been used for single-channel orbital angular momentum and wavelengthto time conversion.
28, 29
Aligned optical cavities havebeen used for time-folded optical imaging modalitieslike multi-pass microscopy.
30, 31
Our implementationinstead employs a re-imaging cavity as the means toobtain temporal resolution for wide-field imaging.An image is in-coupled to a 4 f cavity at the cen-tral focal plane by means of a small mirror M1 asshown in Figure 5. The 4 f configuration re-imagesthe end mirrors (diffraction planes) every round trip.If one end mirror M2 is tilted by angle θ , the imageposition y i at the central focal plane after n roundtrips is displaced by y i = f sin(2 nθ ), where f is thefocal length of the 4 f cavity. The angle θ is set suchthat the resulting images are not blocked by the in-coupling mirror. Each sequentially displaced imageis delayed in turn by an additional round trip. To ex-tract temporal information, the spatially separatedimages need to be either gated externally or simulta-neously out-coupled from the cavity using a PC. Inthe externally gated scheme [schematically shown inFigure 5(a)], light is passively out-coupled each roundtrip through a transmissive mirror. The spatially dis-placed images have a relative time delay ∆ t = 8 f n/c based on their number of round trips n , and an ex-ternal gate is simultaneously applied to all delayed5mages to create temporally distinct frames. A stepfunction gate V(t) allows lifetime measurement fromthe ratios of the time-delayed bins, similar to thetwo-bin case described above. Using the two-bin PCscheme as the external gate gives four image framesfrom each round trip output [Figure 5(c)]. Photon ef-ficiency, the ratio of detected photons to the numberinput to the cavity, with end-mirror reflectivity r isgiven by 1 − r n after n round trips, ignoring intracav-ity loss. This efficiency can be made very high for anappropriate choice of r . For example, 87% efficiencyis obtained with r = 0 . n = 4. It should benoted that the intensity variation between the differ-ent frames is caused by partial transmission after n round trips.Figure 5(c-d) demonstrates the output from an ex-ternally gated tilted mirror cavity. Here a Gaus-sian gate pulse of width less than the round triptime is used. Lifetime in Figure 5(d) is calculatedfrom the ratio R of two frames [Figure 5(b) im-ages (i,4) and (ii,4)] in the gated channel delayedby one cavity round trip time t rt of 4 ns as R =( g ∗ f | t d ) / ( g ∗ f | t d + t rt ). Alternatively, both gated andungated frames could be included in the estimation tomake use of all photons as in equation (1). It is inter-esting to compare n -bin and two-bin lifetime methodsin terms of their theoretical estimation accuracy (seeFigure 6). While the overall accuracies may be closelymatched for monoexponentials, n -bin methods havethe advantage of a wider temporal dynamic range.In a second gated cavity scheme (proposed in Sup-plementary Figure 6), there is instead no transmis-sive mirror, and all input light is simultaneously out-coupled from the cavity with an intra-cavity Pock-els cell and polarizing beamsplitter. Such a schemedirectly gives n images with sequential exposures of t rt = 8 f /c and leaves no light in the cavity. Either athin-crystal or compensated PC would be preferablefor intra-cavity gating since the light passes throughthe PC each round trip.These cavity imaging methods have the advantageof zero dead-time between frames and have no inher-ent limits on collection efficiency beyond intracavityloss. The externally gated cavity is straightforwardto implement with thick-crystal PCs, but has thedisadvantage of indirect temporal gating. Intracav-ity gating instead allows for true n -frame ultrafastimaging where each round trip corresponds to onetemporally distinct image frame. Round trip timesfrom 1 to 10 ns may be achieved with standardoptics. We note that an alternative approach to n-bin imaging could similarly use multiple two-bingates in series (Figure 1) with the added complexityof multiple PCs and detectors. Theoretical estimation accuracy.
Two-binlifetime estimation can perform surprisingly wellwhen compared to the Cram´er-Rao bound for n -binTC-SPC. Both two-bin and n -bin estimationaccuracy scale with photon counting shot noise.Figure 6 shows that n -bin measurements have awider dynamic range of lifetime sensitivity, but thata two-bin PC gate can be nearly as accurate formono-exponential decays when tuned to the appro-priate gate delay. TC-SPC gains a large numberof temporal bins from the bit depth of the ADCwhich dominantly affects the dynamic range. Withideal PC gating, estimation within a factor of twoof the shot noise limit (SNL) may be obtained overa decade of lifetimes with peak sensitivity ∼ . × SNL. In fact, for a step function gate with 1 nsPC rise time, estimation within 2-3 × SNL can beobtained between 1 and 10 ns.
