Under many circumstances an acoustic or electro-magnetic signal is received from a moving source and information as to the location and velocity of the source is desirable. Examples of where this occurs are undersea surveillance and radar surveillance. A common method of representing this is on a graph known as an ambiguity plane, where distance is plotted against velocity as revealed by the relative doppler shift between two signals. The relative time shift and doppler shift between two signals so received can be used to construct this graph.
The ambiguity plane is prepared by evaluating the ambiguity integral which is defined as EQU .chi.(.nu.,.tau.)=.intg.f.sub.1 (t)f.sub.2 *(t-.tau.)e.sup.-i2.pi..nu..omega. dt (1)
In this equation f.sub.1 (t) and f.sub.2 (t) are the two signals being compared expressed as functions of time. The variable .tau. is introduced to correct for the fact that although it is expected that f.sub.1 (t) and f.sub.2 (t) should have a similar form, they will, in general, be shifted in time relative to each other. The function f.sub.2 *(t-.tau.) is the complex conjugate of f.sub.2 (t-.tau.) which is the time shifted version of the signal actually received. The factor e.sup.-i2.pi..nu..tau. is introduced to correct for the frequency difference between f.sub.1 (t) and f.sub.2 (t), caused by the doppler effect. The values of .nu. and .tau. which yield a maximum value of the ambiguity integral may be used to extract information about the velocity and range of the object under surveillance.
In order to be useful for surveillance purposes the information displayed on an ambiguity surface must be as current as possible. For this reason evaluation of the integral (1) must be performed in real time. The ability of optical analog processing to process multiple channels of data rapidly in a parallel fashion has led to its acceptance as a method for ambiguity function calculations. A common procedure involves the preparation of data masks for f.sub.1 (t) and f.sub.2 *(t-.tau.) with t on the horizontal axis and .tau. on the vertical. Optical data processing means perform the multiplication and integration in equation (1) leaving a .nu. dependence on the horizontal axis and a .tau. dependence on the vertical. The graph thus produced is then searched for its greatest value, which is the maximum of the ambiguity integral.
The most important limiting factor on the speed of these prior art devices is the production of the data masks. Although the data mask for f.sub.1 (t) has no .tau. dependence and that for f.sub.2 *(t-.tau.) has only a linear .tau. dependence, they are normally constructed through the use of two-dimensional spatial light modulators (SLM's). Accordingly a simpler and more rapid means of coding the light beam with the data would significantly decrease the time required to produce an ambiguity plane.
The copending application, Ser. No. 105,809, filed Dec. 20, 1979, now U.S. Pat. No. 4,310,894, assigned to the same assignee as the instant invention, reveals a system in which one-dimensional spatial light modulators may be used in place of two-dimensional ones. Although inherently faster than the prior art, that system requires a minimum of four cylindrical lenses, which are more difficult and expensive to produce than spherical ones. It also requires a demagnification stage which significantly increases the path length and, as a result, the size of the apparatus. Therefore it is desirable to build an optical system to perform ambiguity processing retaining the use of one-dimensional spatial light modulators, but eliminating the need for some of the cylindrical lenses and the demagnification stage.