II High-Resolution Techniques in Optical Astronomy

E. WOLF, PROGRESS IN OPTICS XIV 0 NORTH-HOLLAND 1976

I1 HIGH-RESOLUTION TECHNIQUES IN OPTICAL ASTRONOMY BY

A. LABEYRIE Observatoire de Paris, 92190 Meudon, France

CONTENTS PAGE

Q 0. INTRODUCTION . . . . . . . . . . . . . . . . . . .

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Q 1. ATMOSPHERIC OPTICS .

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Q 2 . DIRECT INTERFEROMETRY . . . . . . . . . . . . .

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Q 3 . INTERFEROMETER DESIGNS AND RESULTS . . . . .

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Q 4 . THE IMAGE RECONSTRUCTION PROBLEM . . . . . .

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5 5. CONSTRUCTION OF A SYNTHETIC-APERTURE ARRAY OF OPTICAL TELESCOPES. . . . . . . . . .

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Q 6. INTENSITY INTERFEROMETRY . . . . . . . . . . .

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Q 7 . HETERODYNE INTERFEROMETRY . . . . . . . . . .

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Q 8. CONCLUSIONS . . . . . . . . . . . . . . . . . . . .

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REFERENCES . . . . . . . . . . . . . . . . . . . . . . .

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0. Introduction

0.1. INTRODUCTION

Continued progress in the art of building optical instruments has resulted at about the time of Newton, Herschel and Foucault, in telescopes having better optical quality than the atmosphere. From then on, the subsequent evolution which led to today’s giant telescopes failed to further improve the resolving power of optical observations through the atmosphere. A few obstinate physicists however succeeded in showing that the atmospheric degradation of images can be avoided to some degree by using special observing techniques. Used to observe a few favorably bright stars, these techniques have indeed demonstrated principles which can yield high resolution information beyond the normal atmospheric cut-off. The techniques utilize approaches known as stellar interferometry, intensity interferometry and lunar occultation. The state of the art in these fields has been reviewed by Hanbury Brown in 1968. The present review is more specifically concerned with the more recent developments of stellar interferometry, and the corresponding instruments, generally referred to as coherent synthetic-aperture systems. Pioneering work by A. A. Michelson established the feasibility of large resolution gains, but lack of a mature technology long prevented followers from even repeating Michelson’s observations. Only very recently did the progress of sensors and electronics allow improvements to the original Michelson interferometer. In the last few years, the progress of coherent optics allowed a better understanding of the speckle phenomenon in stellar images, which in turn triggered spectacular developments in both post- and pre-detection image processing methods. The operation of two independent telescopes as a Michelson interferometer, achieved a few months before this review was concluded, indicates that the technology is now ready for operating large arrays of telescopes as optical synthetic apertures. As already experienced at radio wavelengths, telescope arrays are likely to improve enormously the resolution and the luminosity of observations. Their operation from ground-based sites will help designing similar systems for space use. 49

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0.2. HISTORY

The history of attempts to penetrate the turbulent atmosphere dates back to 1868, when Fizeau proposed to observe Young’s fringes in stellar images. Following initial attempts by Stephan, this suggestion was brillantly developed by Michelson using aperture masks on the Yerkes refractor and the 100-inch Hooke reflector. Later,Michelson, Pease and Hale built successively two models of a synthetic aperture system having respectively 20 and 50 feet span, and in which the observer’s eye served as the sensor. Each system involved a pair of small apertures supported by a single steel structure, designed to be as rigid as possible while being mobile around the polar axis of an equatorial mount. After the equality of optical paths had been carefully adjusted, fringes could be observed in stellar images. As we shall see, the phase shifts introduced by the atmosphere induced fast displacements of the fringes, which decreased their apparent contrast. Nevertheless, fringe contrast measurements were possible and these gave apparent stellar diameters for several bright red stars. The observations were difficult and time-consuming, as can be realized from the fact that none has ever succeeded in repeating these experiments. Pease’s measurements of stellar diameters were however confirmed recently by different methods benefiting from the large aperture of the 5-meter Hale telescope, and thus easier to implement. The level of activity in this field dropped near zero between 1930 and 1958. In 1958, Hanbury Brown and Twiss proposed the intensity interferometer method as an alternate approach intended to avoid the problems arising with direct interferometry. In spite of the method’s inherently low sensitivity, the patient work of Hanbury Brown and Davis at Narrabri (Australia) resulted in a major resolution breakthrough. The angular diameters of the 32 brightest southern stars were measured, with resolution of the order of a millisecond of arc. In the meanwhile, interferometric observing techniques underwent considerable development at radio wavelengths. The synthetic-aperture arrays of radio telescopes built in this period by Ryle and his collaborators began to surpass the traditional one-second limit of resolution with optical telescopes, and quickly achieved arc-second, as different groups began to use heterodyning techniques with antennas spaced thousands of kilometers apart. Interest in the direct synthetic-aperture approach at optical wavelengths revived in the year 1965, presumably in relation with the general progress of coherent optics and laboratory interferometry which the invention of lasers has triggered. Summer schools held at Wood’s Hole in 1966 and

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1967, followed by a symposium at Tucson in 1970, stimulated interest in long-baseline interferometers such as proposed by MILLER[19661. A belief emerged that modern technology could solve the problems encountered by Michelson and Pease, and that coherent arrays of telescopes could be operated at optical as well as at radio wavelengths. Several groups, particularly in the USA, USSR and France, began to tackle these problems, investigating in particular the use of artificial sensors to replace the human eye. In 1970, speckle interferometry established a generalized form of Fizeau interferometry, which utilizes the full aperture of large telescopes. Used at the 200-inch Hale telescope by GEZARI, LABEYRIE and STACHNIK [1972], the method provided a confirmation of Pease’s measurements as well as additional hints on color-dependance and limb-darkening effects relating to the two largest apparent stellar disks, Betelgeuse and Mira Ceti. The method also provided diffraction-limited measurements on a dozen binary stars, unresolvable by conventional techniques. Following these initial results, progress in the technology of sensors, and particularly the development of photon-counting television by BOKSENBERG [19721, resulted in considerable gains in both the sensitivity and the accuracy of data reduction. At this point a number of articles discussed further possibilities for improvements, particularly in the direction of image reconstruction. Computer simulations as well as laboratory experiments produced particularly encouraging results in relation with the approach known as “rubber telescope imaging”. In this approach, atmospheric disturbances are actively corrected by servo devices requiring a bright star in the observed field. In the meanwhile, work continued in the direction of long-baseline systems. Preliminary designs were made by MILLER [1966] for a 100-meter interferometer, while the present author attempted to produce interference with two telescopes. The latter project reached its goal in the recent months. It is now undertaken to build a coherent array of telescopes.

0 1. Atmospheric Optics 1 . 1 . THE ATMOSPHERIC HETEROGENEITY

The turbulent behaviour of the atmosphere has been extensively studied in the recent years. Chernov, Tatarsky, LEEand HARP[1969], LAWRENCE and STROHBEHN [19701 and others developped the theory of wave propagation in turbulent air, while HUFNAGEL and STANLEY [1964], FRIED[1966],

