High-resolution ground-based coronagraphy using image-motion …golim/papers/golimowski1992.pdf · 2007. 2. 25. · Then relation (5) may be expressed as 0-1 !S U 2. (7) Using Borgnino's14

High-resolution ground-based coronagraphyusing image-motion compensation

D. A. Golimowski, M. Clampin, S. T. Durrance, and R. H. Barkhouser

The first results of a new approach to ground-based stellar coronagraphy are reported. A coronagraphhas been equipped with an image-motion compensation system for the stabilization of the telescope field,permitting both improved image resolution and contrast at optical wavelengths. By stopping thetelescope aperture D to 4 r, where r is Fried's parameter, the maximum attainable resolution gainfactor of 2.2 was achieved. Gains measured for Diro > 14 were below the theoretical value of 1.3 theoryand were indicative of centroid anisoplanatism, a small spatial coherence outer scale, or both. Theseeffects are also evidenced by diminished power at low frequencies in the power spectrum of image motionover the full telescope aperture. A comparison of stabilized and unstabilized images shows that thiscoronagraph may detect circumstellar objects 2 magnitudes fainter than those detectable with aconventional coronagraph.

Key words: Adaptive optics, image-motion compensation, coronagraphy.

Introduction

The angular resolution of most ground-based opticaltelescopes is ultimately determined by the effects ofatmospheric turbulence rather than the quality of thetelescope optics. Incoming wave fronts from astro-nomical sources are distorted by refractive-indexvariations caused by random temperature and humid-ity fluctuations within the turbulent atmosphericlayers. Phase shifts along the wave front produceblurring and motion of the astronomical image; thedegrees of each depend on the scale of the turbulenceand the size of the telescope aperture. For long-exposure images, the cumulative effect of these wave-front distortions is the degradation of the telescope'spoint-spread function from an Airy diffraction pat-tern to a broader quasi-Gaussian profile.' Forsmaller telescopes (< 1.0 m at optical wavelengths),image motion resulting from wave-front tilt fluctua-tions provides the larger contribution to this imagedegradation, whereas blurring caused by higher-order wave-front aberrations dominates for largerapertures. The effect of atmospheric turbulence onimage quality is commonly termed seeing and istypically characterized by the FVVHM of the stellar

The authors are with the Center for Astrophysical Sciences,Department of Physics and Astronomy, The Johns Hopkins Univer-sity, Baltimore, Maryland 21218.

Received 01/09/92.0003-6935/92/224405-12$05.00/0.a 1992 Optical Society of America.

profile. Seeing causes a significant loss of angularresolution and imaging sensitivity in ground-basedastronomical observations; e.g., optical seeing condi-tions of 1 arcsec produce stellar images 10 to 40 timeslarger than those obtained with diffraction-limited 1-to 4-m aperture telescopes, respectively.

Many techniques have been employed in the effortto overcome the effects of the atmosphere on imagequality, such as the postimaging-reconstruction meth-ods of maximum entropy2 and speckle imaging.3 4

In the last decade, much attention has been given toreal-time correction for seeing through the introduc-tion of adaptive optics into the optical path.5-7 Anadaptive-optics system consists of a wave-front sen-sor and a deformable mirror operating in a closed-loop mode at rates appropriate for the time scale ofthe turbulence. Such a system not only corrects foratmospheric effects, but also compensates for aberra-tions induced by the telescope optics themselves.

An imaging technique that would benefit from theuse of adaptive optics is stellar coronagraphy. Thecoronagraph was first employed by Lyot8 in 1934 toobserve the solar corona. Since then stellar corona-graphs have been successfully used to image faintmaterial around bright stars, which is undetectablethrough direct-imaging techniques. The discoveryof a protoplanetary disk about the star Pictoris witha coronagraph9 has inspired the Johns Hopkins Uni-versity (JHU) to develop a coronagraph incorporatingadaptive optics to conduct a full survey of circumstel-lar disk candidates with nearly diffraction-limited

1 August 1992 / Vol. 31, No. 22 / APPLIED OPTICS 4405

resolution at optical and near-infrared wavelengths.This combination of a coronagraph and adaptiveoptics would also permit the use of smaller occultingmasks, thereby allowing one to image closer to thestar. For P Pictoris, confirmation of a hypothesizedclear zone within 30 astronomical units of the star,where planets may be accreting, should be possiblewith this instrument.

The present configuration of the JHU adaptive-optics coronagraph (AOC) employs an image-motioncompensation system that is based on a quadrant-CCD detector and a piezoelectrically driven tip-tiltmirror to correct the effects of wave-front tilt acrossthe telescope aperture. Thus, the AOC currentlycontains a partially adaptive optics system that re-moves only the lowest degree of image aberration.Ultimately, the AOC will incorporate a fully adaptivesystem, comprising the tip-tilt mirror, an electrostat-ically deformable membrane mirror for phase-errorcorrection, and a wave-front curvature sensor of thetype described by Roddier.10 The partially adaptiveinstrument has been site tested at the EuropeanSouthern Observatory (ESO) and at the Las Campa-nas Observatory. In this paper we present the re-sults of these tests, which to our knowledge includethe largest improvements in the angular resolution ofoptical images reported to date. A comparison ofthese results with the theory of atmosphericallyinduced image motion shows that the AOC effectivelyremoves this component of image distortion for aper-tures < 1 m. The utility of the AOC in performingobservations of the circumstellar environment ofbright stars is also demonstrated.

Image-Motion Compensation

The effects of atmospheric turbulence on image qual-ity have been reviewed by Roddier.11 The spatialspectrum of the turbulence responsible for imagedegradation obeys Kolmogorov statistics, providedthat the spatial frequencies f lie within the inertialrange

apertures 5 m, image motion arising from fluctua-tions of the average wave-front tilt across the apera-ture may be considered the result of a nearly Kolmog-orov spectrum of turbulence filtered by the telescopeaperture D and the outer scale Lo.

