2.1.

Imaging System

The pump-probe technique has been used for decades as a standard nonlinear measurement tool for characterization of light-induced changes in materials’ optical properties and relaxation dynamics of excited states.²¹ The basic concept is that the transmission difference of the probe beam is measured with and without the application of a pump beam. The change in the probe beam signal is caused by the selective excitation of energy states within the molecules.^{10, 21}

Figure 1 shows the experimental setup. The laser has a repetition rate of $80\mathrm{MHz}$ , $100\text{-}\mathrm{fs}$ pulse width, and wavelength tunable range from $780\mathrm{nm}\text{to}920\mathrm{nm}$ . Laser pulses of $100\text{-}\mathrm{mW}$ average power (pulse $\text{energies}=1.25\mathrm{nJ}$ ) are coupled into a holey fiber that is operated in normal-dispersion regime to generate low-noise, broadband, pure self-phase modulation (SPM).²² The beam is then divided into two arms, in which we select two narrow wavelength bands at $800\mathrm{nm}$ and $840\mathrm{nm}$ with high-efficiency notch filters (Semrock FF01-800/12-25 & FF01-840/12-25), as shown in Fig. 1. One signal is delayed in the time domain by a computer-controlled translation stage, and these two wavelength signals are modulated at 980 and $1080\mathrm{kHz}$ , respectively, with electro-optic modulators (Thorlabs, EO-AM-NR-C1). The two arms are combined by a high-efficiency dichroic mirror collinearly and focused onto the object to be studied. The backscattered signals are collected by a large-area silicon PIN photodiode (EG&G SGD-200) in a $45\text{-}\mathrm{deg}$ detection configuration and then detected with a lock-in amplifier at $100\mathrm{kHz}$ , which is the difference frequency. This high-frequency modulation technique provides lower noise and high-sensitivity detection.²³

Fig. 1

Schemetic view of our single-laser, two-color, two-frequency experimental system. A $100\text{-}\mathrm{fs}$ laser (Spectra-Physics Mai-Tai) beam is spectrally broadened in a holey fiber and selected with two notch interference filters in two separate beams. The signals are modulated at 980- and $1080\text{-}\mathrm{kHz}$ frequencies with electro-optic modulators (EOMs) and are recombined and focused into a calibrated scattering cell on the sample. The nonlinear cross-product is detected at the difference frequency with a lock-in amplifier.

The pump and probe arms are collinearly focused onto the dye-filled capillary, which is put inside a $1\text{-}\mathrm{cm}$ cuvette that contains the scattering solution. (Milk solution was used.) The cuvette is attached to a one-dimensional (1-D) translation stage to control the specific depth of the capillary tube relative to the front surface of the cuvette. At each controlled depth, the capillary tube is scanned in the plane vertical to the cuvette moving direction by a two-dimensional (2-D) stage to obtain 2-D images.

2.2.

Sample Calibration

2.2.1.

Image object phantom

Phantoms were prepared with IR125 dye in ethanol contained in capillary tubes with two different inner diameters ( $20\mu \mathrm{m}$ and $300\mu \mathrm{m}$ ). The absorption spectrum of IR125 solution was measured with an Ocean Optics HR4000 spectrometer. The absorption spectrum peaks around $780\mathrm{nm}$ . We adjusted the laser center wavelength and self-phase modulation (SPM) spectrum out of the holey fiber to overlap with the absorption spectrum of the IR125. The pump and probe wavelengths were chosen from the overlap region between the absorption spectrum of IR125 in ethanol and the SPM laser spectrum out of the holey fiber, as shown in Fig. 2 .

Fig. 2

Scheme of the spectra of SPM from holey fiber, absorption of IR125 in ethanol, and selected wavelengths.

2.3.

Monte Carlo–Based Simulation Method

Light propagation in turbid media in this paper are simulated with a Monte Carlo–based method using LightTools software (Optical Research Associates, Inc.). Properties of the turbid media, such as mean-free-path length $L_s$ , absorption coefficient, etc., are defined in the simulations according to the materials used.

3.1.

