10­µm interferometry on the VLTI with MIDI

adapted and updated version of "10 µm interferometry on the VLTI with the MIDI instrument", by Ch. Leinert, U. Graser, L.B.F.M. Waters, G. Perrin, B. Lopez, V. Coudč du Foresto, A. Glazenborg-Kluttig, J. C. de Haas, T. M. Herbst, W. Jaffe, P. J. Lčna, R. Lenzen, R. S. Le Poole, S. Ligori, R. Mundt,  J. W. Pel, I. L. Porro, and O. von der Lühe, published on Proc. SPIE, Vol. 4006, "Interferometry in Optical Astronomy", p. 43, 2000.

HTML version edited by S. Ligori (Feb 25, 2002)

1. BACKGROUND

Interferometry with the ESO Very Large Telescope Interferometer (VLTI) on Paranal will include the four 8 m telescopes of the VLT (called 'unit telescopes' or UTs) as well as three relocatable outrigger telescopes of 1.8 m diameter (called 'auxiliary telescopes' or ATs). Observations with the VLTI started in 2001 (see ESO press release). MIDI, the mid­infrared interferometric instrument covering the astronomical N band from 8 µm to 13 µm, will be the first scientific instrument available at the VLTI. Half a year later, the near­infrared closure­phase imaging instrument, called AMBER2, will arrive on Paranal. A dual­feed system called PRIMA1, 3, which will add faint source and phase­referenced imaging as well as an astrometric mode to the VLTI, will follow in 2003.

 

2. RATIONALE FOR 10 µM INTERFEROMETRY WITH THE VLTI

The high thermal background and the reduced spatial resolution at this comparatively large wavelength are obvious disadvantages connected with 10 µm interferometry, and the need to cool the detector and its environment to very low temperatures adds technical complexity. Probably for these reasons, only two 10 µm interferometers have been built before. The wide­band interferometer SOIRDETE5 could not calibrate its observed fringes because of strong fluctuations in the thermal background. ISI6 succeded with a narrow­band heterodyne technique7, 8, but is limited

in calibrating fringes to N = ­1.8 (200 Jy). Therefore direct interferometry in the 10 µm band, as envisaged by MIDI, still will be a new undertaking, promising new results or results on new type of objects. This attempt will be particularly promising at the VLTI which offers

 

·         big apertures of 8 m diameter (important because in the background­limited case the S/N ratio scales ~D2 )

·         long baselines (up to 130 m, corresponding to a spatial resolution of lambda/D = 16 mas)

·         four telescopes (i.e. six readily available baselines)

 

In this combination the VLTI is unique among present­day observatories, including the Keck interferometer, which has slightly larger telescope dishes but only one 75 m baseline. These prospects led us to propose the mid­infrared interferometric instrument for the VLTI.

3. BASIC PARAMETERS DEFINING THE INSTRUMENT

Most of the parameters defining the operation of the instrument are given by the atmosphere, some by the design of the delay line optics. However, the choice to observe only one baseline at a time was made to keep sensitivity.

 

 

Telescope diameter

UTs

8 m

 

ATs

1.8 m (used for bright sources)

Baselines

UTs

47...130 m

 

ATs

8...200 m

Resolution

Lambda/D for 100 m baseline

20 mas

Wavelength coverage

 

N band (8 µm - 13 µm)

 

expandable to

Q band (17 µm - 26 µm)

Field of view

 

± 1"

Airy disk (FWHM) at 10 µm

for 8 m telescopes

0.26"

 

for 1.8 m telescopes

1.14"

Sampling time for fringe measurements

determined by fringe motion

100 ms

Atmospheric stability

for chopping

200 ms

Differential dispersion

in 100 m of air

0.9 µm (10 µm to 20 µm)

46 µm (1.6 µm to 10 µm)

Input beam diameter

from UTs

80 mm (compressed to 18 mm)

 

from ATs

18 mm

Detector (320x240 pixels)

pixel size

50 µm

 

full well capacity

≈ 2 107 electrons

 

read noise

≈ 1000 electrons

Background at UTs (in Airy disk)

from sky

1.6 1010 photons/s

 

from VLTI mirrors

1.2 1011 photons/s

Limiting N magnitude without fringe tracking

with UTs

4 mag (1 Jy)

 

with ATs

0.8 mag (20 Jy)

