A frequency tripled Q-switched Nd-YAG laser (wavelength 355 nm, pulse duration 12 ns) has been used to pump Coumarin 153 dye solved in ethanol. Simultaneously, a frequency doubled pulse (532 nm) from the same laser is used to probe the solvent perpendicularly resulting in a gain through stimulated laser induced fluorescence (LIF) emission. The resulting gain of the probe beam is recorded using digital holography by blending it with a reference beam on the detector. Two digital holograms without and with the pump beam were recorded. Intensity maps were calculated from the recorded digital holograms and used to calculate the gain of the probe beam due to the stimulated LIF. In addition numerical data of the local temperature rise was calculated from the corresponding phase maps using Radon inversion. It was concluded that about 15% of the pump beam energy is transferred to the dye solution as heat while the rest is consumed in the radiative process. The results show that pulsed digital holography is a promising technique for quantitative study of fluorescent species.
© 2013 Optical Society of America
Laser induced fluorescence (LIF) is the property of some atoms and molecules to absorb monochromatic light at a particular wavelength and to subsequently emit light of longer wavelengths. LIF is a technique widely developed for studying different material properties. It is used as a diagnostic technique to measure fluid flow characteristics such as temperature or species concentration [1,2]. It is also used as an investigation tool in combustion studies  and biomass pyrolysis . Further fluorescence microscopy is widely used in many medical and biological application areas . When a light-molecule interaction takes place the molecule absorbs light in a wavelength band called absorption band. The number of possible electronic and vibrational levels determines the shape of the band. After excitation to an arbitrary electronic state, the molecule relaxes to the lowest vibrational mode of the first electronic state through non-radiative transition called internal conversion. A molecule in the first excited electronic state can return to one of the vibrational modes of the ground state through spontaneous emission of a photon. The manifold of possible transitions gives rise to the fluorescence emission spectrum. Fluorescence emission mainly occurs from the first excited state to the ground state, transitions between higher electronic states are in general non-radiative resulting in temperature rise of the pumped volume . When a volume of excited fluorescent molecules is probed by a certain wavelength included in its spontaneous fluorescence spectrum, the stimulated LIF emission occurs. The stimulated LIF emission is a coherent process as the photons of the probe beam are locally cloned as they pass through the excited volume resulting in a gain of the probe beam. In this paper we investigate the gain dependence on the pump beam energy and the molecules concentration holographically. Pulsed digital holography is a non-invasive and full field method suitable for recording transient events, such as propagation of mechanical waves in solids and shock waves in liquids and gases [7–12]. In digital holography light from a coherent light source, i.e. a laser, is divided into two parts. One part, called the object wave, interacts with the object under study before it falls onto a detector and the second part, called the reference wave, falls directly onto the detector, where the digital hologram is recorded. The interference term between the object and reference wave is the interesting component that is filtered out in the Fourier domain from the digital hologram recorded in an off-axis arrangement. Therefore only the light from the object that is coherent with the source remains. Hence only the gain caused by the stimulated LIF emission will be detected and all spontaneous fluorescence and other disturbances will be filtered out. If we record two holograms without and with the pump beam, an intensity map that shows the gain of the probe beam due to the stimulated LIF emission is produced. In addition the phase difference between the same two recorded holograms can be calculated. The phase change is caused by the refractive index change along the probing laser beam. This projection of the refractive index change in the volume is caused by the temperature rise due to the absorption of the pump beam. In this study pulsed digital holography has been used to investigate the gain of the probe beam due to stimulated LIF emission along the pump beam propagation distance through the dye solution at different pump beam energies and dye concentrations. In addition the thermal effect of the pump beam on the dye solution has been studied.
2. Experimental setup and procedure
Figure 1 shows a sketch of the experimental setup. An injection-seeded, twin oscillator, Q-switched Nd:YAG laser system (Spectron SL804T) is used as light source. The primary wavelength 1064 nm, frequency doubled 532 nm and frequency tripled 355 nm may be accessed through separate apertures. The laser system operates at 10 Hz. Stable single shot operation is not possible. Instead, fast solenoid-activated beam dump shutters allow access to a single, stable, single-frequency pulse. The frequency tripled 355 nm beam with a diameter of about 3 mm is used to pump Coumarin 153 dye solved in ethanol contained in a cuvette with a width of 3 cm in the pump beam direction. The Coumarin 153 dye has a strong absorbance at the pump wavelength 355 nm and its fluorescence spectrum has a peak close to 532 nm. The frequency doubled 532 nm beam from the same laser is used as a probe beam. It is split by a beam splitter (BS1). The reflected part is reflected by mirror M1, expanded by a negative lens (NL), collimated by a positive lens (L1) and illuminates a diffuser (D) after passing through the dye volume. The diffuser is used to give a projective image and to prevent direct light to saturate the detector. As the phase gradients introduced between the recordings are small, the speckles generated by the diffuser are stationary and are filtered away in the subsequent analysis. The light that passes the beam splitter BS1 is used as reference beam and it is guided through a fibre optic cable (Thorlabs 2 m single mode patch fibre) to the beam splitter BS2 from where it illuminates the CCD-detector. The camera is a PCO Sensicam double shutter, with a resolution of 12801024 pixels, a pixel size of 6.7 µm6.7 µm and a dynamic range of 12 bits. The diffuser is imaged onto the CCD detector by a two-element lens system (L) producing an image plane hologram. Each element of the lens system is a plano-convex lens with a focal length of 100 mm. An aperture (A) with a size of 1.34 mm5 mm is placed between the two elements of the lens system. The field of view is 12 mm9.6 mm. The tip of the optical fibre is positioned in such a way that seen from the detector it should appear to come from the same plane as the aperture and one aperture width (1.34 mm) from the edge of the aperture. This is secured by the off-axis angle θ in Fig. 1. In this way the interference pattern between the object and reference light is spatially separated from the object light self-interference term in the Fourier domain, which enables the Fourier transform method to be used for the calculation of the digital holograms .