Discussion
We have presented methods for two and n -bin tem-poral imaging on nanosecond timescales using Pock-els cells. Proof-of-concept experiments with single-molecule lifetime spectroscopy and wide-field FLIMdemonstrate the potential to bring nanosecond res-olution to signal-limited applications. PC imag-ing methods promise to enhance the acquisitionspeed and utility of fluorescence lifetime imaging mi-croscopy.For FLIM applications, nanosecond imaging withPCs enables large improvements in throughput overconventional TC-SPC. Even at low repetition rates,PC FLIM throughput readily surpasses TC-SPC. Forexample, a PC gated image at a low signal level of1 photon/pixel/pulse at 15 kHz for a 1 megapixelimage would take 7500 times longer to acquire ona 20 MHz confocal TC-SPC system operating at a10% count rate (standard to avoid pile-up). Thisthroughput advantage grows linearly with signal andpixel number. Wide-field, high throughput lifetimeimaging with PCs could enable imaging of biologicaldynamics at high frame rate. An example of a rel-evant application would be real-time imaging of cel-lular signaling, especially in neurons.
15, 33–35
FLIMmay also be applied as a clinical or in vivo diagnos-tic and wide-field gating may be readily compatible6igure 5:
Multi-frame nanosecond imaging with a cavity time-to-space converter (a) Externally gated, tiltedmirror 4 f re-imaging cavity. Image input is on small in-coupling mirror M1 in an image plane (i). M2 is tilted at a diffractionplane (f), spatially offsetting the images at the M1 plane each pass. Each round trip, images are passively out-coupled throughpartially transmissive mirror M2. (b) Normalized image intensities for four output images from the cavity showing a 4 ns roundtrip delay. (c) Cavity output on camera (CMOS) shows four images output from the PC analyzer for each round trip outputfrom the cavity (columns numbered 1-4 as in Figure 1). Four round-trips (rows i-iv) are displayed (scale bar 50 µ m). Thesample is a mixture of drop-cast Nile Red 2 µ m beads ( ∼ µ m beads (4.9 ns) that form the diffusefilaments. (d) The ratio of output frames (i,4) and (ii,4) in the gated channel at t g = 5 ns [red line in (b)] is used for singleframe FLIM as described in the text. The two labels are readily differentiated (scale bar 10 µ m). with endoscopic probes. We note that frequencymodulated cameras have recently been developed toenable high-throughput FLIM, but these suffer fromvery high dark currents and read noise. PC modu-lation provides an alternative approach to frequencydomain FLIM which can also allow MHz excitationrates.PC gating may further allow for new microscopytechniques by exploiting the nanosecond temporal di-mension. For example, spectral information has beenused to enable multi-labeling of biological samples,which proves important in understanding complex in-tracellular interactions. Fluorescence lifetime maysimilarly provide an attractive temporal approach forunmixing multi-labeled signals. Confocal FLIM hasalready been applied to this problem. In studyingsingle molecules, the capability to combine parallellifetime measurements with spatial and spectral chan-nels could allow for new types of high-throughputspectroscopy experiments to study molecular pop-ulations and photophysical states.
New infor-mation from lifetime could also be used to enhance Figure 6:
Lifetime estimation error (a) Cram´er-Raobound on lifetime estimation accuracy vs. number of bins fora monoexponential fluorescence decay. Dashed lines comparetwo to n -bin lifetime measurements in the case where mea-surement window is n × t d without finitemeasurement window (i.e. ideal step function gate). Note thatthe range of maximum sensitivity can be shifted with t d . Theblue line indicates the shot noise limit: σ τ /τ = 1 / √ N . (b)Simulated lifetime resolution for a realistic two-bin PC exper-iment with a 1 ns 10-90% logistic rise time PC gate and 1 ns σ e , similar to the red line case in (a). Near shot noise limitedestimation accuracy is obtained for τ > PC rise time. Further, temporal gating could be used to suppressbackground autofluorescence occurring at short life-times. While we have primarily focused on applica-tions in fluorescence microscopy, we also note thatPC nanosecond imaging techniques could be morebroadly applied in quantum optics for fast gating,lock-in detection, event selection, or multi-pass mi-croscopy.