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KORFT, DRYDEN and MILLER[1972] studied the corresponding effects on images. Experimental measurements of scintillation phenomena were made by YOUNG[1969], MIKESELL [1955] and PROTHEROE [1961]. Phase effects were observed by RODDIER and RODDIER [1973] and VERNINand RODDIER [19731. A variety of mechanisms occurring in clear air account for the disturbances which affect optical waves propagating horizontally or vertically. This review is mainly concerned with vertical propagation, and the relevant body of knowledge may be briefly summarized as follows : Air at a uniform pressure and temperature is in principle an excellent optical medium. Apart from the microscopic fluctuations responsible for Rayleigh scattering, the Brownian motion alone introduces negligible wide-scale phase fluctuations on optical waves. However, temperature is not uniform in the atmosphere, and its fluctuations produce optical phase fluctuations on propagating waves, in response to the local variations of the temperature-sensitive refractive index. This temperature effect is predominant at optical wavelengths, but other causes such as humidity or partial pressure fluctuations may contribute at other wavelengths, such as in the infra-red. The temperature fluctuations are caused by a variety of turbulence mechanisms, depending on wheather conditions and terrain topography. Among these are thermal convection, interface turbulence between layers at different temperatures, wind shear turbulence, wake turbulence (downwind from certain”mountain peaks), etc.. As reviewed by LUMLEY and PANOVSKY [1964], the theory of turbulence evolved by fluid dynamics since the 1950’s ascribes a power law to the spatial power spectrum of density fluctuations. The exponent value generally accepted is that obtained theoretically by Kolmogoroff, namely - 11/3. The scale size for turbules ranges between an “inner scale” amounting to a millimeter or so in air at sea level, and an “outer scale” on the order of 10 to 100 meters at sea level. Reasonable agreement exists between theoretical results and experimental measurements, although certain points remain to be clarified. The turbulence parameters which are most significant with respect to optical effects are : 1. the size and the size distribution of turbulence cells; 2. the RMS density fluctuation, integrated along the line of sight; 3. the altitude of turbulent layers; 4. the apparent lifetime of turbules along a given line of sight. In the presence of winds, this lifetime differs from the intrinsic lifetime, since turbules are carried across the line-of-sight by the wind. Concerning the spatial distribution of turbulence cells, these are usually

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organized in random isotropic fashion. However, they sometimes take the form of waves resembling those on water surfaces, and similarly generated by gravity oscillations at the interface between atmospheric layers having different densities (GAVIOLA [19491). The temporal frequency spectrum of atmospheric turbulence is of particular concern to interferometric observers. This is largely governed by wind speeds at ground and altitude levels. Lifetimes vary between 1 and second, depending on wheather conditions. 1.2. WAVE DEFORMATIONS A N D SHADOW PATTERNS

The optical wave received at ground level from a point source located above the atmosphere has both phase and amplitude perturbations. The amplitude fluctuation pattern, also referred to as the shadow pattern, is responsible for the well known twinkling of stars. Because absorption cannot account for the effect, it is generally interpreted as resulting from the action of high-altitude turbulent layers according to elementary stioscopic or Scblieren effects. Both geometric ray deflection and interference may contribute in this effect. A simple method for viewing the high-altitude turbulent layers responsible for the shadow pattern was used extensively by BOYER[unpublished] for wind monitoring purposes. It consists in observing the lunar limb with a small, amateur-type telescope. By defocusing slightly the eyepiece outward, it is possible to focus on the turbulent layers and to see the flowing stream of turbules, their invisible phase pattern being translated into an amplitude pattern by a Schlieren effect. The altitude, velocity and direction of the turbulent flow may thus be determined. More elaborate methods involving large mirrors and shadow pattern correlations have recently been developped by Roddier and his collaborators (MARTIN,BORGNINO and RODDIER [1975]). Phase corrugations on the wave are generated by turbulence at all altitudes, but with increased efficiency at decreasing altitudes. The low-altitude phase cells are observed easily on the aperture of large telescopes when conducting knife-edge tests. In addition to the steady cell flow outside of the dome, a stationary turbulence component occurring inside the dome is also generally observed. RMS values for the fast phase fluctuation have been estimated to vary in the range from 1 to 20 radians. Available data do not cover the long-wave components of phase corrugations. 1.3. THE SPECKLED STRUCTURE OF IMAGES

On good observing nights, small telescopes in the 2 to 10 cm range of

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aperture sizes are smaller than seeing cells. Thus the phase is nearly uniform over their aperture. Consequently, these telescopes are nearly diffraction limited, and star images have the appearance of the classical Airy disk. Considering now the other extreme case of very large instruments, their aperture may cover several thousand seeing cells, having random phases. The Airy-disk pattern is completely destroyed under such conditions ; and classical diffraction experiments, in accordance with elementary Fourier transform analysis, show that the angular spread of the image is of the order of Ajd, d being the characteristic size of seeing cells. 12-cm cells thus correspond to one arc-second as the approximate width of the image projected onto the sky plane; and this figure is rather typical of average observing conditions with large instruments in the best observatory sites. Only very exceptionally are seeing cells larger than 24 cm; and this explains why larger instruments do not benefit from their theoretical resolution performance. Some astronomers, especially binary star observers, have long remarked on the existence of a fast-moving fine structure inside the typical one-second image (Fig. 1). Recently (LABEYRIE [1970]), this structure has been interpreted as a speckle phenomenon, same as the well known effect in diffused laser beams, and this identification led to the interferometric method called “speckle interferometry” (sect. 3.3). As is apparent in the recent review of DAINTY [1976], the speckle phenomenon has been extensively studied in the recent years. In the astronomical case, it results from the fact that any point inside the star image indeed receives coherent contribu-

L

(a)

(b)

Fig. 1. The corrugated optical wave and corresponding image; (a) the full aperture of a large telescope produces a speckled spread function; (b) a Fizeau mask with two small apertures produces Young’s fringes in the image.

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tions from many of the phase cells in the aperture plane. The resulting amplitude at the image point considered is thus a sum of many vibrations with random phases. Summing vibrations with random phases has been a classical problem since Rayleigh: the squared modulus of the sum may have any value between 0 and IZaI2,a being the amplitude of the individual vibrations. In the image plane, the particular value found in the summing process depends on the image point considered since individual vibration phases vary when the point is displaced in the image plane by more than l/a,a being the angular aperture. The scale size for intensity variations in the image plane is thus l/u.As discussed by GOODMAN [1965], in the case of laser speckles, and by KORFF,DRYDEN and MILLER[1972], in the astronomical case, the addition of coherent, but randomly phased, vibrations corresponds to a two-dimensional random walk in the complex plane if component vibrations are represented by vectors in this plane. The sum vector is distributed according to a Gaussian law, and the ampli-

Fig. 2. Speckled images of a non-resolved star (Vega) obtained simultaneously in different colors at the 200-inch telescope. Colors (and spectral bandwidths) are, going clockwise from top left : red (500 A), yellow (250 A), green (250 A) and blue (250 A). Residual atmospheric dispersion is apparent in the blue image. Exposure time is 0.01 second.

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tude A has a Rayleigh distribution of the form ,,/%exp(-A/z2). The distribution of intensities I is exponential e-'/z2. This result is independant of the model assumed for seeing cells, provided random phase variations are present. Indeed, the appearance and the 2"d order statistical properties of laser speckle do not depend on the type of scatterer used. Different scatterers, or qualities of seeing in the stellar case, change only the size of the image envelope, without affecting the statistics of the fine speckle pattern within it. This important property simplifies appreciably simulation experiments carried out in the laboratory or on computers, since real atmospheric seeing does not have to be exactly reproduced. The analysis applies also regardless of aperture shape, and in particular to segmented or multiple apertures such as may be encountered in syntheticaperture systems (§ 2 and Q 4). The shape of speckles however depends on the aperture geometry: the aperture stop may be represented by a multi-

Fig. 3. Synthetic aperture systems and corresponding spread functions : top row - apertures consisting of 1, 2 and 6 telescopes, as well as giant monolithic aperture; middle row - corresponding spread functions, in the absence of atmosphere and optical aberrations; bottom row short-exposure, monochromatic, spread-functions in the presence of the atmosphere. This is a laboratory simulation result obtained by photographing a monochromatic point source (a laser-illuminated pinhole) through a mild diffuser and aperture mask. The conditions simulated correspond to 1.5 'meter telescopes and typical 1 sec. seeing.