Backscattering Image Experimental Results

We imaged a phantom of a single capillary tube ( $300\text{-}\mu \mathrm{m}$ inner diameter) filled with IR125 in ethanol inside a calibrated milk solution $(L_s=448\mu \mathrm{m})$ at different focus depth to the front surface of the turbid medium. The wavelengths for the pump and probe signals are chosen to be $800\mathrm{nm}$ and $840\mathrm{nm}$ , respectively. Each beam contained about $1\text{-}\mathrm{mW}$ average power. The detector was put close to the phantom with $45\text{-}\mathrm{deg}$ angle to the incident laser beams as described earlier. The scanning signals were obtained at a depth from $200\mu \mathrm{m}\text{to}900\mu \mathrm{m}$ below the surface [Figs. 3, 3, 3, 3, 3 ]. Red regions have the highest detected signals, and blue regions are the smallest signals. As expected, the detected signal-to-noise ratio (SNR) decreased as the imaging depth increased, as shown by the $x$ -axis scan signal in Fig. 3. A limiting SNR $\sim 1$ was achieved at $900\mu \mathrm{m}$ , corresponding to more than 2 $L_s$ of the turbid medium. The decreasing signal as a function of focus depth will be compared with simulation results in Sec. 3.2.

Fig. 3

Pump wavelength $800\mathrm{nm}$ ; probe wavelength $840\mathrm{nm}$ . Nonlinear absorption images ( $30\mu \mathrm{m}∕\text{pixel}$ , $40\times 40{\text{pixels}}^2$ ) of a $300\text{-}\mu \mathrm{m}$ -diam capillary tube with $1\text{-}\mathrm{mW}$ power per beam when the capillary tube is at (a) $200\mu \mathrm{m}$ , (b) $400\mu \mathrm{m}$ , (c) $600\mu \mathrm{m}$ , (d) $800\mu \mathrm{m}$ , and (e) $900\mu \mathrm{m}$ below the turbid medium surface. (f) Scan signal along the $x$ axis at different depth $(30\mu \mathrm{m}∕\text{pixel})$ with a logarithmic signal scale. The lock-in time constant was set at $100\mathrm{ms}$ .

Next, a capillary tube with about $20\text{-}\mu \mathrm{m}$ inner diameter filled with IR125 in ethanol was used as the object phantom imaged inside calibrated milk solution $(L_s=330\mu \mathrm{m})$ . Each beam contained about $1\text{-}\mathrm{mW}$ average power with the same wavelengths as before. The same detection configuration was utilized. Images obtained ( $500\times 500\mu {\mathrm{m}}^2$ or $50\times 50{\text{pixels}}^2$ ) are shown in Figs. 4, 4, 4, 4, 4, 4 with capillary tube depth from $100\mu \mathrm{m}\text{to}600\mu \mathrm{m}$ below the surface. The integrated intensity along the $x$ axis at $100\mu \mathrm{m}$ below surface [Fig. 4] was calculated to calibrate the transverse resolution of the image, which is defined by the distance of corresponding $x$ positions at 10% and 90% of the maximum integrated intensity value. This distance was measured to be $22\pm 2\mu \mathrm{m}$ , which matches well with its actual width.

Fig. 4

Pump wavelength $800\mathrm{nm}$ ; probe wavelength $840\mathrm{nm}$ . Nonlinear absorption images $(500\times 500\text{microns})$ of $20\text{-}\mu \mathrm{m}$ -diam capillary tube with $1\text{-}\mathrm{mW}$ power at each beam when the capillary tube is at (a) $100\mu \mathrm{m}$ , (b) $200\mu \mathrm{m}$ , (c) $300\mu \mathrm{m}$ , (d) $400\mu \mathrm{m}$ , (e) $500\mu \mathrm{m}$ , and (f) $600\mu \mathrm{m}$ below the surface. (g) Bright-field image under microscope. (h) Zoomed integrated intensity signal along part of the $x$ axis at $100\mu \mathrm{m}$ below the surface $(10\mu \mathrm{m}∕\text{pixel})$ , from which the width of the capillary tube is calibrated to be $22\mu \mathrm{m}$ . The inset in (h) is the integrated intensity along the whole $x$ axis from the image result.

