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Expected Performance of MCAO

This page addresses the performance of the planned Gemini MCAO system, in terms of sensitivities, image quality and sky coverage. Most of these performance metrics are compared to what would be achieved with Classical Laser Guide Star AO (CAO in the following, with a single deformable mirror, wave front sensor and guide star). Some sensitivities comparisons with HST/NICMOS and JWST are also listed.


  • MCAO performance is very uniform over a 1 square arc minute field, both in terms of Strehl ratios and more general PSF characteristics;

  • Images are basically diffraction-limited, in terms of FWHM, over the full 1 square arcmin field of view, even for the faintest NGS considered here;

  • Strehl ratio under median seeing conditions varies from 45% to 80% in the 1-2.5 micron range and 0-30 degrees zenith angle, with relative uniformity (relative Strehl ratio standard deviation) from 1.5 to 6% ;

  • The Strehl ratio degrades gracefully out of the 1 square arc minute central field. The useable field with Strehl ratio above 50% of the peak value is the full 2 arcmin field in H and K band, and approximately 1.5 arc minute at J band;

  • Three natural guide stars are needed to get the best compensation from the MCAO system but the magnitude limits (R=19) correspond to very useful values of sky coverage (~15% at the galactic pole and over 70% at 30o galatic latitude), even when sky background noise and windshake jitter are taken into account;

  • The overall performance is a weak function of the exact match between the deformable mirror conjugation altitude and the location of the turbulent layers;

  • Under median seeing conditions, MCAO brings a 1.5 to 1.7 magnitude sensitivity gain over the 1-2.5 micron range on point sources with respect to seeing limited imaging. Gains with respect to HST/NICMOS, in the same conditions, are 0.3 (J) and 1.2 (K) magnitudes;

  • For high spectral resolution spectroscopy, MCAO plus a spectrograph will have the same sensitivity as the JWST, insuring a competitive regime for this instrument after the JWST launch;

  • Multiplex gains with respect to CAO are factors of 10 to 20 in area;

1. MCAO Performance

A. Strehl ratio and FWHM

A.1 Strehl, FWHM and Encircled Energy vs Field of View

With a continuous atmospheric turbulence profile, MCAO can significantly reduce but not eliminate the effect on anisoplanatism upon AO system performance. The mean Strehl ratio will decrease with increasing field-of-view if the guide star and deformable mirror configurations are held constant. The relative variability of the Strehl ratio over the field will also increase. Table 12 illustrate these trends as computed for the median Cerro Pachon turbulence profile and the Gemini MCAO baseline wavefront sensor/deformable mirror configuration, but without including the effects of wavefront sensor measurement noise or servo lag. The field-of-view for performance evaluation is a square from 51.5 to 68.5 arc seconds in width, and the five laser guide stars are located at the center and corners of the field. The RMS variability of the Strehl increases fairly rapidly with increasing field-of-view size, approximately by a factor of 1.5 for every increment of 8.5 arc seconds. The field-averaged Strehl ratios also begin to degrade more rapidly as the width of the field is increased beyond 60 arc seconds. This reduction in Strehl takes place across the entire field and is not restricted to the edges. All of these effects become somewhat more pronounced when LGS WFS noise and servo lag are included in the calculation. A one square arc minute field appears to be a soft upper bound on MCAO capability at Cerro Pachon with three deformable mirrors and 5 LGSs. A comparison of the corrected field-of-views for MCAO and conventional AO is presented later in this document.

Table 1:MCAO Strehl ratio vs field span and wavelength: Field averaged value and standard deviation over field (between parenthesis). Note that these Strehl ratio values only include atmospheric turbulence. This does not include noise, telescope and instrument optical aberrations or any kind of alignement error. The main purpose of this table is to illustrate how the level of image quality non-uniformity (see standard deviation over field of view number) and Strehl ratio vary with the covered field of view. The baseline configuration for the Gemini MCAO is 60''.