n, §

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plicative term applied to the infinite incident wave, and the speckles in the image plane are thus convolved, in complex amplitudes, with the diffractionlimited spread function. Speckled images recorded at the Palomar 200-inch telescope are reproduced in Fig. 2. The laboratory equivalent of syntheticaperture systems involving several large telescopes produces the speckled images in Fig. 3. These images were obtained as photographs of a monochromatic point source, using a multi-aperture diaphragm and a mild diffuser in front of the camera lens. Compared to the speckles from the monolithic aperture, these contain an additional finer interference structure which takes the form of fringes with two apertures, of a honeycomb pattern with 3 apertures, etc.. The number of speckles contained within the image envelope increases with aperture size D as (D/dj2.When dealing with low-altitude seeing, no ensemble translation of speckles occurs in the image even when seeing cells are carried as a rigid pattern by the wind flow. Instead, speckles appear and disappear locally much like vapor bubbles at the surface of boiling water. It is apparent from the video images recorded at Palomar that the lifetime of speckles increases at increasing wavelengths, from near ultra-violet to near infra-red. In small telescopes, few seeing cells are present across the aperture at any instant, which results in few speckles in the images. Consistently with simple statistics, experience shows that such images are subject to rapid wander and size fluctuations. In such cases, image selection or exposure triggering techniques such as used by RATT [1957], may improve markedly the image sharpness. Telescopes up to a meter in aperture diameter may thus produce nearly diffraction-limited images durilig a few milliseconds every hour or so. Using short-exposure electronographic photographs of binary stars, R ~ S C HWLERICK , and BOUSSUGI~ [1961] have shown that the instantaneous speckle patterns are identical for closely spaced pairs but different in the case of widely spaced pairs. The angular extent over which speckle is invariant, called the isoplanatic patch, is on the order of 3 to 10 arc-seconds. Patch size .is mainly dependant upon the presence of turbulent layers at high altitudes, since these layers are crossed in different regions by the light beams coming from different stars into the telescope. Temporal and spatial coherence have both been assumed in the above analysis. The size d of speckles being proportional to wavelength, some degree of monochromaticity is indeed required for purity of the pattern. If atmospheric and telescopic aberrations are smaller than the wavelength 2, the requirement may be written I/d2 > D/d. In white light, at the 200-inch telescope, the image of a star close to zenith shows contrasted speckles

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at the center of the typical one-second envelope. The few central speckles are surrounded by radially-oriented coloured streaks generated by the chromatic spreading of speckles at higher interference orders. This is well observable visually in conditions of moderate wind speed, using a strong eyepiece. It takes a filter with 200 fingstrom or narrower bandpass to observe pure speckles all the way to the edge of a one-second image. When pointing at a star lower toward the horizon, dispersion tends to elongate the speckles and it takes a much narrower filter to remove this effect unless some form of prismatic compensation is used. The experimentally-observed proportionality of speckle size to wavelength supports the diffractioninterference interpretation of the speckle phenomenon, as opposed to the ray-deflection interpretation which had sometimes been proposed before the advent of lasers and speckle theory. The optical components of large astronomical telescopes are rarely made to the accuracy meeting the Rayleigh criterion. Residual coma, spherical aberration and astigmatism amounting to 0.5 arc-second are usually tolerated since the effect of the atmosphere is even worse. Such transverse aberrations, as long as they remain inferior to seeing effects, have no influence on the speckle patterns : somewhat paradoxically, bright speckles retain their similarity with Airy peaks in the presence of aberrations which would destroy the Airy peak if they acted alone. Realistic simulations of astronomical speckle phenomena may be carried out in the laboratory using a bright artificial star, a sheet of polyethylene or other diffusing material representing the atmosphere, a lens aperture to represent the telescope, and filters. In addition to laboratory simulations, a number of authors have used computers to derive image spread functions by Fourier-transforming random distributions of phase cells generated across some circular aperture. In all cases, the speckle patterns obtained resemble closely those obtained with large telescopes. 1.4. THE MTF FOR SHORT AND LONG EXPOSURES

The speckled or fringed structure in short-exposure images disappears when dealing with long exposures, due to the averaging of energy distributions in time-dependant speckle patterns. The short-exposure MTF, defined as the Fourier transform of the intensity distribution in the instantaneous spread function, has been studied experimentally (GEZARI, LABEYRIE and STACHNIK [19721) and theoretically (KORFF,DRYDEN,MILLER[1972], DAINTY [1973]). As shown in Fig. 4,it features a central peak and surrounding feet extending all the way to the diffraction-limited cut-off frequency.

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F

Fig. 4.Telescope-atmosphere MTF for alarge aperture : A, diffraction-limited MTF; B, single short exposure; C, long exposure; D, quadratic average from many short exposures.

It has been shown that the RMS profile, obtained by averaging the squared modulus of successive Fourier transforms, is identical to that for the diffraction-limited MTF except in the central region where a central peak is added. The long-exposure MTF, obtained as the simple time-average of the short exposure MTF, or equivalently as the Fourier transform of the long-exposure image, consists of the central peak only, the feet being cancelled in the averaging process. Rather than being Fourier transformed, the star image may be autocorrelated. The central peak appearing in the short-exposure case may be shown to be identical to what would be obtained under diffraction-limited conditions. It follows that the speckle pattern has certain similarities with a random array of diffraction-limited images, i.e. Airy peaks in the case of a circular aperture. Under certain conditions of oceanic storms where organized swell is replaced by random waves, sailors have learned to fear the sudden appearance of “monster waves”, much higher than average (ADLARD COLES[19671). Similarly, and because speckled electromagnetic fields are governed by the same Rayleigh statistics as gravity-induced oscillations at liquid surfaces, there is a rare occurrence of exceptionally bright speckles in astronomical images. These are not dangerous, fortunately, and may in fact be exploited for diffraction-limited imaging purposes. 2.1. BASIC PRINCIPLES

Q 2. Direct Interferometry

As discussed in section 1.4, the stellar images produced by large telescopes

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generally feature an envelope inside which a finer interference structure is present under adequate conditions of temporal coherence and of exposure. The angular size of the envelope is on the order of one to several seconds of arc depending on atmospheric conditions, while the scale size i for the smallest interference details is inversely related to the aperture size d according to the relation i = i / d . With existing large telescopes such as the 200-inch telescope, the interference structure is thus 50 times finer than the one-second image. Ordinary observing procedures ignore the interference structure and thereby do not take any advantage of its presence. Their angular resolution is therefore limited to about one or two seconds, although certain exposures have sometimes succeeded in showing 0.3 sec detail on bright objects such as the sun or planets (it has sometimes been attempted to improve the resolution of long-exposure images with deconvolution procedures, but the more or less Gaussian spread function in this case does not lend itself to significant resolution gains with the noise levels encountered in typical astronomical images). Interferometric observing, on the other hand, concentrates more on the fine interference structure than on the envelope. Indeed, this fine structure contains information on object structures having a comparatively fine scale, and which escape detection if one observes only the envelope. This results, according to widely accepted results of the theory of coherence, from the fact that the interference structure is a spread function which is convolved, in intensities, with the function representing the brightness distribution on the object. Indeed, different object points (within the isoplanatic patch) contribute ideptical patterns in the image. These patterns are translated in the image plane relative to each other in accordance with the source geometry. For ordinary sources (i.e. spatially incoherent sources, which have a coherence time shorter than the exposure time) these contributions add in energy, thereby reducing the contrast or visibility of the interference features according to a convolution operation. Unlike the Gaussian spread functions mentioned earlier, the more complicated interference structures lend themselves to successful deconvolutions down to the size of the finest interference detail, i.e. down to the diffraction limit. The spread function is, however, not completely known, being timedependant, and it is thus generally impossible to directly apply deconvolution procedures. Instead, it is possible to use power spectrum or autocorrelation analysis, but these techniques extract only part of the high resolution information. When dealing in particular with the simple and historically important case of a Fizeau-type apertured telescope, on which a mask reduces the

