Based on the mode expansion theory, a detailed derivation of light transmission properties through fanshaped metallic grating (FMG) is presented. We confirm that all harmonics have considerable transmission coefficients through FMG under limited theoretical assumptions. This means FMG have ability to transmit an image with subwavelength resolution from inner face to outer face. Subsequent simulated results indicate a far-field surperlens by FMG with a resolution better than λ/10 can be obtained. The simulated results are in good agreement with the results of theoretical derivation. Lastly, we demonstrate that clearer image can be reconstructed on the condition of Fabry-Pérot resonance, where both the propagating and evanescent waves almost hold same transmission coefficients. This theory can be applied in designing far-field imaging, highly sensitive detector in biosensing, and research in light-matter interactions.