1. Introduction

Acquiring optical imaging of transient events at the atomic time scale (1ps ∼10fs) is indispensable and invaluable in many research fields, including ultrashort pulse propagation [1,2], femtosecond laser damage and precise machining [3,4], laser-induced plasma [5], femtosecond soliton molecule dynamics [6] and other applications [7,8]. To realize blur-free visualization image of these transient processes, a series of exciting ultrafast imaging methods have been developed in recent decades. Conventionally, the pump-probe technique has been considered as the most widely implemented method for the time-resolved imaging through repeated measurements [9,10]. However, it is not available for non-repeatable or difficult to reproduce events. Fortunately, various single-shot optical imaging methods have been developed, which can record the event in real-time, for instance, sequentially timed all-optical mapping photography (STAMP) [11], spectral filtering in STAMP (SF-STAMP) [12,13], frequency recognition algorithm for multiple exposures imaging (FRAME) [14], and noncollinear optical parametric amplification (NCOPA) [15,16], that operate in the femtosecond scale. Although STAMP has achieved a rate of 4.4Tfps with six frames, the effective frame rate was limited to 1.4Tfps because the exposure time (temporal resolution) is much greater than framing time. SF-STAMP has increased the frame number to 25 with higher frame rate up to 7.5Tfps. However, both of the light throughput and the temporal resolution significantly decrease with the increase of the frame number. FRAME can attain four frames with a rate of 5Tfps and with a spatial resolution of 15lp/mm. Nevertheless, getting sufficient frame number without affecting the spatial resolution or effective frame rate is still a challenge. NCOPA also has attained a frame rate up to 15Tfps with a spatial resolution of 30lp/mm without microscopy, mainly limited the frame number of 4 by the complexity of the system. Compressed ultrafast photography (CUP), including compressed ultrafast photography (CUP) [17], trillion-frame-per-second CUP (T-CUP) system [18], and compressed ultrafast spectral photography (CUSP) [19], is a type of single-shot computational ultrafast imaging technology with a large frame number. However, improving spatial resolution remains a challenge for these CUP techniques due to the spatial-temporal mixture in streak camera and sparsity of scenes. In addition, image reconstruction requires a complex iterative algorithm, Hence, it is valuable to develop a single-shot ultrafast optical technique with both high spatial-temporal resolution and high frame rate / number.

Ultrafast photography with a raster principle has the advantages of high frame rate and sufficient frame number. Existing rotating mirror and rotating pupil are based on a raster framing system [20], whose maximum frame rate is approximately Gfps due to mechanical limitations. Combining streak camera and raster sampling technique, the frame rate can reach 115 Gfps with 50 frames [21]. However, existing ultrafast raster framing cameras cannot operate at the atomic time scale due to the limitations of mechanical mechanisms, spatial-temporal charge effect or intrinsic electronic jitter in electron beam scanning devices. Fortunately, all-optical raster framing imaging method can circumvent these limitations and operate at the atomic time scale.

Here, we developed all-optical photography with a raster principle (OPR)by combining the sampling theory and spectral-time coding techniques, which exhibits high spatial-temporal resolution, high frame rate and sufficient frame number. Meanwhile, compared with a compressed sensing algorithm, the OPR has a more direct and faster reconstruction algorithm with high robustness. We demonstrated the recording of transient scenes with a frame rate of 2 trillion frames per second (Tfps) and a spatial resolution of ∼90lp/mm in single-shot and attained reconstruction data cube size of 1236×1626×12 by a Fourier reconstruction algorithm. Using the developed system, we realized the sub-picosecond scale dynamics image of laser-induced plasma filament in air and captured real-time plasma dynamics in glass. It is a practical technique for studying ultrafast phenomena in physics, chemistry and biology in single-shot.

