存在球差和失焦下电子光学传递函数和脉冲响应函数

根据电子光学理论,球差和失焦引起附加相位移为γ,相干的振幅和相位衬度传递函数为cosγ和sinγ。它们的傅里叶逆变换给出脉冲响应函数的实部和虚部。本文讨论了cosγ和sinγ的零点和极值点,这些点将衍射平面划分为一系列环带。证明了当无量纲失焦量Δ=N^1/2(N为正整数)时各环带上cosγ,sinγ的积分相同,即对脉冲响应函数中心值的贡献相同。本文讨论了使cosγ或sinγ的积分取极大值或极小值,亦即使脉冲响应函数中心值或中心强度取极大值或极小值的条件。本文还讨论了脉冲响应函数最佳均方关键词：

ON ELECTRON OPTICAL TRANSFER FUNCTION AND IMPULSE RESPONSE IN THE PRESENCE OF SPHERICAL ABERRATION AND DEFOCUS

It is well known from electron optics that spherical aberration and defocus modify the diffraction plane wave function by a phase shifty and the coherent amplitude and phase-contrast transfer functions are cosy and siny. Consequently, the inverse Fourier transforms of cosy and siny are the real and imaginary parts of impulse response. The locations of the zeros and extrema of the amplitude- and phase-contrast transfer functions are presented. These zeros and extrema devide the diffraction plane into a series of annular regions. When the value of the dimensionless defocus is selected as △=N^1/2 (N is a positive integer), the integrals of transfer function over corresponding annular regions are equal. Equivalently, their contributions to the central value of the impulse response are of the same value. The conditions for maximizing or minimizing the integrals of cosy on siny (i.e. maximizing or minimizing the central value or intensity of impulse response) has been suggested. In the present paper, the condition for the mean-square optimum approximation of impulse response with the ideal Airy distribution has also been discussed.