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We propose photoacoustic microscopy using ultrashort pulses with two different pulse durations in the range from femtoseconds to picoseconds. The subtraction of images for longer-pulse excitation from those for shorter-pulse excitation extracts two-photon photoacoustic images effectively, based on observation that the intensity ratio of two-photon to one-photon absorption-induced photoacoustic signals depends on the pulse duration in the same manner as the intensity ratio of two-photon and one-photon fluorescence signals. Two-photon photoacoustic microscopy using this subtraction method enables precise observation of the cross-sections of silicone hollows filled with the mixture of one-photon and two-photon absorption solutions.
© 2014 Optical Society of America
1. Introduction
Recently, the combination modality of two-photon (multiphoton) absorption-induced photoacoustic microscopy (TP-PAM) has been proposed [1–8] to improve the penetration depth while keeping high spatial resolution in PAM. Two-photon absorption occurs only at a small focus point and then determines the axial resolution. The detection of two-photon photoacoustic signals enables us to avoid the use of high-frequency photoacoustic components, which do not propagate through long distance in living tissues, and thus makes deep imaging possible. However, due to low probability of two-photon absorption, the detection of two-photon absorption-induced photoacoustic signals is not effective.
To improve the detection efficiency of two-photon absorption-induced photoacoustic signals, we have proposed frequency filtering of photoacoustic signals [1]. Generally, two-photon photoacoustic signals are generated at smaller area than one-photon photoacoustic signals. The high-frequency components in two-photon photoacoustic signals occupy a larger proportion of their spectra than those in one-photon photoacoustic signals. This phenomenon means that the extraction of high-frequency components improves the detection efficiency of two-photon photoacoustic signals. However, the size of the signal-generation area becomes smaller, even for one-photon photoacoustic signals, with decrease in the size of the target and increase in light attenuation. Consequently, the spectra of one-photon photoacoustic signals shift to the higher frequency [9], which reduces the spectral difference between one-photon and two-photon signals. In addition, in contrast to the light frequency filtering in two-photon fluorescence microscopy, acoustical frequency filtering is not based on molecular energy states. Thus, the acoustical frequency filtering is not adequate for the separation of one-photon and two-photon photoacoustic signals.
One of the solutions to extract two-photon photoacoustic signals is to improve the generation efficiency of two-photon photoacoustic signals. The use of femtosecond optical pulses, the peak power of which is normally higher than that of nanosecond optical pulses, has been proposed. Lock-in detection using a repetition rate of a laser source as a reference frequency has been used [4, 6]. However, though the generation efficiency of two-photon photoacoustic signals has been improved, the one-photon photoacoustic signal still remains. Nonlinear photoacoustic microscopy via a loss modulation technique [10] with modulated femtosecond optical pulse trains has also been proposed to remove one-photon photoacoustic background [3]. However, to detect photoacoustic signals induced by two-photon absorption effectively, large photon number and long integration time are required. The reason for the long measurement time is that the lock-in detection requires a long time to detect reliable phase-locked intensity of the signal.
In this report, to extract two-photon photoacoustic signals with low photon consumption, we propose photoacoustic microscopy using small-number low-energy ultrashort pulses with two different pulse durations with the same pulse energies. The subtraction of the image under the condition of longer pulse duration from that under the condition of shorter pulse duration emphasizes the photoacoustic image due to two-photon absorption. This method is based on our observation that the intensity of the two-photon phoatoacoustic signal depends on the pulse duration, while that of one-photon photoacoustic signals is constant independent of the pulse duration. First, we show the effectiveness of femtosecond pulses to reduce the photon number by indicating the minimum pulse energy to obtain photoacoustic images with femtosecond and sub-nanosecond single pulse excitations. Second, we reveal the dependence of one-photon and two-photon photoacoustic signals on pulse duration in the range from femtoseconds to picoseconds. Third, we indicate the power dependence on the pulse duration in one-photon and two-photon photoacoustic signals. Finally, we demonstrate the two-photon photoacoustic image of the cross-section of a silicone hollow filled with a mixture of one-photon and two-photon absorbers using ultrashort pulses with two different pulse durations.