Zenith angle, degrees



Field-of-view, arcsec







J band

0.570 (0.029)

0.532 (0.044)

0.462 (0.075)

0.481 (0.042)

0.434 (0.062)

0.358 (0.101)

H band

0.723 (0.017)

0.695 (0.026)

0.638 (0.043)

0.656 (0.024)

0.618 (0.036)

0.550 (0.056)

K band

0.833 (0.010)

0.814 (0.014)

0.775 (0.024)

0.768 (0.013)

0.762 (0.019)

0.712 (0.032)


Table 2 MCAO overall error budget, including atmospheric turbulence residual, instrument and telescopes aberrations and alignment errors.

[MCAO error budget]

Figure 1: Left: Strehl ratio versus distance from center field at I, J, H and K bands, for the Gemini MCAO with a minimum variance estimator (BLE Code). Right: Strehl ratio, FWHM, Encircled Energy and fraction of flux coupled though a slit of 0.1'' vs the distance from the field center for the Gemini MCAO system (crosses) and a Classical LGS AO system of similar order (triangles, Least square estimator, FR code).

[MCAO Strehl, FWHM, EE and Slit coupling] [MCAO Strehl, FWHM, EE and Slit coupling]

The left hand panel of figure 1 shows how the Strehl ratio varies in the field of view for several wavelength bands. No noise is included, only the error relative to the atmosphere (fitting, servo lag, anisoplanatism). The right hand panel of figure 1 shows an example of Strehl (upper left), FWHM (upper right), 50% encircled energy diameter (bottom left) and percentage of light coupled through a slit (bottom right), versus the field position for a system equivalent to the Gemini baseline system, with realistic noise factors included.

The following figures show:

  • Strehl ratio
  • FWHM [arcsec]
  • 50% Encircled energy diameter [arcsec]
  • Fraction of the total energy coupled through a slit of 0.1''
  • Fraction of the total energy coupled through a IFU "pixel" of size 0.1''x0.1''
  • Fraction of the total energy coupled through a IFU "pixel" of size 0.05''x0.05''

at a given distance r from the center of the field, versus the quantity Pi . r 2, that is, the area defined by this distance (radius) r. This representation was chosen instead of the regular straight distance because it shows better the real area multiplex gain brought by MCAO compared to classical AO. These metrics have been estimated for several bands and for several seeing conditions (50 and 10 percentile seeing). Under operation, and thanks to the optimum scheduling, it is expected that the mean operating seeing for AO will be around the 30 percentile seeing (approximately 0.57 arcsec). Optimum scheduling will also allow to dedicate the best seeing periods (better than 20% seeing) to the more challenging observations, i.e. the shortest wavelengths.

Figure 2a: Strehl, FWHM and encircled energy (see text) for z, J, H and K band under 50% seeing conditions (seeing at 500nm = 0.69 arcsec). The crosses are for the Gemini MCAO system, the triangles for a classical AO system of the same order (same number of subapertures) using a single laser guide star and a single natural guide star for tip-tilt. These figures also exist in Postscript (about 140kB each, z, J, H, K) or PDF format (about 70kB each, z, J, H, K).

[z band MCAO Strehl, FWHM, EE and Slit coupling] [J band MCAO Strehl, FWHM, EE and Slit coupling] [H band MCAO Strehl, FWHM, EE and Slit coupling] [K band MCAO Strehl, FWHM, EE and Slit coupling]

Figure 2b: Strehl, FWHM and encircled energy (see text) for z, J, H and K band under 10% seeing conditions (seeing at 500nm = 0.47 arcsec). These figures also exist in Postscript (about 140kB each, J, H) or PDF format (about 70kB each, J, H).

[J band MCAO Strehl, FWHM, EE and Slit coupling] [H band MCAO Strehl, FWHM, EE and Slit coupling]

A.2 PSF characteristics

The PSF can be formally split into two components: one corresponding to errors in the high order modes controlled by the laser guide stars wavefront sensors and another corresponding to global image motion. The latter is exclusively related to modes controlled using the Tip-Tilt NGS wavefront sensors.

