A synthetic aperture is formed when separate optical systems are combined to function as a single larger aperture. When an aperture is synthesized, independent optical systems are phased to form a common image field with resolution determined by the maximum dimension of the array and therefore exceeding that produced by any single element. In this paper, advantages and disadvantages of synthetic apertures are discussed, imaging properties are described, and implementation techniques are evaluated. Finally, some examples of existing and future phased array systems are presented.

Three generic conceptual approaches to measuring beam path phase differences in a multiple aperture laser transmitter are described.

Very high angular resolution can be achieved in UV/optical astronomy through interfero meters in space. A concept analysis of COSMIC, which may be placed into orbit by the Space Shuttle in the late 19901s, is discussed. The photon-collecting area is three times larger than that of Space Telescope (ST), and exceeds its resolution by approximately on order of magnitude. Several alternative configurations are presented to scope the extent of design approaches which may be achievable within the transportation capability of the Space Shuttle.

We will describe an alignment system for a multimirror telescope array in which an optical light plane provides a synthetic stable platform or optical reference flat upon which are located a series of heterodyne interferometers which measure the relative phasing, tilts, etc., of each element in the array. Several approaches to synthesizing the optical light plane are presented and compared.

Translation insensitive (TI) heterodyne interferometers have the property that a wave-front may be sampled and compared (in phase) at two arbitrary points on a plane without requiring precision control on the reference feed paths to the heterodyne detectors. Several different principles may be employed, some of which exploit nonlinear phase conjugation. The wavefront may be extracted either from pupil planes or focal planes with appropriate changes in the instrumentation.

A wavefront control concept has been developed for piston phase matching of an array of subaperture telescopes such as might be used as a pointer for laser power transmission or for an astronomical telescope. Deep within the optical system, an absolute distance inter-ferometer injects a diagnostic beam into the main beam train. The diagnostic beam is divided into smaller beams which propagate through the subaperture beam trains and exit out of the subaperture telescopes. A metering rod is placed so as to bridge the outgoing diagnostic beams from adjacent subaperture telescopes. If a series of small retro-reflecting corner cubes are attached to the metering rod, these retro-reflectors will return these wavefront samples back through the beam train to the absolute distance interferometer where the samples from one subaperture are compared indirectly to those from the adjacent subaperture through a common reference beam. The absolute distance interferometer is a two wavelength digital heterodyne interferometer. The absolute distance interferometer measures absolute phase, thus establishing the absolute optical path length (OPL) between the inter-ferometer and corner cubes. Differences in beam path are then adjusted to any required zero or non-zero value by optical trombones and an adaptive mirror incorporated in the beam path. Testing for colinearity of the reference corner cubes on the metering rod eliminates errors due to metering rod misalignment.

With the general availability of extensive computer facilities, complex synthetic aperture array problems can be solved to an arbitrary degree of accuracy. Simple approximate models are useful for rapid first order evaluations, but their real value lies in the physical insight which they provide. For illustrative purposes only, the synthetic aperture is treated as a transmitter, directing an optical beam to a remote target. The synthetic optical aperture concept is illustrated in figure 1. Two or more telescopes are pointed at, and focused on, the same remote target. Each individual elementary telescope produces a small section of a spherical wave which converges on the target. The effectiveness of the synthetic aperture is determined by how complete and how perfect is that converging spherical wave.

For the special case of monolithic ranging telescopes, a family of characteristic design curves for various system performance requirements is discussed. The required secondary mirror displacement and the tolerance on this position, as well as the corresponding depth of field for any desTd range can be readily obtained from this normalized family of curves. The hyperfocal distance (closest range within depth of field when infinite range is also in focus) is also displayed on this set of curves and can be used to determine when it is necessary to activate ranging. The degradation in system performance is then plotted vs. range, and the closest effective range is determined. This range is a strong function of telescope diameter and is crucial to certain ranging telescope applications. This degradation in system performance is then determined for various properly phased synthetic aperture systems (multiple mirror telescopes) and compared to the monolithic telescope of equivalent aperture. For certain applications these results provide a strong motivation for going to synthetic aperture telescopes based upon optical performance alone.

The performance of a synthetic aperture array consisting of N identical multiline transmitter apertures is presented using the far-field integrated irradiance as a performance index. Results are presented of the variation of these indices with subaperture separation, number of subapertures, random piston errors and those resulting from pointing of the synthetic aperture for single and multiline transmitters. A brief discussion of the pathlength control requirements generated by this performance analysis will then be given along with a novel multiline focal plane phase retrieval algorithm.

A computer model is described that can generate the Point Spread Function (PSF) for a multiaperture optical system. The model basically does a Fourier transform of the multipupil wavefront to propagate the wave front to the far field. In our model the PSF is synthesized in the far field by squaring the net complex field resulting from the individual relative phase shifts. The wavefront for each subaperture can be expanded in terms of Zernike polynomials. Arbitrary amounts of aberration can be assigned to each individual array telescope. Using the program we did a Monte-Carlo wavefront error analysis that demonstrated general correspondence between RMS wavefront error and encircled energy. The effects of piston on beam steering and shaping are presented.

