Aspects of Far-Field Holography.

Far-field holography has been used as a tool for counting and sizing particles for many years. Still, there are significant gaps in its theoretical development that need to be filled. First, the theory must be developed in a suitably general form. Magnification must be included in both the formation and reconstruction steps. Magnification in the formation step causes information about the object to be encoded to lower spatial frequencies in the hologram. The resolution limits of far-field holography can be derived through geometrical and physical considerations. A resolution cell can be defined giving both lateral and longitudinal resolution. The extent of the hologram determines the size of the cell. The hologram is limited by the interaction of the object's Fourier transform with the granularity of the film--not by the film's MTF. Although this leads to no concise form for the resolution limits, it is possible to make general predictions of resolving power based on film type and object shape. Far-field holography proves to be resistant to noise. Additive noise that enters at the hologram does not affect the resolution in the final image, even though the hologram itself may be rendered indecipherable. If the object is illuminated by a noisy beam the resolution is still not affected provided the variations in the beam are small. Large variations degrade the image to the point where it can no longer be seen. Phased objects may also be visualized with far -field holography. The phase becomes visible in essentially the same manner as conventional coherent imaging. The amplitude impulse response function of the system interacts with abrupt changes in phase to show up the edges as drops in intensity. However, in far-field holography the image of a phase object is itself out of phase with the background and hence is visible. Real-time devices developed for optical processing may be used as holographic media in far-field holography. Although these devices have very low MTF cutoffs, the hologram may be recorded if magnification is used. By judicious use of magnification during formation and reconstruction, small particles may be recorded and working distances kept practical.