High Order Modes

The high order modes are the primary culprit for the well-known Core/Halo PSF shape (see figure 2). To first order for a Strehl ratio > 20%, the percentage of energy in the diffraction limited component of the image is equal to the Strehl ratio. For a telescope with a small central obstruction like Gemini, the fraction of energy in the central peak of a perfect diffraction pattern is 82%. The energy in a diaphragm of diameter 2 lambda/D is 80% of the total energy in the diffraction image, and the energy in a diaphragm of diameter lambda/D is 45%. These numbers, multiplied by the Strehl ratio of the actual short exposure images (determined by the high order LGS-controlled loop) can be used as guidelines in SNR estimations.

The halo has characteristics that vary with wavelength and quality of compensation, noise, etc, and cannot be described simply in an analytical fashion. Its width varies between the seeing width and some fraction (0.25-0.3) of this quantity, being relatively smaller at shorter wavelengths. It is worth noting that in all the AO simulations carried out at Gemini, the halo seems to have a less detrimental effect than for actual images taken with lower order systems on 3.6-m telescopes. This may be because the contrast in width between halo and core is larger for an 8-m telescope, the diffraction limit being twice smaller. This increases the halo/core contrast by a factor of ~ 5. Also, the Strehl ratios planned for the CP MCAO system are slightly higher than those achieved with most AO systems on smaller telescopes, increasing further this contrast.

The stability of the high order PSF component has been addressed in the previous section, and is reported Table 1. The spatial standard deviation of the Strehl ratio is given in this table, and is of the order of 2.5% in H band at zenith for the MCAO baseline. These fluctuations are expected to be quite stable within +/- 1%, so that a first order correction on the photometry could achieve this level of accuracy.

Image Motion

The effect of the NGS-controlled modes on the image is solely to convolve the average high order PSF component by a 2-D gaussian profile. A simulation code has been developped at Gemini to estimate this effect. For example, for 4 magnitude 19th stars, tip and tilt vary from approximately 10 mas to 16 mas within the central 1 square arcmin. It is important to note that this residual image motion will induce an elongation on the image, similar but smaller to what is observed in a one-star compensation system. The amplitude and direction of the elongation depends on location in the field, the relative brightness and location of the NGSs, and the Cn2(h) and wind profile.

The PSF core broadening caused by the residual image motion does not throw energy very far into the halo wings, as is the case for the imperfectly compensated high order modes. For an equivalent reduction in Strehl, the effective loss in resolution, 50% encircled energy, or slit throughput is therefore more benign. For instance, the 50% Strehl ratio loss that we adopt as an arbitrary criteria to estimate sky coverage is equivalent to a broadening of the time-averaged PSF by ~ 40 mas in H band, which increases the FWHM from 43 mas (diffraction limit) to 58 mas. The impact on the encircled energy depends on the exact wavelength. For spectrographs, however, whose pixel elements will probably not resolve the width of the diffraction core, this effect will be very moderate.

Figure 3: Log Cross section of a typical H band MCAO/CAO point spread function, showing the core and the halo. Atmospheric residuals only.

[Log Cross section of typical AO/MCAO PSF]

For those who want to do some numerical evaluation of the MCAO performance and gain with respect to classical AO, below are some PSFs (128x128 images, K band under 50% seeing conditions, pixel size 21.5 mas/pixel). The images corresponds to various locations in the field of view (the numbers between brackets are the X and Y distance to the field center in arcsec). These PSF were computed assuming a randomly generated telescope+instruments optical aberrations (see table 2 above) and include all effects from the atmosphere and the system. All files are 69kB.