Limiting N magnitude with external fringe tracking

with UTs

9 mag (10 mJy)

 

with ATs

5.8 mag (200 mJy)

 

Table 1. Basic parameters of the MIDI instrument

 

 

Figure 1. Optical concept

 

4. GOALS

The scientific promises of a mid­infrared interferometer strongly depend on its limiting sensitivity. Our goal is to achieve the sensitivity limited by the photon noise of thermal emission from the VLTI train (1.5 x 1011 photons/s per Airy disk of radius lambda/D = 0.26" with a VLTI transmission of 40%), assuming that the fringe measurement happens within one coherence time of 100 ms, that the instrumental transmission of MIDI is 60% and that 75% of the light fall into the Airy disk and are useable for the interferometric measurements. This gives the following performance on the UTs with broad band observations (limiting brightness scales like sqrt(n) when splitting the band into n spectral channels):

 

Point source sensitivity:

·         N = 4 mag (1.0 Jy) in self­fringe­tracking mode, with 8 m telescopes and tip/tilt correction

·         N = 9 mag (10 mJy) with external fringe tracking

 

Accuracy of visibility:

·         5 % faint sources

·         1 % bright sources, beam cleaning by spatial filtering

 

Phase measurement: by external referencing

 

The very large gain in sensitivity possible with a fringe tracker (fed by an adaptive optics system) cannot be overemphasised.

To reach these goals, we want to limit the instrumental loss in sensitivity to correlated flux (visibility loss) to less than 25 %. This requires alignment of the beams to 1% of their diameter, ± 5" in their axes, and an optical quality of the surfaces of lambda/8 peak­to­valley, measured at optical wavelengths, e.g. 632 nm10.

 

 

Figure 2. Design of the beam combining optics inside the cryostat. M1 and M2 are confocal paraboloids, M3, M4

and M5 flat mirrors. The beam­combining 50% : 50% coated surface is indicated by a pointer. Not shown: a cold

shutter located about halfway between the cold stops and the entrance windows.

 

5. CONCEPT

A schematic representation of the layout of the instrument is given in Figure 1. Since radiation at 10 µm is dominated by thermal emission from the environment, most of the instruments optics has to be in a dewar and to be cooled to cryogenic temperatures (4 K ­ 8 K for the detector, 40±5 K for the cold bench, 77 K for the outer radiation shield).

Good suppression of the thermal radiation of background and surroundings requires to design for both a cold pupil and a cold field stop inside the instrument.

We choose to have beam combination in (or close to) the pupil and to detect the signal in the image plane. This appeared to us the most promising way to support the baffling against the very high thermal background and to

reduce the effects of variable pixel responsivity, which is common among mid­infrared detectors. This concept is shown schematically in Figure 1:

From the left, the afocal beams from two telescopes of the VLTI are approaching the instrument. Their nominal diameter is 80 mm, and they are reduced to 18 mm by a beam compressor provided as part of the VLTI infrastructure, represented here for simplicity by two lenses.

After the four folding mirrors of a small experiment­internal delay line, the compressed beams enter the cryostat (cold box) through the entrance window (Dewar window). The telescope pupil is imaged by the VLTI delay line

optics onto a cold pupil stop to provide the needed suppression of thermal emission from outside the beams. Next, an intermediate focus is formed, where different masks or spatial filters can be introduced for additional suppression of unwanted radiation. (If no spatial filters are used, the detector pixels, which are much smaller than the Airy disk, still provide an alternative way to limit the spatial region admitted for the measurement). Then the beams are recollimated and move on to combine on the surface of a 50%:50% beam splitter which coating is indicated in the

Figure on the lower back side of the ZnSe plate. This is the heart of the instrument.

From the beam combiner onwards, the two interfering beams have a common optical axis. Actually, there are two of such overlaid beams, one outgoing to each side of the beam combiner. These two outputs are modulated in

flux depending on the optical path difference of the interfering beams, but with opposite sense in because of energy conservation.

We measure the degree of coherence between the interfering beams (i.e. the object visibility at the actual baseline setting) by artificially stepping the optical path difference between the two beams rapidly over at least one wavelength within the coherence time of ≈ 0.1 s. This is done with help of the piezo­driven roof mirrors forming part of the small delay lines just outside the cryostat. Then, for both channels on the detector the fringe amplitude is determined from the modulating signal, usually in one of the methods known from stellar polarimetry9. The large and not precisely

known thermal background forces us to determine the total flux separately by a chopped measurement, chopping between the object and an empty region of the sky. Dividing fringe amplitude by total flux the visibility is obtained.

