Research on Aberration Correction Based on PINN for Secondary Dispersive Objective in GRIN Fibers Spectral Confocal

Precise micro-displacement measurement technology plays a critical role in real-time defect monitoring during manufacturing processes， ensuring adherence to accuracy standards and significantly reducing scrap loss. Chromatic confocal displacement measurement systems operate based on the principles of optical dispersion and confocal technology. Through chromatic encoding， a wavelength-axial position mapping relationship is established， while confocal imaging decodes the reflected spectrum. This enables real-time displacement measurement with sub-micrometer accuracy within a millimeter range， simultaneously providing nanometer-level resolution and robust environmental adaptability. The measurement range and accuracy are constrained by the axial dispersion and aberrations of the dispersive objective. To expand the measurement range and enhance the accuracy of the chromatic confocal displacement sensing system， a secondary dispersion objective based on Gradient-index （GRIN） fiber was designed in this study. The Physics-Informed Neural Network （PINN） algorithm was leveraged in conjunction with ZEMAX software simulation to broaden the system's chromatic dispersion while achieving comprehensive compensation and correction of aberrations in both the secondary dispersion objective and the pre-dispersion GRIN fiber.Firstly， based on the working principle of chromatic confocal displacement sensors， a GRIN fiber-based chromatic confocal system was proposed. A pre-dispersion unit employing GRIN fiber was established according to its refractive index distribution and the Cauchy dispersion model. The relationship between wavelength and axial dispersion was derived. The chromatic focal shift of the GRIN fiber at different pitch numbers was simulated and analyzed. It was determined that at a GRIN fiber pitch number of m=5， an axial pre-dispersion of 1.496 mm could be achieved， with a linearity R² of approximately 95%. Subsequently， based on Hamiltonian optics theory， the aberrations introduced by the GRIN fiber were derived. Based on the calculated equivalent object position of the GRIN fiber pre-dispersion unit and aberration theory， the GRIN fiber aberrations were analyzed. A secondary dispersion objective was then specifically designed. Its dispersion performance was analyzed and aberrations were optimized using ZEMAX. Finally， to improve system resolution and correct aberrations， an aberration correction method employing PINN combined with ZEMAX for closed-loop verification was proposed. A dataset correlating “lens parameters” with “Zernike aberrations” was established using ZEMAX. Combined with aberration data from the pre-dispersion GRIN fiber， PINN was utilized to predict feedback and perform iterative optimization. This facilitated comprehensive aberration correction and optimized axial dispersion linearity.Within the operating wavelength range， the corrected spherical aberration values were significantly lower than pre-correction levels， with particularly pronounced correction in the short-wavelength region. Post-correction spherical aberration values for all wavelengths were markedly optimized， demonstrating effective spherical aberration correction. The aberration correction model demonstrated strong generalization capability， and the overall model training was effective， confirming successful aberration correction. The effectiveness of the aberration correction methodology using ZEMAX software combined with the PINN algorithm for closed-loop verification was thus validated. Following algorithmic optimization， a new optimized dispersive objective lens group was obtained. Results demonstrate that the maximum system aberration was reduced below 10 μm. Total axial dispersion reached 4.34 mm with a linearity R² of 99.84%. Theoretical resolution was approximately 25 nm. In the optimized system， the RMS spot radius at the focal point for each wavelength across the visible spectrum was smaller than the Airy disk， achieving diffraction-limited performance and meeting high-precision displacement measurement requirements. This study provides novel chromatic confocal system optimization， enhancing displacement measurement performance and advancing practical engineering implementation.