Auxiliary lenses may be employed in a modified phase microscope to form additional images of the condenser diaphragm. The images of the condenser diaphragm are called multipupils. They can serve to increase the flexibility of the phase microscope because a diffraction plate may be placed at any one or at all of the multipupils. Multipupil systems serve as effective means for phase microscopy. The bipupil system is of most practical interest because it combines the required flexibility with simplicity. It is shown on general theoretical grounds that the multipupil system is equivalent to a single system of phase microscopy whose over-all magnification is equal to the product of the magnifications of the multipupil system and whose pupil function is the product of the complex pupil functions associated with each of the multipupils. The physical interpretation of the composite pupil function as a product is that the optical paths through corresponding areas of the multipupils are additive, while the corresponding amplitude transmissions are multiplied. The method of proof serves to extend the theory of phase microscopy to multipupil systems.
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