For good accuracy of the visibility determination, the relative fluxes of the combining beams have to be known at the time of the fringe measurement. To this end, part of the incoming light can be extracted out of both of the

incoming beams before beam combination, and these socalled 'photometric beams' are also imaged onto the same detector as the interferometric signal.

Spectral resolution is obtained by filters or with a prism or grism in the parallel beam after beam combination. This provides moderate spectral resolution and at the same time keeps the detector from saturating.

In principle, for the measurements with MIDI the full interferometric field of ±1" is available simultaneously.

This is a small area on the sky, but the point to emphasise is that there is at all an interferometric field beyond the Airy disk of a single telescope.

6. DESIGN

6.1. Detector

For detector we use the 320x240 Si:As Impurity Band Conduction (IBC) array manufactured by Raytheon. Pixel size is 50 µm x 50 µm, peak quantum efficiency over the 2­28 µm response range is > 40%, the active area > 95%, and less than 1% bad pixels are expected. Power consumption is ≈ 60 mW, and maximum frame rate 700 Hz. Detector control is quite flexible but complicated by the large number of controllable parameters. Our laboratory

tests will have to verify the critical quantities of full well capacity of 1.1 x 107 e- and the read noise. This will require fine tuning of signal size for best S/N ratio15.

6.2. Optics

The design of the cold optics16 is shown in Figure 2. For focal plane mask, filter, dispersing element, and camera different elements can be selected by moving a slider or a wheel.

 

cameras

field camera

lambda/D = 3 pixels

 

spectroscopic camera

lambda/D = 1x2 pixels (two in spatial direction)

 

pupil viewing camera

pupil diameter = 40 pixels

 

dispersing elements

grism

resolution per pixel = 520

 

prism

resolution per pixel = 60

 

none

for observations with filter

 

filters

 

10 filters

narrow­band to full N band

focal plane

open

full ±1" field

 

slits

1­4 lambda/D

 

diaphragms

1­4 lambda/D

 

10 µm monomode fiber

best beam cleaning17

 

 

In addition, special setups are available for testing and alignment. The positions for future 20 µm optical components already are provided, allowing an easy upgrade to this second wavelength range.

 

6.3. Cold bench

Figure 3 shows how the mechanisms associated with the different optical components are distributed within the 40 K envelope, and how they are mounted on the so­called cold bench base plate. The main design criterion has been to have a stable, stress­free construction out of one single material, in this case the aluminum alloy Al 6061­T651, where the annotation T651 indicates a special annealing heat treatment. Homologous contraction during cooldown (0.42% from room temperature to 35 K) will preserve the alignment of the optical paths within the 40 K envelope, deferring the alignment and adjustment tasks to the warm parts of the instrument. The 40 K radiation shield connected to the cold bench and the outer radiation shield connected to a liquid nitrogen tank at 77 K are not shown in Figure 3 for clarity, nor is the box­shaped cryostat. The outer dimensions of this cryostat are partially outlined by the the front end of the eight motor/encoder units and by the larger one of the two flanges on the closed cycle cooler. With dimensions of 850 mm x 598 mm on the table, 804 mm height, and a weight of 300 kg ­ 350 kg this is an instrument

of moderate size.

 

 

Figure 3. Design of the cold part of MIDI. The size of the cold bench to which the optical elements and the moving devices are mounted is 596 mm x 428 mm. The weight of the complete assembly, excluding motors and closed cycle cooler, is 28.9 kg.

 

 

Figure 4. MIDI setup in the interferometric laboratory. The optical table carrying the cryostat, external optics and auxiliary equipment has dimensions of 1500 mm x 2100 mm.