2. Materials and methods
2.1 Setup for photoacoustic microscopy using a pulse-duration variable ultrashort pulse laser
Figure 1(a) shows the experimental setup of ultrashort pulse-induced PAM. For generation of photoacoustic signals using ultrashort pulses with two different pulse durations, we employed a femtosecond pulse laser (IFRIT; Cyber Laser Inc.) with a variable pulse duration (200 fs – 7 ps), a pulse repetition rate of 1 kHz, and a center wavelength of 780 nm. Pulse energy was lowered by neutral density (ND) filters (Thorlabs, Inc.) set at a manual filter wheel mount (FW1AB; Thorlabs, Inc.) and continuously variable ND filter wheel (Sigma Koki Co., Ltd.) adequate to not cause laser cavitation and damage samples. The repetition rate and pulse energy were not high enough to produce the Grüneisen effect [11, 12], which causes temperature rise. The beam diameter was expanded by the combination of concave (f = –50 mm) and convex (f = 100 mm) lenses to fill over 70% of the back aperture of the objective lens (10X UPlanFLN; Olympus Corp.) with a numerical aperture of 0.3. We also employed a sub-nanosecond microchip laser with a pulse duration of 600 ps with a collimation convex lens (f = 500 mm) to compare a conventional laser for photoacoustic imaging with the ultrashort pulse laser. Expanded beam diameter was evaluated by a knife-edge method [13]. The beam was focused into samples submerged in a water bath. Generated photoacoustic signals were detected by an ultrasonic transducer (10K6.4I; Japan Probe, Inc.) of which the focal length, resonance frequency, bandwidth, diameter and thickness of the piezo element were 15 mm, 10 MHz, 8 MHz, 6.4 mm and 0.2 mm, respectively. The position of the beam focus was set in accordance with that of the detection by employing a focused ultrasonic transducer to improve the detection efficiency of photoacoustic waves. Photoacoustic signals were amplified by a low-noise wide-band preamplifier (9913; NF Corp., gain; 40 dB, frequency band; < 20 MHz). Sample position was controlled by manipulating an xyz mechanical stage (KS701-30LMS; Suruga Seiki, Ltd.). The photoacoustic signals were measured by the PCI board of a high-speed digitizer (U1082A-AVG; Agilent Technologies, Inc.) set in a computer.
Fig. 1 (a) Experimental setup of ultrashort pulse-induced photoacoustic microscopy. VND1, neutral density (ND) filters set at a manual filter wheel mount; VND2, continuously variable ND filter wheel. (b) Subtraction method using ultrashort pulses with different pulse durations.
Since the signal from the acoustic transducer before amplification is in the micro-volt range, the signal is easily affected by electromagnetic noise from power supply, various switching circuits, and so on. To reduce the electromagnetic noise, all electronic components (the cable between the transducer and amplifier, the amplifier, the cable between the amplifier and computer, and the computer) were set on (or attached to) a large optical bench. Attachment of all electronic components to the same optical bench stabilizes their ground levels. Power cables of the computer and display were frequency filtered to reduce the noise from power supply.
2.2 Time-gated detection of photoacoustic signals with frequency filtering
Two-photon photoacoustic imaging with ultrashort pulse excitation used the temporal profile of photoacoustic signals. Photoacoustic signals are generated only at laser focused points. Consequently the time for the photoacoustic waves to reach the acoustic transducer after their generation is almost constant independent of the sample position. Time-gated detection is therefore valid to improve the detection efficiency of photoacoustic signals caused by two-photon absorption. As the duration of the time gating, 1 μs (or 2 μs) was employed.
Power spectra of measured photoacoustic signals were calculated by Fourier transform of photoacoustic waveforms using Hanning function. In our previous report, we showed the effectiveness of frequency filtering for temporal properties of generated photoacoustic waves to improve the detection efficiency of two-photon photoacoustic signals [1]. To determine the range of frequency filtering, we measured the power spectra of two-photon photoacoustic signals generated from target solutions in a 1-cm silicone cell (as explained in the next subsection in detail) with the 10X objective lens and 10-MHz focus transducer. As a result, we employed the frequency range of 3 to 15 MHz for frequency filtering, because the main frequency components of two-photon photoacoustic signals were over 3 MHz [2]. From the bandwidth of the transducer, 15 MHz was employed as the upper limit of frequency filtering.