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aperture to a pair of small holes, the interference features consist of Young’s fringes (Fig. 1b). The fringes oscillate in response to atmospheric phase shifts, but remain detectable visually under most circumstances of moderate wind. Their contrast is, however, decreased in case of celestial objects larger than the fringe spacing projected onto the sky. The RMS fringe contrast, measured at different aperture separations, can be used to obtain a “visibility curve” which relates to the object’s structure through a Fourier transform. This is the type of analysis which was used successfully by MICHELSON and PEASE [1921] to obtain the first measurements of stellar diameters with baselines up to 15 meters. The response time of the human eye, on the order of 0.1 second, is sufficiently short under favorable circumstances to effectively freeze the fringe motion for efficient visual work. Optical paths in both beams must, however, be equalized to within a few wavelengths when observing in white light. This proved to be a difficult requirement in systems involving segmented rather than monolithic optics : not only are monolithic telescope mirrors very stiff and accurately figured to provide optical path equality, but they are efficiently supported in flotation cells designed to maintain the exact figure within a few wavelengths at all observing angles. In comparison, segmented optics systems such as used by MICHELSON and PEASE[1921] suffer from considerable flexibility requiring frequent readjustments of path equality. 2.2. VISIBILITY MODULUS DETERMINATION

It is of interest to establish in better detail the exact relationship between fringe contrast and object structure. In this section, light will for most purposes be assumed to be effectively monochromatic. More precisely this means that its coherence time is longer than the differential light propagation delays occurring in the interferometer, but shorter than the exposures. Spectral filtering with a bandwidth of the order of an Angstrom produces effectual monochromatic light in most practical circumstances where optical path differences are less than a millimeter and exposures are longer than a microsecond. Within the framework of Zernike’s coherence theory, the concept of degree of mutual coherence has classically been used to relate fringe visibility measurements and object structure (BORN and WOLF [1970]). As an alternate treatment we will use here an equivalent derivation more directly adapted to multiple and large apertures. If S(x,y,A, t ) is the intensity spread function in the focal plane of the instrument, then the intensity in the image Z(x,y , A, t ) of an incoherent object characterized by the apparent

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intensity distribution O(x,y ) is obtained through the convolution I = S 00. The spread function consists of Young’s fringes in the case of a FIZEAU [1868] or MICHELSON [1920] interferometer, of speckles in the case of a single large aperture, of fringed speckles in the case of two large apertures (Fig. 3), of “honeycombed” speckles with 3 large apertures located according to a triangular geometry, etc.. It has been mentioned in section 2.1 that direct image summing, i.e. of the form J t I ( x , y I, , t)dt, results in a loss of the high-resolution detail. Instead, the fringe or speckle information may be preserved and extracted by summing either the power spectra or the autocorrelation functions of images. This becomes apparent by writing the relations simultaneously in the image space and in the Fourier space:

The summed atmospheric term in eq. ( 3 ) tends towards the well defined limit mentioned in sect. 1.4. In the Fourier space, this limit consists of the diffraction limited MTF with an additional central peak. This term being known, frow experiment or theory, a division gives the modulus of the object function, which corresponds to the visibility curve obtained by Michelson and Pease. This general procedure can be applied regardless of aperture geometry and gives spatial information on the object with diffraction-limited MTF characteristics. It can be used not only with a Fizeau interferometer or the full aperture of a large telescope, but also, in principle, with a coherent array of large telescopes (Fig. X). It is interesting to note that early observers seem to have attributed magic virtues to the Fizeau screen, without realizing that information is actually gained when this aperture plate is removed from the top of the telescope. However, some justification of Fizeauaperturing practice lies in the fact that the Fizeau screen simplifies the image structure so that it can be processed by the eyes and brain of the visual observer. Instead the considerable information content in speckled images from a large aperture exceeds the data processing power of the human eye-brain system.

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A

B

C

Fig. X (additional): Principle of synthetic-aperture telescope : the giant (for example 100meter) parabolic mirror in A may be apertured with a multi-aperture mask as shown in B while retaining the same limiting resolution. B is optically equivalent to the array of mirrors shown in C if component mirrors are accurately adjusted in tilt and axial position to reproduce the B geometry with 4 4 accuracy. This difficult tolerance can be relaxed to a few microns when using filtered light. C is also equivalent to the coudi. arrangements in Figs. 12 and 13.

One major limitation to interferometric observing has to do with extended objects, or more generally with objects consisting of more than a few pixels* the size of the diffraction limit. For these objects, the convolution represented by eq. (1) results in a very faintly contrasted image requiring exceptional signal-to-noise ratio for a valid reduction. 2.3. QUANTUM NOISE

The above theory does not take into account the noise component appearing when few photon-events are recorded in each image. However, this happens to be a serious practical limitation to the accuracy of measurements in most practical cases, since the requirements for short exposures, narrow spectral bands and slow focal ratios (highf-numbers) do result in photon-starved images. The problem is especially relevant when observing faint objects with the new generation of image sensors working in the photon-counting mode (BOKSENBERG [19721). Because amplification is virtually noise-free in these receivers, the discrete nature of photon-events becomes the dominant source of noise. The low level image is seen in the form of few bright scintillations occurring on a dark background, and distributed in time and space according to a compounded Poisson law. When observing fringes at decreasing illumination levels, it eventually becomes impossible to decide whether fringes are present or not. If the

*

“Pixel” is a generally adopted word which means “picture element”

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fringe pattern were fixed, prolongated integration would solve the problem. The fringes are however moving in our case, and higher order statistical averages must be performed to extract the fringe signal. The analysis procedure described in section 2.2 may still be used, but the validity of eq. (3) under such conditions may be questioned. Classical results pertaining to compounded Poisson distributions show that the equations are still valid at low level if care is taken to remove the only distorsion arising in the summed autocorrelation function, a narrow central peak appearing at low level due to the correlation of each photon-event with itself. Assuming low levels, pure photon noise, and many images, the signal-to-noise ratio in the summed autocorrelation function is found to be

N,N~N~

(4)

where N , is the number of pho.ton-events per speckle, N , is the number of speckles in the image, and Ni is the total number of images used to build up the summed autocorrelation (LABEYRIE [19741). Applied to speckle interferometry observations with a 200-inch aperture, this expression leads one to expect a limiting magnitude in excess of 20. A more detailed noise analysis published by DAINTY[19741 yields similar conclusions. Not surprisingly, the limiting magnitude derived is much fainter than that found by GUSKOVA and KOROLKOV [19731for the case of photoelectric interferometers involving two small apertures. Because size determinations for the faintest cosmological objects are of crucial importance to modern cosmology,appreciable effort is currently made to reach the above sensibility limits of interferometric observing. Applied now to multi-aperture systems such as described in 8 2.4 and 8 4, expression (4) predicts limiting magnitudes in excess of 15, assuming the 11 to 10 A spectral bandwidth imposed for the fainter objects by the more severe temporal coherence requirements for segmented systems.

0 3. Interferometer Designs and Results 3.1. T H E FIZEAU A N D MICHELSON INTERFEROMETERS

The original Fizeau interferometer, used for the first time by Stephan at Marseilles in 1873, involved only the aperture screen as special equipment on the telescope. A strong eyepiece was used to observe the fringes. Telescope optics are usually sufficiently good to meet the one-micron or so tolerance on path equality which allows fringe observations in white light.

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Problems are created by the prismatic dispersion of the atmosphere when observing stars at low elevation. Michelson, Pease and Anderson first used a Fizeau interferometer at the Mt Wilson 100-inch reflector (1920-1933). In order to avoid difficulties with a 100-inch mask, they installed a small mask some distance above the focal plane, in the converging beam. It could be rotated in position angle, and atmospheric dispersion was corrected with a glass plate that could be tilted. This system failed to resolve any stellar disk but was successful in resolving the conspicuous spectroscopic binary Capella, spaced by approximately 0.05”. The fringes were found to disappear for certain baseline orientations, allowing precise measurement of the separation and position angle between the component stars. This was the first instance, and is still one of the very few cases, where stellar masses could be determined directly. Several variants of this interferometer have continued to be used by double s t q observers (FINSEN [1964]), but their contribution to double star observing in general has been of somewhat secondary importance in comparison with conventional visual work. In order to increase the possible baseline span beyond the maximum size of available telescopes, Michelson equiped the 100-inch reflector with a 20-foot beam. The beam carried four flat mirrors designed to reflect the light beams in perioscopic fashion. These could be positioned, with about 50 microns accuracy, for optical path equality. Further adjustment for

Fig. 5. Diagram of the 50-foot Michelson interferometer built by Hale and Pease at MtWilson.

