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Existing computational spectral imaging systems typically rely on coded aperture and beam splitters that block a substantial fraction of incident light, degrading reconstruction quality under light-starved conditions. To address this limitation, we develop the Oscillating Dispersion Imaging Spectrometer (ODIS), which for the first time achieves near-full light throughput by axially translating a disperser between the conjugate image plane and a defocused position, sequentially capturing a panchromatic (PAN) image and a dispersed measurement along a single optical path. We further propose a PAN-guided Dispersion-Aware Deep Unfolding Network (PDAUN) that recovers high-fidelity spectral information from maskless dispersion under PAN structural guidance. Its data-fidelity step derives an FFT-Woodbury preconditioned solver by exploiting the cyclic-convolution property of the ODIS forward model, while a Dispersion-Aware Deformable Convolution module (DADC) corrects sub-pixel spectral misalignment using PAN features. Experiments show state-of-the-art performance on standard benchmarks, and cross-system comparisons confirm that ODIS yields decisive gains under low illumination. High-fidelity reconstruction is validated on a physical prototype.