 

6.4. MIDI in the interferometric laboratory

Figure 4 shows how the cryostat18, with turbomolecular pump mounted, is arranged on the optical table of MIDI in the interferometric laboratory. The closed­cycle cooler, connected to the cryostat by a bellow (appearing black) is rigidly mounted to a separate massive block of cast material just next to the MIDI table. With respect to Figure 4, the delay lines of the VLTI would run left/right near the bottom the page. Dedicated beam compressors more to the right of the MIDI table in the interferometric laboratory keep the image of the telescope pupils on the cold pupil

stops inside the MIDI dewar with alongitudinal precision of ≈1 cm. The beams from the telescopes (any telescope pair can be chosen for the two input beams) approach the cryostat from the lower part of the figure, passing over the so­called warm optics bench, a separate breadbord with two corners cut out, and mounted directly on the large optical table. The small four­mirror internal delay lines close to the dewar are laid out asymmetrically in order to compensate for asymmetries in the way the beams are directed towards the instrument. The two alignment plates on the warm optics bench are removed during the observations. In addition to the calibration provided by the VLTI system LEONARDO, which is situated a couple of meters upstream of the instrument, MIDI has two calibrating

units of its own: a black­body screen which can be moved in and out of the field­of­view of the instrument, and a laser in the neighbouring room, the radiation of which can be made replacing the interferometric beams by moving in a small plate carrying the necessary optics. The path of the laser beam through the laboratory wall to the warm optics bench can be seen in the upper right of the figure.

 

Figure 5. The standard fringe sampling mode (``ABCD method'').

The optical path difference (OPD) between the interfering beams is modulated by the equivalent of one wavelength, either by having four steps, separated by lambda/4 (middle panel, measurement taken at dotted position), or by a continuous linear sweep (ramp) one wavelength (lower panel, integration over the shaded interval); and this modulation pattern

is repeated as needed. In both cases, the phase of the modulating signal signal is equal to tan-1 [(A-C)/(B-D)]+p/4, and the visibility proportional to sqrt[(A-C)2 + (B-D)2], with proportionality factors of 1.0 and 2*sqrt(2)/p, respectively.

 

7. OBSERVING WITH MIDI

Because 10 µm arrays have the bad reputation of unstable flat fields, the main observing modes for MIDI are using on­the­pixel comparison for background subtraction. In the so­called ``ABCD'' method (see Figure 5) the optical path difference (OPD) between the incoming beams is stepped or scanned through one wavelength. The detector pixels in the Airy disk of a sufficiently unresolved object then will experience a sinusoidal flux variation, with four measurements being taken per period. Since the method works from differences between these flux values measured

on the same pixel(s), it is comparatively insensitive to flatfield effects.

If the interferometric measurements are performed with dispersion, different ways of deriving the modulation can be applied. For non­zero OPD, constructive and destructive interference will follow each other when moving along the spectrum. This gives rise to a ``channeled'' (i.e. transversed by dark lines) appearance of the spectrum. The

distance between adjacent minima or maxima in the channeled spectrum is constant in optical frequency space and inversely proportional to the momentaneous OPD value. With some knowledge or assumption on the nature of the OPD fluctuations and on the wavelength dependence of visibility for the object then both, the OPD history during the measurement and the object visibility can be obtained by a fitting procedure11. The expectation is that by the associated increase in effective integration time, when compared to self­fringe tracking measurements, one magnitude

or more can be gained in limiting sensitivity. These so­called coherent integration procedures, which will as a side effect allow slow (a few s) OPD tracking, will also be available for observations with MIDI.

Table 2 gives an indication how the limiting magnitude for self­fringe tracking depends on the circumstances of the observations. Read noise and transmission of optics lead to the result that the achievable S/N ratio and hence limiting magnitude depends on spectral resolution, which should not occur in the truly background limited case.

 

Table 2. Estimated point source sensitivities for 100 ms integration time

 

 

Therefore, best sensitivity, N = 4.3 mag (slightly less than 1 Jy) may be expected for broad band observations. On the other extreme, one could decide to observe with fibers (60% coupling efficiency), using the grism with photometric channels (taking 35% of the light) and reading out the detector at its maximum rate of 4 ms per measurement. The resulting limiting magnitude for self­fringe tracking then would be N = ­1.1 mag (110 Jy) for an individual resolution element and N = 0.1 mag (43 Jy) for the combined signal of 10 resolution elements.

In all cases, external fringe tracking over a time interval T will improve the sensitivity considerably, theoretically by at least a factor of sqrt(T/0.1s) or already by 2.5 mag for even a modest 10 s interval of fringe stabilisation.

