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This paper presents a novel heterodyne grating interferometer designed to meet the precise measurement requirements of next-generation lithography systems and large-scale atomic-level manufacturing. Utilizing a dual-frequency light source, the interferometer enables simultaneous measurement of three degrees of freedom. Key advancements include a compact zero Dead-Zone optical path configuration, significantly enhancing measurement reliability by mitigating the impact of light source fluctuations and air refractive index variations. A comprehensive crosstalk error analysis was conducted, resulting in a robust correction algorithm that reduces errors to below 5%. Performance testing of the prototype, size of 90mm*90mm*40mm, demonstrated exceptional resolution (0.25 nm in the XY-axis and 0.3 nm in the Z-axis), superior linearity (6.9e-5, 8.1e-5 and 16.2e-5 for the X, Y, and Z axes, respectively), high repeatability (0.8 nm/1000 nm for the three axes) and stability (20 nm for the XY-axis and 60 nm for the Z-axis over 1000 seconds). Comparative analysis with existing measurement sensors highlights the proposed method's significant advantages in integration, multidimensional capabilities, and is expected to be widely used in fields such as integrated circuits, atomic-level manufacturing and aerospace technology.