Indirect holographic imaging consists of two stages. The first stage is the recording of a sampled intensity pattern, whilst the second stage is concerned with image reconstruction. The recording of a sampled intensity pattern, I(x,y), is formed by combining the scattered signal from the object, E(x,y), with a reference signal, R(x,y). For antenna measurements, the object to be imaged was an active source of microwave radiation. However, for imaging of passive objects, the object must be illuminated with a source of microwave radiation. At optical frequencies, image reconstruction is performed by reilluminating the hologram with the original reference signal. In order to obtain an unobscured image of the original object, this reference signal must be introduced at an offset angle [11]. The adoption of a similar technique at microwave frequencies has proved difficult due to the practical problems associated with providing an offset reference wave. To overcome this, in the proposed system the radiated reference wave is replaced by an electronically synthesised reference signal. An outline of the system used to achieve this is shown in figure 1.
Figure 1: Experimental Arrangement for Intensity Pattern Collection
The form of the resultant intensity pattern is given by:
(1)
The first stage in the process to reconstruct a high quality image of the original object is to take the Fourier Transform of this intensity pattern (1) to obtain a pattern in the spatial frequency domain (2).
(2)
The first two terms of equation (2) correspond to the auto-correlation of the scattered object wave and the reference wave respectively. The third and fourth terms of this equation relate to the convolution of the reference wave with the scattered wave and it’s complex conjugate. These are offset from the origin by an amount related to the angle of reference wave and contain sufficient information to reconstruct the image. The use of a synthesised offset reference plane wave allows the third and fourth terms of equation (2) to be separated in the spatial frequency domain. This is shown diagrammatically in figure 2.
Figure 2: Spectral Representation of Off-Axis Hologram
In the optical case these correspond to the upright and inverted images upon reconstruction. By selecting either of these two terms, filtering off the remaining terms, centralising the remaining term and performing an Inverse Fourier Transform, the original complex scattered field at the measurement plane can be reconstructed. To obtain a focused image of the tumor at its origin, the information contained in the hologram is then back-projected to the object plane using postprocessing software routines.