The Gemini MCAO Performance

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 NGST are also listed.

Summary:

• 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 term of FWHM, over the full 1 square arcmin field of view, even for the faintest NGS considered here;
• Strehl ratio under median seeing conditions vary 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 30^o 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 NGST, insuring a competitive regime for this instrument after the NGST 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

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''.

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

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).

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.

• 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''

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).

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).

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.

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 19^th 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 C_n²(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.

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 randomnly 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.

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 (see the Strawnman Instrument page).

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).

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

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.

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

A. Point source Sensitivities

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

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

Last update September 6, 2000; Francois Rigaut