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 △=N1/2 (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.