In the classical diffraction theory, the Debye integral is an important formula for analyzing the characteristics of the light field near the focal point of a converging light wave. However, since the effect of the inclination angle of the wave vector of the convergent light wave on the diffraction integral formula is ignored, the Debye integral is an approximation formula. In order to further clarify the necessity of the inclination factor on observation side of the diffraction integral formula for calculating the characteristics of light field near the focal point of nonparaxial convergent light wave, a nonparaxial convergent light wave whose amplitude varies with the square root of the cosine of the inclination angle of wave vector limited by a circular aperture is used as the diffraction source, the diffraction integral formula with normalized inclination factor expressed by the square root of the cosine of inclination angle on observation side and the Debye integral are engaged to analyze the characteristics of light field on the focal plane of this diffraction source respectively.Based on the diffraction integral formula with the normalized inclination factor on observation side expressed by the square root of the cosine of the inclination angle of wave vector, the functional expression of light field distribution on focal plane of this diffraction source is presented. Such light field distribution on the focal plane of this special diffracted source is in the form of the Airy spot. Moreover, the total power of the focal plane light field is equal to the total power of the light field of this special diffracted source. It satisfies the law of conservation of radiation energy of traveling wave field, and verifies the rationality of the normalized inclination factor expressed by the cosine square root of the inclination angle on observation side. It shows that the diffraction integral formula with the normalized inclination factor expressed by the square root of the cosine of inclination angle on observation side is suitable for analyzing the characteristics of optical field on focal plane of paraxial and nonparaxial converging light wave.When the Debye integral is used to analyze the characteristics of light field on the focal plane of the same diffraction source, the light field distribution on the focal plane of the same diffraction source deviates from the Airy spot form, the amplitude of focal point deduced by the Debye integral is greater than the actual value, and the total power of the focal plane light field is greater than the total power of the light field of this special diffraction source. It does not satisfy the law of conservation of energy, and thus identifies the limitation of the Debye integral. It shows that the Debye integral is not suitable for analyzing the characteristics of light field on focal plane of the nonparaxial convergent light wave.When the diffraction integral formula with normalized inclination factor expressed by the square root of the cosine of inclination angle on observation side is used to analyze the characteristics of light field on the vertical facet which very close to the focal plane and the characteristics of light field at the point on axis which very close to the focal point of this diffraction source, the amplitudes of light field on several vertical facet which very close to the focal plane of the nonparaxial convergent light wave with a maximum inclination angle of (1/3)π rad are computed, the amplitudes and phases of light field at point on axis which very close to the focal point of this nonparaxial convergent light wave with a maximum inclination angle of (1/3)π rad are also computed. If the maximum inclination angle of this nonparaxial convergent light wave is equal to theoretical value 0.5π rad, the expression of complex amplitude of light field at point on axis which very close to the focal point is derived, the characteristics of amplitude and phase of light field at point on axis which very close to the focal point of this nonparaxial convergent light wave are presented. Thereinto, when the absolute value of axial defocusing is far greater than the wavelength of light wave, the characteristic of phase of light field at point on axis of this nonparaxial convergent light wave with a maximum inclination of 0.5π rad is similar to the Gouy phase shift of the fundamental mode Gaussian beam, this characteristic has its physical meaning and indicates that this formula is worthy of further study.Based on the condition of paraxial approximation, the expression of complex amplitude of light field at point on axis which very close to the focal point of a paraxial convergent light wave whose amplitude varies with the square root of the cosine of the inclination angle of wave vector limited by a circular aperture is derived. The characteristics of amplitude and phase of light field at the point on axis which very close to the focal point of this paraxial convergent light wave are also presented. It shows that the diffraction integral formula with the normalized inclination factor expressed by the square root of the cosine of inclination angle on observation side is suitable for analyzing the characteristics of light field near the focal point which diffracted from a paraxial convergent light wave and a nonparaxial convergent light wave whose amplitude varies with the square root of the cosine of the inclination angle of wave vector within a certain inclination angle.