In this paper, the ultrasonic frequency coordination relation has been re-designed in the high-dimensional space by the principle of Kernel function nonlinear mapping. The relative deviation of ultrasonic frequency coordination relation from the original formula has been obtained by analyzing I.C.Chang theoretical model and P.A.Gass revised theoretical model concretely, theraby indicating the inadequacy of the two theoretical models; Using the principle of the nonlinear mapping to map the original data samples into a high dimensional kernel space, in other words, translating the nonlinear problem into a linear problem can clarify the relationships not only between ultrasonic frequency and incident angle but also between ultrasonic frequency and optical wavelength, leading to an appropriate kernel function and the improved coordination of the ultrasonic frequency relation.

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