The Study of the Fractional Talbot Effect of a Grating and a Lens under Spherical Lightwave Illumination

We study the fractional Talbot effect of a grating and a lens under sphere lightwave illumination in this paper. Our analysis is based on the scalar theory of optical diffraction. For simplicity we omit the influence of the finite size of the grating and the lens on the optical diffraction. We use comparing method. We change the diffraction of the optical system under sphere lightwave illumination into the diffraction of a single grating under parallel lightwave illumination. Then we present the fractional Talbot effect condition of the system under spherical lightwave illumination and analyse its characteristics. Analysis shows that the fractional Talbot effect of the system connects to wavelength of the incite light, the period of the grating, the position and the focal length of the lens and the distance of the spherical lightwave. Because more parameters are related to the fractional Talbot effect of the system, we can adjust and control the fractional Talbot effect more easily than the situation of a single grating under parallel lightwave illumination.