An alternative extension to the Gaussian-beam expansion technique is provided to simplify the computation of the ~esnel field integral for rectangular symmetric sources. From a known result that the circle or rectangl...An alternative extension to the Gaussian-beam expansion technique is provided to simplify the computation of the ~esnel field integral for rectangular symmetric sources. From a known result that the circle or rectangle function is approximately decomposed into a sum of Gaussian functions, the cosine function is similarly expanded by the Bessel Fourier transform. Two expansions are together inserted in this field integral, it is then expressible in terms of the simple algebraic functions. As examples, the numerical results for the sound pressure field are presented for the uniform rectangular piston transducer, in a good agreement with those directly evaluated from the Fresnel integral. A wide applicability of this approach is discussed in treatment of the ultrasonic field radiation problem for a large and important group of piston sources in acoustics.展开更多
The electron optical column for the variable rectangular-shaped beam lithographysystem DJ-2 is described,with emphasis on the analysis of the optical configuration and theshaping deflection compensation.In this column...The electron optical column for the variable rectangular-shaped beam lithographysystem DJ-2 is described,with emphasis on the analysis of the optical configuration and theshaping deflection compensation.In this column the variable spot shaping is performed with aminimum number of lenses by a more reasonable optical scheme.A high-sensitivity electrostaticshaping deflector with sequential parallel-plates is implemented for high-speed spot shaping.With a precise linear and rotational approach,the spot current density,the edge resolution aswell as the position of spot origin remain unchanged when the spot size varies.Experiments showthat the spot current density of over 0.4 A/cm^2 is obtained with a tungsten hairpin cathode,andthe edge resolution is better than 0.2μm within a 2×2 mm^2 field size.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11074038 and 11374051
文摘An alternative extension to the Gaussian-beam expansion technique is provided to simplify the computation of the ~esnel field integral for rectangular symmetric sources. From a known result that the circle or rectangle function is approximately decomposed into a sum of Gaussian functions, the cosine function is similarly expanded by the Bessel Fourier transform. Two expansions are together inserted in this field integral, it is then expressible in terms of the simple algebraic functions. As examples, the numerical results for the sound pressure field are presented for the uniform rectangular piston transducer, in a good agreement with those directly evaluated from the Fresnel integral. A wide applicability of this approach is discussed in treatment of the ultrasonic field radiation problem for a large and important group of piston sources in acoustics.
文摘The electron optical column for the variable rectangular-shaped beam lithographysystem DJ-2 is described,with emphasis on the analysis of the optical configuration and theshaping deflection compensation.In this column the variable spot shaping is performed with aminimum number of lenses by a more reasonable optical scheme.A high-sensitivity electrostaticshaping deflector with sequential parallel-plates is implemented for high-speed spot shaping.With a precise linear and rotational approach,the spot current density,the edge resolution aswell as the position of spot origin remain unchanged when the spot size varies.Experiments showthat the spot current density of over 0.4 A/cm^2 is obtained with a tungsten hairpin cathode,andthe edge resolution is better than 0.2μm within a 2×2 mm^2 field size.