2.3 Target samples
As imaging targets, we employed transparent blocks (height: 24 mm, width: 19 mm, depth: 5 mm) made of silicone elastomer (SYLGARD 184; Dow Corning Toray Co., Ltd.) with a cylindrically-shaped hollow [1]. As filling solutions for two-photon absorption, we employed Rhodamine B (R6626; Sigma-Aldrich, Inc.; molar extinction coefficient, 1.05 X 105 M−1 cm−1 at 550 nm)/ethanol, which has large two-photon cross-section (1 X 10−48 and 3 X 10−49 cm4 s/photon for 780-nm and 1064-nm excitations, respectively) [14] and is transparent in the infrared region. As filling solution for the one-photon absorption at 780 nm, we employed IR780 iodide (425311-1G; Sigma-Aldrich, Inc.; molar extinction coefficient, 2.8 X 105 M−1cm−1 at 780 nm)/ethanol, for which the absorption peak is near 780 nm. For comparison between photoacoustic signals generated by one-photon and two-photon absorptions, target solutions in a 1-cm silicone cell through which light entrance was provided by a cover slip were employed.
2.4 Evaluation of characteristics of ultrashort optical pulses
Pulse duration was estimated using an autocorrelator (Mini; A•P•E GmbH) from the measured autocorrelation width under the assumption that ultrashort pulses have transform-limited Gaussian shape. The average power after passing through the objective lens was measured by an optical power meter (Q8230; Advantest Corp.). Pulse energy was calculated by dividing the average power by the laser repetition rate. ND filters of which transmittances were calibrated by a spectrophotometer (UV-3600; Shimadzu Corp.) were used for precise alteration of the pulse energy to investigate the pulse energy dependence.
2.5 Image reconstruction using two different pulse durations
Based on our findings described in the next section, we propose a subtraction method employing two images obtained by ultrashort pulses with two different pulse durations to extract the two-photon photoacoustic signals, as shown in Fig. 1(b). Here we designate Images 1 and 2 as those obtained by short-pulse and long-pulse excitations, respectively. Image brightness at each xyz coordinate was determined by the integral of the power spectrum in the entire frequency range between 0 and 15 MHz in the photoacoustic signal. The final Image 3 is obtained by subtracting Image 2 from Image 1. We compared the frequency-filtering and subtraction methods by measuring the cross-section of the silicone hollow filled with the mixture of one-photon and two-photon absorbers described in subsection 2.3.
3. Experimental results and discussion
First, to estimate the required number of photons for PAM with ultrashort pulses compared with conventional sub-nanosecond pulses, we investigated the dependence of the cross-sectional image for the silicone hollow filled with Rhodamine B/ethanol (30 mM) on pulse energy with 250-fs and 600-ps pulse durations. Cross-sectional images obtained by single-pulse excitation per pixel with the range from 3 to 15 MHz for frequency filtering are shown for the conditions of 250-fs [Figs. 2(a) and 2(b)] and 600-ps [Figs. 2(c) and 2(d)] pulse excitations. Under the condition of 250 fs, the pulse with energy of 3.2 nJ visualized the precise cross-sectional structure [Fig. 2(a)], while the pulse with energy of 2.0 nJ did not [Fig. 2(b)]. On the other hand, under the condition of 600 ps, the energy of 3.0 μJ was needed to visualize the precise cross-sectional structure [Fig. 2(c)]; the pulse with energy of 2.1 μJ did not [Fig. 2(d)]. The cross-sectional images by ultrashort pulse-induced PAM using femtosecond optical pulses were obtained even at 1/1000 of pulse energy required for PAM using sub-nanosecond optical pulses. The peak power of 250-fs optical pulses at 3.2 nJ is about 13 kW. On the other hand, the peak power of 600-ps optical pulses at 3.0 μJ is about 5 kW. The fluorescence signal intensity caused by two-photon absorption is generally proportional to the product of the square of the peak power and the pulse duration [15]. However, the relation between the signal intensity of two-photon photoacoustic signals and pulse duration is unknown. The product at pulse duration of 250 fs and peak power of 13 kW was 4.1 X 10−5 J2/s, while that at 600 ps and 5 kW was 1.5 X 10−2 J2/s. The product in the case of 250 fs was about 300 times lower than that at 600 ps. This means that femtosecond optical pulses generated effectively larger two-photon photoacoustic signal than sub-nanosecond optical pulses, even considering the difference between two-photon cross-sections at 1064 nm and 780 nm.