  • [0'',0''] (centered), MCAO, AO;
  • [0'',22.5''] (centered), MCAO, AO;
  • [0,45''] (centered), MCAO, AO;
  • [22.5'',22.5''] (centered), MCAO, AO;
  • [45'',45''] (centered), MCAO, AO;

B. NGS Magnitude Limits

The performance of the low-order NGS loop may be determined using modal control. At present we have developed at Gemini numerical codes and performed analyses to evaluate and optimize (a) the residual mean-square error in each NGS-controlled mode and (b) the overall residual field-averaged phase variance. The statistics of the residual tip/tilt jitter at each point in the field of view can be computed from the statistics of the residual errors in the NGS-controlled modes, and the corresponding Strehl ratio reduction determined. Figure 4 illustrates sample results for triangular constellations of three magnitude 18 to 19 NGS. The NGS WFS noise model used for these results assumes quadrant detector APD tip/tilt sensors. No sharpening of the NGS image on the quadrant detector by the adaptive optics is included, which is a conservative assumption, even if the tip/tilt sensing is performed in the visible.

Figure 4: Strehl ratio reductions in H band due to noise and servo lag errors in the NGS loop for two sample guide star constellations. The curves are iso-Strehl contours. The NGS locations and magnitudes are indicated by the annotated triangles. The smaller square is the 1 arcminute field.

[TT NGS Strehl loss for mag=[19,19,19] ] [TT NGS Strehl loss for mag=[19,19,18] ]

The above figures illustrate that the Strehl ratio reduction due to the errors in the NGS-controlled tilt and tilt anisoplanatism modes is not uniform across the field of view. For imaging instruments, we expect that the nature of the nonuniformity may be determined and taken into account in the post-processing based upon the statistics of the residual tip/tilt errors measured by the NGS WFSs. For spectroscopy the reduction in Strehl due to this residual image motion should have a negligible effect, since moderate amounts of tip/tilt jitter will broaden the central core of the PSF without reducing the fraction of PSF energy coupled through slit, on the order of 0.1 arc second in width.

A simpler, scalar indication of the performance of the NGS loop is the overall Strehl ratio corresponding to the residual field-averaged phase variance in the NGS-controlled modes. For a fixed observing scenario and set of AO system parameters, this Strehl will be a function of (i) the magnitudes and locations of the three NGS, (ii) the sky background, and (iii) the disturbance spectrum for windshake-induced tip/tilt jitter. A reasonable definition of the NGS magnitude limit for MCAO is the value yielding a field-averaged Strehl ratio reduction of 0.5 in H band. Figure 5 illustrates the field-averaged Strehl ratio in H band for the NGS loop with a sample NGS constellation and two different sets of values for sky background and telescope windshake. The NGS constellation consists of three stars of equal magnitude located at the corners of an equilateral triangle with base 0.87 arcmin that is centered within the 1 square arc minute field-of-view. The limiting NGS magnitude is about 20.3 for the optimistic case of an 80% sky background (for Mauna Kea), and no windshake-induced jitter. The limiting magnitude falls to about 19.1 for the more representative case of a 50% sky background and the "typical windshake" disturbance spectrum specified for Gemini-North. MCAO does not appear to be dramatically more or less sensitive to these error sources than conventional LGS AO. More detailled studies will be carried out as more accurate estimates/measurements of windshake at Cerro Pachon become available.

Figure 5:Field-averaged Strehl ratios in H band for the NGS loop as a function of NGS magnitude for median seeing, a 0 degree zenith angle, and a triangular guide star constellation with a base of 0.87 arcmin. Solid: No windshake jitter, 80% sky background (dark sky). Dashed: Typical Mauna Kea jitter, 50% sky background (grey sky).

[Field-averaged Strehl Loss vs TTNGS magnitude]

The effect of a less favorable constellation geometry on the NGS magnitude limits has also been studied. Reducing the base of the equilateral triangle from 0.87 to 0.43 arcmin degrades the magnitude limit from 19.1 to about 18.4. Displacing the equilateral triangle from the center to one side of the 1 arcmin field increases the limit by a further 0.2. Additional results illustrating the impact of the constellation geometry upon the performance of the NGS control loop are given in the appendix. Based upon these calculations, we have specified a limiting magnitude of 19 and a minimum triangle area of 0.25 square arcmin (corresponding to an equilateral triangle with base 0.75 arcmin) for the sky coverage estimates presented below.