The spatial coherence of the distorted wave front istypically characterized by Fried's parameter ro, whichat zenith is given by"

ro-513 = 16.70A-2 f dhCN2(h), (2)

where X is the wavelength of light, h is the heightabove the ground, and CN2(h) is the refractive-indexstructure constant. For given seeing conditions, rocorresponds to the aperture size below which theshort-exposure image resolution is diffraction limitedand above which it is seeing limited. The angulardiameter (FWHM) of the seeing-degraded long-exposure image is related to r0 by15

0 = 0.976 -i) (3)

and varies with wavelength as A-1/5. The variance ofthe wave-front tilt with respect to the plane of thetelescope aperture has been expressed as'1

(4)

where the altitude dependence of Lo is shown explic-itly. Performing the integration over f and substitut-ing Eq. (2) yields

0.36X2 rO-5/3[D-1/3 - So-1/3]' (5)

where Yo is the spatial coherence outer scale14 definedas

fO dhLo(h-" 3CN2(h)

fO dhCN2(h)(1)

where lo and Lo are the inner and outer scales of theturbulence, respectively. The inner scale, defined asthe length at which the mechanism of kinetic-energydissipation changes from turbulent breakup to fric-tional heating, is < 1 cm for all heights." The outerscale reflects the size of the largest eddies that can besupported by the energy of the turbulent motion.In the troposphere, Lo is generally thought to be ofthe order of the thickness of the turbulent layer,ranging from a few decameters to 100 meters.1""12

Near the ground, Lo is of the order of the height abovethe ground." Recent reports based on in situ mea-surements of the atmospheric pressure, temperature,and refractive-index profiles have shown a systematicaltitude dependence of Lo, with an upper limit for Loabove 1 km of 5 .13'3 4 Thus, for telescope

and the constant of proportionality has been insertedto provide agreement with more rigorous derivationsof cr2 for an infinite outer scale.'6

Borgnino14 has introduced 2Y as an estimator ofthe distance at which the structure function of phasefluctuations saturates (i.e., the self-coherence of thephase is zero). Relations (5) and (6) indicate thatvalues of So obtained from simultaneous ground-based measurements of ro and u2 cannot be directlycompared with in situ measurements of Lo unless asingle layer of homogeneous turbulence is assumed.However, 2Y is a useful parameter for estimating thedegree to which Lo reduces the amount of imagemotion otherwise expected from fully developed Kol-mogorov turbulence. To illustrate this point, let oru

2

be the wave-front tilt variance as Lo c- for all h.

4406 APPLIED OPTICS / Vol. 31, No. 22 / 1 August 1992

lo << <

(6)

0-2 0C f- dhCN2(h) rD_1_ 1 dff-2/3,0 Ao(h)

. -1/3_

Then relation (5) may be expressed as

0-1 !S U 2. (7)

Using Borgnino's1 4 overestimate of Yo = 7.67 m, wefind that the rms image motion recorded with a 2-mtelescope would be 60% of that expected for fullydeveloped turbulence. Thus, failure to account forsuch a finite outer scale would lead to an overestima-tion of the role of image motion in image degradation.

(It should be noted that relation (4) assumes aKolmogorov spectrum of turbulence for all spatialscales, which is in violation of relation (1). Lessimage motion is expected for f L(h)-' than ispredicted by Kolmogorov theory. Further, relation(4) assumes that contributions to the image-motionpower spectrum from scale lengths less than D arezero as a result of spatial averaging over the aperture.Having computed nonnegligible increases in the Strehlratios of short-exposure images over those of long-exposure images for values of D/Lo as much as 4,Valley17 has shown that this assumption is onlyapproximate for a single layer of homogeneous turbu-lence. Thus, Yo must be considered a diagnosticmeasurement, not an accurate measurement, of theeffect of Lo on image motion.)

The time between wave-front tilt fluctuations withinwhich an adaptive correction must be applied isdetermined by the flow of frozen-in turbulence acrossthe telescope aperture:

stellar coronagraphy is the ability to use smallerocculting masks, permitting high-resolution imagingcloser to the star.

The expected gains in resolution using image-motion compensation for various values of Diro arerepresented by the dashed curve in Fig. 1. Thesegains have been computed from Fried's tabulations oflong- and short-exposure image resolutions18 ; how-ever, our resolution pertains to the physically measur-able image spread and is therefore inversely propor-tional to the square root of Fried's resolution."Although Fried based his calculations on theinaccurate assumption that wave-front tilt is statisti-cally independent from higher-order wave-front aber-rations, his resolution gains have been characterizedas being low by no more than 10% at peak gain.1920

For lack of better-tabulated resolution values, werefer to Fig. 1 with appropriate caution. WhenDiro 3-4, the image may be sharpened by a factorof 2. However, as Diro increases the resolutiongain rapidly decreases, because spatial averaging ofthe tilt contributions from smaller scales of turbu-lence produces little overall tilt across the telescopeaperture. When Diro < 3, the telescope's diffrac-tion limit becomes comparable with the size of theblurred image, so the gain achieved by image-motioncompensation again decreases. The favorable re-gime for image-motion compensation is Diro 1-10,where gains between 1.4 and 2.1 may be achieved.Note that these expected values also require D << and are diminished if the condition is not satisfied.

D7r= - 'U - (8)

where is the average velocity of the turbulentlayers. The angular extent of the sky over whichimage-motion compensation is effective, or the corre-lation angle, is by geometry

Dh

2.5

.5112(9)

where h is the average height of the turbulent layers.For typical values of , a correlation angle of 1.5arcmin is possible on a 2-m telescope, which reflects afactor of Diro increase over the correlation (or isopla-natic) angle for fully adaptive systems.