2. Principle, system and experiment

2.1 Principle of OPR

The OPR was designed based on the sampling theory and spectral-time coding techniques. The sampling theory is briefly described in Fig. 1(a). The signal of an object should be sampled at least twice as fast as the highest frequency component in the signal. After that, a raster image can be formed, and the original signal of the object can be reconstructed by a Fourier transform algorithm. OPR is a practical under sampled optical imaging system. It is still capable of operating in this way due to bandwidth limitations of digital images. In this case, effective information capacity of the detector increases by reducing data redundancy. Therefore, this method of compressing measured data is feasible to record multiple images on a detector. The principle of OPR is presented in Fig. 1(b). OPR operates in two steps: data cube acquisition and data cube reconstruction. The data cube acquisition can be described by a raster framing camera (RFC), as shown in Fig. 1(c). The transient scene can be expressed as discretized sequence depth frames $O(x,y,{t_i})\textrm{ }i = 1,2, \cdots n,$ and can be illuminated by the linearly chirped pulse $I(x,y,t{(\lambda )_i}),$ in which $t$ and $\lambda $ are interchangeable. The target is then imaged on the plane of a microlens array by the objective lens and a relay image can be formed. and then the microlens array images, a raster image can be formed through the entrance pupil of objective lens (an array of sub-pupil images, where each lenslet images the entrance pupil of objective lens forming a raster image pixel) $R(x,y,{\lambda _i})\textrm{ }i = 1,2, \cdots n,$ for a single wavelength raster image, which is denoted by

 

Fig. 1. The principle of OPR. (a) Demonstration of sampling theory. ${\cal F}$, Fourier reconstruction algorithm; (b) The operating principle of OPR. (c) The raster framing camera (RFC). CL, collimating lens; G, grating; FL, Fourier lens.

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The data cube reconstruction was performed by a Fourier transform algorithm. We extracted each single wavelength raster image $R(x^{\prime\prime},y^{\prime\prime},{\lambda _i})\textrm{ }$ from $R(x^{\prime\prime},y^{\prime\prime})$ by system calibration. Finally, the reconstructed transient scene $O(x,y,{t_i})\textrm{ }$ can be expressed as follows

Here ${\cal F}$ and H denote the Fourier transform and Filtering operations, respectively. Supposing that the dispersion axis of the grating is the $x$-axis, the grating is rotated by a designated angle with respect to $x$-axis to avoid the spatial overlap of spectrally dispersed pixels on the detection plane. Equation (3) indicates that the shift size of adjacent frames is $\delta x = ({f / d})\delta \lambda ,$ where $\delta x$ is the pixel size of the raster image on the detection plane and $\delta \lambda $ is the corresponding wavelength difference. The relation between time and wavelength of linearly chirped pulses is determined by the equation $\delta t = \eta \delta \lambda $, where $\eta $ is a chirp parameter. Therefore, the frame interval (δt) can be estimated according to $\delta t = ({{\eta d} / {f)}}\delta x$. Based on our OPR, a high frame rate (≥10Tfps)/number (more than 50 frames) can be achieved due to framing pixel by pixel and the increased detector capacity.