28, 30, 49
Other useful operation modes maybe realized with the two-bin PC scheme by apply-ing different modulations V(t). For example, a linearramp of V(t) creates a unique mapping of time tooutput intensity to temporally localize photon bursts(e.g. molecule blinking) by polarization streaking(see Supplementary Figure 3). Periodic V(t) couldalso be used to implement wide-field lock-in detec-tion. Traditional fast-imaging applications in plasmaphysics, LIBS spectroscopy, combustion, time-of-flight techniques, and fluid dynamics could also ben-efit from sensitive single-shot imaging.
6, 31, 50–52
The n -frame tilted mirror re-imaging cavity is particu-larly unique in its ability to perform single-shot ul-trafast imaging of weak, non-repetitive events withzero deadtime between frames when using an inter-nal PC gate (Supplementary Figure 6). It could alsoprove useful for wide dynamic range lifetime imag-ing. We note that strategies for time-of-flight imag-ing and LIDAR have also been recently demonstratedusing PC modulation for the timing of reflected lightpulses. In summary, wide-field PC FLIM was demon-strated in single-frame and time trace modalities.Single-molecule lifetime spectroscopy showed com-patibility with signal limited applications. By us-ing a thin PC crystal, the technique was extendedto ultra wide-field FLIM with single frame acquisi-tion. FLIM images were acquired on a standard bi-ological benchmark with exposure times down to 2ms and acquisition speeds to the camera frame rate.Finally, a new method using re-imaging cavities toenable ultrafast imaging by time-to-space multiplex-ing was shown. These techniques promise to openthe nanosecond regime to signal-limited applicationslike wide-field and single-molecule fluorescence mi-croscopy. Further, they are broadly compatible withany imaging system and sensor, giving potential ap-plications in a variety of fields.
Methods
Experimental setup.
FLIM was performed with a home-made fluorescence microscope for figures 2, 3, and 5. A NikonPlanApo 100x VC 1.4 NA oil-immersion objective was usedfor single-molecule microscopy. All other data was taken witha 20x, 0.8 NA Zeiss PlanApo objective. Excitation pulses(1 ns FWHM) at 532 nm were generated by a Q-switchedNd:YAG at 5 kHz repetition (15 kHz for single-molecule data)(Standa Q10-SH). The detector was a machine vision CMOScamera (FLIR BFS-U3-32S4M-C). A 10 mm aperture, 40 mmthick dual crystal longitudinal KD*P PC embedded in a 50 Ωtransmission line was used (Lasermetrics 1072). High voltagegating pulses were generated into 50 Ω with an amplitudeof 1.3 kV, 2.8 ns FWHM (FID GmbH) attaining 85% of V π and σ IRF = 1 . <
100 ps. Long transmission lines wereused to prevent spurious pulse reflections during fluorescencedecay. For single-molecule data, only two of the outputframes (one output from first PBS) were used to maximizeFOV through the PC, limiting photon efficiency to ∼ f re-imaging cavity used for the n -bin demonstra-tion used a 3 mm prism mirror (Thorlabs MRA03-G01) forin-coupling and f = 150 mm ( t rt = 8 f/c = 4 . R = 0 . T = 0 . Sample preparation.
Alexa 532 single-molecule sam-ples were prepared by drop casting dilute solution onto ahydrophobic substrate, then placing and removing a pristinecoverslip. A dense field was photobleached to the point thatsingle, diffraction-limited emitters were observed. Step-likephotobleaching is shown in the Supplementary Figures 4 and 5along with blink-on dynamics. While multi-molecule emissionwithin a diffraction limited spot was certainly also seen, amajority of the emitters were single molecules. Fluorescentbead samples were prepared by drop-casting directly ontocoverglass. Invitrogen IR bead solution formed crystals asseen in Figure 2.
Data analysis.
