The microscopic image of illuminated objects results from a twofold diffraction, at the object and at the lens-aperture. The theories of Rayleigh and of Abbe differ only as to the order in which they consider these diffractions. The Abbe method is here used to calculate the image of a coarse transparent grating with shallow grooves of arbitrary form (phase grating). In the ideal case the image is invisible. The formulae are successively applied to the following practical methods to make the image visible: the schlieren method, where the diffraction spectra of the grating are intercepted on one side, the ordinary oblique dark ground illumination, where the central image is intercepted also, the central dark ground illumination, with intercepts the central image only, and the bright ground observation with illumination by a narrow pencil, where the visibility is caused by out-of-focus observation. It is found that none of these methods can show the real groove form. This is possible by the new method of phase contrast, where a path difference of λ/4 is introduced between the spectra and the central image by passing the last through a slightly thicker or thinner part (phase-strip) of a glass plate.

In Part II the new method is treated in another way which applies to objects of arbitrary irregular structure. The general result is that by the phase-contrast method transparent details of the object which differ in thickness or in refractive index appear as differences of intensity in the image. An important increase of sensitivity can further be obtained by the use of an absorbing phase strip. The effect of the diffraction by the phase strip is then considered and practical methods discussed to make the resulting diffraction-halo as faint as possible. Various reasons are found why the strip should preferably be of circular form, with a corresponding annular diaphragm in the condenser. Finally the methods of preparing phase strips and of placing and adjusting them in the microscope are discussed.