C. Sensitivity to Vertical turbulence distribution

The baseline conjugate ranges for the three deformable mirrors are 0.0, 4.5, and 9.0 km. Fine-tuning or real-time adjustment of the selected conjugate ranges is unnecessary. As illustrated in the Figure below, MCAO performance is not a strong function of the exact match between the DM conjugate ranges and the atmospheric profile.

Figure 6: MCAO performance (for a sample system configuration) is a relatively week function of the exact match between the turbulence profile and the DM conjugate ranges.

[MCAO Strehl, FWHM, EE and Slit coupling]

2. MCAO gains and sensitivity compared to CAO and space-based instruments

A. Point source Sensitivities

Table 1 below presents the limiting fluxes of a ground-based telescope with MCAO/AO or without AO at Cerro Pachon, the Hubble Space telescope with NICMOS, and the yardstick NGST. We list the 5-sigma, 1 hour limiting magnitudes for spectral resolutions of R=5 (broad band imaging) and R=10000 (between-the-OH-lines spectra). The backgrounds were taken from either the expected sky backgrounds for Gemini, the NICMOS manual, or from Gillett & Mountain (1997). The encircled energy fraction in the central 2x2 pixels is taken from simulated PSFs for the MCAO, NICMOS NIC2 growth curves (HST Instrument Science Report NICMOS-99-007), or estimated in the case of NGST ("NGST science instrument capability report", Dec 29, 1999). We reconfirm the results of Gillett and Mountain that at low resolutions NGST has a significant advantage (2.5 - 3 magnitudes) while at high spectral resolutions there is no SNR advantage. At these spectral resolutions detector noise is important and the Gemini advantage arises from the lower cosmic ray flux and hence fewer frame readouts. In broadband imaging at 2.2 microns MCAO has a 1.2-1.7 magnitude advantage over NICMOS and no AO cases respectively. Note that at high spectral resolution the no-AO case has a fainter limiting magnitude than the MCAO but this is through a slit which is 12 times larger (i.e. a 2 pixel slit width).

Table 1:Limiting sensitivities on point sources for MCAO/AO and no AO at CP, HST, and NGST.





Telescope diameter [m]










Background [mag/arcsec2, between parenthesis in Jy/arcsec2]

2.1 mic, R=5

13.8 (2e-3)

13.8 (2e-3)

16.9 (1.1e-4)

20.3 (5e-6)

1.25 mic, R=5

16.2 (5.5e-4)

16.2 (5.5e-4)

20.9 (7e-6)

20.9 (7e-6)

2.1 mic, R=10000

17.1 (1e-4)

17.1 (1e-4)

16.9 (1.1e-4)

20.3 (5e-6)

1.25 mic, R=10000

18.0 (1e-4)

18.0 (1e-4)

20.9 (7e-6)

20.9 (7e-6)


Pixel size





Longest Integration, R=5 [s]





Longest Integration, R=10000 [s]





PSF, Fraction of Energy in 2x2 pixels

2.1 microns





1.25 microns





Limiting magnitudes, 5 sigma, 3600 sec, aperture=2x2 pixels [Vega magnitude, between parenthesis in nJy]

2.1 mic, R=5

23.2 (370)

24.9 (76)

23.7 (230)

28.0 (4.4)

1.25 mic, R=5

24.8 (190)

26.3 (50)

26.0 (66)

28.6 (6.0)

2.1 micron, R=10000

20.4 (4.8)

20.3 (4.8)

17.2 (92)

20.1 (6.1)

1.25 mic, R=10000

21.3 (4.7)

20.5 (9.7)

