Optical processor for the very large array (VLA) radiotelescope: system concept

Optical Fourier transform processing of radiotelescope visibility function data is reviewed. Emphasis is placed on the aspects of the processor design that arise from the unusual characteristics of the data. The complex visibility function is available only over a partially filled aperture consisting of a set of elliptical paths. It is recorded at the input to the optical processor on a carrier frequency as a real nonnegative transmittance. Since a bipolar sky brightness function output is to be computed, the output of the optical Fourier transform channel is mixed with a reference beam and the difference is taken of two successive measurements differing in reference phase by 1800. Experimental results demonstrating processor concepts are shown and a processor system design approach is described. Introduction Basic to radio astronomy is the determination of the distribution of radiated power from celestial sources with the radiotelescope. This power distribution or sky brightness, B, is a measure of the power per unit solid angle for the temporal frequency band under observation. The sky brightness data obtained serves a primary role in the scientific research on the physics of celestial bodies. Over the past few decades, radiotelescopes have evolved from radio receivers of modest performance having simple antennas of limited angular resolution to present day receivers of high sensitivity and stability, with fine angular resolution obtained by synthetic aperture antenna concepts. These systems utilize a ground -based large array antenna with array elements operated as interferometer pairs. As the antenna array moves, due to earth's rotation, an extensive received signal history is collected from which a high resolution receiving aperture is synthesized. As an example, the very large array radiotelescope (VLA) currently under development near Soccorro, New Mexico, by the National Radio Astronomy Observatory (NRAO) employs the aperture synthesis concept. This VLA will make use of up to 27 ground -based antenna elements; each element being a steerable 25 meter diameter parabolic dish located along the arms of a wyeshaped array pattern. Four basic array arrangements (A, B, C, D) are planned which are denoted according to a ground distance over which the array elements are spread. This system provides as its output a signal history called the visibility function V. It is related to the desired measure of the sky brightness function B through the Fourier transform. Thus, Fourier transform processing of the radiotelescope output V allows recovery of a measured version of B. We will describe a design concept for an optical Fourier transform processor system for radiotelescope visibility function data, starting first with a review of sky brightness image and visibility function properties and then going on to a processor configuration and supporting experimental data. Sky brightness The sky brightness1t2 can be taken as a two -dimensional spatial distribution B(x, y) for the purposes of this discussion. The x and y variables define orthogonal position coordinates relative to a fixed reference direction within the field of observation of the radiotelescope. B(x, y) has physical units of power per unit area and per unit solid angle for the location (x, y). It is a real valued function and its spatial variation encompasses point -like (stars) as well as highly dispersed distributions. The magnitude of the brightness function must be generated with an accuracy of one per cent of its peak value or better. An example of sky brightness map data is shown in Figure 1. L.E. Somers is with the Lawrence Livermore Laboratory, Livermore, California 94550. 38 / SPIE Vol. 231 1980 International Optical Computing Conference (1980) l l ) i t l sc e: t i , . R. Fien , L. E r nd ptics ivision, ir ntal earch Instit t f . . Box 8618, Ann Arbor, ichigan 4 str t al ier m is f l d y o a se of elliptical paths. t e al al er l n e ° ts ing r s f al o s bri B, ure f e r r e y ss s, o ance ing e s r h ivity d lity, utili a ground based ant with array p t ion, n sive d l y i sy le, r orro, w ico, l u of up to 27 ground e ts; h nt ng r r a wye-shaped r ( C ch e ed ing e . s m des s l ed o e ed e ss , V r y B s r telescope ibility ion ta, ing t h e ity tness^-» b ta as a two-dimensional tial , di e d les e s ive o d e n , f (x, t s l d n l -like (stars) as wel as highly ed s ion st e ed cy m da is show in Figure 1. * .E. "Sb~me ry, , S / ol. n e n ion O t c C put ng f ) Downloaded From: http://spiedigitallibrary.org/ on 11/25/2015 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx OPTICAL PROCESSOR FOR THE VERY