To evaluate the benefits of image-motion compensa-tion, Fried18 has calculated the expected improve-ment in image resolution for short exposures as afunction of Dro. These calculations apply equallywell to the expected improvement in the resolution oflong-exposure images obtained with real-time wave-front tilt correction by means of a tip-tilt mirror.The principal advantage of real-time tilt correctionover a posteriori shift-and-add processing of short-exposure images is the enhanced ratio of signal tonoise in the resulting image, which improves thechances of resolving faint objects with a noise-limiteddetector. Another advantage that is important for

1.5

10 20 30

Fig. 1. The gain in angular resolution when the effects ofwave-front tilt are removed. The dashed curve depicts the ratio ofFried's calculated short- and long-exposure resolutions for variousvalues ofD/ro. The symbols represent the gains measured forAOCimages obtained with the following telescope apertures: ESO2.2-m MPI telescope at full aperture (open circles), ESO 2.2-m MPItelescope stopped to 0.6 m (open squares), ESO 2.2-m MPItelescope stopped to 0.5 m (open triangle), 2.54-m DuPont tele-scope at full aperture (filled square), and the 2.54-m DuPonttelescope stopped to 0.7 m (filled triangles). The error bars foreach datum reflect the uncertainty in the measurements of theimage FWHM's and the width of the filter bandpass.


1

The Adaptive-Optics Coronagraph

The AOC consists of two major components: anadaptive-optics system used to sense and correctwave-front distortion, and a stellar coronagraph usedto search for faint circumstellar emission. An occult-ing mask is the element common to both components,serving to prevent the light of a bright star fromentering the coronagraph and reflecting that lightinto the wave-front sensor. The present AOC incor-porates only those elements necessary for image-motion compensation, but the instrument has beenconstructed to easily accommodate future elementsthat will render the AOC fully adaptive. A sche-matic of the AOC and its peripheral control system isshown in Fig. 2. Light from the focal plane of thetelescope is collimated by lens Li onto the flat mirrorsMI and M2. Ml will ultimately be replaced by the

LI

Ml

membrane mirror in the fully adaptive instrument.M2 is driven by three piezoelectric actuators designedto provide rapid tip-tilt adjustment for removingoverall wave-front tilt. The tip-tilt mirror is manu-factured by Burleigh Instruments, Inc. and is capableof operating at rates in excess of 1 kHz. The tele-scope focal plane is reimaged with unit magnificationby lens L2 onto the occulting mask M3. This smallmirrored disk reflects the light of the bright star intothe image-motion compensation system, permittingonly the light from the circumstellar region to pass tothe imaging camera.

The Image-Motion Compensation System

The image-motion compensation system is used tostabilize a stellar image once it has been positionedbehind the occulting mask. The system consists of a

L CORONAGRAPH .

Fig. 2. Schematic of the JHU AOC configured for image-motion compensation: HV, high-voltage.


2 x 2 pixel quadrant-CCD detector, a control systembased on an IBM-AT compatible personal computer(PC1), and the tip-tilt mirror. Lenses L3 and L4reimage the star onto the quadrant-CCD, with L4replaceable to provide a magnification suitable for thetelescope plate scale. A neutral-density filter F1may be inserted between L3 and L4 to preventsaturation of the detector. After each readout of thequadrant-CCD, the PC1 calculates the coordinates ofthe image centroid relative to the center of thequadrant-CCD. The PCI then outputs voltage sig-nals to the tip-tilt mirror necessary to return theimage to the center position. The quadrant-CCD ismounted on a remotely controllable x-y translationstage to permit precise centering of the star behindthe occulting mask. The closed-loop system typi-cally operates at a sampling frequency of 100 Hz, witha 1.2 ms lag between each readout of the quadrant-CCD and the corresponding adjustment of the tip-tiltmirror. A detailed discussion of the characteristicsof the quadrant-CCD detector has been given byClampin et al.

21; therefore, only a brief description

follows.Because the frequency spectrum of the image mo-

tion may contain significant power out to 50 Hz forsmaller-aperture telescopes, closed-loop correctionrates up to 300 Hz may be required to sample theturbulence well. Thus a sensor capable of detectingthe motion of a point source at such rates is needed.We selected the quadrant-CCD built by Tektronix foran investigation of alternative fine-guidance sensorsfor the Hubble Space Telescope.22 The quadrant-CCD is a three-phase front-side-illuminated devicehaving four 100 ,tm x 100gm pixels that can be readout through a serial register at rates in excess of 1kHz. The device has a peak quantum efficiency of

40% and a read noise of approximately 10 e- rms.Cooling to -40 C is accomplished by using a four-stage thermoelectric stack and yields negligible darknoise for integration times < 100 ins. The perfor-mance of the quadrant-CCD is determined by analy-ses of the x and y transfer functions and of the noiseequivalent angle (NEA). Each transfer function re-flects the response of the quadrant-CCD as an appro-priately sized image is slewed across the chip. Theregion of each transfer function in which the re-sponse changes polarity has been shown to be quitelinear and encompasses the expected range of imagemotion.2 ' These characteristics make the quadrant-CCD extremely suitable for image-motion sensing.The NEA is a measure of the uncertainty in the imagecentroid arising from photon and read noise. It isdefined as

NEA= (10)T x SN (0

where T is the slope of the transfer function and S/Nis the signal-to-noise ratio of the image. The sys-tem's limiting magnitude is determined from thepoint at which the NEA becomes comparable with theimage-motion amplitude measured by the system.

For the ESO 2.2-m Max Planck Institute (MPI)telescope, the NEA becomes appreciable at visiblemagnitudes of 10-11 for 10-ms exposures. Thislimiting magnitude could be extended by improvingthe quadrant-CCD quantum efficiency through thin-ning and antireflection coating the device, but it isquite suitable for our current scientific objectives.

