REDUCTION OF SIDELOBES IN OPTICAL ARRAYS

Abstract: To reduce the sidelobe levels in a beam produced by an optical phased array, the array is arranged so that the output fields of the emitters have the amplitude and phase given by the inverse Fourier transform of the desired radiation pattern.

Description: REDUCTION OF SIDELOBES IN OPTICAL ARRAYS BACKGROUND OF THE INVENTION The present invention relates to optical phased arrays, and more particularly to a technique for reducing sidelobes in an optical beam generated by an optical phased array. Optical phased arrays are presently under development, and will become increasingly important as low cost, compact coherent radiation sources. For example, arrays are under development which employ surface emitting diodes or edge emitting diodes as the light emitters. An information sheet apparently issued by the Defense Technology Enter¬ prises, Ltd., Royal Signals and Radar Establishment, Worcestershire, UK, describes a linear optical array which gives a steerable beam in one dimension. One of the problems associated with optical arrays, however, is the presence of sidelobes. A conventional optical array, e.g., of laser diodes, gives undesirable sidelobes in addition to the desired main lobe of radia- tion. Pending application serial number 07/773,471, "Optical Phased Arrays," filed October 9, 1991, by V. Vali et al. and assigned to a common assignee with the present inven¬ tion, describes a technique for reduction of sidelobes wherein the individual array elements are not specially placed so that sidelobes remain a concern. The present invention is an improvement on the sidelobe problems inherent in using prior placements of the array elements. SUMMARY OF THE INVENTION The invention comprises a method for determining the spacing, amplitude and phasing of optical array elements in order to obtain a desired radiation pattern and reduce undesirable sidelobes. An exemplary embodiment comprises the following steps: obtaining the inverse Fourier transform of the desired radiation pattern; spacing said array elements in dependence on the inverse Fourier transform; and driving said array elements so that the output of the array elements has the amplitude and phase given by the inverse Fourier transform. The invention is further characterized by an optical array system having a desired radiation pattern and reduced undesirable sidelobes. The array comprises an array of optical emitter elements spaced in dependence on the inverse Fourier transform of the desired radiation pattern. The array further includes a means for exciting the array elements such that the output of the array has the ampli- tude and phase given by the inverse Fourier transform. As a result, the array system produces the desired radiation pattern with reduced undesirable sidelobe levels. BRIEF DESCRIPTION OF THE DRAWING These and other features and advantages of the present invention will become more apparent from the following detailed description of an exemplary embodiment thereof, as illustrated in the accompanying drawings, in which: FIG. 1 illustrates the coordinates for describing the radiation at a distance f from an optical array whose elements are at positions denoted by f 0 . FIG. 2 shows an exemplary desired angular distribution of radiation as a function of an angle from the normal to an optical phased array. FIG. 3 is a graph depicting the amplitude and phase distribution of an optical array output as a function of distance of the array element from the array center in accordance with the invention to achieve the radiation pattern of FIG. 2. FIG. 4 illustrates a cylindrically symmetric array of optical emitter elements comprising an optical array system in accordance with the invention. FIG. 5 is a simplified schematic diagram illustrative of an optical array embodying the invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT Referring to FIG. 1, the radiation at f from the optical array whose elements are at positions denoted by r 0 can be calculated by integrating a Green's function G(f-f 0 ) = (e ikP )/p), p=|f-f c (1) over the source fields (S(f 0 )) , where the "source fields" designate the fields at the antenna array, and k = ω/c, with ω the angular frequency of the radiation and c the speed of light. Thus, denoting the radiation potential at f by p(F) , 0(F) - / G(r-r 0 )S(r 0 ) d J r 0 (2) If the distance between the observation point and the source is much larger than the dimensions of the source, p ,2^ _ = (r-r 0 ) ■ (r-r 0 ) - 2r, ( 3 ) and p = r - (2/2) (f 0 - f/r) . (4) If K = k(f/r) , <P (r) ~ (l/r) J e ikr e~ i r o S(f 0 )d 3 r 0 (5) From the desired radiation potential φ {x ) , this equation (5) provides a means of optimizing the source distribution S(r 0 ). As an example, suppose