Fig. 2 Photoacoustic imaging of the cross-section of the silicone hollow filled with Rhodamine B/ethanol (30 mM) using 250-fs [(a) and (b)] and 600-ps [(c) and (d)] single pulse excitations with 3 - 15 MHz frequency filtering. Excitation pulse energies for (a), (b), (c) and (d) are 3.2 nJ, 2.0 nJ, 3.0 μJ and 2.1 μJ, respectively. Scale bar is 150 μm.
To investigate whether the pulse duration alters the intensity ratio between one-photon and two-photon photoacoustic signals, we investigated the dependence of one-photon and two-photon photoacoustic waveforms on the pulse duration while preserving the pulse energy of 20 nJ (one-photon absorption) and 44 nJ (two-photon absorption), as shown in Fig. 3. Red lines show photoacoustic waveforms averaged by using 100 photoacoustic signals generated by single optical pulses for precise investigation of waveforms and signal intensities in this experiment. Grey areas denote the standard deviations of photoacoustic signals at each time point. Target solutions were in a 1-cm silicone cell in order not to induce temperature rise [11, 12]. The optical focus was set in the middle of the silicone cell. As a result, the one-photon absorption-induced photoacoustic signal from IR780 iodide/ethanol, with concentration of 0.34 mM, was constant in spite of the pulse duration, as shown in Figs. 3(a)–3(d). On the other hand, the two-photon photoacoustic signal from Rhodamine B/ethanol, with concentration of 19 mM, was increased with decrease in pulse duration, as shown in Figs. 3(e)–3(h). Figure 3 makes it clear that the intensity ratio of one-photon and two-photon photoacoustic signals depends on the pulse duration.
Fig. 3 (a)-(d) Dependence of one-photon absorption-induced photoacoustic signal from IR780 iodide/ethanol (0.34 mM) on pulse duration [(a) 250 fs; (b) 770 fs; (c) 1.7 ps; (d) 4.2 ps]. (e)-(h) Dependence of two-photon absorption-induced photoacoustic signal from Rhodamine B/ethanol (19 mM) on pulse duration [(e) 250 fs; (f) 770 fs; (g) 1.7 ps; (h) 4.2 ps]. Red lines show 100-times averaged photoacoustic signals. Grey areas denote the standard deviations of photoacoustic signals at each time point. arb., arbitrary.
Figure 4 shows the dependence of signal intensity on the pulse duration for (a) one-photon and (b) two-photon photoacoustic signals. The signal intensity of the generated photoacoustic signal was measured as explained below. First, precise photoacoustic waveforms were obtained by 100-times averaging using a pre-installed program inside the FPGA on a high-speed digitizer board. Second, the zero value offset of the photoacoustic signal was determined as the average value of the intensity when there is no photoacoustic signal. Third, the absolute values of the measured signal intensity at each time point after subtracting the zero value offset were time-integrated. Fourth, time-integrated signal intensities were averaged 100 times and then the precise photoacoustic intensities and standard deviations were obtained. Solid lines in Fig. 4 denote fitting curves by power function. Noise levels, shown by the dashed lines in Fig. 4, were determined by the time-integral of the detected signal within the same time window without pulse excitation. The data point near the noise level was excluded for the fitting. As a result, we found that the signal intensity generated by one-photon absorption is almost constant, as predicted based on Figs. 3(a)–3(d). On the other hand, the signal intensity generated by two-photon absorption [Figs. 3(e)–3(h)] decreases with increase of the pulse duration. The obtained power coefficient was about - 0.7.
Fig. 4 Time-integrated intensity of photoacoustic signal (open dots with error bars) generated by (a) one-photon (IR780 iodide/ethanol, 0.34 mM) and (b) two-photon (Rhodamine B/ethanol, 19 mM) absorption solutions as a function of pulse duration. Solid lines denote fitting curves by power function. Dashed lines denote the noise level. arb., arbitrary.
Figure 5 shows the dependence of the two-photon photoacoustic signal on the energy of pulses with different pulse durations (250 fs, 770 fs, and 1.7 ps). Time-integrated signal intensities and their standard deviations were determined by 10-times measurement of precise waveforms at each pulse duration. Precise waveforms were determined by 1000-times averaging of waveforms obtained by single optical pulses. Solid lines show the fitting curves for power function. In the same way as in Fig. 4, data points for which time-integrated photoacoustic intensities are near and below the noise level were excluded for the fitting. Noise level, shown by the dashed line in Fig. 5, was determined by the time-integral of the detected signal within the same time window without pulse excitation. The obtained power coefficients were 1.6, 1.8 and 1.9 for 250 fs, 770 fs and 1.7 ps, respectively.