 

8. SCIENCE PROGRAMME

The scientific Potential of MIDI observations will be discussed in more detail elsewhere in these conference proceedings13. Apart from the spatial resolution given by the geometry of the VLTI array, it strongly depends on the sensitivity of the instrument and on the accuracy of visibility calibration. Before fringe tracking will be available on the VLTI in 2003, the limiting magnitude will be N = 4 mag (1 Jy) at best (see Table 2). When fringe stabilisation becomes available, fringe motion due to atmospheric turbulence will be compensated, and interferograms can blindly be added together without smearing the fringe signal. A total integration time of 15 min should improve the sensitivity by a factor of 100 to N = 9 mag (10 mJy). With this kind of performances, extragalactic studies come within reach of the instrument. However, it has to be stressed that these are point source sensitivities, related to correlated flux, and a somewhat extended source may have to be much brighter to produce measurable fringe

signals. Moderate accuracies of ≈ 5% ­ 10% in visibility are expected in general, although on bright sources, using photometric monitoring of the input beams by means of the photometric channels of the instrument, accuracies of 1% appear feasible.

 

 

Objects

Topic

Number with(without) fringe tracker

required telescopes

Active Galactic Nuclei

dust tori

5* (≈ 12)

UTs only

Young Stellar Objects

geometry and disk structure

6 (≈ 15)

UTs mostly

Extrasolar planets

detection by shift of light center

(2)

UTs only

AGB stars

spatial distribution of dust components

≈ 10

 

Smaller programs

Galactic center, hot stars very low mass stars

(≤ 5)

UTs mostly

*NGC 253, NGC 1068, NGC 3758, NGC 5128, Circinus (J1413-6520)

 

Table 3.

Outline of first scientific observations planned with MIDI

 

This will require a similar accuracy in total flux determination, which has to be achieved by chopping against an empty part of the sky, a complicated procedure within an interferometer. From these considerations, we identified as main goals for the first two to three years of observations with MIDI (see Table 3) the study of nearby active galactic nuclei and the study of circumstellar material around young stars.

Defining the spatial distribution of different dust components around asymptotic giant branch stars will be another important topic. Following the orbits of close young binaries for mass determination and studying the history of dust formation in red giants are also promising studies, but because of the long time base needed they are less well suited as one of the first science programms. Measuring the spatial separation of an extrasolar planet from its central star is an exciting project, but very, very challenging for an instrument like MIDI, because the signature will be well below 1% even for the biggest extrasolar planets known14. Finally, small projects on individual targets of astrophysical interest will help to demonstrate the scientific capabilities of the instrument.

9. STATUS AND SCHEDULE

MIDI is being built by a european consortium led by the Max­Planck­Institut für Astronomie in Heidelberg (PI team),including astronomical institutes in the Netherlands coordinated by the Netherlands School for Astronomy

(Co­PI), Observatoire de Paris (Co­PI for the French contribution), the Kiepenheuer­Institut für Sonnenphysik in

Freiburg, the Thüringische Landessternwarte in Tautenburg, and Observatoire de la Côte d'Azur (chair of the science group).

The final design review for the optics has been passed in July 1999, the remaining parts of the final design review happened at the end of February 2000. Integration of the instrument in Heidelberg has been completed in July, 2001, and the first fringes were obtained in the lab on October 30th, 2001. Shipment to Paranal is now foreseen in October, 2002, and commissioning with the siderostats of the VLTI is planned starting before the end of 2002. Commisioning with the 8 m telescopes will then follow in the first half of 2003, and with the 1.8 m auxiliary telescopes later the same year. MIDI therefore should begin science observations by the end of 2003.

10. OUTLOOK

The possible future development of the instrument includes

·         Addition of a wavelength band at 20 µm. Space for the necessary optical components has already be reserved in the optical and mechanical design

·         Phase measurements by external referencing. This has to await the implementation of the VLTI subsystem PRIMA1,3 , which will become operational in 2003

·         High spectral resolution (lambda/Delta lambda = 10 000), to allow gas phase and kinematical studies.

·         Simultaneous measurements on several baselines for closure phase imaging

·         A nulling option. The very accurate beam cleaning to be expected from the use of single­mode fibers should be an advantage when developing this option12

While the first two upgrades can be obtained with modest modifications on the present instrument, the three

latter ones will require substantial changes or a complete redesign.