Lifetimes were computed by both ratiometriccalculation from image intensities and by time-trace fitting.In ratiometric calculation, a numerically generated lookuptable is used to convert between the measured ratio andestimated lifetime according to the equations in the text andthe pre-characterized IRF. Due to our specific t d and Gaussiangate pulse in Figure 3, lifetimes below 1.1 ns are redundant ith those above 1.1 ns in the numerical conversion. Wereport the larger lifetime value. In timing trace calculation,fitting by least squares was used to estimate lifetime. ThePC applies a time-varying retardance to linearly polarizedinput as δ = 2 πr V n o /λ , where the birefringent phase shift δ is determined by the applied voltage V, ordinary index ofrefraction n o , and the longitudinal electro-optic coefficient r .Transmission in the parallel and perpendicular beamsplitterchannels is T (cid:107) = sin ( δ/
2) and T ⊥ = cos ( δ/ N p pixels corresponding to eachmolecule region of interest after background subtraction.Error bars in Figure 3(c) account for shot noise in the gated(G) and ungated (U) frames and for the background standarddeviations σ g and σ u in the ratio SE σ R as σ R = GU (cid:115) G + 1 U + N p ( σ g G + σ u U ) . Background is the dominant error term here combiningbackground signal with a high camera dark current.The Cram´er-Rao bound for n -bin lifetime estimation ina fixed time window of width T may be directly calculatedfrom a multinomial probability distribution. Fixed windowbounds in Figure 6 were found by setting T = n × t rt for n round trips. The photon normalized Cram´er-Rao bound for n bins is √ Nσ τ τ = nτT (cid:113) (1 − e − T/τ ) (cid:20) e Tnτ (1 − e − T/τ )( e Tnτ − − n e T/τ − (cid:21) − / . Acknowledgements
We thank Yonatan Israel andRachel Gruenke. This research was funded by the Gordon andBetty Moore Foundation. AB and BK acknowledge supportfrom the Stanford Graduate Fellowship. AB acknowledges sup-port from the National Science Foundation Graduate ResearchFellowship Program under grant 1656518.
Author contributions
AB conceived the idea andperformed the experiments. BK and TJ performed initial workon PC gating. AB and MK prepared the manuscript.
Data availability
The data that support the findings of this study are availablefrom the corresponding author upon request.
Competing financial interests
The authors declare no competing financial interests.
References Elson, D. S. et al.
Real-time time-domain fluorescence life-time imaging including single-shot acquisition with a seg-mented optical image intensifier.
New Journal of Physics (2004). Esposito, A., Gerritsen, H. C. & Wouters, F. S. Optimiz-ing frequency-domain fluorescence lifetime sensing for high-throughput applications: photon economy and acquisitionspeed.
J. Opt. Soc. Am. A , 3261–3273 (2007). Hirvonen, L. M. & Suhling, K. Wide-field TCSPC: methodsand applications.
Meas. Sci. Technol , 012003 (2017). Sparks, H. et al.
Characterisation of new gated optical im-age intensifiers for fluorescence lifetime imaging.
Review ofScientific Instruments , 013707 (2017). Gao, L., Liang, J., Li, C. & Wang, L. V. Single-shot com-pressed ultrafast photography at one hundred billion framesper second.
Nature , 74–77 (2014). Heshmat, B., Satat, G., Barsi, C. & Raskar, R. Single-shot ultrafast imaging using parallax-free alignment with atilted lenslet array. In
CLEO: Science and Innovations , pp.STu3E–7 (2014). Burri, S. et al.
A 65k pixel, 150k frames-per-second camerawith global gating and micro-lenses suitable for fluorescencelifetime imaging. In
Proc. SPIE 9141, Optical Sensing andDetection III , 914109 (2014). Ulku, A. C. et al.
A 512 x 512 SPAD Image Sensor withIntegrated Gating for Widefield FLIM.
IEEE Journal ofSelected Topics in Quantum Electronics , 1–12 (2018). Berezin, M. Y. & Achilefu, S. Fluorescence Lifetime Mea-surements and Biological Imaging.
Chemical Reviews ,2641–2684 (2010). Becker, W. Fluorescence lifetime imaging - techniques andapplications.
Journal of Microscopy , 119–136 (2012). Liu, Z., Lavis, L. D. & Betzig, E. Imaging Live-Cell Dynam-ics and Structure at the Single-Molecule Level.