For the preceding experiments, the pump and probe beams were set to be linearly polarized. The backscattered light would be depolarized after propagation in a strongly scattering turbid medium,²⁸ and our detection method was independent of the polarization of the backscattering light.

Previously, Warren’s group demonstrated the use of the nonlinear pump-probe technique for biological imaging.^{8, 9, 10} We believe that this technique can be even more applicable to important biological imaging problems if it can be made to work efficiently in backscattering mode. The current phantom experiments help us to understand the limitations of the backscattering mode detection.

3.2.

Analysis by Monte Carlo–Based Simulation

To understand and analyze the nonlinear absorption signal’s propagation in turbid media for the case of a backscattering detection, we applied a Monte Carlo–based method using the software LightTools. Turbid media having an $L_s$ of $448\mu \mathrm{m}$ was held inside a $1\text{-}\mathrm{cm}$ cuvette.

For our first simulation, 1,000,000 rays were focused into the turbid medium by a singlet with a focus length of $\sim 1.5\mathrm{cm}$ , as illustrated in Fig. 5 . (Only 50 rays are shown of the 1,000,000 used in the calculation.) A dummy surface was inserted inside the turbid medium at the focus point so that the distribution of rays at the focus point surface could be measured.

Fig. 5

Monte Carlo–based simulation for signal versus focus depth. (a) Side view of the simulation setup. (b) Comparison of experimental results with simulation ones: signals decrease exponentially at similar rate as the depth increases.

By moving the cuvette along the $z$ axis, the focus depth relative to the front surface of the turbid medium was changed accordingly. The number of rays incident at the focus point for focus depth varying from $200\mu \mathrm{m}\text{to}1\mathrm{mm}$ below the surface had been obtained by simulation. The simulation was repeated for wavelengths $800\mathrm{nm}$ $\left(I_1\right)$ and $840\mathrm{nm}$ $\left(I_2\right)$ , the wavelengths used for the pump and probe signals in the experiment. The product of the two focused intensities for the two wavelengths at corresponding depths was normalized to compare with the normalized $x$ -axis scan peak values of the $300\text{-}\mu \mathrm{m}$ capillary tube images [Fig. 3] obtained from our experiment, where the turbid medium had the same $L_s$ length. This is appropriate since the nonlinear absorption signal is generated only by the product of the two focused intensities.

By plotting the nonlinear absorption image signal values as a function of different focus depth, both our experimental data and our simulation data could be fit well with similar exponential curves [Fig. 5]. The experimental curve is fit with $y=2.4\exp$ $(-x∕250)$ , and the simulation data is fit with $y=2.8\exp$ $(-x∕200)$ , where $x$ is the depth of the focus with units of microns. The variance of the two curves is within a reasonable range, which might be caused by the errors of experimental measurement.

A second simulation is done to estimate the collection efficiency of our $45\text{-}\mathrm{deg}$ detection method. A detector was put at a $45\text{-}\mathrm{deg}$ angle to the cuvette, as shown in the top view in Fig. 6 . 1,000,000 rays were generated at the focus point with forward directions falling inside a $5\text{-}\mathrm{deg}$ cone, which corresponds to the NA of the focus lens. The focus point was assumed to be $1\mathrm{mm}$ below the turbid medium surface. The backscattered signal reemitted to the detector was calculated by the ratio of power integrated to the initial total signal power generated at the focus point as a function of the radius of the detector.

Fig. 6

Monte Carlo-based simulation for detection process. (a) Top view of the simulation setup (only 30 rays visible). (b) Simulation results of the percentages of integrated power on the detector to the total signal power as a function of radius to the center of the detector.

Figure 6 shows that as the radius of the detector increases, more signals are collected by the detector, as expected, but only about 2% of the signal photons are collected on a $5\text{-}\mathrm{mm}$ -radius detector. We are investigating multiple-detector schemes that can increase this fraction; however, clearly our results show that backscattering mode detection does indeed work with moderate pump and probe signal powers, benefiting from the high-frequency detection technique.