 

REFERENCES

1. A. Glindemann and 17 co­authors, The VLTI - The Observatory of the 21st Century, ESO Messenger No. 98, pp. 1-7, December 1999

2. R. Petrov, F. Malbet, A. Richichi, and K.­H. Hofmann, AMBER, the Near­Infrared/Red Focal Instrument, ESO Messenger No. 92, pp.11-14, June 1998

3. A. Quirrenbach, V. Coudč du Foresto, G. Daigne, K.­H. Hofmann, R. Lattanzi, M. Osterbart, R. le Poole, D. Queloz, and F. Vakili, PRIMA - Study for a Daul­Beam Instrument for the VLTI interferometer, in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE 3350, pp. 807-817, 1993

4. Ch. Leinert, and U. Graser, MIDI -- the Mid­infrared interferometric instrument for the VLTI, in Astronomical Interferometry, R. D. Reasenberg, ed., Proc. SPIE 3350, pp. 389-393, 1993

5. Y. Rabbia, D. Mekarnia, and J. Gay, Infrared interferometry at Observatoire de la Côte d'Azur, France, in Infrared Technology XVI Proc. SPIE 1341, pp. 172­182, 1993

6. W.C. Danchi, M. Bester, C.G. Degiacomi, P.R. Mc Cullogh, and C.H. Townes, Visibility curves at 10 microns wavelength for stars with dust shells, Amplitude and intensity spatial interferometry, Proc. SPIE 1237, pp. 327­334, 1990

7. W.C. Danchi, M. Bester, C.G. Degiacomi, P.R. Mc Cullogh, and C.H. Townes, Location and phase of dust formation in IRC +10216 indicated by 11 micron spatial interferometry, ApJ Letters 359, L59­L63, 1990

8. M. Bester, W.C. Danchi, C.G. Degiacomi, C.H. Townes, and T.R. Geballe, Distribution of dust about o Ceti and ff Orionis based on 11 micron spatial interferometry. ApJ Letters 367, L27­L31, 1991

9. M. Shao et al., The Mark III stellar interferometer, Astron. Astrophys. 193, 357­371, 1988

10. I. Porro, U. Graser, Ch. Leinert, Estimated performance for 10­micron interferometry at the VLTI with the MIDI instrument, in Working on the fringe: an international conference on Optical and IR interferometry from ground and space eds. S. Unwin and R. Stachnik, Astronomical Society of the Pacific Conference series, San Francisco 1999, p.34

11. J.A. Meisner, Coherent estimation of complex fringe visibility: a generalized approach, in Interferometry in Optical Astronomy, Proc. SPIE, Vol. 4006, p. 1068, 2000

12. G. Perrin, Ch/ Leinert, U. Graser, L.B.F.M. Waters, and B. Lopez, MIDI, the 10 µm interferometer of the VLT: a step towards mid­infrared interferometry in space, Proceedings of the DARWIN conference, Stockholm, November 1999

13. B. Lopez et al., Astrophysical potentials of the MIDI VLTI instrument, in Interferometry in Optical Astronomy, Proc. SPIE, Vol. 4006, p. 54, 2000

14. B. Lopez and R. Petrov, Direct detection of hot extrasolar planets with the VLTI using differential interferometry, in Interferometry in Optical Astronomy, Proc. SPIE, Vol. 4006, p. 407, 2000

15. S. Ligori, U. Graser, B. Grimm, R. Klein, Design and tests of the MIDI detector subsystem, in Interferometry in Optical Astronomy, Proc. SPIE, Vol. 4006, p. 136, 2000

16. J.­W. Pel, A. Glazenborg­Kluttig, J.C. de Haas, H. Hanenburg, and R. Lenzen, Cold optics of MIDI: the mid­infrared interferometric instrument for the VLTI, in Interferometry in Optical Astronomy, Proc. SPIE, Vol. 4006, p. 164, 2000

17. G. Perrin, V. Coud'e du Foresto, and M. Olivier, Spatial filtering for 10 µm interferometry, in Interferometry in Optical Astronomy, Proc. SPIE, Vol. 4006, p. 1007, 2000

18. R.­R. Rohloff, U. Graser, N. Ortlieb, M. Lebong, and W. Laun, Cryo design for the VLTI MIDI instrument, in Interferometry in Optical Astronomy, Proc. SPIE, Vol. 4006, p. 277, 2000