The controller electronics for the quadrant-CCDare a modified version of the Palomar Observatorysystem described in detail by Gunn et al.23 PCicontrols the quadrant-CCD system through a direct-memory access card, which interfaces to the quadrant-CCD controller electronics. Because it takes 1.2 msto read the chip, compute the centroid, and output theappropriate correction signals to the tip-tilt mirror,CCD integration times > 2 ms are required for theoperation of the feedback loop. During the computa-tion of the centroid, the pixel values are thresholdedto discriminate cosmic-ray events. If the rms imagemotion exceeds a predefined value, the imaging cam-era's shutter is closed, permitting short periods of badseeing to be rejected in real time and thereby improv-ing the quality of the final image. For 1- to 2-intelescopes, typical integration times of 10-20 ms areused to sample the image-motion power spectrumadequately. During operation of the feedback loop,the PCI software provides a real-time graphic displayof the centroids and image-motion statistics. Image-centroid data may also be stored for subsequentpower-spectrum analysis.

The Coronagraph

The coronagraph section of the AOC is shown con-tained within the dashed box in Fig. 2. The occult-ing mask M3, located at the reimaged telescope focalplane, marks the entrance to the coronagraph. It ismounted on a remotely controllable x-y translationstage to permit precise positioning anywhere in thefield. The occulting mask is made by evaporatingaluminum through a small pinhole onto a clear glasswindow. Masks ranging in size from 1 to 6 arcsec(depending on the telescope plate scale) have beenmade and are easily interchangeable with evolvingseeing conditions. The occulting mask may be re-placed with a beam splitter or dichroic to permitdirect imaging and image-motion sensing of a singleobject.

An apodizing mask is placed at the plane of thereimaged telescope exit pupil following M3. Thismask is a Lyot stop used to suppress the lightdiffracted by the telescope aperture and secondarymirror-support assembly. At the focal plane, suchdiffracted light from a bright star inhibits the detec-tion of faint circumstellar emission. An apodizingmask that reduces the pupil radius by 20% willeffectively reduce the diffracted light at the focalplane by more than an order of magnitude. Thesuppression of diffracted light, however, comes at theexpense of a smaller effective aperture. This smalleraperture may present difficulties for the detection offaint circumstellar material with conventional corona-


graphs, but these difficulties are countered by theimproved signal-to-noise ratio in the images obtainedwith the AOC.

Lens L5 reimages the circumstellar field onto theimaging camera with a magnification of 6. Thelight is spectrally filtered by F2 for broad- or narrow-wavelength band imaging. The imaging camera sys-tem is manufactured by Photometrics Ltd. and em-ploys a Thomson-CSF 384 x 576 pixel CCD. TheCCD has a spectral range of 0.4-1.02 p1m, with a peakquantum efficiency of 38% at 0.70 pum. The pixelsize is 23 tim, which with the magnification from L5provides for a well-sampled point-spread function.The format of the CCD has permitted fields of view of20-60 arcsec, depending on the telescope Plate scale.The read noize of 6 e- and a dark count of < 1 normalweight h-1 when the CCD is cooled to -120 C areboth adequate for the detection of faint circumstellarmaterial.

Image acquisition and storage is controlled fromPC2 through a general purpose interface bus to theCCD camera controller. Supporting software hasbeen written to assist in observing tasks, such astarget acquisition and telescope focusing. Once thetarget has been acquired, camera control is switchedto PC1, which is part of the image-motion compensa-tion system. As we described previously, PC1 sus-pends the exposure during periods of particularly badseeing or errant telescope tracking. Once the expo-sure is completed, control is returned to PC2 forimage storage.

Performance of the AOC

Demonstration of Image-Motion Compensation

Observations using the AOC were conducted duringthe nights of 24-30 May 1990 with the ESO 2.2-mMPI telescope at La Silla, Chile, and again during 1-6December 1990 with the 2.54-m DuPont telescope atthe Las Campanas Observatory in Chile. During thecourse of the scientific program (a survey of circum-stellar disks around infrared excess stars), additionalimages were obtained to evaluate the image-motioncompensation system. The telescopes are fi8 andf/7.5, respectively, both yielding a plate scale of 0.04arcsec pixel-' at the imaging camera. Because theAOC is designed to sample diffraction-limited imagesadequately, the images were oversampled and suit-able for high-precision-resolution comparisons. Fur-ther, the entire imaged field lay within the correlationregion for image-motion compensation determinedfrom relation (9). Observations of several stars weremade with R-band (XA 650 mm, AX 100 nm) andI-band (XA 830 nm, AX 200 nm) filters, whichwere placed at the location marked F2 in Fig. 2. Foreach star, an exposure was taken with the image-motion compensation system operational; the expo-sure was immediately followed by another taken withthe system off. A closed-loop sampling frequency of100 Hz was used for all observations in which theimage-motion compensation system was operational.The quadrant-CCD beam was only neutrally filtered,

so the effective bandpass was determined by theCCD's spectral response over 500-900 nm. Thestars were sufficiently bright to ensure that thequadrant-CCD NEA was negligible for each observa-tion. The size of the stellar image at the quadrantCCD was limited by lens L4 to less than one pixel for 1arcsec seeing conditions. This limitation guaran-teed accurate computation of the image centroid.To investigate the system performance as a functionof Diro, we made observations with the full 2.2-m and2.54-m apertures and also with subapertures of 0.7,0.6, and 0.5 m, which were obtained by insertingstops at the reimaged telescope exit pupil correspond-ing to the position of mirror Ml. The maximumstop diameter was constrained by the dimensions ofthe unobscured region of the telescope primary mir-ror.

