Numerical processing of time-varying holographic information

In optical imaging systems, waves diffracted by an object may be focused into an image by the eye. In most situations where non-optical wavelengths are used, the diffracted waves must be measured and converted to a visible representation of the object. Since the measurements are made at discrete points, a large number are normally required for good resolution and image aperture. It is desirable, therefore, to decrease the number of points, while retaining the image quality, so that the cost of the measurements may be reduced. A method is described which achieves this. If continuous wave illumination is limited to a finite number of cycles, the wave-front created by an object becomes time dependent at the sample points. By taking the samples at selected times, a set of values can be obtained which relates to a common volume in the object space. This volume will be only a small portion of the space and thus requires measurements from relatively few sample points in order to describe it. A complete reconstruction can thus be obtained by moving the common volume through the object space using sets of samples from the same detector points but taken at different selected times. The required numerical manipulation of wave information is illustrated by the generation of a kinoform. This is a physical device from which an optical image can be obtained using coherent light illumination and is constructed using information calculated from a digital description of an object. Similar mathematical techniques can be used for the reverse process of computing reconstructions from continuous wave data. The suggested method has been applied to simulated wave data. There is a large reduction in the number of sample positions required to obtain reconstructions of similar quality to those of the continuous wave method.