Fig. 5 Dependence of time-integrated intensity of photoacoustic signal on pulse energy with various pulse durations (closed circles, 250 fs; closed squares, 770 fs; open squares, 1.7 ps) with error bars and fitting solid lines. arb., arbitrary.
If the photoacoustic signal is proportional to the two-photon absorption energy, the intensity of the photoacoustic signal is inversely proportional to the pulse duration (power coefficient: −1) while the pulse energy is kept constant, as inferred from the theory of two-photon absorption [15]. Also the photoacoustic signal is proportional to the square of the pulse energy (power coefficient: 2) while the pulse duration is kept constant. The dependence on pulse duration [Fig. 4(b)] and pulse energy [Fig. 5] shows that the two-photon photoacoustic signal is generated mostly in proportion to the two-photon absorbed energy. However there are small deviations of the obtained power coefficients between theoretical and experimental results. The possible reasons for such small deviations are (a) the change of the beam diameter at the focus point due to self-focusing and -defocusing [16], (b) deformation of optical pulses depending on pulse duration, (c) saturation of the two-photon absorption, and (d) interfusion of the one-photon photoacoustic signals in two-photon photoacoustic signals.
(a) The diameter at the focus point is affected by self-focusing and -defocusing. These effects deviate from the ideal focusing by using an objective lens. With decrease of the pulse duration while the pulse energy is kept constant, the peak power of the optical pulses increases. Since the effect of self-focusing and -defocusing increases with increase of the peak power, the focus diameter becomes larger and then the photoacoustic signal becomes smaller. Thus the power coefficient of the pulse duration dependence rises above −1. The power coefficient of the pulse energy dependence decreases below 2. (b) Group-velocity dispersion (GVD) with self-phase modulation (SPM) broadens the pulse duration [17]. The broadening of the pulses increases with decrease of the pulse duration. However, measured autocorrelation traces for 250-fs pulses with 36 nJ energy in front of (without) and behind (with) the 5-mm cell filled with 19-mM Rhodamine B/ethanol were the same. GVD with SPM does not broaden the pulse duration on passage through the half of the 1-cm cell and thus does not decrease the photoacoustic signals. (c) Saturation of two-photon absorption occurs when the number of molecules in the ground state is small. When a 10X objective lens (NA: 0.3), 44-nJ pulse energy, and 250-fs pulse duration are used, the photon intensity at the focal point is 2 X 1031 photon s−1 cm−2. Using the two-photon absorption cross-section of the Rhodamine B/methanol (1 X 10−48 cm4 s/photon [14]), we can calculate the number of two-photon excited molecules as 3 X 1010 in a focal volume (3 X 10−11 cm3) [15]. The number of Rhodamine B molecules in 19-mM Rhodamine B/ethanol in the focal volume is 3 X 108. Because the calculated number of two-photon excited molecules in the focal volume is higher than that of total Rhodamine B molecules, the saturation of the two-photon absorption carries a possibility of decreasing the photoacoustic signals. (d) If the interfusion of the one-photon photoacoustic signal occurs, the slope of the pulse energy dependence of the photoacoustic signal decreases below 2. Since the shorter pulses generate larger two-photon photoacoustic signals, the slope of the pulse energy dependence with shorter pulses is predicted to be steeper than that with longer pulses. However, the experimental results showed that the slope of the pulse energy dependence was more gentle for shorter pulse duration. Thus, saturation due to the interfusion of one-photon photoacoustic signals has low probability. The most probable reasons for saturation of the photoacoustic signals are (a) the self-focusing and -defocusing and (c) saturation of two-photon absorption. These effects decrease the signal intensity.
Based on the observations that one-photon photoacoustic signals are generated with a constant intensity independent of the pulse duration and that two-photon photoacoustic signals are generated in proportion to the two-photon absorbed energy, we can eliminate the contribution of one-photon photoacoustic signals from the photoacoustic image at short pulse duration by the simple subtraction of the longer-pulse image from the shorter-pulse image. By the same means of the subtraction method using two pulse durations, the subtraction of the photoacoustic image with low pulse energy from that with high pulse energy seems to extract two-photon photoacoustic signals. However, this simple subtraction cannot be accomplished because the nonlinear photoacoustic signal generated by one-photon absorption [18] cannot be eliminated.
