Spontaneous loss versus stimulation gain in pump-probe microscopy: a proof of concept demonstration

Abstract. Significance: The large background, narrow dynamic range, and detector saturation have been the common limiting factors in stimulated emission (SE)-based pump-probe microscopy, attributed to the very small signal overriding the very intense laser probe beam. To better differentiate the signal of interest from the background, lock-in detection is used to measure the fluorescence quenching, which is termed spontaneous loss (SL). The advantages are manifold. The spontaneous fluorescence signal can be well separated from both the pump and the probe beams with filters, thus eliminating the background, enlarging the dynamic range, and avoiding the saturation of the detector. Aim: We propose and demonstrate an integrated pump-probe microscopy technique based on lock-in detection for background removal and dynamic range enhancement through SL detection. Approach: The experimental setup is configured with a pulsed diode laser at a wavelength λpu=635  nm, acting as a pump (excitation) and a mode-locked Ti:sapphire laser at a central wavelength λpr=780  nm, serving as the probe beam (stimulation). Both pulse trains are temporally synchronized through high precision delay control by adjusting the length of the triggering cables. The pump and probe beams are alternatively modulated at different frequencies f1 and f2 to extract the stimulated gain (SG) and SL signal. Results: SG signal shows saturation due to the irradiation of the intense probe beam onto the photodetector. However, the detector saturation does not occur at high probe beam power for SL detection. The fluorescence lifetime images are acquired with reduced background. The theoretical signal-to-noise ratios for SG and SL are also estimated by photon statistics. Conclusion: We have confirmed that the detection of SL allows the elimination of the large background without photodetector saturation, which commonly exists in SG configuration. This modality would allow unprecedented manipulation and investigation of fluorophores in fluorescence imaging.

stimulated Raman scattering (SRS) 6 and TA. 7 These imaging modalities have been shown to reveal the structural features and transient phenomena in biology and chemistry at picosecond or femtosecond time scales. [8][9][10][11][12] In the pump-probe technique, the pump pulse is used to excite the sample and the induced changes are then monitored by the synchronized probe pulse. Notably, lock-in detection is used throughout the pump-probe microscopy for both labeled and label-free imaging to recover the relatively small modulated signals from the very large background.
Among the above-mentioned modalities, SE is one of the most versatile techniques for scanning optical microscopy, with its renowned application in stimulated emission depletion (STED) microscopy to allow spatial resolution far beyond the diffraction limit. 13 In STED microscopy, a common approach is to excite the electrons from ground states to excited states and another laser beam at a wavelength that partially overlaps the emission spectrum of the fluorophore is then used to turn the excited fluorophores to a nonfluorescent state (dark state) by SE. In this way, SE increases the number of photons (gain) in the probe beam (stimulated gain, SG), while it also quenches the fluorescence emission process, known as spontaneous loss (SL). In this case, the rate equations for populations of the ground state ðS 0 Þ and of the excited state ðS 1 Þ can be written as 14 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 2 ; 1 1 6 ; 4 9 2 where k exc ¼ σ abs I exc , k fl ¼ 1∕τ, and k STED ¼ σ STED I STED are the rate of excitation caused by the pump beam, rate of spontaneous emission, and rate of SE caused by the STED beam, respectively. Therefore, increasing the STED beam would shorten the excited state lifetime, τ ¼ 1 k fl þk STED . This feature of STED with a low intensity STED beam has been used to improve image resolution. 14 Note that the transitions of SE take place in both real states (fluorescence) and virtual states (SRS). In SRS, the pump and Stokes beams are illuminated on the sample when the frequency difference between the pump and the Stokes matches the specific molecular vibrational frequency of a chemical bond. As a result, the Stokes beam experiences photon gain (stimulated Raman gain). On the other hand, the pump beam experiences photon loss (stimulated Raman loss).
In addition, SE-based pump-probe microscopy was carried out for undetectable fluorophores detection, 15 subdiffraction fluorescence lifetime imaging, 16 and background-free fluorescence imaging. 17 SE is also a two-photon process working through real state transition, which has an equivalent cross section several orders of magnitude greater than the virtual ones. Note that in scanning optical microscopy, the penetration depth and signal-to-background ratio are two key advantages claimed by two-photon (2P) excitation due to the nonlinear intensity dependence of the absorption. SE reduced fluorescence microscopy was demonstrated to extend the fundamental depth limit of 2P fluorescence imaging. 18 A femtosecond laser is often required to achieve effective excitation efficiency since the transition is through virtual states, which renders such an imaging system being costly, bulky, and complex. In comparison, SE could realize the 2P process with the use of gain-switched laser diodes, greatly reducing the cost and the complexity of operating a femtosecond laser.
In this paper, we are presenting an integrated pump-probe microscopy setup for the detection of both the SG and the SL. Critically, SL detection allows the reduction of high background in the signal and more flexibility in selecting detectors and the corresponding electronics for signal processing. A comparison between SG and SL is highlighted in Table 1.