LARGE ARRAY (VLA) RADIOTELESCOPE: SYSTEM CONCEPT Visibility function The measured visibility function V, available at the radiotelescope system output, is a composite of signals associated with the antenna array elements. We will discuss some of the salient properties of V pertinent to its processing. The derivation of V is described in the literaturel'2. The NRAO /Soccorro system concept will be used as a basis for our discussion. Each signal of the visibility function composite is derived from correlation processing of the reception from selected pairs of antennas of the 27 element array. Correlation is performed over a succession of short time intervals thus causing V to be a sampled function. Signals from 351 antenna pairs, i.e., n(n 1)/2 for n = 27, which are derived simultaneously in parallel channels of the radiotelescope system constitute V. The time history of V corresponds to the movement of the antenna array due to the earth's rotation. Typically during the observation interval over which the visibility function is being collected, data is accumulated in buffer storage. It is then read out' of buffer storage over a short time interval for Fourier transform processing to generate the sky brightness map B. The broad temporal bandwidth of the radiotelescope can be divided into as many as 256 individual narrow spectral bands or lines with a visibility function generated for each line. Fewer bands of broader bandwidth, about eight, may also be generated and are referred to as the continuum case. In the following, the description of the visibility function processing applies to each individual spectral line. Each spectral line is processed separately. As will be explained in greater detail below, the visibility function may be considered as a time varying signal or as a spatially varying signal defined in a (u, v) spatial domain. A simulated example of the elliptical paths on which V(u, v) is measured is shown in Figure 2 where each individual signal, of the total composite of 351 signals which make up V, occurs along one of the curved paths shown. The ratio of the maximum value to the minimum value (noise) of the magnitude of V will be about 10:1 for about two -thirds of the spectral line visibility functions expected. Normally the remaining third of the expected visibility functions will have a ratio of about 100:1. The space -bandwidth product of V for the A -array over a viewing field extending to the -3 dB width of the beam pattern for an individual array element is 3000 in each of its two dimensions. The time domain representation of the visibility function will be written as 351 V(tn) _ Vk(tn) k=1 (1) where k identifies an antenna element pair of a particular baseline (separation) length and to the n -th discrete sample of the continuous succession of equally spaced samples in each Vk More appropriate to the Fourier transform processing to be performed on V is the spatial domain representation of the visibility function, V(u, v), which we can write as 351 V(un, vn) _ Vk(un, vn) k=1 (2) The variables u, v have the form of a distance normalized by the operating wavelength of the radiotelescope. More specifically, the radiotelescope spatial domain related to u and v is a plane that is normal to the reference pointing direction of the radiotelescope. Defining orthogonal coordinate unit vectors u and v in this plane, we have u as the normalized component of an antenna baseline in the u direction, and similarly for v. As noted previously, the signal history of the visibility function in the spatial domain falls along a set of elliptical paths (or tracks), one path for each of the 351 baselines (antenna pairs). These u, v plane paths are well defined in terms of the earth's rotational angle (hour angle h), the declination angle of the reference pointing direction of the radiotelescope (s), the latitude angle of the antenna site location (2), and the east west and south -north component lengths of the antenna baseline at the earth's surface (BEW and BSN). Operating wavelength is X. Path coordinates in the u, v plane are given by the following expressions. SPIE Vol. 231 1980 International Optical Computing Conference (1980) / 39 R E Y E R I E: f e ed ty , e ut, wi th ante array element s o to it proce ^ > 2 . /Soc or o system concept will e d f fr sele pair of antennas of the 27 element a ray. f a pa i. n(n l)/2 a i chan of the radiotelescope system constitute V. e y d, i a in buff stora rea ou * i fo Four transform processing to generate the sky m B y lin h, , ca g, o th vi a to eac individu spectral line. l ll ed l w, y d g u, ) d , e l, , s p sh e o e e) l two-thirds f e l function expected. lly e ing d ty s -bandwidth f th A-array fie exten g e 3 h al h