Single-Shot Femtosecond Raster-Framing Imaging with High Spatio-Temporal Resolution Using Wavelength/Polarization Time Coding

Abstract

This paper introduces a single-shot ultrafast imaging technique termed wavelength and polarization time-encoded ultrafast raster imaging (WP-URI). By integrating raster imaging principles with wavelength- and polarization-based temporal encoding, the system uses a spatial raster mask and time–space mapping to aggregate multiple two-dimensional temporal raster images onto a single detector plane, thereby enabling the effective spatial separation and extraction of target information. Finally, the target dynamics are recovered using a reconstruction algorithm based on the Nyquist–Shannon sampling theorem. Numerical simulations demonstrate the single-shot acquisition of four dynamic frames at 25 trillion frames per second (Tfps) with an intrinsic spatial resolution of 50 line pairs per millimeter (lp/mm) and a wide field of view. The WP-URI technique achieves unparalleled spatio-temporal resolution and frame rates, offering significant potential for investigating ultrafast phenomena such as matter interactions, carrier dynamics in semiconductor devices, and femtosecond laser–matter processes.

1. Introduction

Ultrafast optical imaging characterized by high spatial resolution on atomic timescales (from picoseconds to femtoseconds) has emerged as an essential method for capturing transient phenomena in various disciplines, including ultrafast physics, chemistry, and biology [1,2,3,4,5]. This capability is critical for visualizing dynamic processes, such as carrier dynamics in semiconductors [6], ultrafast optical responses in quantum well microstructures [7], femtosecond soliton molecules [8], laser-induced plasma formation [9], and bond formation and breakage in chemical reactions [10,11,12]. These insights provide foundational knowledge for both advancing fundamental science and enabling transformative technologies.

The most widely used technique, pump-probe imaging, achieves temporal resolutions in the order of femtoseconds to attoseconds [13,14,15]. However, despite their effectiveness, pump-probe methods necessitate repetitive measurements, rendering them unsuitable for stochastic or non-reproducible events owing to their dependence on temporal scanning and multiple exposures. To address these limitations, numerous single-shot ultrafast imaging techniques have emerged. Notably, compressed ultrafast photography (CUP) and its variants, such as T-CUP, CUST, and CUSP [16,17,18,19,20,21,22,23,24], have received considerable attention. These techniques use electron beam scanning or all-optical strategies combined with compressed sensing algorithms, achieving up to 219 trillion frames per second (Tfps) and ~1000 frames per acquisition. Despite their advantages, these techniques are inherently limited by spatial resolution constraints stemming from the fundamental trade-off between temporal and spatial resolution, as well as the substantial computational demands of image reconstruction algorithms. An alternative class of ultrafast imaging methodologies leverages spectral time-encoding strategies, exemplified by approaches such as STAMP, SF-STAMP, OPR, and SS-AUOI [25,26,27,28,29,30,31]. These approaches encode temporal information into different spectral components of ultrashort laser pulses, enabling temporal-to-spatial conversion for frame-resolved imaging. This technology is currently delivering significant improvements in temporal resolution and frame rate. For instance, SF-STAMP demonstrates a frame rate of 7.5 Tfps (25 frames) with a temporal resolution of 465 fs. While they achieve high frame rates, these methods are fundamentally limited by the uncertainty principle, which imposes a theoretical boundary on effective frame rates and temporal resolution. Spatial frequency multiplexing techniques [32,33] exploit partial dispersion to encode temporal information at different spatial frequencies. For example, a system operating at 5 Tfps with 200 fs exposures captures four frames at a 15 lp/mm spatial resolution [32]. However, this method introduces a trade-off: increasing the frame count degrades spatial resolution, thereby constraining performance enhancements. Non collinear optical parametric amplification (NOPA) techniques [34,35,36,37], leveraging non collinear frequency conversion, attain frame rates of up to 15 Tfps and a 30 lp/mm spatial resolution. However, nonlinear conversion constraints (e.g., phase-matching bandwidth, spatial walk-off) hinder further spatial resolution improvements. Despite these challenges, current advancements enable single-shot ultrafast imaging at terahertz-scale frame rates (Tfps) with picosecond-to-femtosecond temporal resolutions. Nevertheless, key challenges persist, including spatio-temporal overlap artifacts, resolution trade-offs, and inherent physical limitations, which collectively hinder the realization of a single-shot system that simultaneously delivers high spatio-temporal resolution, extreme frame rates, and practical simplicity.

