Circular Apertures and Resolving Power

 If a parallel beam of light (where all rays are parallel to each other) passes through an aperture in an opaque screen, it broadens due to diffraction, and ceases to be parallel. On the focal plane of a lens that is placed behind the screen, the image of the source becomes diffused due to diffraction. In the case of a circular aperture, the diffraction image consists of the central bright spot (the so called Airy disk) and a number of concentric circles around it. The radius of the central spot on the focal plane of the lens is r1=1.22(λ/D)f Where λ is the wavelength, D is the diameter of the aperture, and f is the focal length. If the rays from a distant source fall on a lens directly, the aperture of the lens plays the role of the screen. In this case, D is the diameter of the lens. The size of the diffraction spot increases with an increase in the wavelength λ and with a decrease in the lens' diameter D. The diffraction character of the image limits the abilities of optical instruments. For example, the diffraction images of two nearby stars may strongly overlap so that it is hard to distinguish whether there is one star or two. If the light from two stars at angular separation θ strikes the objective of a telescope, the centers of diffraction maxima will be Δl=fθ apart (for small angles θ) in the focal plane of the objective lens of diameter D with the focal length f. If this distance equals the radius r1 of the central spot, the diffraction patterns strongly overlap so that one cannot easily distinguish the image of two stars from the image of one star. According to this criterion (called Rayleigh's criterion), the quantity θmin=r1/f=1.22λ/D is called the diffraction limit of resolution of a lens. In a similar fashion, wave nature of light limits our ability to distinguish close details of an object that is viewed through a microscope.