# Adaptive optics control strategies for extremely large telescopes

Abstract: Adaptive optics for the 30-100 meter class telescopes now being considered will require an extension in almost every area of AO system component technology. In this paper, we present scaling laws and strawman error budgets for AO systems on extremely large telescopes (ELTs) and discuss the implications for component technology and computational architecture. In the component technology area, we discuss the advanced efforts being pursued at the NSF Center for Adaptive Optics (CfAO) in the development of large number of degrees of freedom deformable mirrors, wavefront sensors, and guidestar lasers. It is important to note that the scaling of present wavefront reconstructor algorithms will become computationally intractable for ELTs and will require the development of new algorithms and advanced numerical mathematics techniques. We present the computational issues and discuss the characteristics of new algorithmic approaches that show promise in scaling to ELT AO systems.

## Summary (2 min read)

### 1. INTRODUCTION

- The authors can start the discussion with a broad-brush overview of the A 0 system concepts for extremely large telescopes (ELTs) and, from well-known scaling laws, determine the requirements for basic system components.
- The authors then consider the state of the art in these component areas and ask if rates of technology development will meet the ELT timelines.

### 2. A 0 CONCEPTS FOR ELT'S

- Other large telescope projects may follow along similar baseline A 0 paths.
- One can envision building A 0 systems into each instrument package.

### 4.1 Deformable mirrors

- The requirement for multi-conjugate adaptive optics (MCAO) on the 30-meter telescope is 10,000 degrees of freedom.
- This would be possible on a 200 mm MEMs device with 0.6 mm actuator spacing, which is'a reasonable extrapolation for this technology over the next 10 years or so.
- A 100-meter telescope needs this size device for routine MCAO (scaled to 30 cm subapertures).

### 4.2 Wave front sensors

- Since the 64 x 64 and 128 x 128 Lincoln Lab chips have 4 and 16 readout ports respectively to achieve their high frame rates, let us say the authors want to scale the number of amplifiers to achieve similar frame and pixel read rates with the 600 x 600 array.
- The number of readout ports required is around 300.
- The frame transfer latency manifests itself as smearing of guidestar light along the direction of frame transfer and may become a significant contributor to the wavefi-ont sensor error budget.

### 4.3 Lasers

- To first order, the single-laser power requirement scales with subaperture size d2 and wavefront sampling fiequencyA.
- Unfortunately, as the telescope diameter gets larger the average distance of the laser beam launch aperture from any subaperture get larger, and this results in an apparent elongation of beacon.
- Since the wavefront measurement error is directly proportional to beacon size, this elongation drives a higher laser power requirement.
- There are methods that have been proposed for compensating for the elongation, which the authors discuss in section 6.

### s = Ha

- Weighted least squares, Optimal (A++), and Modal (if all modes are retained) reconstructors all have similar computational structure to the leastsquares formulation above, which requires O(nDo:) operations to perform the matrix multiplication.
- Keep in mind that for multi-conjugate AO, all the sensor readings are strung into the vector s and all the DM actuator values are strung into the vector a.
- Even with the fast-paced growth of processor power, it's hard to imaging a scaling of computational power to this degree.
- The authors explore this more in the next section.

### 6. LASER GUIDESTARS' SPECIAL PROBLEMS

- Another solution was suggested by Jerry Nelson.
- The authors project lasers from two separated launch locations but to the same point in the sodium layer so that the elongated beacons form cross patterns on the Hartmann wavefiont sensor detector.
- The centroid across only the thin dimension of the elongated guide star is just as accurate as that of a non-elongated guide star.
- The lasers are pulsed so measurements of each are taken separately.
- Of course, this technique uses twice as much power to reproduce the accuracy of a non-elongated guidestar, but this is much better than using 25 times the power to recover from 5 times elongation.

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