In this paper, we propose a novel single-shot ultrafast imaging scheme based on the raster imaging principle combined with wavelength and polarization time encoding, termed wavelength/polarization time-encoded ultrafast raster imaging (WP-URI). The WP-URI system demonstrates single-shot imaging of transient phenomena at 25 trillion frames per second (Tfps) with an intrinsic spatial resolution of 50 line pairs per millimeter (lp/mm). Crucially, the imaging field of view matches the detector’s effective area, achieving an unprecedented spatio-temporal bandwidth product (SBWP). These unprecedented performance metrics make our system an exceptionally powerful tool for in-depth studies of ultrafast dynamics in materials science, photonics, and chemical processes, notably including femtosecond lasers’ interactions with matter and carrier dynamics in semiconductor devices.

2. Principle and System

2.1. Principle of WP-URI

The methodology of wavelength/polarization time-encoded ultrafast raster imaging (WP-URI) is shown schematically in Figure 1. This approach synergistically combines raster imaging principles with wavelength- and polarization-based temporal encoding. As depicted in Figure 1a, the fundamental raster imaging principle involves spatially sampling a 2D object through a periodic mask to generate an encoded raster image. The spatial frequency components of the original object are subsequently reconstructed via Fourier transform-based algorithms. According to the Nyquist–Shannon sampling theorem, faithful signal recovery from the raster image requires the sampling rate to exceed twice the highest spatial frequency of the object’s band-limited signal. In practice, however, high-speed raster imaging systems typically operate in an under-sampled regime, yielding approximate reconstructions that remain sufficient for most applications. To enable effective frame-resolved imaging, a critical design criterion mandates a proportional relationship between the sampling point spacing and the spatial extent within the raster image. The operating mechanism of WP-URI is shown in Figure 1b. The system employs four output femtosecond pulses with equidistant temporal intervals, uniform intensity distribution, and different wavelength/polarization encodings. These pulses, denoted as P_i I (x, y, λ_j, t − nΔt) (where n = 1, 2,…, 4; i, j = 1, 2; P_i represents the polarization encoding, λ_j indicates the central wavelength, and Δt denotes the time interval between adjacent pulses), illuminate the ultrafast process. This process can be discretized into a series of sequential frames, O (x, y, t − nΔt) (where n = 1, 2,…, 4). After being spatial sampled by the mask S (x, y) and imaged, the recorded composite signal R (x, y) integrates four wavelength/polarization-coded raster images R_n (x − x_n, y − y_n), where x_n and y_n denote spatial offsets, and the sampling points of different raster images are located at different pixel positions on the detector plane. This process can be concisely expressed as follows:

R (x, y) = Σⁿ R_n (x − x_n, y − y_n) = Σⁿ P_i I (x, y, λ_j, t − nΔt) O (x, y, t − nΔt) S (x − x_n, y − y_n).

(1)

During reconstruction, each wavelength/polarization time-encoded raster image R_n (x − x_n, y − y_n) is extracted from R (x, y) by system calibration. A Fourier transform is then applied to each R_n (x − x_n, y − y_n), and the ultrafast dynamics for each frame are reconstructed as follows:

O (x, y, t − nΔt) = F⁻¹(H [F (R_n (x − x_n, y − y_n))]), n = 1, 2, 3, 4.

(2)

Here, F, F⁻¹, and H represent the Fourier transform, inverse Fourier transform, and filtering, respectively. Crucially, these primary parameters—spatial resolution, frame rate, and imaging area—are governed by distinct experimental variables. Specifically, the spatial resolution is primarily determined by the sampling pitch and geometric configuration of the spatial encoding mask, while the frame rate is dictated by both the temporal interval (Δt) and the duration of the encoded probe pulses. The imaging area, conversely, scales directly with the detector’s effective dimensions. This parametric independence enables the WP-URI technique to simultaneously achieve high spatial resolution, ultrahigh frame rates, and a wide field of view, thereby offering unique advantages for resolving intricate transient phenomena with exceptional spatio-temporal fidelity.