The results of the image-motion compensation testobservations are summarized in Table 1. Columns1-5 provide information concerning the object, date,filter, telescope aperture, and exposure time for eachobservation. For I Velorum and HR 394, which arevisual binaries with respective separations of 7.2 and5.0 arcsec, image-motion sensing was performed us-ing the occulted brighter star, and resolution measure-ments were made on the fainter companion. Image-motion sensing and direct imaging of the remainingtwo stars, HR 7575 and p. PsA, were conductd using abeam splitter transmitting approximately 10% of thelight to the coronagraph and 90% to the quadrantCCD. Columns 6 and 7 list the FWHM's of theimage profiles in arcseconds for the uncorrected andimage-motion corrected images, respectively. Thesevalues reflect the averages of the FWHM's measuredalong orthogonal CCD directions without removal ofany contribution to the image spread from the tele-scope optics. Column 8 lists the resolution gain,defined as the ratio of the FVHM's of the uncorrectedand corrected images, for each observation. Inspec-tion of these gains shows that in all but one case animprovement in resolution was obtained. To ourknowledge, the gain of 2.16 achieved with the ESO2.2-m telescope stopped to 0.6 m is the highest yet

Table 1. Performance of the Image-Motion Compensation System

Expo- Un-sure corrected Corrected

D time FVHM FWHMObject Date Filter (m) (s) (arcsec) (arcsec) Gain

I Vel 5/25/90 R 2.2 120 1.20 0.97 1.24I Vel 5/26/90 R 2.2 30 1.46 1.45 1.01HR 7575 5/27/90 R 2.2 60 1.23 1.13 1.09HR 7575 5/27/90 R 2.2 60 1.46 1.17 1.25HR 7575 5/27/90 R 2.2 60 1.31 1.19 1.10HR 7575 5/27/90 R 2.2 60 1.39 1.21 1.15HR 7575 5/27/90 R 0.5 120 1.07 0.62 1.73I. PsA 5/27/90 R 0.6 120 1.06 0.49 2.16. PsA 5/27/90 R 0.6 180 0.91 0.44 2.07HR 394 12/7/90 I 2.54 60 0.95 0.78 1.22HR 394 12/7/90 I 0.7 100 0.94 0.47 2.00HR 394 12/7/90 I 0.7 100 0.89 0.46 1.93


reported for wave-front tilt correction at optical wave-lengths.2 >27 The tests conducted with the 0.5-, 0.6-,and 0.7-m subapertures produced gains between 1.73and 2.16, implying that D/ro 3-4 and that themaximum resolution improvement predicted byFried18 was attained.

Profiles of the pair of uncorrected and correctedimages of . PsA with the measured gain of 2.16 areshown in Fig. 3. These profiles illustrate an improve-ment in the Strehl ratio (defined as the peak intensityof the aberrated image divided by the peak intensityof a diffraction-limited image) from 0.037 to 0.092.The corrected-image profile contains a sharp centralpeak and low-level wings that have the same angularextent as the seeing disk of the uncorrected image.These wings are typical of images obtained withpartially adaptive optics systems in which there arean insufficient number of actuated mirror elementsto correct for wave-front phase errors caused by smallspatial scales of turbulence.2 8

The determination of r from each uncorrectedimage is complicated by the uncertainty of the contri-butions to the image size from local facility (dome)seeing and the telescope optics. If facility seeing isignored, the atmospherically degraded image sizemay be estimated by deconvolving in quadrature thetelescope point-spread function from the uncorrectedimage. The corresponding value of r may then becalculated using Eq. (3). Facility seeing generallycannot be ignored, however, so the resulting value ofro reflects the combined effects of turbulence causedby both the atmosphere and local thermal gradients.

Because the contribution of the telescope optics tothe image spread was not measured during eitherobserving period, r has been estimated for eachobservation using the uncorrected-image FWHM'slisted in Table 1. (The presence of the telescopecomponent renders each computed value of r anunderestimate of the true value.) Each gain has

1000

800

600

400

200

u . . I , -3 -2 -1 0 1 2 3

Arcsec

Fig. 3. Stellar profiles of AOC images of p. PsA taken with(solid curve) and without (dashed curve) image-motion compensa-tion. The profiles reflect a reduction in image width from 1.06 to0.49 arcsec and a 149% increase in the Strehl ratio. The imageswere obtained with the ESO 2.2-m MPI telescope stopped to 0.6 m.

been plotted against its respective value of Diro inFig. 1 to permit comparison with theory. The errorbars for each datum reflect the uncertainty in themeasurements of the image FWHM's and the widthof the filter bandpass. For the observations madewith the full aperture of each telescope (i.e., for Diro> 14), the gains were lower than predicted. Theeffect of an underestimated value of ro on this resultcan be investigated. For the ESO 2.2-m telescope,Maaswinkel et al.25 previously adopted a figure of 0.5arcsec for the image size caused by the telescopeoptics at full aperture for zenith angles of 30 to 45.Each observation conducted with the full 2.2-m aper-ture was done at a zenith angle within this range.When this value of the telescope component and anadditional 0.04 arcsec (obtained from ray-tracing theAOC optics) are deconvolved from the FWHM of eachuncorrected image, at most a 6% increase in theresolution gain is obtained. After computing thenew values for r based on the deconvolved imageFWHM's, we find that the resulting values of Diro arereduced by no more than 9%. These revisions areinsufficient to alter significantly the location of thefull 2.2-m aperture data with respect to the theoreti-cal gain curve in Fig. 1. The same is probably truefor the observation made with the full-aperture 2.54-mtelescope. The data obtained with the telescopesubapertures are scattered about the peak of thetheoretical gain curve. Estimated changes in thegains and computed values of r after deconvolutionalso affect the location of these data in Fig. 1 inconse-quentially. However, as is discussed in Section 2,Fried's calculation of the maximum resolution gain islow by 10%, implying that the peak of the curveshown in Fig. 1 should be higher by 5%. Thesubaperture data, therefore, generally lie at or justbelow the predicted maximum gain obtainable throughimage-motion compensation.