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fringe acquisition in white light was achieved by observing the star image through a direct-view prism. Reference fringes of adjustable contrast were provided by an auxiliary Fizeau interferometer for visual contrast measurements, and corrections had to be made for a systematic effect which decreased the apparent fringe contrast at long baseline settings. In spite of appreciable operating difficulties, Michelson and Pease succeeded in resolving and measuring nine stars. These angular measurements confirmed the enormous linear dimensions of objects such as Betelgeuse in comparison to our sun, and gave the foundations for a scale of stellar temperatures. A second interferometer having a 50-feet beam was later constructed by Hale and Pease at Mt Wilson (Fig. 5). Similar in its principle to the 20-foot system, the larger interferometer failed to produce many additional results for reasons which are not completely clear but seem related to operational difficulties greater than were expected. During a recent visit to Mt Wilson, I found the interferometer well preserved in its building. In spite of some very excellent design features, it appears that the 50-foot cantilever beam may have suffered from poor stability about its symmetry axis. The instrument could be revived at moderate cost, and modern electronics for guiding and fringe sensing could certainly make its operation much easier than in Pease’s days. It is not clear, however, whether the modernized interferometer could compete with recent instruments involving two independently mounted telescopes. 3.2. PHOTOELECTRIC FIZEAU INTERFEROMETERS

Photomultiplier tubes are hardly more sensitive than the human eye for short exposure work at medium illumination levels, but they have faster response and better photometric accuracy. Before the newer generation of television sensors appeared, these advantages led several groups to develop photoelectric fringe sensors replacing the human eye in Fizeau-type systems. ELLIOTT and GLASS[1970] have used a picket-fence mask to generate a photoelectric signal from Young’s fringes, but most workers in the field have preferred beam-splitter arrangements to obtain a flat interference field (Fig. 6), following Michelson who had already considered using beam-splitters for variants of the basic Fizeau arrangement. He apparently found no advantage in doing so for visual work, but the single-pixel nature of photomultiplier tubes obviously makes it easier to work on flat interference fwlds than on Young’s fringes. This advantage of beam-splitter arrangements no longer holds with the new generation of multi-pixel sensors. A wide variety of configurations are possible with beam-splitter arrange-

INTERFEROMETER D E S I G N S A N D RESULTS

-14-

61

-1-1-

(C)

Fig. 6 . Types of single-pixel photoelectric fringe sensors: a, Kosters prism (K) arrangement used by Currie with two polarizers (P), the waves made to interfere have opposite orientations in the figure plane; b, system used by Cagnet, in which waves are identically oriented and polarizers unnecessary; c, “standing wave phototube” used by the author, in which the thin S11 film probes a standing-wave pattern produced by the two beams; d, picket-fence mask used by Elliott and Glass in a Young’s fringe pattern.

ments. These fall in several classes depending on their symmetry properties : 1. lateral shear; 2. radial shear; 3. axisymmetricflip; 4.centrosymmetric flip. Lateral shear applied to the aperture of a large telescope produces an interference field in which the interferometric baseline is everywhere the same. A single-pixel sensor could suffice to probe the entire wave in the absence of seeing. In the axisymmetric case no interference occurs in natural light since interference maxima for one of the polarization vectors correspond to minima for the other polarization. This situation arises in all single-pass

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beam splitter arrangements where the two incident beams are subjected to equal numbers of reflexions before meeting the beam-splitter. The phenomenon has been responsible for appreciable frustration in some attempts at operating stellar interferometers. Once the effect is understood however, fringes may be retrieved easily by using an additional mirror or polarizing element. In the centrosymmetric case, a two-dimensional display of the object’s visibility function may be obtained directly if the waves are tilted so as to produce narrow fringes : the fringe contrast varies locally in proportion to the local visibility value. The shadow pattern on the wave however destroys somewhat this display. Devices belonging to the first class have been used on telescopes by KULAGIN[1970], CAGNET [1973] and C. RODDIER[1971]. The fringe signal in the Cagnet system is obtained as the difference between the outputs of two photomultipliers located on each side of the beam splitter (Fig. 6b). The device was operated in the Fizeau mode at the Haute Provence 193 cm reflector. C. RODDIER [19711 worked with a different system which in fact uses the full aperture of the telescope ; interference thus tends to vanish when using large apertures with a single-pixel sensor. CURRIE,KNAPPand LIEWER[1974] have developped an axisymetry interferometer (Fig. 6a) which they mounted on the 100-inch and 200-inch telescopes of the Hale observatories. They used a differential detection scheme similar to that of Cagnet, but working in the photon-counting mode with an on-line digital processor. With a pair of 2-cm apertures and 10 Angstroms spectral bandwidth, they were able to measure visibility curves on Betelgeuse and alpha Hercules. In this system, polarizers are used to avoid the above mentioned polarization incoherence problem associated with axisymmetry devices. The system appears to work at rather low counting rates, and this leads to expect considerable sensitivity for future large-aperture, multi-pixel, devices working in the photon-counting mode. Centrosymmetry systems have been operated in the laboratory by different authors. BEAVERS [1963] has experimented with several forms of photoelectric fringe sensing on the reduced-scale version of the Michelson 20-feet interferometer which he has built. Yet another type of single-pixel sensor was used by the author concurrently with a Cagnet-type device in initial attempts with the two-telescope interferometer at Meudon. As shown in Fig. 6c, the device is based upon a special photomultiplier tube (built to the author’s specifications by the collaborators of Prof. Lallemand at Observatoire de Paris). The S11 photocathode may be illuminated from both sides with plane waves. If these are coherent, they interfere in the form of a standing-wave pattern

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which is probed by the semi-transparent and very thin S11 film. For flat interference, the photocathode plane has to be parallel to the nodal planes of the standing waves much as is the case with the beam-splitter films used by CAGNET [1973] and CURRIE,KNAPPand LIEWER[1974]. If the phase is made to oscillate with 180” amplitude by an auxiliary mirror drive, the phototube signal may be submitted to lock-in detection, thus providing with a single phototube the equivalence of the two-photomultiplier systems mentioned above. Used concurrently with the Cagnet-type sensor, the standing-wave sensor was generally preferred. However, both sensors were discarded after a photon-counting television sensor was built and its superiority was recognized (sect. 3.3). 3.3. THE SPECKLE INTERFEROMETER

The principle of speckle interferometry follows immediately from the discussion of image speckles (sects. 1-3 and 2-2). As proposed by Labeyrie in 1970, the method consists in recording speckled images at the focus of a large telescope. The images are then analyzed statistically according to eq. (3), to obtain diffraction-limited information in the form of a twodimensional “visibility function” formally similar to Michelson’s visibility curve. Although the very existence of speckles appears to have long remained ignored by many experienced astronomers, including perhaps Michelson himself, the principle had already been used on a some,qhat intuitive basis by double-star observers working visually on large refractors. With adequate training, and because of the moderate aperture size, the brain of these observers could perform the second order statistical analysis required, and detect stellar companions spaced by 0.1’’ under 0.5” seeing conditions. They could notice the double character of the granules or “condensations” which moved inside the image of close binary stars. It has however been impossible to record the phenomenon until receivers more sensitive than photographic plates appeared. Using a Lallemand-Duchesne electronographic tube, ROSCH,WLERICK and BOUSSUG~~ [1961] were first to succeed, and started a double-star program with the one-meter telescope at Pic du Midi. The speckle interferometer which I use at the prime focus of the 200-inch [1974]), telescope is represented in Fig. 7. As described previously (LABEYRIE it includes essentially a magnifying lens and a field-grating arrangement serving as a tunable filter, and also to correct atmospheric dispersion. Different types of sensors have been used successively: 1. photographic film with an image intensifier; 2. a standard television camera equipped

