Deformable mirror

In the design of MOEMS components, various parameters have to be tuned. These parameters differ according to the functionality of the component. We will consider two different family of devices, programmable slits for Multi-Object Spectroscopy, including Micro-Mirror Arrays (MMA) and Micro-Shutters Arrays (MSA), and Micro-Deformable Mirrors (MDM) for Adaptive Optics systems. 

However this technology has also some limitation. For example, pupil diameter is an overall parameter and for a 100 m primary telescope, the internal pupil diameter cannot be reduced below 1 m. According to the maximal size of the wafers (8 inches), a deformable mirror based on MOEMS technology cannot be build into one piece. New AO architectures are under investigation to avoid this limitation (Zamkotsian and Dohlen, 2001). 

Table 1. Deformable Mirror parameters for Extremely Large Telescopes...

Since September 2000, we have engaged an active collaboration with a French laboratory expert in micro-technologies, the Laboratoire d Analyse et d Architecture des Systfemes (LAAS) in Toulouse, France, for the conception and the realization of micro-deformable mirror (MDM) prototypes. Our design is based on three elementary buildings blocks (Fig. 6). From top to bottom ... 

Figure 6. Schematic view of our Micro-Deformable Mirror architecture.

Micro-Opto-Electro-Mechanical Systems (MOEMS) will be widely integrated in new astronomical instruments for future Extremely Large Telescopes, as well as for existing lOm-class telescopes. The two major applications are programmable slit masks for Multi-Object Spectroscopy (see Ch. 12) and deformable mirrors for Adaptive Optics systems. Eirst prototypes have shown their capabilities. However, big efforts have stiU to be done in order to reach the requirements and to realize reliable devices. 

Figure 1 outlines the basic AO system. Wavefronts incoming from the telescope are shown to be corrugated implying that they have phase errors. Part of the light is extracted to a wavefront phase sensor (usually referred to as a wavefront sensor, WFS). The wavefront phase is estimated and a wavefront corrector is used to cancel the phase errors by introducing compensating optical paths. The most common wavefront compensator is a deformable mirror. The idea of adaptive optics was first published by Babcock (1953) and shortly after by Linnik (1957). 

In order to compensate for the distortions in the wavefront due to the atmosphere we must introduce a phase correction device into the optical beam. These phase correction devices operate by producing an optical path difference in the beam by varying either the refractive index of the phase corrector (refractive devices) or by introducing a variable geometrical path difference (reflective devices, i.e. deformable mirrors). Almost all AO systems use deformable mirrors, although there has been considerable research about liquid crystal devices in which the refractive index is electrically controlled. 

The main characteristics which determine the performance of a wavefront corrector are the number of actuators, actuator stroke and the temporal response. The number of actuators will determine the maximum Strehl ratio which can be obtained with the AO system. The price of a deformable mirror is directly related to the number of actuators. The actuator stroke should be enough to compensate wavefront errors when the seeing is moderately poor. This can be derived from the Noll formula with ao = 1.03. For example, on a 10m telescope with ro = 0.05m at 0.5 m, the rms wavefront error is 6.7 /xm. The deformable mirror stroke should be a factor of at least three times this. It should also include some margin for correction of errors introduced by the telescope itself. The required stroke is too large for most types of deformable mirror, and it is common practice to off-load the tip-tilt component of the wave-front error to a separate tip-tilt mirror. The Noll coefficient a2 = 0.134 and... 

Deformable mirrors are usually placed at a greatly reduced image of the telescope entrance pupil - the typical diameter of PZT or PMN based deformable mirrors is in the range 10-20 cm. A completely different approach is to make one of the telescope mirrors deformable, and the best choice is the secondary mirror (relatively small and usually coincides with the aperture stop for in-... 

Increasing the diameter, d, increases the number of photons in the wavefront measurement, and therefore reduces the error due to photon noise. However, increasing the diameter also increases aliasing in the wavefront sensor measurement. If the deformable mirror actuator spacing is matched to the subaperture size, then the fitting error will also depend on the subaperture diameter. There is therefore an optimum subaperture diameter which depends on the... 

Figure 8. Isoplanatic angle at 2.2pm as a function of conjugate altitude of the deformable mirror for different turbulence profiles obtained at the Observatorio del Roque de los Muchachos.

Some practical complications are introduced when this technique is used since the deformable mirror is not conjugate to the pupil it has to be made... 

The idea of optimal conjugation can be extended by using multiple deformable mirrors-this is referred to as multi-conjugate AO or MCAO. Again, the question arises as to the optimal altitudes of the deformable mirrors. Toko-vinin et al. (2000) showed that if the turbulence in the volume defined by fhe field of view and fhe felescope aperfure is perfectly known, then the isoplanatic error in an MCAO system with M deformable mirrors is given by... 

In the layer-oriented approach each wavefront sensor sees all the guide stars but each is coupled to a single deformable mirror. Each wavefront sensor... 

The basic layout of a laser guided AO system is shown in Fig. 1. Implementation of LGS referencing requires the addition of a laser and launch telescope, plus one or more additional wavefront sensors (WFS), including a tip-tilt sensor. Multiple LGSs require additional lasers and launch systems, or a multiplexing scheme. Multi-conjugate AO (MCAO) requires additional deformable mirrors, operating in series, plus multiple WFSs. 

Figure 1. Schematic of a laser guide adaptive optics system. The laser is pr( jected along or parallel to the telescope ax onto the science object. The deformable mirror can be a separate entity, or can be an adaptive secondary. The light is split among the cameras by dichroics.

Figure 3. Sky coverage of an adaptive optics at an 8m telescope. Pupil sampling by the actuators of the deformable mirror 0,5m, 0 = 0,17m, From top to bottom in a direction of galactic latitude 6 = Of (the Milky Way), b = 20f and b = 90f (the galactic pole). From left to right K, 1 and V bands.

The only 3D mapping system with LGSs under constmction today is that for the Gemini South 8m telescope at Cerro Pachon, Chile (Lllerbroek et al., 2002). It consists of 5 LGSs, 3 deformable mirrors with a total of 769 actuators and one 1020 subapertures wavefront sensor per LGS (Fig. 11). It is expected to be the most performing MCAO device. 

These probabilities are shown in Fig. 14 for the case of an AO device with several LGSs and 2 deformable mirrors. The corrected field is 6 . 3 NGSs... 

Figure 14. Sky coverage for a LGSs + 2 deformable mirrors AO. Field 6 . 3 NGS sense...

Figure 15. Sky coverage for a LGSs + 1 deformable mirrors AO device. Field is 6 wide. 1 NGS is required to sense the tilt. Same symbols as Fig. 14.

With a single deformable mirror AO, and if a single NGS is used (see Le Louam and Hubin, 2004), the point spread function is quite peaked in the corrected field, but the probability to find if is much higher from fa 10 toward the galactic pole for observations in the visible to 50% toward the galactic plane for observations in the near infrared. 

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