Effects of Centroid Anisoplanatism and Finite YoAlthough the resolution gains measured with thetelescope subapertures matched theoretical expecta-tion, those recorded with the full apertures fell short.Two possible explanations for this dichotomy are that(1) the effectiveness of the AOC image-motion compen-sation system is reduced for larger values of Dro, and(2) the role of image motion in the degradation of thefull-aperture image is overestimated. Yura andTavis' 6 have addressed the first issue by investigatingthe ability of image-centroid tracking sensors to yieldaccurate overall wave-front tilt information. By com-paring the variances of the wave-front tilt and theinstantaneous image centroid, they concluded thatthe wave-front tilt angle is not completely correlatedto the angular position of the image centroid.Although the discrepancy between the variances issmall (the wave-front tilt variance is greater by 7%,independent of Dro), this centroid anisoplanatismsignificantly reduces the improvement in the Strehlratio expected from wave-front tilt correction forDiro 10. According to Fig. 2 of Ref. 16, the Strehl


I

Iq

19

2�1

5�.Ei

ratios of the corrected images obtained with the full2.54-m and 2.2-m apertures should have been dimin-ished by factors of 5 and 10, respectively. If theFWHM of each corrected image is assumed to beinversely proportional to its peak intensity (as in thecase of a Gaussian profile), then the resolution gainsrecorded for these observations should also have beenlower than expected by factors of 5 and 10. How-ever, as we see in Fig. 1, only one of the gainsmeasured with the full apertures was reduced soseverely. It is possible that these gains primarilyreflect the removal of image motion induced fromnonatmospheric sources (such as telescope vibra-tion); however, without proper characterization ofsuch image motion, the effect of centroid anisopla-natism on AOC performance cannot be fully assessed.

The presence of centroid anisoplanatism does notpreclude an investigation of reduced image motion forlarger values of Diro. For the 0.6-m and 0.7-msubaperture observations, the measured gains of1.93-2.16 imply that any reduction of image motioncaused by a finite outer scale Yo must be small. (The

0.4

0.2

0

-0.2

-0.4

-0.6102 4 6

Time (ec)

(a)

lower gain recorded for the single 0.5-m subaperturetest is not understood, but may be a result of aberra-tions induced by the off-axis aperture stop.) How-ever, the effect of a finite 2 o on the full-aperture gainsmay be evident, given Bornino's' 4 estimate of 2 <7.67 m. This possibility can be checked by usingsimultaneous measurements of the image-centroidvariance and r. During the 0.7-m and 2.54-maperture observations of HR 394, the quadrant-CCDimage centroid was recorded every 10 ms for a periodof 10.24 s. The components of the image centroidmeasured along one axis of the quadrant-CCD foreach aperture are shown in Figs 4(a) and 4(b). Thedominant influence of high-frequency image motionon the long-exposure image spread for small telescopeapertures is clearly shown. The centroid variancesare 0.043 arcsec2 and 0.013 arcsec2 for the 0.7-m and2.54-m aperture observations, respectively. The cor-responding values of ro are obtained from the FWHM'sof the uncorrected images of HR 394 recorded inTable 1. These images were recorded at positionssufficiently near zenith to validate their use in this

0.6

0.4

0.2

0

-0.2

-0.4

-0.60 2 4 6

Time (sec)

(b)

. . . . . . . I . . . I . . l I 8 1 0 I

0.1

0.01

0.001

2 0.0001

*V 1 0

F 1 0

10

o -

to L0.1 10 100

0.1

0.01

- 0.001

2 0.0001

vi 1 0

I

, Il -t

10 -

10-0.1 10 100

Frequency (Hz) Frequency (Hz)

(c) (d)

Fig. 4. Image motion of the star HR 394 recorded at 10-ms intervals for 10.24 s: (a), (b) Change in the image centroid for observations

with the 0.7-m subaperture and the 2.54-m aperture, respectively; (c), (d) Computed one-sided power spectral density per unit time for the

image centroids of (a) and (b). The long-dashed lines represent the f-2 3 power law for Kolmogorov turbulence. The short-dashed linesindicate the level of the system noise.


. ~ ~ ~ ~ ~ ~ . .. . . . . .

,3'1I

Z.92I

I11

.9

:9

EI

ii

8 10

analysis. Using relation (5), with an appropriatecorrection for centroid anisoplanatism, we estimate2o to be 1.5 m from the subaperture data and 3.5 mfrom the full-aperture data. These estimates arequite disparate, and the value of 2Y obtained for the0.7-m subaperture is remarkably small given theresolution gains measured at that aperture.

It is evident from relation (5) that estimates of Y'are sensitive to errors in the measurements of U 2, ,and r. Because the image size at the quadrant CCDcould not be precisely measured on the telescope,calibration of the image centroid for each aperturewas performed using a laboratory-generated transfercurve obtained for the corresponding corrected-imagesize from Table 1. Assuming an uncertainty of 0.1arcsec for the quadrant-CCD image size and employ-ing the previously adopted uncertainties for and r,we find that the estimated uncertainties for the twovalues of 2Y are 0.8 m and ± 0.7 m, respectively.These uncertainties are insufficient to bring thevalues of 2Y for the two apertures into agreement.The remaining discrepancy may be attributed to thebrevity of the centroid measurements compared withthe uncorrected-image exposure time, which mayhave caused an undersampling of the low-frequencyimage motion. The disparity may also be a result ofthe added degradation of the long-exposure imagefrom nonatmospheric sources. The long-exposureimage size has been observed to be more sensitivethan the image-motion variance to facility seeing29

and telescope focus30; without proper characteriza-tion and removal of these components of the imagespread, 2Y will be underestimated. Telescope vibra-tion must also be characterized and eliminated fromthe analysis. These factors were not measured dur-ing the observations, so the degree to which a finite2Y affected the full-aperture resolution gains remainsambiguous.

