The Resolution of Two Particles in a Bright Field by Coated Microscope Objectives

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Abstract
A theory is presented for determining the diffraction image of two, identical, opaque or transmitting, uniform, individually unresolved particles of finite area located in a uniform, transmitting surround. Numerical calculations are included for the classical Airy type objective, for center-blocked Airy type objectives and for simplified Sonine type objectives which have been coated so as to produce diffraction patterns having central disks of reduced diameter. It is shown that marked improvement in the resolution of two particles can be expected by such coated objectives. The resolving power for two particles increases rapidly with the area of the particles and has unexpectedly steep dependence upon the relative amplitude and phase transmission of particle and surround. The theory, subject to experimental verification, forms a basis for explaining why a microscope as used with transmitted light can resolve considerably better than is indicated by the Airy limit.

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