2.2 System and experiment

The experimental setup for OPR is shown in Fig. 2(a), in which the femtosecond pulses (35 fs, 1000 Hz, 800 nm) with a chirped pulsed amplifier (CPA) system (Legend Ellite, Coherent Inc.) were used as an excitation source, and the energy per pulse is 2.5mJ. The amplified ultrafast laser pulses were spilt into pump and probe beams by a wedge plate with a beam splitting ratio of 99:1. The pump pulses (99% energy) were reflected from a wedge plate and were then frequency doubled (a 400nm pulse) by a BBO nonlinear crystal. With the help of a half-wave plate (HWP), the polarizations of pump and probe pulses are perpendicular to each other. Then the pump pulses were focused onto the sample by a spherical convex lens (L3, f = 25 mm). The probe pulses (1% energy, gaussian distribution) were stretched to linearly positive chirped pulsed duration (6ps) by the STM consisting of a high dispersion prism pair (ZF52, a refractive index of 1.82) [22], which passed through the SSM (a zero-dispersed 4f system) with a pair of gratings (G1, and G2, 1200 lines/mm@800 nm), two lenses (L1, and L2, f1=f2 = 75mm), and the tunable slit placed in the Fourier plane. The target was then illuminated by the output linear chirped pulses and was magnified with a microscopic objective (5X, Thorlabs, Inc., MY5X-802). Next, the probe beam was incident to a raster framing camera (RFC). The magnified target was imaged by the objective lens, and a relay image was formed on the plane of the microlens array. Here, the microlens array (12 mm × 12 mm, 300 ×300) consists of many lenslets (diameter∼40 µm; focal length∼220μm; NA=0.18; the distance between adjacent lenslets ∼40 μm), which are used for sampling the target and forming a raster image (an array of sub- pupil image). The probe pulses passed through a collimating lens (f = 50 mm) and were incident to a diffraction grating (50lp/mm) placed in the Fourier plane. Finally, the Fourier lens (f = 75 mm) transferred the spectrally dispersed raster image onto the CCD camera (1626×1236 pixels; pixel size∼ 4.4×4.4 µm; Basler, acA1600-20gm). To avoid spatial overlap of the spectrally dispersed pixels on the CCD plane, the slit width was adjusted to 4.5 mm for selecting a designed spectral range of 28 nm (782 - 810 nm), and the dispersion axis of the grating was set ∼26.5° with respect to $x$- axis, Fig. 2(b) is the raw spectrally dispersed raster of probe pulses without any object. The details in the yellow dotted box in Fig. 2(b) are magnified and are shown in Fig. 2(c). Figure 2(d) shows a single wavelength (sub-bandwidth) raster image, we selected a sub-bandwidth $\delta \lambda $∼2.3 nm of the probe pulse by adjusting the slit width (0.375 mm) of SSM (spectral-shaping module). The corresponding raster image pixel size $\delta x$ is ∼8.8μm (2×2 binning CCD pixel), which is larger than the diffraction limit of each microlens. The frame interval $\delta t = ({{\eta d} / {f)}}\delta x = 500\textrm{fs}$ (chirp parameter $\eta $=0.22ps/nm), so the frame rate is 2Tfps. We reconstructed a single wavelength frame with 1236 ×1626 pixels by a Fourier reconstruction algorithm of the raster image. Similarly, we got a calibrated data cube of size 1236×1626×12 (frame number $n = \textrm{ceil}{{(({\lambda _{\max }} - {\lambda _{\min }})} / {\delta \lambda )}}$ by tuning the slit position (slit width∼ 0.375 mm; step length ∼ 0.375 mm) on the Fourier plane in a pump-probe mode. In single-shot mode, we can extract 12 sequentially timed raster images from a spectrally dispersed raster image by a calibrated data cube. The reconstruction image strategy is the same as pump-probe mode. In theory, the specification of the two models is consistent. In order to verify the excellent characteristics of OPR, the following experiment was performed to realize the sub-picosecond scale dynamics image of the laser-induced plasma filament in air and capture the real-time plasma dynamics in glass in single-shot.

 

Fig. 2. The experimental setup of OPR. (a) Schematic diagram for the ultrafast imaging in single-shot. WP, wedge plate; HWP, half wave plate; G1, G2, grating; DL, delay line; MO, microscope objective. (b) The raw spectrally dispersed raster of probe pulse without object. (c) The details in the yellow dotted box in Fig. 2(b). (d) The sub-bandwidth raster of probe pulse.