Working Principle of Lock-In Detection for Signal Extraction from Stimulated Gain and Spontaneous Loss
The working principle of modulation transfer that carries the SE signal in pump-probe microscopy for SG and SL is shown in Fig. 1. The pump and the probe beams are alternatively modulated at a selected frequency, f, to extract SG and SL, respectively.
For SG detection, the sample is irradiated with the modulated pump beam and SG is then detected by demodulating the probe beam at the same frequency by a lock-in amplifier. In the same way, when the sample is excited with the unmodulated pump and the modulated probe beam, the loss in spontaneous emission due to SE is extracted by demodulation with the modulation frequency (on the probe beam).

Spectral Detection Scheme for Both Stimulated Gain and Spontaneous Loss
The versatile and robust ATTO 647N fluorescent dye (ATTO 647N, ATTO-TEC, Germany) is used for demonstration. The absorption and fluorescence emission spectra of the red fluorescent dye along with the pump (excitation) and probe (stimulated) laser beams are shown in Fig. 2. The pump (λ pu ¼ 635 nm) and the probe (λ pr ¼ 780 nm) beams are selected at two different  wavelengths that match well with the absorption and emission band spectra of the dye. The spectral filter sets are used in the experiment for two functions: (i) blocking the pump beam completely and allowing the probe beam only that carries SE signal and (ii) blocking both the pump and the probe beams and allowing only fluorescence emission. Critically, in the detection of SL, a band pass filter (marked by green) is used to reject both the pump and the probe wavelengths and pass only the spontaneous emission. While for the detection of SG, a band pass filter (marked by blue) is used to block the pump beam completely and pass the probe beam along with the florescence emission (which is a substantial source of background in SG detection).

Optical Microscope Setup
The schematic of the experimental setup for the SG and the SL is shown in Fig. 3. Our pumpprobe microscope is configured with a pulse diode laser (LDH-D-C-635M, PicoQuant, Germany) with the pump (excitation) beam at a wavelength of λ pu ¼ 635 nm and a pulse width of ∼120 ps, which is synchronized with the mode-locked Ti-sapphire laser (Mira F-900, Coherent Inc.), serving as the probe beam operated at a central wavelength of λ pr ¼ 780 nm through a trigger diode (TDA200A, PicoQuant, Germany). The maximum pump and probe beams power are set at 2.6 and 50 mW accordingly. The time delay (τ) between the pump and probe pulses are precisely controlled by adjusting the length of the triggering cable and setting the nanosecond delay box (Ortec 425A, Ametek). Two laser line filters (FL635-10 and FL780-10, Thorlabs) are used to remove the unwanted wavelengths that are associated with the pump and probe beams. The probe beam pulses (200 fs) are passed through two 15-cm long dispersive glass rods (SF-6) for pulse width stretch (to ∼2.6 ps) to avoid 2P excitation. An anamorphic prism (PS875-A, Thorlabs) is used to transform the elliptical mode of the pump beam into a circular one for better mode matching and tighter focusing. Both beams are coupled into a laser scanning unit (FV300, Olympus, Japan) through a dichroic mirror (FF01-720/SP, Semrock). The combined beams are focused onto the sample by an objective lens (UPlanFL 10X 0.30, Olympus, Japan) and the transmitted light is collected by another objective lens (UPlanFL 10X 0.30, Olympus, Japan). For SG, the pump beam is modulated with a lock-in amplifier (HF2LI, Zurich Instrument, Switzerland) at the frequency of 100 KHz. A bandpass filter (FF01-769/41-25, Semrock) is used to block the pump beam completely and let only the probe beam along with some fluorescence to pass through the filter. The SE photons gained by the probe beam propagating in the transmission direction are detected by a silicon photodiode (PDA36A, Thorlabs). For comparison, in SL, the probe beam is modulated with an electro-optic modulator (M350-80LA, Conoptics Inc.) also at the frequency of 100 KHz. The spontaneous emission is reflected in the backscattered direction by a dichroic mirror (ZT685dcrb, Chroma Technology). A bandpass filter (FF01-700/13-25, Semrock) is placed before the photomultiplier tube (PMT) to completely block the pump and the probe beams. The SL signal is detected by demodulating the output of the PMT (R376, Hamamatsu, Japan) with the lock-in amplifier. The time constant of the lock-in amplifier is set at 2 ms. The output of the lock-in amplifier is connected to the analog-to-digital channel of the scanning unit to reconstruct the images. For SG and SL signals' measurements, the fluorescent ATTO 647N dye is dissolved in deionized water with various concentrations (0.1 to 1 mM). The dye solution is injected into the microchannel slide (15μ-slide, ibidi GmbH, Germany) for testing. A piece of lens cleaning tissue paper is immersed inside the ATTO 647N dye solution and sandwiched between two cover glass slides for timeresolved imaging.