To reveal the effectiveness of the subtraction of the image with longer pulse duration from the image with shorter pulse duration, we visualized the images of the cross-section of the silicone hollow filled with the mixture of two-photon (Rhodamine B/ethanol, 30 mM) and one-photon (IR780 iodide/ethanol, 0.14 mM) absorbers with 10-times on-board averaging, as shown in Fig. 6. As representative images, we show the results under the conditions of (a) 250 fs and (b) 1.7 ps with the pulse energy of 33 nJ without frequency filtering (using entire frequency components, 0 - 15 MHz). Figure 6(c) shows the cross-sectional image in the case of 250 fs with frequency filtering (3 - 15 MHz). Though the image in Fig. 6(c) with frequency filtering is more precise than the image in Fig. 6(a) without frequency filtering, blurring of the edge of the cross-section is still apparent even when the frequency filtering is used. The subtraction of the image in Fig. 6(b) with longer pulse duration (1.7 ps) from the image in Fig. 6(a) with shorter pulse duration (250 fs) shows a clear edge of the cross-section and reproduces the cross-sectional structure more precisely than that with shorter pulse duration with 3 - 15 MHz frequency filtering [Fig. 6(c)], as shown in Fig. 6(d). Figure 6(e) shows the depth profiles of the photoacoustic signals obtained using (c) 3 - 15 MHz frequency-filtering and (d) subtraction methods. Maximum signal intensity was normalized in Fig. 6(e). The width of the line through the center of the hollow used for the depth-profile calculation was set at 30 μm. From Fig. 6(e), we found that the signal intensity in the front (outside) of the hollow in the case of the subtraction method was reduced more markedly than in the case of the frequency filtering. This means that the one-photon photoacoustic signals were excluded effectively by the subtraction method. Thus the subtraction method using ultrashort pulses with two different pulse durations demonstrated effectiveness for extracting precise cross-sectional images.
Fig. 6 (a) Photoacoustic images for the cross-section of the silicone hollow filled with the mixture of one-photon (Rhodamine B/ethanol solution, 30 mM) and two-photon (IR780 iodide/ethanol solution, 0.14 mM) absorbers using 250-fs pulse excitations without frequency filtering (0 - 15 MHz). (b) Photoacoustic image using 1.7-ps pulse excitation without frequency filtering. (c) Photoacoustic images using 250-fs pulse excitation with 3 - 15 MHz frequency filtering. (d) Image subtraction of the image in (b) with 1.7-ps pulse excitation from the image in (a) with 250-fs pulse excitation. Scale bar is 150 μm. (e) Depth profiles of photoacoustic images obtained using (c) 3 - 15 MHz frequency filtering (black line) and (d) subtraction (red line) methods on the line with a width of 30 μm passing through the center of the silicone hollow.
4. Conclusions
We demonstrated photoacoustic microscopy using small-number low-energy ultrashort pulses with two different durations. Required number of photons for PAM using ultrashort optical pulses (pulse duration: 250 fs) was about 1/1000 lower than that for PAM using sub-nanosecond optical pulses (pulse duration: 600 ps). We also found that the intensity of the photoacoustic signal generated by one-photon absorption is constant, while that generated by two-photon absorption is increased with decrease in pulse duration. Due to these dependences on pulse duration, the subtraction of the image for longer pulse duration from that for shorter pulse duration extracts the two-photon photoacoustic images. Such subtraction method with small-number low-energy ultrashort pulses will improve the imaging contrast of TP-PAM.
Acknowledgments
Our helpful discussion about femtosecond optical pulses with Prof. Kiyotaka Miura of Kyoto University is gratefully acknowledged. We also thank Dr. Keisuke Kametani of the Next Generation Laser Processing Technology Research Association at Kyoto University for the use of the infrared femtosecond pulse laser. This work was partially supported by a grant-in-aid for scientific research (C) from the Japan Society for the Promotion of Science (JSPS), Japan (23500525). This work is partially based on a previous SPIE conference proceeding [2]. The content is fully expanded, developed and corrected.
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