Achromatic cascaded diffractive optical elements for microlens system design

Chromatic aberration, originating from wavelength-dependent optical path differences, fundamentally limits imaging performance of diffractive optical elements (DOEs) under multi-wavelength illumination. In this work, we propose an achromatic design framework based on cascaded DOE, in which chromatic aberration is compensated through a wavelength-multiplexed optimization strategy. By treating wavelength as an additional design degree of freedom, the cascaded DOE is designed to produce identical output images under multi-wavelength illumination. The far-field coupling between cascaded DOEs is exploited to provide enhanced flexibility for wavelength-dependent phase compensation. Numerical simulations demonstrate that the proposed cascaded DOE achieves a high and stable correlation of 0.8296 ± 0.0066 across three representative wavelengths (633 nm, 550 nm, and 450 nm), whereas single-layer DOEs exhibit significantly lower correlation coefficients with much larger wavelength-dependent variations (∼0.02−0.05). These results verify the feasibility of the proposed cascaded DOE framework for near-achromatic diffractive imaging and highlight its potential for multi-wavelength optical system design.