用偶幂级数处理Abel变换问题

USING EVEN POWER SERIES TO TREAT ABEL INVERSION

本文提出了用偶幂级数代替对称分布函数,使其线积分成为递推可积,从而简化了Abel逆变换。引进权函数使本方法简单地过渡到非对称问题。对一组假想相移信号进行变换,获得了可靠的密度分布结果,并对影响变换精度的各种因素作了讨论。

A new method is presented in which a even power series replaces the symmetrical function so that the Abel inversion can be done easily. A weight function is introduced to expand this method into asymmetrical region. A very believable local density distribution is obtained when this method is applied to an artificial phaseshift function. Some factors influencing the inversion accuracy are discussed.