Results and Discussions
Figure 4(a) shows the SG signal as a function of the probe beam power. When the probe laser power reaches 3.5 mW, the SG signal starts to show saturation due to the intense power of the probe beam on the photodetector. In such a high NA setting, the SG contains a large background, which is attributed to the spontaneous emission caused by the pump beam. Notably, the SE is also the dominant fluorescence quenching process with the wavelength-dependent SE cross section. 19 The SG and the SL are thus correlated with each other. The fluorescence reduction rate of a single molecule can be described as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 1 1 6 ; 2 1 1 where R SERF , f rep , k exc , τ exc , η, k SE , and k fl are the fluorescence reduction rate, repetition rate, excitation rate, pulse width, fluorescence quantum yield, SE rate, and fluorescence emission rate, respectively. 18 In SG measurements, some spontaneous fluorescence signal (forming the background) is always present along with the SE signal and cannot be filtered out since the probe beam lies within the emission band of the fluorescent dye. For comparison, Fig. 4(b) shows the SL signal increases linearly with the probe beam power. The SL signal does not saturate at a high laser power of ∼50 mW, and the detected SL dose not contribute to any background or detector saturation. The SL signal as a function of time delay between two pulses is shown in Fig. 5(a). In a fluorescence quenching experiment, the fluorescence intensity and relative delay are given as E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 1 1 6 ; 5 1 8 where I 0 and I are the intensities in the absence and presence of SE pulses, q is the extent of quenching, t d is the relative time delay between the pump and probe pulses, and τ is the  fluorescence lifetime of the fluorophore. 20 The fluorescence lifetime images with different delay times are shown in Fig. 5(b). When compared with the data acquired in our previous work, 21 the lifetime images are obtained with greatly reduced backgrounds.
In SG detection, the probe beam carrying the SE signal directly irradiates the photodetector and contributes substantial noise due to its high intensity and fluctuation. The noise level due to the probe beam is evaluated by switching off the pump beam. The root-mean-square noise, which is the standard deviation of the detected signal over a period of time, is measured as the input power of the probe beam, as shown in Fig. 6. The experimental result is compared with the theoretical shot noise level, which is evaluated by Eq. (5) with the following parameters for the photodetector: gain, G ¼ 0.75 × 10 3 V∕A, elementary charge, q ¼ 1.6 × 10 −19 C, responsivity ðrÞ ¼ 0.49 A∕W at 780 nm, and optical power, P. In this condition, the shot noise level is limited at a very low optical probe power (∼110 to 160 μW). As the power of the probe beam increases, the main source of noise is switched to the laser noise. However, the laser intensity noise does not affect the SL signal except for shot noise.
In an optical imaging system, signal-to-noise ratio (SNR) is a critical parameter, which is also estimated by theoretical calculation. Here, we used Poisson statistics to evaluate the theoretical SNRs of the SG and SL. The experimental parameters for theoretical calculation are listed in Table 2.
The number of spontaneous photons per pulse in the pump beam waist is estimated as The SNR of SG can be estimated as The SNR of SG is limited by the photodetector saturation window due to the strong probe beam power.  The SNR of SL can be calculated as E Q -T A R G E T ; t e m p : i n t r a l i n k -; s e c 3 ; In SL, the selection of a high gain detector, such as a PMT, would improve the SNR. As discussed above, the benefits and limitations of SL are illustrated using conventional analog lock-in detection mode. Notably, the analog measurements are always affected by the detector's gain [such as a photodiode (PD) and PMT] and the electronics noise (such as thermal noise, flicker noise, and shot noise). For a sine wave modulation, the effective count rate ðr T Þ over a bin time (T) can be expressed as 22 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 1 1 6 ; 5 5 8 where r 0 is a constant rate, A is the modulation depth, and f m is the modulation frequency. Therefore, a high count rate can be obtained with a longer bin time. The gated photon counting approach can also be used to increase the count rate with a short gating interval to provide high detection efficiency and SNR.
Note that the lock-in amplifier extracts the SL signal from an extremely noisy background. The electronic noise is one of the predominant noises for lock-in detection. In addition, lock-in detection is analog signal processing in nature and is more susceptible to noise and signal distortion. Alternatively, digitally detecting the signal through photon counting will greatly improve the electronic noise and the reliability. The gated photon counting can be an advantageous alternative for lock-in detection under the pump-probe scheme. 12 Notably, the lifetime of the fluorescence dye is in the nanosecond time regime, which allows synchronization of the pump pulses with the probe pulses at half of the repetition frequency (∼38 MHz). 23 In this way, the highest possible modulation can be achieved and is termed subharmonic synchronization.

