What follows is some material that I have used in talking about adaptive optics. The first Figure (1) is a chart that I first prepared for the WIYN Board to explain what AO is, why it is difficult to make a decison and why we deceided not to submit a proposal to NSF at this time.
The density fluctuations characteritically occur in the atmosphere at 5 to 10 km and then again near the ground. If the local seeing is taken care of than it doesn't matter where on the earth you are. For the purpose of AO the seeing effects are characterized by the Fried coherence length r0, which is distance over which wavefront errors are less than 1/4 wave. this is also the radius of the isoplanatic surface. The corresponding angular patch is the isoplanatic angle. The time over which phase perturbations are coherent tauo = r0/v(wind). These angles and times are quite small which are the things that limit the usefullness of AO. (The spectrum of turbulence is fairly well described by Kolmogorov turbulence which says that on scales smaller than the dimensions of the system the spectrum is not determined by the boundary conditions but by the kinematic viscosity and power feed in to the large scale motions is transfered to smaller and smaller eddies or wavelengths until it is dissipated in heat at the molecular level. A simple dimensional argument yields the spectrum and shows that the power is small in the smallest eddies.) Sorry this was a needless digresion. To correct the wavefront distortion we must first measure it, on a time short with respect to the coherence time (tauo). We must measure it over sizes comparable to the smallest wavelength that produce significant (1/4 wave) disturbance. to do so requires N sensors and to correct it N actuators or sub apertures. The order of correction is N ; which is also the degree of freedom.
The Number of degrees of freedom is ~ (D/ro)^2 where D is the telescope aperture. For a 4 meter class telescope and good seeing N is ~1000 in B, ~ 500 in V and ~ 15 at K. The coherency time is a few hundred in the visible and a few tens in the IR.
The next two columns are more model dependent but a a reasonable representation of the gains that could be achieved in image size and in central intensity with an AO system of order 20. J is about the optimum wavelength at shorter wavelengths ro is too small at longer wavelengths you are running into the diffration limit (i.e. it is all ready as good as your going to get). For high order systems you approach diffraction limited image width and Strehl ratios greater than 50 % but lower over all thruput and smaller isoplanatic angle than at lower order. On the other side just tip-tilt can produce 0.6" images and a Strehl of .004 for 0.75 " natural seeing and 0.38 witha 0.01 Strehl at 0.5 " seeing. All of which is not insignificant depending upon pixel size you can get a 40% increase in intensity in the central pixel. Tip-tilt is effective over the isokinetic angle (angle for image motion which can be as large as 5 arc min.
The next two charts (Fig 3 and 4) are just a quick view of ro vs FWHM and of the isoplanatic angle. Most of the above information concentrates on partial correction which is more difficult to model. The expected PSF was a broad seeing profile with a central diffraction type spike. The worst case modeling of this is to assume for each actuator an exact correction is made over an area with a radius ro. The ratio of broad PSF to the central diffraction limited PSF would then be the ratio off areas of N ro^2 to telescope area. Actually results appear to be better than this because other areas of the mirror are pulled along .
Next come cost $800 K seems very low especially for ESO. When Rigaut was here we could not pin him down on costs they were all too diffuse. The program had been going on so long and carried out by CFHT, DAO, Obs. de Paris, Laserdot etc. When we costed ours out we based it on PUEO with the assumption we did not have to carry out any development efforts. Derrick Salmon came to Tucson and worked with us. Derrick was the Project manager throughout the entire development, and is now the CFHT manager. When Francois arrived he had just finished his thesis on COM-ON AO and knew the theory and moved the CFHT project along rapidly. It was, however built upon experience obtained over years starting with HRCAM and DAOCAM. The price we arrived at to essentially clone PUEO and test and integrate it was 4.6 million. This included all known costs fringe benefits, overhead, contracts etc. I believe it was a realistic budget and that PUEO actually cost considerably more than that. We than looked at what of our costs would actually show and where we could cut costs.