70

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I

< -

\

Irn

F300

&

Fig. 7. Speckle interferometer used at the prime focus of the 200-inch telescope M, fieldfinder mirror, with 0.1 mm hole; L, magnifying lens; G, concave field grating (Jobin-Yvon holographic type) in plane of magnified image;U, spherical mirror; S , spectral mask; TV, television camera ; R, auxiliary spectrum-viewing lens ;C, geometry-calibration grid. The optics provides magnification and tunable filtering (color and bandwidth are separately adjustable). Atmospheric dispersion is corrected by translating TV axially and rotating the complete system about the telescope axis.

with a SIT tube; 3. a photon-counting television camera. Because standard television image frequencies are close to the optimum values, determined by atmospheric frequencies, television-type sensors are particularly efficient for this application. Initially, optical analog techniques were used to reduce speckle interferometry data. This was required on account of the high information content in the numerous two-dimensional images which had to be processed. The images recorded on film, or transferred from video tape to film, were Fourier transformed in a laser processor, and their power spectra were summed by multiple-exposing a photographic plate. 200 to 6000 exposures were typically used in the summation for residual noise on the order of a few per cent. Fringes in the summed pattern were interpreted as evidence of stellar duplicity, while attenuation of the outer edges indicated a resolved stellar disk (Fig. 8). The power spectrum of the object could, in principle, be obtained by dividing the summed power spectra obtained respectively for the object and an unresolved reference star. In practice, the difficulty of insuring the required sensitometric gamma resulted in unavoidable photometric distorsions in the processed data. Nevertheless, the sensitivity and two-dimensional character of the method permitted a number of findings: 200 objects were observed as of December 1974, 90 of which in the course of only two nights. Twelve stars were found to be binaries (LABEYRIE, BONNEAU, STACHNIK and GEZARI [1974]), allowing stellar mass determinations in five cases. Most of the supergiant stars resolved by Michelson and Pease were also resolved in spite of slightly inferior resolution with the 200-inch telescope. Two of these (Betelgeuse and Mira Ceti) were found to feature a markedly limbdarkened profile, the width of which increases from red to blue wavelengths

Fig. 8. Stellar structure evidenced from time-averaged power spectra. Speckled images on top with corresponding power spectra below. From left to right : Betelgeuse (resolved disk), Capella (resolved binary), unresolved reference star. The power spectra presented here are relatively noisy due 2 to the small number of frames used in the average.

N -4

Fig. 9. Typical integrated power spectra of 200-inch images. obtained optically, showing resolution of six sellar disks and two binaries. Object-reference pairs are indicated by a bar. The alteration in the case of p Canis Majoris is believed to result from aberrations resulting from flexure of the 200-inch mirror for certain orientations. A mirror mask suppresses the bright central peak.

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(BONNEAUand LABEYRIE [1973]). All the resolved disks were found to be revolution symmetrical, with the possible exception of Mira (Fig. 9). It is currently attempted to improve the image analysis procedures. High-speed digital correlators have been used in real time, but they provided only one dimension. A two-dimensional technique applicable to digital video signals at extremely low pulse rates has been worked out for work on faint objects or attenuated bright ones. As discussed in sect. 2.3, it appears indeed that interferometric information may be recovered at extremely low counting rates, down to 2 photon-events per image, or even less. Part of the information in high-level analog images must be sacrificed due to rate limitations in digital processing techniques. It appears that beam attenuation, for the brighter objects, is the optimum way of sacrificing information if it allows digital reduction in the photon-counting mode. The expression (4) shows that minutes of observation suffice to provide adequate signal-to-noise ratio at counting rates on the order of 100 per image, which are compatible with on-line digital processing. A software and a hardware autocorrelation system using a special algorithm are currently developped along these lines at Meudon. R. Lynds and his collaborators (1973) at Kitt Peak National Observatory have developped a digital two-dimensional correlator which they use to reduce their analog speckle interferometry data. Steps have been taken in a different direction by STACHNIK and NISENSON [1973] : they use electro-optic crystals as transducers for optical reduction of speckle data in real time. 3.4. INTERFEROMETRY WITH TWO TELESCOPES

Because self-supporting structures such as the 50-foot interferometer at Mt Wilson cannot be extrapolated for baselines on the order of 100 meters, it has been suggested by MILLER [I9661 and others to use separately mounted collectors for long-baseline work. Miller has studied configurations involving a pair of heliostats and a central station equipped with optical delay lines. Following this general philosophy, I have constructed an interferometer utilizing two telexcopes. Installed at Nice, the system recently produced fringes on Vega (LABEYRIE [1975]). The instrument was intended to test design concepts suitable for future extrapolation toward long baselines, large component apertures, and progressive growth into an array including perhaps 40 telescopes. It consists of two 25-cm telescopes located on each side of a laboratory building, along a 12 meter baseline oriented in the

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North-South direction. The telescopes have a Cassegrain-Coudt configuration, both caude beams being received in the laboratory building at focal ratio f: 3000, and recombined on an optical table as shown in Figs. 10, 11 and 12. The table is mobile on tracks to compensate the optical path variations occurring as the star follows its diurnal motion. It carries a twin .autoguider system and a roof-mirror arrangement for recombining the two images in order to produce Young’s fringes similar to those observed with his instrument by Michelson. The telescope mounts are of a special altitude-altitude design providing adequate stiffness with a minimum number of coude flats. Considerable care has been taken to avoid possible mount vibrations. The synthetic image, or a fringed spectrum, are observed either visually or with the photon-counting television camera. The camera is interfaced to a PDP8 minicomputer through a preprocessor. The fringes observed repeatedly on Vega were found to be of very good contrast, suggesting that the subjacent limestone soil at Nice provides adequate stability. Also, it appears that the narrow coudk beams are essentially insensitive to turbulence

Fig. 10. The two-telescope interferometer at Nice. Narrow coudC beams from both telescopes are received in the central building, where they recombine to produce Young’s fringes in the synthetic image. The telescopes have special alt-alt mounts built from heavy-gage materials for dimensional stability. Tracks are currently being designed for a variable baseline.

INTERFEROMETER D E S I G N S A N D RESULTS

Fig. 11. One of the two tclescopes operated as a Michelson interferometer. The coudii beam exits through the hearing visible in front. Also visible are the massive secondary spider, yoke and concrete support.

in the horizontal path, implying that no piping should be required with this configuration at long baseline settings. In contrast with some of the beam-splitter arrangements used to recombine beams, the simple optical configuration can be adapted for work with N telescopes. This requires replacing the roof-mirror by a pyramid mirror. Optical delay lines such as proposed by Miller may prove necessary

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[n. 0 4

,=I Fig. 12. Optical layout of the Meudon/Nice two-telescope interferometer: Tn, TS- Northland South telescope; M- primary mirror cf= 850 mm); m- Cassegrain secondary cf= 7.5 mm); F- coude flat; L-field lens; rm-roof mirror in pupil plane; D-dichroic mirror; TV1-guiding camera; bl-bilens serving to separate the North and South guiding fields; S and P- slit and direct view prism used for fringe acquisition; TV2- photon counting camera (tunable filter or disperser not represented); Tr- tracks on which table moves (programming mechanism not represented).

in this case. Making accurate contrast measurements on inherently variable fringes has been a standing problem since Michelson and Pease. Systematic errors may be caused by incomplete temporal coherence, atmospheric dispersion, polarization effects, differential field rotation, vibrations, insufficiently short exposures, and guiding errors. The problem of avoiding all these effects has not yet been solved at Nice, but it appears that the use of larger component apertures with digital reduction methods in the photon-counting mode should attain a level of accuracy sufficient for many astrophysical problems. Steps are currently being taken to replace the small telescopes by 60-inch ones. Also, railway tracks are being installed for variable and progressively longer baselines.

