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Molecular structure determination of chemical reactions or processes has been one of the grand challenges in physics, chemistry, and biology. To image these processes, it typically requires sub-Angstrom spatial and femtosecond temporal resolutions. One of the standard imaging techniques, X-ray diffraction, however, currently suffers from temporal jitters and is available only at large facilities. Furthermore, it also suffers from very low elastic scattering cross sections, which make it difficult to apply to gas phase molecules. Another technique, ultrafast electron diffraction (UED), overcomes this low cross section problem, but the temporal resolution is still limited to hundreds of femtoseconds, mainly due to Coulomb repulsion in electron beam and velocity mismatch between laser-pump pulse and electron probe pulse in a typical pump-probe scheme. The recently proposed laser-induced electron diffraction (LIED) is based on two basic ideas. First, an electron wave packet can be generated from a target itself by an intense laser pulse and driven back within the subsequent half-cycle of the laser to rescatter from the parent ion, thus realizing a self-imaging process. Laser-free elastic differential cross sections (DCS) can then be extracted from high-energy electron spectra, as demonstrated by the Quantitative Rescattering theory (QRS). Second, the target structure information can be retrieved from the DCS. This retrieval is further simplified by using back-scattered electrons with collision energy of about 100 eV, for which the independent-atom model (IAM) can be employed to quite accurately simulate the DCS. Demonstration of ultrafast imaging with the LIED has been reported so far on simple diatomic molecules. Here we discuss recent progress in LIED with polyatomic molecules in two examples. The first one is aligned acetylene (C2H2) and the second one is benzene (C6H6). In both cases, two bond lengths, C-C and C-H have been successfully retrieved. For even more complex polyatomic molecules with many bond lengths and bond angles, the method using simple fitting to DCS would not work, while the 1D Fourier transform method cannot resolve bonds of similar lengths. We show that these difficulties can be overcome by using the 2D Fourier transform method which allows retrieving 2D information from laser aligned polyatomic molecules.
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