Power-Spectrum Analysis

The amount of image motion at a frequenty f can bedetermined through the computation of the one-sidedpower spectral density (PSD) per unit time of theimage centroid. The PSD's for the centroids ob-tained with the 0.7- and 2.54-m apertures are shownin Figs. 4(c) and 4(d). Each PSD is normalized to themean-squared centroid. For Kolmogorov turbu-lence, the PSD c -2/3, regardless of wind directionsThe dashed line in each figure represents the Kolmog-orov power law scaled to best fit the low-frequencyend of the 0.7-m aperture PSD. Despite the exist-ence of a finite outer scale, the fit to the 0.7-maperture PSD is quite good up to 3.7 Hz. At thisfrequency the PSD drops considerably, reflecting thepoint at which spatial averaging over the aperturebecomes significant. (The PSD ultimately falls tothe level of the system noise, which is represented bythe short-dashed line.) This turnover frequency, fo,is related to the aperture size and to v11, which is thecomponent of the wind velocity parallel to the direc-

tion of image motion, by15

fo 0.2 . (11)

The wind speed along the given axis of the quadrantCCD for D = 0.7 m and fo = 3.7 Hz is approximately13 m s1. Within the 0.1-3.7-Hz region of the2.54-m aperture PSD the overall power is diminished,again revealing the combined effects of centroid aniso-planatism and a finite outer scale on low-frequencyimage motion. For this aperture fo 0.8 Hz.From relation (11), we see that v- 10 m/s-1, whichis in rough agreement with the subaperture case.

Comparison of Results

Several other systems designed to stabilize telescopeimages at optical wavelengths have been developedand tested, beginning in 1983 with the ISIS ofThompson and Ryerson.24 More recent publicationsof performance tests have reported varying degrees ofsuccess. Maaswinkel et al.2 5 have developed theDISCO adapter for the ESO 2.2-m MPI telescope,employing a fast mirror unit and an ICCD camerawith electronics to calculate the image centroid.Operating at a 50-Hz correction rate and with the fulltelescope aperture, they reported an improvement inimage resolution in 44% of their trials, with a bestcorrection from 0.8 to 0.66 arcsec FWHM. Using ananalysis of image centroids and uncorrected-imagewidths, they determined the outer scale of turbulenceto be 5-20 m. (In retrospect, these values apply toan estimate of 2Y, not Lo.) The effects of centroidanisoplanatism were not considered.

Racine and McClure26 have reported the results of asimilar experiment at the 3.6-m Canada-France-Hawaii Telescope using HRCam, a system employingessentially the same elements for image-motion sens-ing and correction as the AOC. They achieved reso-lution improvements from 0.61 and 0.56 arcsec forthe full aperture, and from 0.45 to 0.35 arcsec for a1.2-m subaperture. They concluded that the tele-scope optics and facility seeing were responsible forthe failure to achieve more significant improvementsgiven the excellent seeing conditions (ro 40 cm).In their analysis, Racine and McClure did not con-sider the effects of centroid anisoplanatism or a finiteouter scale, which for a 3.6-m aperture may limit therole of image-motion compensation to the removal ofsome elements of facility seeing and telescope vibra-tion.

Doel et al.27 addressed the problem of a finite orderscale for the 4.2-m William Herschel Telescope withthe MARTINI instrument, which separately cor-rected for image motion across each of six 0.6-msubapertures. Image-motion sensing for all the sub-apertures was accomplished with a single photon-counting detector, and corrective signals were sent tosix piezoelectrically driven mirrors located at a conju-gate plane of the turbulent layer. The system permit-ted comparison of postexposure-sharpened imagesconstructed from photon-arrival data with real-time

1 August 1992 I Vol. 31, No. 22 / APPLIED OPTICS 4413

sharpened images recorded by the detector for each ofthe six subapertures. From an uncorrected-imageFWHM of 0.6 arcsec, Doel et al. reported a bestreal-time correction of 0.35 arcsec (a resolution gainof 1.7) and a best postexposure reconstruction of 0.25arcsec. The failure to achieve maximal correction inreal time was attributed to unrefined mirror-position-ing algorithms.

Coronagraphic Performance

The performance of a coronagraph is assessed by itsability to image an object of low surface brightness inthe proximity of a comparatively bright star. Thedegree to which a coronagraph can limit the effects ofdiffracted and scattered light at the focal plane gov-erns this performance. As is discussed in Section 3,suppression of light diffracted by the telescope aper-ture and secondary-mirror support assembly is accom-plished by placing an apodizing mask at a location ofthe reimaged exit pupil within the AOC. Becausethe location of this diffracted light at the pupil planeis unaffected by wave-front tilt, image-motion compen-sation does not improve the efficiency of pupil planeapodization over that of conventional coronagraphs.For all the observations described above, diffractedlight was satisfactorally suppressed using apodizingmasks that reduced the effective telescope apertureby no more than 30%.

Image-motion compensation does, however, en-hance coronagraphic performance by reducing theamount of light scattered into the outer regions of theseeing disk. This enhancement affords two advan-tages when imaging with the AOC instead of aconventional coronagraph. First, for a given expo-sure length (determined, e.g., by the saturation of theimaging detector) a smaller occulting mask may beused, thereby exposing regions closer to the brightcentral star. This point is illustrated by again exam-ining the stellar profiles shown in Fig. 3. To occultthe region of the uncorrected image with pixel intensi-ties greater than 100 photons s-1 would require amask with a diameter of 1.6 arsec. To do the samewith the corrected image would require a 1.4 arcsecmask. Although this reduction in mask size ismodest (even for these images obtained with optimalDiro), it does predict a greater benefit when higher-order aberrations are corrected by the fully adaptiveAOC.