0 4. The Image Reconstruction Problem 4.1. THE VISIBILITY PHASE PROBLEM WITH DIRECT INTERFEROMETRY

The equations in sect. 2.2 show how the autocorrelation function of objects, or equivalently their power spectrum, may be obtained. This is generally insufficient for reconstructing images. The information missing is the relative phase of the varied spatial frequency components, i.e., the exact location of the component fringe patterns on the sky plane. In the

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Fizeau interferometer for example, the phase cannot be determined since the fringes observed for any baseline value oscillate in such a way that no average position exists. Due to turbulence and tracking instabilities, it is not practicable to pin-down some average fringe position on the sky plane. Thus, fringe positions on the sky plane at different baseline settings cannot be compared. A similar problem is classically encountered in the interpretation of X-ray diffraction data for mapping crystal structures. The X-ray spot diagrams do not contain phase information, and considerable effort has been invested in trying to obtain indirectly this information in order to deduce the electron density distribution in crystals. The absence of a well defined average fringe position may be explained by the random walk character of the operation which consists in adding fringed images. This addition has the form c i [ l + sin(2nx/s + q,)] which is equal to N+xisin(2nx/s+cp,). The latter term may be represented by a sum of randomly oriented vectors in the complex plane, and the resulting phase keeps varying wildly as N increases. MCGLAMERY [19671 and others have proposed to average directly the phases cpi . This might be feasible in the absence of amplitude variations. However, these variations cut the fringe contrast repeatedly during the integration period, thus creating 360" ambiguities which are likely to affect the average result. Although the visibility phase information is generally necessary to reconstruct images, there are a number of special object geometry cases where the phase is not needed if a certain a priori knowledge of the object exists. Such cases include : 1. centrosymmetrical objects, for which the Fourier spectrum is purely real; 2. objects with a reference star in the immediate vicinity. The application of speckle interferometry in the latter case has been discussed and explored through laboratory experiments by BATES, GOUGH and NAPIER [1973]. When a reference star is present at a suitable distance, the autocorrelation function indeed contains a pair of sideterms consisting of cross-correlations between the object and the reference star. The reference star being a delta function, these side terms turn-out to be reconstructed images of the object. Chosing which side term corresponds to the actual object orientation is normally impossible, unless one uses the image envelope, and this introduces a 180" ambiguity in the orientation of the object. LIUand LOHMANN [19731 have discussed the case of speckle interferometry on objects which contain a dark background interrupted by relatively small islands, one of these at least being a point star. They show that a high-resolution image may be reconstructed by utilizing image envelopes to eliminate unwanted cross-correlation terms. Stellar configurations

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suitable for imagery by the last two methods are not too unfrequent due to the high occurrence of multiple star systems. With the new generation of very sensitive receivers, many sources should become amenable to highresolution imaging by these methods. We shall see in section 3.3 that these observations are potentially more sensitive than those with pre-detection compensation systems. One more possible method, which has not been very much investigated yet, involves the exceptionally bright speckles which are likely to appear sometimes in the image according to Rayleigh statistics. These superspeckles may be considered as diffraction-limited images of the source. 4.2. THE TRIPLE INTERFEROMETER

Rogstadt proposed to use for visibility phase measurements in the optical region the 3-antenna method worked out by JENNISON [1967] at radio wavelengths. The concept was further developped by GOODMAN and RHODES[1973] with the help of laboratory and computer experiments. The principle of the triple interferometer may be explained in the context of a Fizeau interferometer with 3 apertures instead of the conventional two. Holes are obturated in sequence according to a circular permutation scheme in such a way that only two holes are used simultaneously. The permutation time is shorter than atmospheric lifetimes. Three possible fringe systems are recorded in sequence, with a cycle time shorter than the atmospheric lifetime. With a point source, whenever atmospheric phase shifts are so arranged that fringe systems 1 and 2 coincide, then every second maximum of 3 should also coincide with the maximas of 1 and 2. Lack of coincidence implies that the source is not a point source, and gives the relative phases of its Fourier components at spatial frequencies f and 2f. Due to lack of experience in real astronomical situations, it is unclear yet how this method will compare with the seeing compensation and superspeckle selection methods. 4.3. THE SEEING COMPENSATION APPROACH

One of the most attractive approaches to diffraction-limited imaging through the atmosphere is that suggested by BABCOCK [1953]. The idea is to remove atmospheric phase fluctuations by means of active phasing devices. The servo loop originally proposed by Babcock involved a rotating knife-edge to map wave defects, with a television camera and an Eidophor optical transducer for applying phase corrections on the wave. The state

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of the art has long been incompatible with such attempts, but the idea has recently been revived by different groups at Berkeley (Lawrence Radiation Laboratory), Itek Corp. and Hughes Labs.. MULLERand BUFFINGTON 119741 at Berkeley, in collaboration with DYSON[1974] used computer simulations to study the performance of arrays having a few dozen aperture elements with individually controllable phases. A parameter suitable for deriving an error signal was found to be the intensity at one preselected image pixel: the first aperture is phased to maximize intensity, than the second, etc., and a few cycles of adjustments performed within the seeing lifetime suffice to increase dramatically the image sharpness, even though no attempt is made to suppress the shadow pattern on the aperture. A different system, resembling more the original Babcock device has been demonstrated in the laboratory by HARDY,FEINLrEB and WYANT [1974] at Itek. In this seeing compensator, a wavefront-shearing interferometer serves to measure the phase distribution on the wave. A simple analog computer derives correction signals, and these are supplied to a deformable piezoelectric mirror. The spectacular image improvement already obtained with this other simple system in its present stage of development suggests a bright future for the seeing compensation approach. A rather modest limiting magnitude, of the order of 10 to 13, has been predicted for devices of that kind. However, for bright enough objects, not only imaging cameras but also spectrographic equipment should benefit from reconcentrating the energy which is scattered by the atmosphere.

0 5. Construction of a Synthetic-Aperture Array of Optical Telescopes In the past few years, interest has arised in building optical telescopes much larger than those in existence. As discussed by CODE119731, it has generally been felt that the conventional monolithic approach is not suitable for building such giant instruments. The construction costs with the conventional approach indeed appear to increase faster than collecting area. Instead, it has been seriously envisaged to build arrays of optical telescopes resembling those used in radio astronomy. ODGERS and RICHARDSON 119723, for example, have proposed an incoherent array consisting of fourty 1.5 meter telescopes. In their project, a synthetic image is produced at a common focus where the coudC beams meet. The usable field is small but the array is primarily intended for feeding light into a spectrograph. The advantages and limitations of telescope arrays have been discussed by CODE119731, primarily from the incoherent synthesis point of view. Code pointed out a unique advantage of array over monolithic telescopes : they

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can grow, i.e., it is possible to start with a relatively modest system and progressively expand it once satisfactory operation is demonstrated. However, the greatest potential interest of the array approach lies perhaps in the coherent synthesis applications. Interferometric baselines on the order of 100 meters can indeed be envisaged with an array since system cost depends mostly on the total collecting area and not on the telescope spacing. C6mpOnent telescopes for an array do not need to involve unduely novel techniques, except perhaps for the coudC beam arrangements, which should require as few reflexions as possible. Telescopes should preferably be movable for a flexible baseline geometry, unless their individual size is excessive. Optical path equality can be achieved by means of tunable delay lines, as discussed by MILLER[1971]. Fringe detection in the image may be achieved by speckle interferometry or using any of the numerous possible beam-splitter arrangements. Figure 3 shows, under conditions of laboratory simulation, the possible appearance of images produced by a two-telescope arrays and a 6-telescope array, component apertures being on the order of 1.5 meter. More complicated interference structures would be observed within the speckles in the case of more than 6 telescopes, but the image analysis procedures used with a single telescope remain valid. Fig. 13 shows the general layout of an array proposed by the author. The array will have variable baseline geometries. Altitude-altitude or spherical mounts are envisaged for the telescopes. These are 1.5 meter Cassegrainians with a small interchangeable secondary and single-flat

Fig. 13. Proposed synthetic-aperture array of telescopes. Narrow coudB beams propagate from each telescope into the central station, where they recombine. The telescope mounts represented consist of ferro-cement spheres tracked on fluid pads. They are expected to provide better dimensional stability than conventional coudi. mounts. Sphere surfaces are precision ground. Conventional 1.5 meter (60-inch) telescope optics are mounted inside the spheres.