MolecularCell , 644–659 (2015). Chen, B.-C. et al.
Lattice light-sheet microscopy: Imag-ing molecules to embryos at high spatiotemporal resolution.
Science , 1257998 (2014). Gadella, T. W. J., Jovin, T. M. & Clegg, R. M. Fluorescencelifetime imaging microscopy (FLIM) Spatial resolution ofmicrostructures on the nanosecond time scale.
BiophysicalChemistry , 221–239 (1993). Chen, H., Holst, G. & Gratton, E. Modulated CMOS Cam-era for Fluorescence Lifetime Microscopy.
Microsc. Res.Tech , 1075–1081 (2015). Raspe, M. et al. siFlim: single-image frequency-domainFLIM provides fast and photon- efficient lifetime data.
Na-ture Methods , 501–504 (2016). Davis, C. C.
Lasers and electro-optics: fundamentals andengineering (Cambridge University Press, 2014). Kr¨uger, E. & Krijger, E. High-repetition-rate electro-opticcavity dumping.
Review of Scientific Instruments , 1028(1995). Kleinbauer, J., Knappe, . R. & Wallenstein, R. 13-W pi-cosecond Nd:GdVO 4 regenerative amplifier with 200-kHzrepetition rate.
Appl. Phys. B , 163–166 (2005). Yan, R. et al.
100 kHz, 3.1 ns, 1.89 J cavity-dumped burst-mode Nd:YAG MOPA laser.
Optics Express , 761–769(2015). Bergmann, F. et al.
MHz Repetion Rate Yb:YAG andYb:CaF2 Regenerative Picosecond Laser Amplifiers with aBBO Pockels Cell.
Applied Sciences , 761–769 (2015). Bass, M.
Handbook of Optics, Volume 1: Geometric andPhysical Optics, Polarized Light, Components and Instru-ments (McGraw-Hill, 2010). West, E. A. Extending the field of view of KD*P electroopticmodulators.
Applied Optics , 3010–3013 (1978). West, E. A., Gary, G. A., Noble, M., Choudhary, D. &Robinson, B. Large field-of-view KD*P modulator for solarpolarization measurements. In
Proc. SPIE 5888, Polariza-tion Science and Remote Sensing II , 588806 (2005). Lee, M., Kim, J., Tang, J. & Hochstrasser, R. M. Flu-orescence quenching and lifetime distributions of singlemolecules on glass surfaces.
Chemical Physics Letters ,412–419 (2002). Xu, B. et al.
Probing the inhomogeneity and intermedi-ates in the photosensitized degradation of rhodamine B byAg3PO4 nanoparticles from an ensemble to a single moleculeapproach.
RSC Adv. , 40896 (2017). Luong, A. K., Gradinaru, C. C., Chandler, D. W. & Hayden,C. C. Simultaneous Time-and Wavelength-Resolved Fluo-rescence Microscopy of Single Molecules.
J. Phys. Chem. B. , 15691–15698 (2005). Arnaud, J. A. Degenerate Optical Cavities.
Applied Optics , 189–196 (1969). Klopfer, B. B., Juffmann, T. & Kasevich, M. A. Iterativecreation and sensing of twisted light.
Optics Letters ,5744–5747 (2016). Poem, E., Hiemstra, T., Eckstein, A., Jin, X.-M. & Walm-sley, I. A. Free-space spectro-temporal and spatio-temporalconversion for pulsed light.
Optics Letters , 4328–4331(2016). Juffmann, T., Klopfer, B. B., Frankort, T. L. I., Haslinger,P. & Kasevich, M. A. Multi-pass microscopy.
Nature Com-munications , 12858 (2016). Heshmat, B., Tancik, M., Satat, G. & Raskar, R. Photog-raphy optics in the time dimension.
Nature Photonics ,560–566 (2018). K¨ollner, M. & Wolfrum, J. How many photons are necessaryfor fluorescence-lifetime measurements?
Chemical PhysicsLetters , 199–204 (1992). Brinks, D., Klein, A. J. & Cohen, A. E. Two-Photon Life-time Imaging of Voltage Indicating Proteins as a Probe ofAbsolute Membrane Voltage.