the origin is placed in the plane of the array and suppose this array is cylindrically symmetric about the axis through the origin and perpendicular to the plane. Then, denoting the angle between the axis and the observation point by θ, F(θ)≡ rø(r)e ~ikr = J e iksinΘr o S(f 0 )df 0 (6) = 2π J e iksinΘr o S(r 0 )r 0 dr 0 For a desired F(θ) , where F(θ) denotes the radiation potential multiplied by r with the phase removed, an inverse Fourier transform gives the necessary S(r 0 ) . For instance, if a directed pencil beam without side lobes is desired, this would give an Airy-type function for S(r 0 ) . S(r 0 ) describes what the optimum phase and spatial distribution of the optical array elements should be, i.e., S(r 0 ) describes the optical phase and amplitude distribution of the emitter signal. FIG. 2 is a graphical illustration of an exemplary desired radiation pattern from an optical phased array of emitters whose placement, amplitude, and signal phase are to be determined in accordance with the invention. FIG. 3 represents the inverse Fourier transform of the radiation pattern of FIG. 2', and indicates the placement, signal amplitude and phasing of the optical emitters to obtain the radiation pattern of FIG. 2. The invention may be employed in the following manner to determine the location of the emitters in order to obtain the desired radiation pattern while minimizing the sidelobe level. As an example, if the array includes a number of equally spaced emitters on a grid, then in accordance with the pattern for S(r σ ) indicated in FIG. 3, the amplitude of the signal to be provided to any particular element in the array is determined by the height of S(r 0 ) at the distance of the element from the center of the array. The amplitude of the signal of any particular element can be determined by the amplification of an amplifier hooked to that ele¬ ment. The sign of the signal is likewise determined by the sign of S(r 0 ) indicated at r 0 in FIG. 3. FIG. 4 shows a cylindrically symmetric array 30 of elements 32 as a simple example. It is necessary to specify the amplitude and phase of each element in the array. In the illustration of FIG. 4, the array is depict¬ ed as having an equal number of elements per unit area. To achieve the desired result, i.e., obtain a particular radiation pattern, different amplitude signals are typical¬ ly needed at each element. It would also be possible to use constant amplitude feeds to the elements, in which case, the density of the elements would need to be varied. For the cylindrically symmetric case of FIG. 4, and for a beam aimed in the direction perpendicular to the plane of the arrays, eq. 6 provides F(θ) == 22ττττ iJ e e ikJtsSiinIlΘwrr oo rr D0 SS((rr 00 ))ddrr 0 _.. (7) Hence, r 0 S(r 0 ) = k J e ~ikr o Ω F(θ)dΩ (8) where Ω = sinθ. If F(θ) is a constant for θ<θ 1 and zero otherwise, as an example, i.e., then S(r 0 ), the inverse Fourier transform of F(θ) , is given by S(r 0 ) = (-constant/ir 0 2 ) [ e - ikr o sinΘ l - e +i r o sinΘ l] = (2 constant/r 0 2 ) sin [kr 0 sinθ 1 ] . (9) For this circular symmetric case, an element at a distance r 0 from the center would be fed a signal equal in amplitude to S(r 0 ), (2 constant/r 0 2 ) |sin[kr 0 sinθ 1 ] I and would have a phase of 0 or it depending on whether the sign of sin(kr Q sin θ ) was plus or minus. Another way of achieving the amplitude effect using constant amplitude signals to each element is to vary the density of elements in accordance with the amplitude indicated for S(r 0 ) . If for the distribution F(θ) described above in eq. 7, it is desired to use signals of constant amplitude to feed the elements, then the density of the elements would be varied to mimic S(r 0 ), i.e., the density of the elements would be proportional to (2/r 0 2 )sin[kr 0 sinθ 1 ] The phase of the signal to be supplied to each element would again be determined in the same way as described above for the equal element spacing case. The means of supplying signals of different amplitude and phase to the elements can be any of the standard means of varying amplitude and phase using off-the-shelf equip¬ ment. For instance, phase can be varied by using delay lines and amplitude can be raised by use of amplifiers. FIG. 5 illustrates an exemplary means for setting the amplitude and phase of the signal driving the emitter elements of an optical phased array 50 in accordance with the invention. For simplicity, only two elements 52 and 62 are shown in FIG. 5. In this embodiment, equal drive signals are applied to the respective amplifiers 54 and 64 corresponding to the respective emitters 52 and 62. The amplifiers are used to set the amplitude for the respective emitter as determined by the inverse Fourier transform of the desired radiation pattern. The