2.2. System of WP-URI

The experimental configuration of the WP-URI system is shown in Figure 2. A femtosecond laser pulse (800 nm, 35 fs) is generated by a Ti:sapphire femtosecond laser amplifier. This pulse enters a wavelength-polarization (W-P) time encoder (dashed box in Figure 2), where a small fraction of its energy is converted to its second harmonic (400 nm, 35 fs) using a nonlinear crystal, typically β-BaB₂O₄ (BBO). The combined 800 nm and 400 nm beams then pass through an optical wedge characterized by a 1:10 transmission to reflection energy ratio. The transmitted portion (~10% energy) serves as the probe pulse, while the reflected portion (~90% energy) acts as the pump pulse to excite ultrafast dynamics in the sample. Subsequently, an adjustable neutral density (ND) filter equalizes the energy between 800 nm and 400 nm components within the probe pulse by selectively attenuating 800 nm light, ensuring matched signal intensities. The probe pulses propagate through a 50:50 beam splitter (BS1) and two orthogonally oriented polarizers (P1 and P2). The resulting pulses then traverse two fused silica (FS) delay stages and are recombined at a second 50:50 beam splitter (BS2). A dispersion compensator adjusts the group velocity dispersion to maintain near-transform-limited pulse durations (~35 fs) for all four output probe pulses. The W-P time encoder ultimately delivers four collinear probe pulses, each encoded with distinct wavelength/polarization states and temporally separated by uniform intervals (Δt), for target illumination. A wavelength/polarization sampling mask is positioned at the first image plane to perform spatially periodic raster sampling. This mask comprises two integrated components: (1) a micro-polarizer array with 5 μm × 5 μm units alternating between horizontal and vertical transmission axes (indicated by bidirectional arrows), and (2) a spectral filter array with 5 μm × 5 μm units selectively transmitting either 800 nm (light red) or 400 nm (light blue) wavelengths. This modular design reduces fabrication complexity and cost, as both components can be manufactured using existing lithography and thin-film deposition processes, with commercially available techniques readily achieving the required 5 μm feature size. The modulated signal is subsequently relayed through a second imaging lens onto the CCD detector plane.

3. Results and Discussion

3.1. Characterization of the Temporal and Spatial Resolution

Temporal and spatial resolutions represent critical performance metrics in high-speed imaging systems. In WP-URI, the temporal resolution is governed by the probe pulse duration. The spatial resolution depends on the sampling mask pitch and optical magnification. To validate spatial performance, we conducted numerical simulations imaging a USAF-1951 resolution chart (512 × 512 pixels, 5 μm pixel size, 100 lp/mm). The optical system employs two lenses (L1, L2; f = 100 mm, NA = 0.125) in a 1:1 magnification configuration. Both the sampling mask S (x, y) and the CCD detector comprise 512 × 512 pixels (5 μm pitch). Background white noise was set to 0.6 intensity, with an additional 0.2 noise contribution from the sampling mask. The simulations were performed with a Fourier-optics propagation model based on the Fresnel diffraction integral, augmented by Nyquist-limited sampling and a wavelength/polarization time-encoding scheme; rectangular frequency-window filtering and additive Gaussian noise were applied to confirm the system’s intrinsic spatial resolution and its single-shot, multi-frame imaging capability (see ‘Simulation Methodology’ in the Supplementary Materials for details). The simulation results are presented in Figure 3. Figure 3a displays the raster image under 800 nm horizontally polarized illumination, while Figure 3b shows its reconstructed image. Figure 3c,d show the intensity distributions along lines a and b in Figure 3b, respectively. The grid stripes exhibit a spatial period of ~4 pixels (20 μm), corresponding to an intrinsic resolution of 50 lp/mm, consistent with theoretical predictions. Figure 3e demonstrates four reconstructed 2D frames via wavelength/polarization time encoding, each spanning 2.56 × 2.56 mm² and matching the CCD’s effective resolution (512 × 512 pixels). These results validate the system’s capability to simultaneously deliver high spatial resolution (50 lp/mm), a wide field of view, and multi-frame single-shot acquisition.

3.2. Single-Shot Imaging of an Object’s Uniform Motion

To verify WP-URI’s single-shot multi-frame capability, we numerically simulated a uniformly moving target comprising the letters “A”, “B”, and “C”. The object was translated horizontally from right to left at 0.64 μm/ps over a 4 ps temporal window. The simulation employed four probe pulses (35 fs duration, 1 ps temporal spacing) encoded with distinct wavelength/polarization states. The optical setup utilized two lenses (f₁ = f₂ = 100 mm, NA = 0.125, 1× magnification) with matched spatial sampling components: a 512 × 512 pixel mask (S(x,y)) and a CCD detector (5 μm pixel pitch). To emulate realistic conditions, we introduced system-level white noise (intensity ratio: 0.6) and mask-induced noise (ratio: 0.2). Figure 4a displays the integrated CCD-recorded data from a single instance of exposure, combining four temporally encoded raster images with distinct wavelength/polarization states. Figure 4b provides a magnified view of the yellow-boxed region in Figure 4a. Computational demultiplexing was used to reconstruct four consecutive frames (Figure 4c), resolving the object’s translational motion at 1 Tfps with 1 ps inter-frame intervals. Notably, the simulations spanned a wide field of view (FOV: 2.56 mm²). These results confirm WP-URI’s framing imaging capability and its performance in single-shot multi-frame imaging.

