Fig. 1. (a) The operational principle of the spatiotemporal profiler for ultrashort pulses. The femtosecond pulse to be measured undergoes multi-beam interference through a beam-splitting module. The modulated pulse, which has a comb-like spectral structure, is directed into a coherent diffraction imaging module combined with a spectral phase measuring device for spatiotemporal reconstruction. (b)–(e) Modulated spectra for interferences with different pulse numbers. (f)–(i) Differences between the initial spatial chirp beam center coordinates and the centroids of the reconstructed beams for different WCs, corresponding to the modulation spectra in the above row. (j)–(m) The corresponding reconstructed object functions. In the simulation, 301 points were selected across the whole spectrum at equal intervals to generate the diffraction pattern, with each point representing a two-dimensional Gaussian beam with a 2.34 mm diameter. A total of 121 diffraction patterns were simulated, with a step size of 208 μm, an overlap rate of 88.5%, and a pixel size of 6.5 μm, matching the actual camera specifications. The object-image distance was 5 cm. Additionally, each beam of different wavelengths included a lateral displacement of one pixel to simulate spatial chirp.

Fig. 2. Experimental schematic of the spatiotemporal profiler for ultrashort pulses. The spatiotemporal laser beam passes through a Mach–Zehnder interferometer for spectral modulation, with the number of interference peaks controlled by a pair of wedge mirrors. The spectral phase at the beam center is then measured using FROG. Finally, the beam enters the ptychography imaging module for high-precision spatial phase retrieval. The spatial spectrum of the laser beam is also recorded by a spectrometer mounted on a motorized stage.

Fig. 3. The measured spatio-spectral profile of a femtosecond laser beam using a modulated spectrum consisting of six peaks. (a) The blue (red) line represents the spectrum before (after) modulation. (b) Comparison of the reconstruction results for each WC component, with the green (black) bars representing the reconstructed (measured) spatially averaged intensity distribution of the spectral components. (c) The amplitude of reconstructed object, with an inset showing the 10.7 μm resolution fit at the red line position. (d) The laser beam captured directly by the camera after removing the test target. (e) The reconstructed beam consisting of three different WCs; the color bar represents the normalized intensity for each WC. (f) Comparison of spatial chirp results: the red (blue) line represents the centroids of the reconstructed beam for each WC under conditions with (without) spectral modulation. The yellow line indicates the maximum intensity positions of each WC measured directly from the spectrometer. (g) The beam reconstructed from the modulated spectrum. (h) The beam reconstructed from the unmodulated spectrum. (i) The spectrally resolved spatial intensity distributions measured by the spectrometer mounted on a 2D translation stage.

Fig. 4. Same as Fig. 3 but for a modulated spectrum consisting of 14 peaks by increasing the optical path difference of the Mach–Zehnder interferometer.

Fig. 5. Spatiotemporal reconstruction of a femtosecond laser beam. (a) The modulated and unmodulated spectra. (b) The measured and reconstructed FROG traces. (c) The spectral intensity and phase reconstructed using FROG. (d) The beam of each WC in the reconstructed image plane. (e) The beam back propagating 0.5 m from the image plane. (f) The phases of each beam on the plane are displayed.