• [Special Report] Wave front Reconstruction Using Small Lenses II


    gradientaberration can be accurately obtained combining the wavefront sloping towardx axis and that sloping toward the y axis. Results indicate that the Hudgin and Fried model yields errors due to an algorithm that fails to use the entire gradient information at thewavefront edge. We can also see that the relative values of the phase of the Fried modelinhibit natural progression. <Figure 2> d) shows comparison of each model and clear differences between them. On the other hand, the Southwell model that obtained the phase based on the entire gradient informationproduces symmetrical phase information.

    We compared the relationship of wavefront reconstruction of each model based on the phase information of deformable mirror measured using Fizeauinterferometer. We included two systems within adaptive optics in order to analyze the difference of phase of wavefront distortion and reference wavefront under identical conditions usingFizeauinterferometer and Shack-Hartmann wavefront sensor.We applied 10,000 digital voltage (9.2 V) to the channel 19 actuator at the center of the deformable mirror to change the Laser beam phase. <Figure 3> and<Figure 4> show phase results obtained fromFizeauinterferometer andwavefrontreconstruction from Shack-Hartmann wavefront sensor. It seems that the wave reconstruction results of wavefront sensor is greater than the full width at half maximum (FWHM) of Fizeauinterferometer results due tozonal sensing.


    Figure 3.Phase information obtained from Fizeauinterferometer.a) phase information b) shape information at center location


    Figure 4.Phase information obtained from Shack-Hartmann wavefront sensor.a) Southwellmodel’swavefrontreconstruction b) Comparison with shape information at center location


    Wavefrontreconstruction using modal sensing

    Noll et al. proposed modal sensing where the coefficient of each wavefrotn mode was computed from Zernike polynomial equation for wavefrontreconstruction. Herrmann and Hunt computed wavefront error and phase of least norm by using repetition of least square estimation andmatrix computation.We obtained aberration information using coefficients of Zernike polynomial equation based on measuredwavefrontgradient information for wavefront reconstruction. Wavefront sensor generally extracts wavefront information from acircular aperture. Using Zernike polynomial equation which is vertical to the unit circle enables expressingwavefrontaberration in the modal form. Zernike polynomial equation can be expressed in the multiplicationof angular function and radial function. When each term of Zernike polynomial equationis orthogonal to thewavefront at given conditions, wavefront information can be obtained usingleast square estimation.



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    -To be continued-

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