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3. Experimental results and discussions

3.1 Characterization of the temporal and spatial resolution

In order to achieve optimal performance of OPR, appropriate parameters must be selected. In this system, the framing exposure time relies on the Fourier-transform limit of femtosecond pulse and sub-bandwidth per frame of the linearly chirped pulse. There is an optimal exposure time (τ) estimated as 460 fs by the equation $\tau \textrm{ = }\sqrt {t{}_0{t_c}} $[23,24], where ${t_0}$ is the Fourier-limited duration of the original femtosecond pulse, ${t_\textrm{c}}$ is the FWHM of the chirped pulse. To achieve the best image quality, the modified temporal qualify factor ${g^{{2 / 3}}}$ ($g = {{{\tau _f}} / \tau }$, ${\tau _f}$ is the frame interval) should be greater than 1 [25]. However, in T-CUP, STAMP and SF-STAMP, in order to achieve a higher frame rate, the value of g^2/3 should be less than 1. In OPR, the interval time (τ_f) between adjacent frames is 500 fs, so the value of g^2/3 can be estimated as ∼ 1.06, which can ensure optimized image quality. The spatial resolution of the system is mainly determined by the system magnification and raster image pixel pitch (60µm in our system). As shown in Figure 3(a) and (b), it can reach 90lp/mm by 10 times magnification in this system. Figures 3(a) and 3(b) show a single wavelength raster image and reconstructed image, respectively. Figure 3(c) shows the relationship between the magnification and spatial resolution of the system. When the magnification is less than 20 times, the spatial resolution and the magnification have a linear relationship approximately. The spatial resolution is also related to frame rate and frame number. We can get more frames by enlarging the pixel pitch of the raster image. However, the spatial resolution of the image will also decline proportionally. In addition, higher frame rate and larger frame numbers can be realized by adjusting the size of raster image pixel to be smaller. In this case, a lower spatial resolution will be caused due to the sacrifice of high spatial frequency information of the image. Moreover, the modified temporal qualify factor ${g^{{2 / 3}}}$ will be less than 1. Therefore, the trade-off between the parameters of an optimized system must be considered.

 

Fig. 3. The#spatial resolution of OPR. (a) The sub-bandwidth raster image. Scale bar: 220 µm. (b) The reconstructed image of (a). (c) The relationship between the spatial resolution and magnification of the system.

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3.2 Shadowgraph imaging of the plasma string by the pump-probe method

To verify the feasibility and accuracy of OPR in a single-shot mode, we first implemented a dynamic time-resolved shadowgraph imaging of laser-induced plasma in air by pump–probe method, i.e., monitoring the transient transmittance of the probe pulses by the pump-induced air plasma string. The relevant schematic diagram is shown in Fig. 4(a). The pump pulses (800 nm, 1.75mJ/pulse) were focused by the spherical convex lens L3 (f = 25 mm) to air. The linearly frequency-time encoded pulses illuminated the plasma string as a probe beam. In SSM, we adjusted the slit width to 0.375 mm (corresponding sub-bandwidth∼2.3nm) and performed a spectral sweep from 810 to 782 nm by tuning the slit position with 0.375 mm step length on the Fourier plane. We acquired 12 frames with 500 fs interval time in the sequential timed raster image. Figure 4(b) shows the raw sub-bandwidth raster image and reconstruction data cube obtained by a Fourier reconstruction algorithm. The 12 sequentially timed frames are shown in Fig. 4(c). It can be seen that the evolution of plasma string is clearly visible in real-time. In the first image, t=0ps, the pump pulse arrives at the field of view, and the intensity of the electron density increases gradually until 3.5 ps. The time-dependent modulation of plasma string along the yellow lines in each image was shown in Fig. 4(d). It is noteworthy that the modulation increases from 0 to 3ps, and we can consider that a self-focusing effect occurs at 3 ps.

 

Fig. 4. Shadowgraph imaging of plasma string in the air by pump-probe method. (a) Schematic diagram. (b) the raw sub-bandwidth raster image, where the center of the slit position is located at 2.4375mm. The inset is the magnified image indicated by yellow dotted line. Scale bar: 880 µm. (c) Reconstruction sequentially timed image in the Fourier domain. (d) The time-dependent modulation of plasma string along the yellow lines.