The second advantage of coronagraphic imagingwith the AOC is improved contrast in the circumstel-lar region. Image stabilization and reduction ofscattered light together result in a much-enhancedratio of signal from the circumstellar material tophoton noise from the occulted star. Consequently,the brightness limit for the detection of a faint objectnear the occulted star (after proper subtraction of theocculted stellar profile) is lowered. Figure 5 showsthe R-band magnitude detection limit for a hypothet-ical star as a function of distance from the R = 4.45magnitude star p. PsA. The upper and lower curvesare based, respectively, on the radially averaged pro-

86;

E

T

10

12

14

160 2 4 6

Radial Distance (arcsec)

Fig.5. LimitingR-band magnitude for detection of a hypotheticalstar as a function of distance from 1i PsA. The curves are basedupon radial averages of the 180-s exposures listed in Table 1. Thesolid curve represents the uncorrected (conventional coronagraph)case, whereas the dashed curve represents the image-motioncorrected (AOC) case; p PsA itself has an R magnitude of 4.45.

files of the uncorrected and corrected 180-s exposuresof p PsA recorded in Table 1. The detection limit ata given distance was defined by the point at which thepeak of the hypothetical star profile equalled twicethe photon noise of the p PsA image. The hypothet-ical star image was given the same Strehl ratio as thecorresponding image of pu PsA. Figure 5 shows thatthe AOC may reveal stellar sources up to 2 magni-tudes fainter than those detectable with a conven-tional coronagraph throughout the immediate circum-stellar environment.

Three-dimensional surface plots of actual corona-graphic images, which give an exaggerated demonstra-tion of the improved image contrast obtainable withthe AOC, are shown in Figs. 6(a) and 6(b). Theocculted star in each figure is e Sagittarii, a B-typestar with a visual magnitude of 1.85. The observa-tions of e Sgr were conducted at ESO as part of oursurvey of infrared excess stars and other circumstel-lar disk candidates.3 ' Several 60-s exposures wereobtained using the 0.6-m subaperture of the2.2-m MPI telescope and a 4.7-arcsec occulting mask.Such a large mask was necessary because of thebrightness of E Sgr and the less-than-favorable seeingconditions. Figure 6(a) shows the surface plot ofthe uncorrected image of e Sgr. Inspection of thehalo of light surrounding the occulting mask showsthat the mask was well centered on the star andsuggests the presence of an unresolved feature at theedge of the mask. Figure 6(b) shows the correctedimage of e Sgr. This plot reveals the unresolvedfeature to be a star with a visual magnitude of 8.This star, whether a companion to E Sgr or a fieldstar, is a likely cause of the measured infrared excessof e Sgr. Further analysis of these images will bereported in an astronomical journal.


(a)

(b)Fig. 6. Three-dimensional surface plots of AOC images of theinfrared-excess star e Sgr, obtained with the ESO 2.2-m MPItelescope stopped to 0.6 m and a 4.7-arcsec occulting mask. (a)Plot of the uncorrected image, showing an unresolved feature atthe edge of the occulting mask. (b) The corrected image, whichreveals the feature to be a star and a likely cause of the measuredinfrared excess. The two images illustrate the improved contrastin the circumstellar region obtainable with the AOC.

Concluding Remarks

Through successful implementation of an image-motion compensation system, the AOC has demon-strated significant improvement in the angularresolution and contrast of coronagraphic images.Performance tests under mediocre seeing conditions(0.9-1.5 arcsec) showed maximal resolution gainswhen Dro 3-4, which is in accordance withtheoretical predictions. Tests conducted for D/r >14 resulted in gains lower than those predicted. Thelatter results, together with an analysis of short-exposure image-centroid data, indicate that (1) cen-troid anisoplanatism may indeed restrict the effective-ness of centroid trackers as wave-front tilt sensors forlarge values of Diro, and (2) the role of image motionin the degradation of long-exposure images for D > 2m may be smaller than expected under conditions offully developed Kolmogorov turbulence.

Because centroid anisoplanatism and a finite outerscale together reduce the effectiveness of image-motion compensation for intermediate-size tele-scopes, such correction is most beneficial for aper-tures less than 2 m. In particular, 1-m-classtelescopes based at good sites may achieve 0.3-0.4arcsec images during subarcsecond seeing conditionswith a relatively small investment in technology.The use of image-motion compensation for largeapertures, however, may be feasible for the nextgeneration of new technology telescopes, for whichthe telescope-tracking specifications preclude the useof traditional autoguiding systems. In such cases,fine guidance with a tip-tilt mirror would offer an

effective alternative to an autoguider, thereby permit-ting optimum telescope performance. Although im-age-motion compensation at optical wavelengths isgenerally not well suited for telescope aperturesgreater than 2 m, such correction at near-infraredwavelengths (1.0-5.0 m) is quite appropriate. Atthese wavelengths r typically ranges from 30-360cm, and values of Diro favorable for optimal image-motion compensation are available even for 4-m-classtelescopes.

The authors thank the Seaver Institute forits support of adaptive-optics development at TheJohns Hopkins University. We are grateful to theobservations of the Carnegie Institution of Washing-ton for providing observing time at Las Campanas aswell as to the observatory staff for its dedicatedassistance. Observing time at the ESO 2.2-m MPItelescope was awarded by the Max Planck Institute incollaboration with F. Paresce and J. Staude. Fi-nally, we acknowledge the enthusiastic support ofadaptive-optics development at The Johns HopkinsUniversity by the Center for Astrophysical Sciences.This paper is based on data obtained at the ESO andthe Las Campanas Observatory.

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High-resolution ground-based coronagraphy using image-motion …golim/papers/golimowski1992.pdf · 2007. 2. 25. · Then relation (5) may be expressed as 0-1 !S U 2. (7) Using Borgnino's14