Summary and Future Perspective
In summary, we have successfully established a new pump-probe microscopy technique for the detection of SG and SL signals. In addition, detection of SL allows a much wider dynamic range without saturating the detector and the elimination of the large background, which commonly exists in the SE signal. In this way, fluorescence lifetime images can be obtained with greatly reduced backgrounds.
Finally, and critically, our ultimate goal is to insert the pump-probe microscopy system into a fully digital data acquisition scheme based on photon-counting detection. The pump-probe imaging is equivalent to 2P imaging, which provides optical sectioning capability with high contrast. In particular, our technique is expected to investigate fluorophores and improve SNR in pump-probe microscopy.

Disclosures
We have no competing financial interests.
respectively. He received his PhD in biophotonics from the Institute of Biophotonics, National Yang-Ming University, Taiwan, in 2019. His current research interests include advanced optical microscopy, optical beam-induced current microscopy, and ultrasound imaging. He was the president of the OSA student chapter at National Yang-Ming University from 2017 to 2018. He is a member of SPIE, OSA, and IEEE.
Khalil Ur Rehman is currently pursuing his PhD at the Institute of Biophotonics, National Yang-Ming University, Taipei, Taiwan, under the supervision of Professor Fu-Jen Kao. He received his MPhil degree in applied physics from the Centre for Advanced Studies in Physics, Government College University, Lahore, Pakistan, in 2015. He has expertise in light-matter interactions, fluorescence lifetime imaging, and fluorescence resonance energy transfer. His current research in the field of polarization-resolved based stimulated emission pump-probe microscopy.
Guan-Yu Zhuo is now an assistant professor in the Institute of New Drug Development, China Medical University (CMU). He directs the Biophotonics Laboratory at CMU for advanced science and optical imaging technology. He received his BS and MS degrees in physics from the National Chung Cheng University, Taiwan, in 2005 and 2007, respectively. He received his PhD in physics from the National Taiwan University in 2012. He studied high-end microscopy techniques with Professor Fu-Jen Kao for more than 5 years.
Fu-Jen Kao received his BA degree from the National Taiwan University in 1983 and his MA and PhD degrees from Cornell University, in 1988 and 1993, respectively, all in physics. He is currently a professor at the Institute of Biophotonics, National Yang-Ming University, Taiwan. He was also the former director of the Institute of Biophotonics, National Yang-Ming University, and the former president of the Physics Society of ROC, Taiwan. He was the vice president of the Association of Asia Pacific Physical Societies from 2017 to 2019. In addition, he has served as the chief of research and planning, Office of Research Affairs, a professor at the Institute of Electro-Optical Engineering, and a professor at the Department of Physics, National Sun Yat-sen University. The research laboratory led by him has successfully developed many advanced techniques based on multiphoton microscopy with a wide variety of imaging modalities, including two-photon, OBIC, SHG, THG, CARS, stimulated emission, FLIM/FRET, etc. In addition to championing these developments, he has transferred many of the above techniques to a large number of interested research groups both domestically and internationally. He has authored more than 100 SCI journal papers, edited two books, and presented his research at more than 100 international conferences. He is a fellow of Royal Microscopy Society, Taiwan Physical Society, and SPIE, and a reviewer of a number of international research journals.