This paper presents a fast, high-fidelity single-atom imaging method in optical lattice arrays, achieving 99.4% fidelity in distinguishing between 0 and 1 atoms per site within 2.4 microseconds. The method uses accordion lattices to increase atom spacing beyond the diffraction limit, enabling resolution of small-spacing lattices. It also demonstrates parity-projection-free imaging, allowing full atom number detection without parity projection. The technique enables the study of extended Hubbard models, multi-band or SU(N) Fermi-Hubbard models, and quantum link models. The imaging method uses alternating pulsed beams to minimize momentum spread and improve imaging fidelity. The method also employs binarization of EM CCD counts to enhance signal-to-noise ratio and achieve high-fidelity imaging with few photons. The technique is applicable to any atom or molecule with optical cycling in optical tweezers or lattices. The method reduces the total imaging duration for tweezers to a few microseconds, and for small-spacing lattices, the duration is still favorable compared to established techniques. The work also enables repeated use of accordion lattices to magnify the system without the need for diffraction-limited imaging. The results demonstrate that site-resolved imaging does not suffer from parity projection, simplifying the technical challenges of studying a wide range of physics, including entanglement entropy measurement in 2D to study quantum phase transitions and quantum critical points, multi-band Fermi Hubbard models, SU(N) physics, charge density wave and topological phases like Haldane Insulator, and quantum link model simulations. The work also shows that accordion lattices can be used to expand the lattice spacing for easier imaging, making it possible to study the phases enabled by the relatively weak dipolar interactions between magnetic atoms in optical lattices. The method is supported by simulations and experimental data, and the results are consistent with theoretical predictions. The work has potential applications in quantum simulation and computation, and the technique could be further improved with novel camera technology and expanded accordion lattice spacing.This paper presents a fast, high-fidelity single-atom imaging method in optical lattice arrays, achieving 99.4% fidelity in distinguishing between 0 and 1 atoms per site within 2.4 microseconds. The method uses accordion lattices to increase atom spacing beyond the diffraction limit, enabling resolution of small-spacing lattices. It also demonstrates parity-projection-free imaging, allowing full atom number detection without parity projection. The technique enables the study of extended Hubbard models, multi-band or SU(N) Fermi-Hubbard models, and quantum link models. The imaging method uses alternating pulsed beams to minimize momentum spread and improve imaging fidelity. The method also employs binarization of EM CCD counts to enhance signal-to-noise ratio and achieve high-fidelity imaging with few photons. The technique is applicable to any atom or molecule with optical cycling in optical tweezers or lattices. The method reduces the total imaging duration for tweezers to a few microseconds, and for small-spacing lattices, the duration is still favorable compared to established techniques. The work also enables repeated use of accordion lattices to magnify the system without the need for diffraction-limited imaging. The results demonstrate that site-resolved imaging does not suffer from parity projection, simplifying the technical challenges of studying a wide range of physics, including entanglement entropy measurement in 2D to study quantum phase transitions and quantum critical points, multi-band Fermi Hubbard models, SU(N) physics, charge density wave and topological phases like Haldane Insulator, and quantum link model simulations. The work also shows that accordion lattices can be used to expand the lattice spacing for easier imaging, making it possible to study the phases enabled by the relatively weak dipolar interactions between magnetic atoms in optical lattices. The method is supported by simulations and experimental data, and the results are consistent with theoretical predictions. The work has potential applications in quantum simulation and computation, and the technique could be further improved with novel camera technology and expanded accordion lattice spacing.