Relative wavefront phasing errors between the beam trains that make up a synthetic aperture beam expander can be estimated from the far-field interference patterns produced by samples of wavefronts propagated through adjacent beam trains. Wavefront sensor and estimation algorithms are presented, and the effect of noise and higher-order errors on performance is described.

This paper describes an experiment, currently in progress at the Air Force Weapons Laboratory, on the testing of telescope systems using multiple subapertures for the auto-collimating optics. This method of optical testing is being considered as a cost-effective means for testing large aperture telescope systems of the future. While much progress has been made in finding analytical techniques for reconstructing the full-aperture wavefront from the subaperture data, no experiment has been performed to verify these analytical techniques. Several theoretical aspects of subaperture testing are described with the help of the Thunen-Kwon analytical technique and a covariance matrix calculation. Among these aspects are the contribution of each full-aperture Zernike polynomial to subaperture tilt, and the difficulty in detecting certain Zernike aberrations due to the symmetry of the subaperture configuration. No experimental results were available at the time of this writing, but the experiment plan is described. The aim of the experiment is to show that aberrations introduced into a wavefront by an optical system may be correctly retrieved using subaperture testing.

Subaperture testing provides an attractive alternative to large monolithic test optics for evaluation of large optical systems. In this paper, we present a method for reducing subaperture testing data that requires no a priori knowledge of the relative piston and tilt of the subapertures. Results of applying this method to analyze subaperture testing interferograms are presented. In particular, the behavior of this method in the presence of data noise is studied.

We addressed the question of whether half aperture data could be used for testing a large active segmented primary mirror. Our study indicates that modal control with Zernike coefficients will be difficult, whereas modal control with Gram-Schmidt coefficients may be practicable.

The Research and Development Laboratory at BDM Albuquerque, in cooperation with and for the Air Force Weapons Laboratory has designed and developed an optical phase measurement instrument capable of providing a phase error signal with a resolution of 3 nm at an update rate of 1 kHz. This phase error measurement of better than 1/160th of a wave detects the optical path difference (OPD) between two laser beams operating in the 0.5 micron region. The error measurement is used to translate mirrors which adjust the OPD to maintain phase coherence between the beams. By using several mirrors, each corrected to a reference, a large aperture can be synthesized. The 1 kHz update rate provides a high speed control signal for closing the mirror control loop. The design is part of a proof-of-concept program which will identify the feasibility of using feedback control techniques to simulate a large optical aperture with multiple small apertures.

A concept is described for phasing the outputs of a multiple telescope array used as a laser transmitter. The technique uses samples of the transmitted beams to control optical path lengths through the separate telescopes so that the beams add coherently at the receiver. The phasing concept is applicable both to systems which provide inputs to the multiple telescopes by dividing a single laser beam and to systems in which the inputs to the telescopes and multiple, phase-locked laser beams. The approach is also compatible with single line and multi-line lasers, and it does not entail stringent alignment requirements. The concept uses a three step procedure to find the zero optical path difference condition and to effect fine control of the optical path lengths through the different telescopes. Algorithms are described for estimating the phase mismatch from focal plane measurements. The technique is susceptible to errors induced by local aberrations within the individual telescopes. The errors and one possible solution, the use of redundant measurements, are discussed. Performance requirements for a phased array laser transmitter are described.

In the course of the design of a laboratory proof-of-concept demonstration of a synthetic aperture optical telescope array for a multi-wavelength laser transmitter, a number of design considerations have become apparent which will be important in full-scale systems and other synthetic aperture experiments. These considerations, discussed here, include polarization effects, beam rotation, packaging, lateral beam translation due to OPD adjustment, matching of transmissive components, and mechanical and thermal stability. An approach is given for dealing with each potential problem discussed.

The concept for a phased array laser transmitter described in Reference 1 interferes samples of the transmitted beams from adjacent telescopes to determine the relative phase of the two beams from which the samples are taken. This information is then used to con-trol optical path length adjusters to keep all of the beams in phase so that they will add constructively in the far field. A laboratory breadboard phased array transmitter utilizing this approach is currently being assembled and tested at the Air Force Weapons Laboratory. This breadboard is described in Reference 2. A study was performed in support of this experiment to formulate and assess various algorithms for estimating the phase mismatch of two laser beams from measurements of the irradiance pattern created by inter-fering samples of the beams. The results of that study are described here.