17.9 (107)

20.5 (9.7)

+ The following assumptions were used for the throughput calculations: Tatm = 0.92, Ttel = 0.8, Taos = 0.75 and Tinst = 0.6
++ The following common detector characteristics were assumed : Ndark = 0.01 e-/s, Nread = 15 e-

B. Sky coverage

Table 1 summarizes the sky coverage for classical LGS AO (CAO) and MCAO, for two galactic latitude and the three near-infrared bands

Table 2: Classical AO and MCAO sky coverage

CAO / MCAO Sky Coverage [%]




7 / 12

21 / 67


16 / 14

44 / 69


35 / 24

74 / 82

Both for CAO and MCAO, the sky coverage is computed as the fraction of the sky within which the Strehl ratio loss is < 50% with respect with the noiseless performance -on bright stars-. For instance, for the MCAO system, with a K band Strehl ratio of 60% under median seeing, a Strehl of 30% will be achieved over 24% of the sky at galactic pole latitudes. This table shows that the requirements for 3 Tip-Tilt NGS does not impact the sky coverage compared to classical LGS AO. CAO shows some gain at high galactic latitude for the longest wavelengths but MCAO recovers the advantage at shortest wavelengths and shows larger sky coverage for low galactic latitudes. The fact that it is less wavelength dependant is also significant, as the sky coverage at J band is the limiting factor for multi-wavelength studies (e.g. CMD).

C. Field of view Multiplex gain

Table 3 belows shows that, for programs that need field of view, MCAO provides a 10-20 multiplex gain compared to CAO. Such a large gain can enable programs that were not tractable previously -because of the time required to complete-. It can also simply increase efficiency, e.g. translate into more time spent on the object(s). This of course requires that this multiplex gain can be exploited, that is, adequate ~ 2 arcmin instrumentation follows.

Table 3: MCAO and CAO compensated surface area





MCAO FoV Diameter [arcsec]




CAO FoV Diameter [arcsec]




Area gain




We note that this multiplexing gain is not simply a matter of doing CAO science faster: the field covered by MCAO enables new opportunities. In particular, for some science programs, the information is spread over a wide area (1-2 arcmin), and the science goal can only be achieved by imaging the entire object (e.g. microlensing of dense clusters, image reconstruction of lensed objects in gravitationnal arc systems, spatial evolution of star formation regions in nearby galaxies). For these objects, the probability to have enough guide stars to cover the entire object is equal to the CAO sky coverage to the n-th power, n being the number of field needed to cover the object with adequate image quality. For example, to mosaic a field with Strehl > Speak/2 at 1.65 microns of a galaxy that is 1 arcmin in diameter requires four CAO fields. Using the numbers in Table 2, the probability that there will be guide stars in each of these fields is less than 4% at 30 degrees galactic latitude and considerably less than 1% at the galactic pole.

D. Uniform PSF

This feature is, as such, unique to MCAO. Although 0.1 magnitude error can be achieved in some cases on field of 10-30'' with CAO (c.f. Davidge), a uniform PSF will vastly improve the accuracy of the image/spectra analysis. More generally, it is the experience AO users that data reduction is a critical problem, because of (1) the lack of proper and simultaneous PSF calibration and (2) PSF spatial variability in the field. For some programs (e.g. stellar population, sparse to moderately crowded field) a PSF can be found in the field itself, by definition, however small the field is. For the majority of the wide field programs (high Z clusters, galaxy morphology/evolution, YSOs, solar system, ISM), this is not the case. Having a large, uniform field goes a long way toward solving this problem: if a star is present in the field of view (e.g. 80''x80'' of the strawman imager), it can be used for the whole 80''x80'' uniform field. Since, by definition there are three m < 19 stars to serve as tip-tilt guide stars in a 2 arcmin diameter field, the probability of having at least one in the central 1 square arcmin field is high (60%).

- Francois Rigaut, Sep 6, 2000

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