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A generalized model for beam-path variation analyzed with vector method in square ring resonators is established. The model can be applied to analyze beam-path variation in various ring resonators induced by all the possible perturbation sources. The generalized model is useful for the cavity design, cavity improvement, alignment of planar ring resonators and research on backscattering coupling effect. Backscattering coupling effect in square ring resonator has been chosen as examples to show its application. Backscattering coupling coefficient r is obtained as a function of mirror's axial displacements. Some novel results of backscattering coupling effect have been acquired. The results indicate that r can not be reduced to zero because of the initial machining errors of surfaces of plane mirrors. However, r can be reduced to zero almost when stabilizing frequency of laser gyro by take the suitable values of axial displacements of plane mirrors. These results are important for high precision laser gyro.

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Leaf pigment content retrieval is negatively affected by specular reflectance. To alleviate this effect, some specific techniques that take specular reflectance or specular effects into account have been proposed. In this study, continuous wavelet transform (CWT) and specific techniques including some vegetation indices (VIs), radiative transfer (RT), and hybrid models, were examined and compared in the nadir and near the mirror-like direction, with a 30° incident zenith angle. Results show that the RT and hybrid models appeared to be ill-posed, and they were not applicable at this high-incident zenith angle (>20°). Most VIs effectively alleviated the specular disturbance in the forward 35° direction, and comparable accuracy was obtained between the two viewing directions. Multiple linear regression (MLR), derivative transformation, and CWT were effective for specular interference alleviation. The MLR-based methods (reflectance, derivatives, etc., as the independent variables and pigment content as the response) generally obtained higher retrieval accuracies than the VIs. With MLR-based methods, the retrieval was more accurate for chlorophylls than for carotenoids. CWT plus MLR (MLR on wavelet coefficients) was the most prominent among all the methods, and it generally obtained the highest accuracy. The results are 2.68 and 0.88 μg/cm² for chlorophylls and carotenoids, respectively, in the nadir direction, and 2.42 and 0.86 μg/cm² in the forward 35° direction, with reflectance or the first derivative input for CWT. In the retrieval, wavelet coefficients at the optimal decomposition scale may achieve a balance in corresponding to fine, and broad absorption features, and the overall reflectance properties.