Elimination of the Unwanted Image in Diffraction Microscopy

Abstract

DURING a discussion at Cambridge, the idea was put forward that it might be possible to eliminate the effects of the unwanted image in diffraction microscopy by taking a subsidiary hologram and subtracting it from the reconstruction. In Gabor's method^1,2 a single hologram is used, and he has shown how two images are formed, when coherent light traverses this hologram, so that the image in sharp focus has as a background a confused pattern due to the other image. In a recent note in Nature³, an elementary explanation of the origin of these two images is given; the confusion they cause is the necessary price paid for the loss of information as to the phase of the disturbance in the plane in which the main hologram is taken. But in a coherent beam, if the amplitude and phase are known over a surface 1, they can be calculated over a subsequent surface 2 by Huyghens's principle. In general, the two patterns differ from one another, yet they both contain essentially the same information. This opens up the possibility that the confusion due to loss of information about phase in one plane, the main hologram plane, may be cleared up by measuring the amplitude in another plane which we call that of the auxiliary hologram. In other words, two suitably separated amplitude patterns will do service for a single pattern giving both amplitude and phase. While one hologram gives two images, two holograms can be made to give one image.