amplifier outputs are in turn fed to respective optical delay lines 56 and 66, which are used to set the phase required by the inverse Fourier transform for the particular element. For each of the emitters comprising the array 50, an amplifier and delay line are provided to set the amplitude and phase of the emitter output signal in accordance with the inverse Fourier transform. Of course, if the array employs equal amplitude signals, the amplifiers may be omitted, or may simply provide the same gain for all emitters, with the amplitude distribution being achieved by selecting the emitter density as described above. In the foregoing example of FIG. 4, the desired beam described by F(θ) is assumed to be cylindrically symmetric about an axis perpendicular to the plane of the array. But it is obvious from eqs. (5) and (6) how to have the beam directed in any general polar direction instead by polar angles (θ, ) . Again, it is a matter of performing the transform of the desired distribution. The amplitude and phase indicated by the inverse Fourier transform will vary as the beam is steered to different angles. It is understood that the above-described embodiments are merely illustrative of the possible specific embodi¬ ments which may represent principles of the present inven¬ tion. Other arrangements may readily be devised in accor¬ dance with these principles by those skilled in the art without departing from the scope and spirit of the inven¬ tion.

Claims: 763 CLAIMS What is claimed is: 1. A method for determining the spacing, amplitude and phasing of optical array elements in order to obtain a desired radiation pattern and reduce undesirable sidelobes, comprising the following steps: obtaining the inverse Fourier transform of said desired radiation pattern; spacing said array elem nts in dependence on said inverse Fourier transform; and driving said array elements so that the respec- tive outputs of said array elements have the amplitude and phase given by said inverse Fourier transform. 2. An optical system comprising: an array of optical emitter elements spaced in dependence on an inverse Fourier transform; and means for driving the array elements such that the respective outputs of the array elements have the amplitude and phase given by said inverse Fourier transform. 3. An optical array system having a desired radia¬ tion pattern and reduced undesirable sidelobes, comprising: an array of optical emitter elements spaced in dependence on the inverse Fourier transform of said desired radiation pattern; and means for exciting the array elements such that the output of said array has the amplitude and phase spatial distribution given by said inverse Fourier transform, whereby said array system produces said desired radiation pattern with reduced undesirable sidelobe levels. 10 4. A method for determining the amplitude and phasing of equally spaced radiating elements in an optical array in order to Obtain a desired radiation pattern and reduce undesirable sidelobes, comprising the following steps: obtaining the inverse Fourier transform of said desired radiation pattern; and driving said array elements so that the output of respective ones of said array elements has the ampli- tude and phase given by said inverse Fourier trans¬ form. 5. An optical array having a desired radiation pattern and reduced undesirable sidelobes, comprising: a plurality of equally spaced radiating elements; and means for exciting the array elements such that the output of said respective array elements has the amplitude and phase given by the inverse Fourier transform of said radiation pattern. 6. An optical array having a desired radiation pattern and reduced sidelobes, comprising: an array of radiating elements; means for feeding equal amplitude drive signals to said radiating elements; said radiating elements further characterized by element spacings determined by the inverse Fourier transform of said desired radiation pattern; and means for setting the relative phase of said equal amplitude drive signals in dependence on said inverse Fourier transform. 7. A method for determining the spacing and phasing of optical array elements driven by equal amplitude drive signal in order to' obtain a desired radiation pattern and reduce undesirable sidelobes, comprising the following steps: obtaining the inverse Fourier transform of said desired radiation pattern; spacing said elements in accordance with said inverse Fourier transform; and setting the phase of said drive signals in accor¬ dance with said inverse Fourier transform.

Inventors: CHANG DAVID B, VALI VICTOR, CHANG, DAVID, B., VALI, VICTOR
Applicants: HUGHES AIRCRAFT CO, HUGHES AIRCRAFT COMPANY
Application year: 1993
Main classification: H01Q21
IPC codes: H01Q3, H01Q21, H01S3, H01S5