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coudt focus. Because the mounts are not equatorial, photoelectric or computer-controlled guiding is needed. Also, the coudt flat must be rotated along the alt-2 axis during observing. This is automatically achieved by a gear mechanism, and satisfactory operation has been achieved with the prototype telescopes installed at Nice. The array design is such that telescopes may be utilized : 1. individually, for conventional observing with each telescope separately ; 2. collectively in the incoherent mode, as proposed by ODGERSand RICHARDSON [1972] for their array; 3. collectively in the coherent mode. The Meudon/Nice interferometer is a prototype intended for evaluating the concept. Its operation has been demonstrated and found satisfactory using photoelectric guiding to maintain the superposition of the two star images. The mechanical design of telescope mounts must be unusually stiff in order to

Fig. 14. Cross-section of concrete spherical mount studied for the array of 1.5 telescopes. Reinforced concrete has good vibration damping characteristics, short-term stability and low cost. The outer sphere surface is ground smooth and supported on rollers, water bearings, or piezoelectric pads.

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avoid vibrations at the 0.1 micron scale. This implies particularly thick spider arms and a very rigid yoke or sphere. In the prototype system, it was found necessary to sacrifice partially the possibility of operating at low elevation angles in order to meet these requirements. This is no great loss for coherent work, since atmospheric turbulence and dispersion increase sharply at large zenith angles. An attractive alternate design involves spherical mounts. For low-cost production and excellent vibration-damping characteristics, these mounts could consist of a shell made of reinforced concrete or ferro-cement and supported on three rollers or fluid pads, as shown in Fig. 14. This design appears to have attractive advantages, and the unusual tracking problems appear to be quite solvable with the help of modern minicomputers. Among the advantages are : 1. structural simplicity; 2. no dome is needed since the sphere includes self-enclosed laboratory space; 3.’ the spherical mount may be tracked either in the alt-alt, equatorial, or even alt-az modes. A project along these lines is currently being worked out at Meudon. A 3.5 meter ferro-cement sphere has been constructed and will shortly be equipped with a 1.5 meter mirror to develop the spherical tracking technology. A second telescope will then be built, and institutions from different countries will later be invited to contribute additional telescopes for progressive array growth. The system’s luminosity will surpass that of Mt Palomar’s 200-inch instrument if the array grows to include eleven 1.5 meter telescopes or six 2-meter telescopes. Because it is still difficult to predict the maximum baseline dimensions that will be usable, some flat expanse of terrain at least one square kilometer should be selected, in a region having low nebulosity and jet-stream activity in addition to other desirable astronomical characteristics.

0

6. Intensity Interferometry

In order to overcome the problems which stellar interferometry had to face in the years 1950, Hanbury Brown and Twiss proposed the novel method which they called “intensity interferometry”. The principle may be presented in the following elementary fashion, readers being referred to Hanbury Brown’s articles for more details. Neglecting atmospheric effects, which have no influence on this method, the illumination produced on the ground by a stellar source is not uniform if mapped during a period shorter than the coherence time z = l/f of the beam ( f being the frequency bandwidth). The non-uniformity results from interference of light emitted by different parts of the source. Indeed, the

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electric field behaves as if the source were spatially coherent during such a short interval. The phase is however not uniform on the source, so that the emitter may be compared to a piece of diffusing glass illuminated by a laser beam. If the diffusing glass is further assumed to fluctuate randomly with lifetime z, an accurate model of the beam’s spatio-temporal structure is obtained. The theory of speckle phenomena mentioned in section 1.3 applies to this case and shows that a distant screen, the terrestrial ground in the present case, is illuminated with a speckle pattern fluctuating with the time-constant z. The size of the speckles d is related to the angular size M of the source by the usual relation d = A/M. This is equivalent to saying that the whole spatio-temporal structure of an incoherent beam is speckled: temporal as well as spatial speckles are present. The beam structure may be described as a flow of random cells or speckles (also known as field modes or coherence cells) propagating in space with velocity c while deforming themselves. Fast detectors located on a transverse surface (the terrestrial ground) see simultaneous intensity fluctuations if they are spaced by less then the transverse dimension of speckles. They see uncorrelated fluctuations in the opposite case. The cell size may thus be determined by comparing the signals from two detectors having a variable spacing. This is the technique used by HANBURY BROWN,DAVIS and ALLEN[1974] at Narrabri observatory. A pair of 6.5-meter light collectors mobile on a 300-meters diameter circular track are each equipped with a fast photomultiplier and narrow-band filter. The two photoelectric signals are multiplied, and the result is integrated for several hours or days until adequate signal-to-noise ratio is obtained. Because of the limited electrical bandwidth in the photomultipliers and amplifier circuits, the optical frequency bandwidth effectively utilized is extremely narrow, on the order of Angstroms. This implies a comfortable tolerance on the dimensional stability of mechanical structures, but also a very inefficient use of the incident energy. For this last reason, the method has been applicable only to the very brightest blue stars up to magnitude 2.5. It nevertheless permitted remarkably accurate measurements on 32 stars with the unrivaled resolution of l o p 3 arc-second. Following the recent results with two telescopes operated as a Michelson interferometer (sect. 3.4), J. Davis and myself have discussed the potential applicability of both methods for work at very long baselines, on the order of 2 kilometers. Whereas baselines as long as one kilometer may be usable with direct interferometry, it seems that propagation of an electrical signal is easier over long distances than the undisturbed coherent propagation of

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[II,

§ 8

an optical beam. For 2 kilometers baseline, the optical beam produced by a 1.5 meter (60 inch) telescope may be propagated in 10 cm piping (no periscope-type relay lenses being required). Vacuum is also unnecessary, especially if the pipe structure includes thermal insulation. In spite of their remarkably low loss characteristics, state-of-the-art fiber-optics light guides cannot be used since they distroy the temporal coherence. Single-mode fibers may however become available before interferometric baselines grow enough to require their use. It is thus difficult to predict the result of the competition between direct and intensity interferometry in the coming years, although short baselines appear to favor direct interferometry at this time.

0 7. Heterodyne Interferometry Heterodyning techniques have been successfully employed at radio wavelengths for the very-long-baseline observations involving antennas located several thousand kilometers apart. The method consists in beating light from the star with that from a local oscillator, on a suitable sensor. Simultaneous work at two stations using the same oscillator frequency, provides interference information. Heterodyne interferometers for work at 10.6 microns are currently developped by TOWNES and his collaborators [1974] at Berkeley, as well as by GAYand JOURNET [1973] at Observatoire de Paris. At the University of Utrecht, VANDE STADT[1973] and Nieuwenhuyzen build a system intended for work at 3.4 microns. Like intensity interferometry, and for the same reason, the heterodyne approach restricts considerably the spectral band used. Its potential usefulness is generally considered as marginal in the ultra-violet, visible and near infra-red regions where photoemissive sensors are available. In the 2 to 10 micron infra-red range, heterodyning becomes more efficient, but even there it is not yet clear how it will compete with direct interferometry. Work on direct interferometry at 10 microns is carried out at Berkeley by D. Cudaback and J. Franck.

0

8. Conclusions

Present trends in the fields concerned with high-resolution observation at optical wavelengths indicate the likelihood of major improvements in the coming decade. The directions which appear to hold most promise are: 1. synthetic-aperture arrays of telescopes. It is unclear yet how far it will be possible to push this technique which is still in its infancy, but orders

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of magnitudes will probably be gained in the resolution and luminosity of interferometric work; 2. imaging techniques related to the “rubber telescope” concept may succeed in providing improved images of the bright stars and fainter sources in their vicinity. The corresponding devices may become useful accessories to spectrographic equipment and also to telescopes participating in array work. Satellite-based telescopes such as NASA’s proposed Large Space Telescope also provide remarkable new possibilities. Concerning synthetic aperture arrays, however, it is likely that ground-based systems in the 100-metersrange of size will be operational before equivalent space systems. The experience gathered with them should help designing space systems for completely diffraction-limited performance. Such systems will open a new era in optical astronomy.

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