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3.3 Shadowgraph imaging of the plasma string in single-shot mode

The OPR of plasma string in the air in single-shot mode was further performed. We selected a single pulse exposure by setting the CCD recording rate the same as the repetition rate (1 kHz) of amplified Ti: sapphire laser. The single-shot raw image is shown in Fig. 5(a). It can be concluded that sequential multi-spectral raster images were accumulated during the camera exposure. The inset is the magnified image indicated by yellow dotted line. By employing spectral calibrated raster images, a series of sequential timed raster images were extracted. The images in the frequency-domain were reconstructed and 12 sequential timed image was obtained (Fig. 5(b)). The time-dependent modulation results are consistent with those in Fig. 4(c). Compared with the pump-probe mode, the experimental results of the two modes are basically consistent. Therefore, it is reliable to capture three-dimensional transient scenes in single-shot method.

 

Fig. 5. Shadowgraph imaging of plasma string in the air by single-shot method. (a) The raw multi-spectral raster images. (b) The time-dependent modulation of plasma string along the yellow lines. (c) Reconstructed sequential image in the Frequency-domain. Scale bar: 880 µm.

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3.4 Observation of plasma dynamics in glass

After verifying the consistency of single-shot mode and pump-probe mode by observing the evolution process of plasma in air, we further visualized the transient scenes of plasma dynamics in glass (a non-repetitive process). The schematic diagram of the experimental setup is shown in Fig. 6(a). The pump pulses (400 nm, 0.75mJ/pulse) that have a certain angle with respect to the substrate plane were focused on the glass substrate (BK7 with a thickness of 5mm) by the spherical convex lens L3 (f=25 mm). Probe pulses illuminated plasma strings and were collected by microscopic optical system, which were then fed into raster camera for imaging. Figure 6(b) show the raw spectrally dispersed raster image, which is the accumulation of multi-spectral raster images. The reconstruction method for the sequentially timed images is the same as in the above demonstration, and data cube size of 1236×1626×12 was reconstructed by a Fourier transform algorithm, with high spatial resolution (90lp/mm) and frame rate (2T fps). As shown in Fig. 6(c), 12 frames sequentially timed image were recorded in a single-shot exposure, and the dynamic of laser induced plasma filaments in glass were clearly visible. Our experimental results implied that this advanced system could be a useful tool for capturing ultrafast three- dimensional imaging in sub-picosecond scale, even shorter or longer.

 

Fig. 6. Observation of plasma dynamics in silica glass. (a) Schematic diagram for observation of plasma dynamics in silica glass. (b) The raw multi-spectral raster images of laser induced plasma filaments in silica glass. (c) Reconstructed sequential timed image in the frequency-domain. Scale bar: 880 µm.

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4. Conclusion

We presented a single-shot ultrafast all-optical photography with a raster principle (OPR) that can capture real-time imaging of dynamics at the atomic time scale (10fs∼1ps). In a proof-of-principle demonstration, we recorded time-resolved shadowgraph imaging of plasma filaments in air and visualized the transient scenes of plasma dynamics in glass, respectively. The reconstruction data cube size of 1236×1626×12 by a Fourier transform algorithm, with 90lp/mm spatial resolution and 2Tfps frame rate, was obtained in a single-shot exposure. The maximum number of frames can be up to 30 by theoretically optimizing the design. In addition, due to its flexible operating characteristics, the frame rate of 10Tfps with more than 50 frames can be achieved by adjusting the designed parameters (diffraction grating (300lp/mm), namely, a 200µm spacing of microlens array, a shorter FWHM of femtosecond pulse source, and a larger detector array plane) of the system. This is a significant advantage with its high spatial-temporal resolution, high frame rate, and sufficient frame number. We believe that the OPR will be widely applied to capture the three-dimensional transient scenes in non-reproducible events at the atomic time scale (10fs∼1ps) by taking advantage of its unique characteristics.