Wavefront sensor

Adaptive optics. atmospheric turbulence, residuals Metrology Wavefront sensor(s)... 

The idea is to select light beams coming from the elongated LGS in such a way that taken individually, they have the same properties as if they were coming from an infinite distance, as seen by the wavefront sensor. The concept is called PIGS for Pseudo-Infinite Guide Stars and should be tested on-sky in 2003. 

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 real curvature sensors, a vibrating membrane mirror is placed at the telescope focus, followed by a collimating lens, and a lens array. At the extremes of the membrane throw, the lens array is conjugate to the required planes. The defocus distance can be chosen by adjusting the vibration amplitude. The advantage of the collimated beam is that the beam size does not depend on the defocus distance. Optical fibers are attached to the individual lenses of the lens array, and each fiber leads to an avalanche photodiode (APD). These detectors are employed because they have zero readout noise. This wavefront sensor is practically insensitive to errors in the wavefront amplitude (by virtue of normahzing the intensity difference). 

The pyramid wavefront sensor has recently been proposed (Ragazzoni, 1996). A four-sided p5n amid is placed with its vertex at the telescope focus, and following the pyramid is some optics to image the pupil plane onto a detec-torSince a four-sided prism is employed, four pupil images will be formed... 

Figure 5. Pyramid wavefront sensor concept. Wavefront tilt causes the corresponding zone to be brighter in one pupil image and darker in the other.

The main error sources are noise in the wavefront sensor measurement, imperfect wavefront correction due to the finite number of actuators and bandwidth error due to the finite time required to measure and correct the wavefront error. Other errors include errors in the telescope optics which are not corrected by the AO system (e.g. high frequency vibrations, high spatial frequency errors), scintillation and non-common path errors. The latter are wavefront errors introduced in the corrected beam after light has been extracted to the wavefront sensor. Since the wavefront sensor does not sense these errors they will not be corrected. Since the non-common path errors are usually static, they can be measured off-line and taken into account in the wavefront correction. 

The accuracy with which a wavefront sensor measures phase errors will be limited by noise in the measurement. The main sources of noise are photon noise, readout noise (see Ch. 11) and background noise. The general form of the phase measurement error (in square radians) on an aperture of size d due to photon noise is... 

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... 

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... 

Figure 9. Schematic diagram of Star-Oriented MCAO there is one wavefront sensor for each reference star.

In order to evaluate system performance it is useful to plot SR as a function of fo. This may be compared to simulations or model predictions and deviations indicate that there are problems. When this occurs, what are the diagnostics that can be examined There is a great deal of information in the wavefront sensor measurements and provision should be made to store them. Zemike decomposition of the residuals helps to identify if there are problems... 

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. 

When the piston is assumed to be measured from the LGSs (top eurve), the corresponding mode is singular because one cannot measure the contribution of each layer to the total piston. This case is not realistic, since no wavefront sensor measures the piston. When the tilts are measured from the LGSs (case of the polychromatic LGS), the odd piston is not measured again. The even piston is no longer available. And the two odd tilt modes are not also, because whereas the tilt is measured, the differential tilt between the two DMs is not one does not know where the tilt forms. Thus there are 4 zero eigenvalues. 

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. 

Abstract Wavefront sensing for adaptive optics is addressed. The most popular wavefront sensors are described. Restoring the wavefront is an inverse problem, of which the bases are explained. An estimator of the slope of the wavefront is the image centroid. The Cramer-Rao lower bound is evaluated for several probability distribution function... 

Keywords wavefront sensing, wavefront sensors, image centroid, Cramer-Rao, maximum... 

In order to accurately estimate the wavefront a number of properties are desirable in a wavefront sensor (Marcos, 2002). These are ... 

Broadband The wavefront sensor should be able to operate across a wide range of wavelengths. Often light is limited and it is important to use every available photon to minimize the noise. 

Rather than attempting to focus on all aspects of wavefront sensing in this chapter we will focus on the problem of estimating parameters from the measurements. This is a problem that underlies all wavefront sensors, and indeed most instruments. 

For a circular aperture a typical set of basis functions are the Zemike polynomials (Noll, 1976), but for other geometries alternative basis functions may be more appropriate. The objective of most wavefront sensors is to produce a set of measurements, m, that can be related to the wavefront by a set of linear equations... 

The second problem is how we can obtain a linear relationship between the coefficients describing the wavefront and our measurements. It is how this linear relationship is obtained that differentiates, for example, a Shack-Hartmann and a curvature sensor. In all wavefront sensors to transform a wavefront aberration into a measurable intensity fluctuation it is necessary to propagate the wavefront. As a first approximation this propagation is described by geometric optics, and we discuss the linear relationship between the wavefront slope and the image displacement in Section 24.3. 

The problem we face is that we have to estimate a wavefront, which has an infinite number of degrees of freedom, from a finite number of measurements. At first this may seem impossible, but in reality an infinite range of possible solutions describes most practical situations, not just wavefront sensing. The key to solving the problem is that we need to make an assumption about the relative likelihood of the solutions. As an example of how this is done, consider a wavefront sensor which makes a single measurement that is sensitive to only two basis functions. 

Unfortunately, there is not a linear relationship between the light intensity in the measurement plane and the wavefront. This is shown in Fig. 2 which shows the intensities measured at the focal plane for a wavefront equal to pure tilt and coma terms individually. It is apparent that scaling the wavefront by a (in this case 5) does not result in a linear increase in the measured intensity by a factor a. The key difference between existing existing wavefront sensors such as the Shack-Hartmann, curvature and pyramid sensors is how they transform the measured intensity data to produce a linear relationship between the measurements and the wavefront. 

P. D. Pulaski, J. P. Roller, D. R. Neal, and K. Ratte, "Measuremenst of aberrations in microlenses using a Shack-Haitmann wavefront sensor," Proceedings ofSPIE, vol. 4767, pp. 1-9,2002. 

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