In digital holography the intensity in the recorded hologram may be written as I = IO + IR + JRO + J*RO, where IO is the intensity of the object wave, IR is the intensity of the reference wave, JRO is the interference term between the object and reference waves and * represents complex conjugation. In pulsed digital holography the interesting component is JRO (or its conjugate) that is separated in the Fourier domain from the rest of the components in the off-axis arrangement shown in Fig. 1. Therefore only the light from the object that is coherent with the source remains. Two digital holograms without (reference image) and with (deformed image) the pump beam (355 nm) are recorded. The interference term in the recorded hologram may be expressed as,Eq. (1) subscript i = 1 refers to the reference image and subscript i = 2 refers to the deformed image, respectively, and we have assumed perfect coherence between the two waves. If we assume the reference wave to be a smooth deterministic wave we see that the hologram becomes a magnified and phase delayed replica of the probe wave. Combining the interference terms of the reference and deformed holograms as,
3. Results and discussion
Intensity maps showing the gain of the probe beam (532 nm) caused by the stimulated LIF emission at different pump beam energies (Ep) and dye concentrations (c) are shown in Fig. 2. In Fig. 2(a) Ep is 8.3 mJ and c is 0.32 g/L. In Fig. 2(b) Ep is 0.94 mJ and c is 0.32 g/L and in Fig. 2(c) Ep is 8.3 mJ and c is 0.05 g/L. The corresponding intensity profiles (an average from Y = 4.2 mm to Y = 4.3 mm) are shown in Fig. 3.
We expect to be larger than unity in the regions where the pump beam (355 nm) interacts with the dye solution. The intensity maps in Fig. 2 show that there is a bright volume () with a width close to the pump beam diameter (3 mm) in the Y direction compared to the surrounding undisturbed dye. The intensity of the probe beam (532 nm) increases at this volume due to the stimulated LIF. All spontaneous fluorescence and other disturbances have been filtered out during the interferometric detection. The bright volume shows the propagation of the pump beam through the dye solution. At high dye concentration (0.32 g/L) the pump beam is completely absorbed a short distance from the cuvette wall (X = 0), see Figs. 2(a) and 2(b) while for lower concentration (0.05 g/L) the pump beam propagates longer distance through the dye solution, see Fig. 2(c). Figure 3 shows that at high dye concentration (0.32 g/L) the gain is high close to the cuvette wall and decreases gradually with the distance until about 5 mm from the cuvette wall. Therefore one may conclude that the pump beam is completely absorbed after about 5 mm from the cuvette wall. The maximum gain is about 85% at a pump beam energy of 8.3 mJ compared to about 30% at a pump beam energy of 0.94 mJ close to the cuvette wall. On the other hand at lower concentration (0.05 g/L) the gain is almost constant (about 25%) along the propagation distance, hence the pump beam propagates homogenously through the dye volume.
In addition to the intensity maps, phase maps showing the change in refractive index due to the thermal effect caused by the pump beam are recorded. Part of the pump beam energy is transferred to the dye solution through non-radiative transitions. The time-scale of the non-radiative transitions is 10−13 - 10−11 s  and as the pulse length of the pump beam is 12 ns; the heat caused by the non-radiative transitions changes the refractive index of the dye solution during the pulse duration, which changes the optical path of the probe beam. Figures 4(a) and 4(b) show phase maps recorded after two different numbers of pump pulses with an energy of 8.3 mJ and a dye concentration of 0.32 g/L. In Fig. 4(a) the phase map is recorded after 3 pump pulses and in Fig. 4(b) it is recorded after 10 pump pulses. Figure 4(c) shows the corresponding phase difference profiles (an average from Y = 4.6 mm to 4.7 mm). Figure 5 shows phase maps recorded after two different numbers of the pump pulses with an energy of 8.3 mJ and a dye concentration of 0.05 g/L. In Fig. 5(a) the phase map is recorded after 3 pump pulses and in Fig. 5(b) it is recorded after 10 pump pulses.