We summarize the experiments which have used the Multiple Mirror Telescope (MMT) subapertures as a phased array in the optical, infrared, and submillimeter spectrum regions. Those experiments exploit the unique, very high angular resolution of the MMT being equivalent to that of a conventional telescope 686 cm in diameter. The operation of the MMT as a phased array is not only important for obtaining high angular resolution but also for obtaining the higher detection sensitivity which results from the better discrimination against the sky emission background for infrared diffraction limited images. We describe future plans to make the MMT into a phased telescope.

The first physical demonstration of the principle of image reconstruction using a set of images from a diffraction-blurred elongated aperture is reported. This is an optical validation of previous theoretical and numerical simulations of the COSMIC telescope array (coherent optical system of modular imaging collectors). The present experiment utilizes 17 diffraction blurred exposures of a laboratory light source, as imaged by a lens covered by a narrow-slit aperture; the aperture is rotated 10 degrees between each exposure. The images are recorded in digitized form by a CCD camera, Fourier transformed, numerically filtered, and added; the sum is then filtered and inverse Fourier transformed to form the final image. The image reconstruction process is found to be stable with respect to uncertainties in values of all physical parameters such as effective wavelength, rotation angle, pointing jitter, and aperture shape. Future experiments will explore the effects of low counting rates, autoguiding on the image, various aperture configurations, and separated optics.

Recently a concept has emerged which may significantly change large scale laser beam expander technology. The phased array synthetic aperture beam expander concept seeks to create a large synthetic aperture by phasing and aligning several smaller subaperture telescopes. This concept may offer enormous advantages in the cost and feasibility of optics fabrication, and on a system level provides greater modularity, as well as a more compact and optomechanically stable structure. Along with these advantages come scientific and technical issues regarding system feasibility, control, and comparative performance. The Air Force PHASAR experiment will answer many questions about the application of this beam expander concept. Any application of a PASABE system may utilize the far-field intensity pattern as a measure of effective system performance, as it is a quantitative measure of the way in which energy is delivered to the reciever or target. By incorporating important aspects of system operation, such as subaperture misalignment into a far-field propagation simulation we may learn a great deal about the performance of a system under various conditions. In order to support the design and testing of the Air Force PHASAR, a specialized propagation code called OPALS was developed to simulate far-field performance of multiaperture bex systems. The purpose of this paper is to present a perspective on the objectives, constraints and methods used in developing such a simu-lation.

The concept of coupled resonator beam combining is introduced via laboratory experiments and a model based on the coupled laser theory of Spencer and Lamb. In the laboratory experiments a pair of half-symmetric CO₂ unstable resonators were coupled to provide a pair of mutually coherent output beams. The coupling was introduced in the symmetry plane of the resonators with either beamsplitters or hole couplers. The beamsplitter coupling configurations were used to experimentally verify the stability region of the coupled lasers, predicted by the Spencer-Lamb model, as a function of the coupling coefficient. The corresponding behavior was then investigated for the hole coupled lasers with hole size and position as parameters.

The instrument described here is fundamentally a stellar interferometer employing fiber optic links to combine very high resolution with high sensitivity. In a typical (Michelson's) stellar interferometer, outriggers and mirrors are attached to an astronomical telescope so that objects with small angular subtense (binary stars, star diameters) can he observed by each of two mirrors separated by an adjustable distance. The spacing of the resulting interference pattern depends on the angle between the two incident beams, and the visibility or contrast of the frinse pattern depends on the separation of the mirrors and the angular subtense of the astronomical object.(1) Binary stars with a subtense a observed at a mean wavelength A show a steadily decreasing visibility with increasing mirror separation until the separation s is s = λ/2a (1) where the visibility is zero. These conventional stellar instruments have a number of shortcomings. (a) The mechanical structure required to support the outriggers, etc. is interferometrically unstable resulting in random changes in the fringe pattern which increase the difficulty of quantitatively assessing fringe visibility. This instability limits the practical size of the interferometer to less than 10 meters. (h) A large telescope is required, even though its full aperture is not utilized. (c) The relatively small amount of light collected by the outrigger mirrors is spread over a relatively large number of fringes, and is thus wasteful of light. (d) Turbulence with frequency components higher than the eye can temporally resolve causes rapid fringe motions which impair the observer's ability to estimate fringe contrast. Other stellar instruments or measurement techniques, such as intensity interferometry(2) and speckle interferometry(3), avoid some of these problems but require bright sources. The instrument described here avoids these problems and collects substantially larger quantities of light, permitting much fainter objects to he measured. The experimental measurements described here demonstrate the feasibility of the instrument.

This paper describes preliminary results from an on-going PHASAR experiment at the Air Force Weapons Laboratory. The implementation of two phasing algorithms is discussed, one algorithm is for measuring the optical path difference to better than λ/100 but cyclical every λ. The second algorithm is used in a global search to find the zero fringe within λ/2. The second algorithm requires multiline sources, the first works with single or multiline sources. Optical and electrical configurations are discussed and experimental results are presented.