Examples are that the Project Scientist salery and support would be paid elsewhere as would some of the others working on it. Some hardware could come from contributions , like computers etc. Some things that should be done would be deffered like proper documentation, commissioning etc. But let me suggest that you carry out the following exercise. Imagine that what ever you are going to create will take 3 years and that the Project Scientist and Project Manager will both be full time for the three years. Then at some time some where you will need to involve the following mix of people. An Optical Engineer, Optical Tech., Mech. Engineer, Machinist, Electrical Engineer, Electronic TecH., a System Analyist, Programer and Servo Engineer. Try to estimate how much time each skill will be needed. I did and came out with 1,3 million and I haven't paid a penny for hardware, and know full well that software will be twice what ever effort I guess at. Also is your imager a part of AO are you going to have a CCD and an IR imager ? How much will these cost ?
Now as to copying PUEO that is not pratical or advisable. If CFHT were building PUEO and had a free hand they wouldn't build it. The project started out with doimensional constraints which involved a lot of folding of optics and the use of tiny toroidal optics which were very expensive. But of course you will have different constraints CFHT is f/8 you are probably F/10 . SOAR is also an alti-az telescope with different structural features. CFHT intially had a lot of problems with deflection which is very important for some of the AO components. SOAR intends to have tip-tilt to start with probably by controlling the tertiary, You will adopted particular protocols in S/W interfaces and the decisions on electronic modules control system I/F deployment of other instruments and a host of other considerations will impact the AO design. When does it get done are you already in operation ? How long is the telescope down when testing mounting and commissioning the AO ? It will mimimize the impact on the rest of SOAR and in the testing debugging and learning if you have a test bench a hardware SOAR simulator (or at least light source) and a SOAR software simulator. Is an optical lab for this in your budget.
The basic elements of an AO system are of course the wavefront sensor and the deformable mirror PUEO used a 19 element bimorph mirror made by laserdot I believe that is now part of CILAS in france. In the early days they had a number of failures of bimorphs, which is why CHOS (Ed Kibblewhite made his own repairable mirrors using the eidaphor technology i belive, anyway sort of a thin mirror with a charge.) Thw wavefront sensing can be a Shack Hartmann or a curvature sensor. The curvature sensor maps well onto the bimorph and does a lot of the calculating for you although you still need a matrix in the calaculations. We prefeered curvature because that is what we were already doing for our active optics system. Shack Hartmann, however, has its advantages as well as drawbacks and is used in ACE at Mt. Wilson and since Chris Shelton, who dewveloped the AO efforts at Mt. Wilson and after abrief stay at the MMT is now at Keck, will probably be the choice for Keck. How Many actuator should you have and should you think about be able to upgrade to laser guide stars. First the reason that PUEO was 19 actuators was that was the design of the bimorph and the matching lenslets (central circular area, an inner annular ring with six 60 degree sector areas and outter ring with 12 sectors. You can now buy a bimorph with an additional ring giving 35 subapertures. How many do you need earlier I suggested that that depends upon the amount of distortion in the small wavelengths and you might not be making much gain for the additional expenses complication and limitations introduced. Kibblewhite and Shelton do apparently do not agree with Rigaut on the limitation when using lasers since they upgraded for laser applications and operat above 100 subapertures ther may be other reasons but it is worth exploring. What kind of laser. ? Rayleigh scattering, Gated Rayleigh scattering, Sodium ? How many lasers ? All of this is somewhat mute, however, until laser technology for astronomy is further along. Of course there is also the problems with laser involving sattelites aircrafts and other observers which currently introduces interesting administrative problems.
Science is, I think, the big thing in a decision for SOAR. What are the prime programs for SOAR ? Is AO going to help the SOAR members do research that they are targeting SOAR for better. Or do you have to invent programs to use the capabilities of the AO. One would expect that photometry is always going to be difficult with spatial and temporal varying PSF and resolution variations in crowded field etc. Resolution of relatively faint structures, galaxies etc. will require the use of a guide star within , what 5" . In the case of WIYN we have a serious scattered light problem with a bright enough guide star for many of our programs. Now I recall that at least initially SOAR was intending to capitalize on very low scattered light problems so if this is still so than maybe this is not a problem. The configuration with the clasical Nasymth ports looks subject N we believe that the tertiary may be a major contributor to our scattered light. The configuration with the tertiary behind your primary looks a bit better from this standpoint.
I hope that I have highlighted some of the features of AO today. What you must do is measure these things against the scintific goals of SOAR.