Figure 4(a) shows that after 3 pump pulses the heated volume is almost a cylinder extended in X direction. After 10 pump pulses heat transfer by convection toward the dye surface takes place, see Fig. 4(b). The corresponding phase difference profiles seen in Fig. 4(c) show that, the phase difference is about −2.2 ± 0.15 radians after 3 pulses and increases with number of pulses to be about −4 ± 0.15 radians after 10 pulses. By increasing the number of pulses, the corresponding input energy to the dye volume through non-radiative transitions increases and hence the change of the dye temperature will increase the change in refractive index. Figure 5 shows that at lower dye concentration (0.05 g/L) when the pump beam propagates longer distance along the dye solution (see Fig. 2(c)) the heated volume is elongated. With increasing number of pulses the convective heat transfer is seen in Fig. 5(b). The uncertainty in phase is estimated to about 0.15 radians considering the random error in an undisturbed region of the phase map (calculated to be 0.05 radians) and shot to shot stability of the laser. The uncertainty in the following quantities is calculated by error propagation of the phase.
When the heated volume is almost a cylinder (see Figs. 4(a) and 5(a)) Radon inversion can be used to estimate the 3D refractive index fields measured from the projections assuming rotational symmetry [14–16]. The reconstructed refractive index difference profiles at Y = 0.28 mm at different positions from the cuvette wall at two different dye concentrations and a pump energy of 8.3 mJ are shown in Fig. 6. In Fig. 6(a) the dye concentration is 0.32 g/L and in Fig. 6(b) it is 0.05 g/L.
The pump beam is almost Gaussian shaped; it is seen in Fig. 6 that the change in refractive index is larger at the centre of the beam and reduces towards the edges. Figure 6(a) shows that the refractive index change is large close to the cuvette wall, it is about (−8.8 ± 0.6) × 10−5 and decreases gradually with the propagation distance at the dye concentration of 0.32 g/L. In contrast Fig. 6(b) shows that at lower dye concentration (0.05 g/L) the refractive index change is almost the same at different positions from the cuvette wall with a value of about (−3.3 ± 0.6) × 10−5. The results of the refractive index change are consistent with the results from the intensity maps. Since Fig. 3 shows that the pump beam is gradually absorbed short distance from the cuvette wall at a dye concentration of 0.32 g/L, while at low dye concentration (0.05 g/L) the pump beam propagates homogenously through the dye volume.
From the refractive index change, the temperature change can be calculated. Kim et al.  reported the change of refractive index with temperature for ethanol to be about 3.3 × 10−4 /K. From the reconstructed refractive index at pulse energy of 8.31 mJ and dye concentration of 0.32 g/L the change of refractive index close to the cuvette wall is about (−8.8 ± 0.6) × 10−5 resulting in a temperature change of approximately (0.26 ± 0.02) K. The corresponding change for a dye concentration of 0.05 g/L is about (0.1 ± 0.02) K. The amount of the pump beam energy E transferred to the dye solution through the non-radiative transition causing the temperature change ∆T can be calculated using the following formula:Eq. (3) by integrating the temperature change along the heated volume. For a dye concentration of 0.32 g/L, the amount of the pump beam energy that causes the temperature change is about 3.6 ± 0.2 mJ. The energy input is three times the pulse energy; 24.9 mJ (the phase map is recorded after three pulses). Therefore about 15 ± 1% of the pump beam energy is transferred to the dye solution through non-radiative transitions and causes a temperature rise while the rest is consumed in the radiated process (spontaneous and stimulated LIF). For the dye concentration of 0.05 g/L, the amount of the pump beam energy that causes the temperature rise is about 3.9 ± 0.7 mJ. Hence about 16 ± 3% of the pump beam energy is transferred to the dye volume through the non-radiative process.
The results show a qualitative similarity between intensity and phase maps. The gain (from intensity maps) and the phase change (from phase maps) follow in essence the Beer-Lambert decay along the propagation distance from the cuvette wall. However, as the local gain coefficient will depend on the dye concentration as well as the pump and probe beams energy , a slight divergence from a classical Beer-Lambert decay is expected. As a consequence a quantitative comparison between intensity and phase maps will be more complicated and excluded from this paper.
The possibility of using pulsed digital holography for quantitative study of fluorescent species has been studied. Intensity maps showing the gain of the probe beam as a result of the stimulated LIF emission at the positions where the pump beam (355 nm) interacts with the dye volume are recorded. The gain is about 85% close to the cuvette wall for a dye concentration of 0.32 g/L and pump beam energy of 8.3 mJ and decreases gradually with the distance from the cuvette wall. At a lower dye concentration of 0.05 g/L the gain is almost constant along the distance from the cuvette wall and it is about 25%. In addition the phase change caused by the thermal effect of the pump beam has been measured simultaneously. Assuming rotational symmetry, Radon inversion has been used to estimate the 3D refractive index field and the corresponding temperature change. By integrating through the pump beam, it was estimated that about 15% of the pump beam energy was transferred to the dye solution by the non-radiative process. The remaining part of the pump beam energy is consumed in the radiative process (spontaneous and stimulated LIF). The results show that pulsed digital holography is a promising technique for quantitative studies (species concentration, temperature, diffusion, transient heat transfer problems, etc.) of fluorescent species.
We would like to acknowledge Bio4Energy, a strategic research environment appointed by the Swedish government, for supporting this work.
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