3.3. Single-Shot Imaging of Objects with Spatial Structure

In high-speed imaging, object motion typically generates motion blur, causing direction-dependent resolution anisotropy. Resolution degrades significantly along the axis of motion while remaining largely intact perpendicular to it, mainly due to the interplay between exposure time and object velocity. To validate this effect, we performed numerical simulations using the WP-URI system under the optical configuration described in Section 3.2 (f₁ = f₂ = 100 mm, NA = 0.125, 1× magnification). This setup included matching spatial sampling devices—a 512 × 512 pixel mask (S(x,y)) and a CCD detector, each with 5 μm × 5 μm pixel dimensions—and used four illumination pulses with a duration of 35 fs with 40 fs inter-pulse intervals. Figure 5a illustrates the imaging of horizontally translating grating (40 μm period) with a horizontal orientation. When the imaging time window (T) was reduced from 2 ps to 1 ps—doubling the object speed—the vertical spatial resolution remained almost unchanged, confirming the ability of the system to maintain high orthogonal resolution even at higher speeds. Importantly, the use of illumination pulses spaced 40 fs apart enabled an imaging rate of 25 Tfps, providing the temporal resolution required to capture ultrafast dynamics. Figure 5b presents reconstructed images under a 2 ps time window for horizontal grating periods G = 150 μm, 120 μm, and 90 μm along the horizontal axis. The results demonstrate that stripe structures with periods of 150 μm and 120 μm remain clearly distinguishable, whereas the 90 μm periodic structure becomes virtually unresolvable. This indicates that the transverse spatial resolution does not exceed 90 μm under these experimental conditions. These findings establish velocity-dependent resolution degradation along the motion axis, with preserved orthogonal resolution.

Therefore, explicit consideration of motion-related resolution degradation is critical in the design of high-speed imaging systems. By optimizing exposure settings, temporal sampling, and system configurations, one can ensure accurate imaging of ultrafast phenomena. These controlled experiments extend the basic performance metrics detailed in Section 3.2 to structured targets and provide a critical validation of the WP-URI system’s suitability for spatially patterned ultrafast imaging applications.

3.4. Single-Shot Imaging of the Uniform Rotation Object

To demonstrate the exceptional performance of the WP-URI system in single-shot multi-frame imaging with high temporal resolution, we simulated a rotating sector-shaped object using the parameters defined in Section 3.2. The system used four illumination pulses (35 fs duration) encoded by different wavelengths and polarizations, with pulse intervals set to 40 fs and 100 fs, to acquire sequential four-frame snapshots. Given the 360° rotation of the object within 1 ps, these ultrashort sampling windows allowed precise tracking of its rotational dynamics. Figure 6a shows four reconstructed frames at 40 fs intervals (t = 0, 40, 80, 120 fs), corresponding to rotation angles of 90°, 76°, 61°, and 46°, respectively. Similarly, Figure 6b shows the results for a 100 fs interval (t = 100, 200, 300, 400 fs) with angles of 54°, 18°, 342°, and 306°. The data confirm the uniform rotation of the object while highlighting the dual resolution capabilities of the system: the 25 Tfps mode (40 fs intervals) resolves subtle positional shifts between frames, while the 10 Tfps mode (100 fs intervals) captures broader rotational trends. Crucially, this high temporal resolution reveals previously inaccessible transient states and nanoscale variations in ultrafast processes, setting a new benchmark for high-speed imaging.

4. Conclusions

This paper presents an imaging system designed to capture transient events with high frame rates and spatio-temporal resolution on atomic time scales. Numerical simulations validate the system’s performance in imaging uniformly moving objects, spatially structured targets, and rotating sector-shaped objects. The system achieves 25 Tfps frame rates, 50 lp/mm spatial resolution, and four-frame single-shot acquisition. Key parameters exhibit intrinsic decoupling: the spatial resolution is determined by the sampling interval of the raster plate; the frame rate depends on the fixed time interval between the probe laser pulses; the temporal resolution is limited only by the probe pulse width, allowing potential improvements with shorter femtosecond laser sources; and the frame count depends on the number of wavelength-/polarization-encoded femtosecond laser pulses. In addition, the large area imaging capability of the WP-URI system demonstrates significant advantages for documenting large-scale phenomena. These combined features position WP-URI as a powerful tool for studying ultrafast dynamics in plasma physics, advanced materials, and semiconductor nanodevices.