Biophysical journal , 914–921 (2015). Gong, Y., Wagner, M. J., Zhong Li, J. & Schnitzer, M. J.Imaging neural spiking in brain tissue using FRET-opsinprotein voltage sensors.
Nature Communications , 3674(2014). Laviv, T. et al.
Simultaneous dual-color fluorescence lifetimeimaging with novel red-shifted fluorescent proteins.
NatureMethods , 989–992 (2016). Munro, I. et al.
Toward the clinical application of time-domain fluorescence lifetime imaging.
Journal of BiomedicalOptics , 051403 (2005). Sun, Y. et al.
Fluorescence lifetime imaging microscopy forbrain tumor image-guided surgery.
Journal of biomedicaloptics , 056022 (2010). Sun, Y. et al.
Endoscopic fluorescence lifetime imaging for invivo intraoperative diagnosis of oral carcinoma.
Microscopyand microanalysis , 791–8 (2013). Valm, A. M. et al.
Applying systems-level spectral imagingand analysis to reveal the organelle interactome.
Nature , 162–167 (2017). Fan, Y. et al.
Lifetime-engineered NIR-II nanoparticles un-lock multiplexed in vivo imaging.
Nature Nanotechnology , 941–946 (2018). Niehorster, T. et al.
Multi-target spectrally resolved fluores-cence lifetime imaging microscopy.
Nat Meth , 257–262(2016). Wang, Q. & Moerner, W. E. Lifetime and Spectrally Re-solved Characterization of the Photodynamics of Single Flu-orophores in Solution Using the Anti-Brownian Electroki-netic Trap.
J. Phys. Chem. B. , 4641–4648 (2013). Zhang, Z., Kenny, S. J., Hauser, M., Li, W. & Xu,K. Ultrahigh-throughput single-molecule spectroscopy andspectrally resolved super-resolution microscopy.
NatureMethods (2015). Mlodzianoski, M. J., Curthoys, N. M., Gunewardene, M. S.,Carter, S. & Hess, S. T. Super-Resolution Imaging of Molec-ular Emission Spectra and Single Molecule Spectral Fluctu-ations.
PLoS ONE , 0147506 (2016). Squires, A. H. & Moerner, W. E. Direct single-molecule mea-surements of phycocyanobilin photophysics in monomeric C-phycocyanin.
PNAS , 9779–9784 (2017). Yan, R., Moon, S., Kenny, S. J. & Xu, K. SpectrallyResolved and Functional Super-resolution Microscopy viaUltrahigh-Throughput Single-Molecule Spectroscopy.
Acc.Chem. Res. , 697–705 (2018). Dong, B. et al.
Super-resolution spectroscopic microscopyvia photon localization.
Nature Communications , 12290(2016). Cordina, N. M. et al.
Reduced background autofluores-cence for cell imaging using nanodiamonds and lanthanidechelates.
Scientific Reports , 4521 (2018). Fickler, R., Campbell, G., Buchler, B., Lam, P. K. &Zeilinger, A. Quantum entanglement of angular momentumstates with quantum numbers up to 10,010.
PNAS ,13642–13647 (2016). Hahn, D. W. & Omenetto, N. Laser-Induced BreakdownSpectroscopy (LIBS), Part II: Review of Instrumental andMethodological Approaches to Material Analysis and Appli-cations to Different Fields.
Applied Spectroscopy , 347–419 (2012). Gao, L. & Wang, L. V. A review of snapshot multidimen-sional optical imaging: measuring photon tags in parallel.
Physics reports , 1–37 (2016). Liang, J. & Wang, L. V. Single-shot ultrafast optical imag-ing.
Optica , 1113–1127 (2018). Jo, S. et al.
High resolution three-dimensional flash LIDARsystem using a polarization modulating Pockels cell and amicro-polarizer CCD camera.
Optics Express , 1580–1585(2016). Zhang, P. et al.
High resolution flash three-dimensional LI-DAR systems based on polarization modulation.
AppliedOptics , 3889–3894 (2017). Chen, Z., Liu, B. O., Wang, S. & Liu, E. Polarization-modulated three-dimensional imaging using a large-apertureelectro-optic modulator.
Applied Optics , 7750–7757(2018)., 7750–7757(2018).