Atmospheric Dispersion Correction Based on Electrowetting Liquid Prism
Objective The atmosphere has varying refractive indices for different wavelengths of light,causing light emitted from a star to broaden as it passes through,leading to atmospheric dispersion.An increase in zenith distance results in greater atmospheric dispersion.When the atmospheric dispersion exceeds the diffraction limit of a telescope,the imaging quality significantly declines.As modern telescopes'apertures increase,the effect of atmospheric dispersion on imaging quality becomes more pronounced.To counteract atmospheric dispersion,atmospheric dispersion correctors(ADCs)are developed to generate compensatory dispersion.The two popular types of ADCs are linear atmospheric dispersion correctors(LADCs)and rotating atmospheric dispersion correctors(RADCs).Traditionally,ADCs are made of glass,but they face challenges such as high-accuracy mechanical moving parts,complex structures,bulkiness,wear issues,and high cost.We propose an atmospheric dispersion corrector based on electrowetting liquid prisms(ELADC),which offers fast response time,no mechanical movement,and effective dispersion correction at common zenith distances.Method The ELADC consists of two immiscible liquids with the same refractive index at a center wavelength of 589 nm but different Abbe numbers.The contact angles between the sidewalls and the liquid-liquid interface follow the Young-Lippmann equation.When the contact angle,controlled by the working voltage,is 90° and the interface is planar,this voltage is defined as the critical voltage.The two immiscible liquids form a planar interface with varying deflection angles under different critical voltage combinations.We theoretically deduce the relationship between the liquid prism's deflection angle and atmospheric dispersion.The ELADC model is established in COMSOL,and simulations of the liquid-liquid interface deflection under various voltage combinations are performed.We analyze the atmospheric dispersion correction for 3.50"in the visible spectrum under different deflection angles and compare the results with ZEMAX simulations.The error between the simulated and theoretical results is analyzed in detail.Results and Discussions By measuring the refractive indices and Abbe numbers of candidate liquids,we select a combination of alkyl silicone oils used as the insulating liquid and 1-Decyl-3-methylimidazole tetrafluoroborate solution used as the conductive liquid,with refractive indices of 1.431 at D light and Abbe numbers of 50.73 and 55.12,respectively.The deflection of the liquid-liquid interface inside the liquid prism varies with changing voltage combinations(Fig.5).We analyze the influence of ELADC's different deflection angles on 3.50"atmospheric dispersion correction using COMSOL and determine the optimal deflection angle(Fig.7).The liquid prism performs best in dispersion correction when the deflection angle is between 1.419° and 1.423°,with 1.421° being optimal.ZEMAX validates that a deflection angle of 1.42° achieves the best dispersion correction for 3.5"(Fig.8).COMSOL and ZEMAX provide a series of optimal deflection angles for correcting various dispersions(Fig.9).Conclusions We propose an atmospheric dispersion correction device based on electrowetting liquid prisms,detailing its working principle.Using the Elden model,we calculate atmospheric dispersion values in the visible band at a 66.5° zenith distance and derive the relationship between the liquid prism's deflection angle and atmospheric dispersion values.COMSOL simulations construct physical and optical models of the electrowetting-based liquid prism and analyze the effects of dispersion correction.The optimal deflection angles for atmospheric dispersion correction at different zenith distances are verified by simulation in ZEMAX simulations and compared with theoretical results.The results show that the ELADC effectively corrects atmospheric dispersion.For 3.50"dispersion,the ELADC with a 1.421° deflection angle compensates residual dispersion to approximately 0.001238",significantly below the diffraction limit of common telescopes.The dispersion correction value increases linearly with the deflection angle of ELADC,with simulated values aligning closely with theoretical calculations.This study provides a new approach to atmospheric dispersion correction,offering significant theoretical and practical values for developing dispersion correction technologies.
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