FAQ ADAPTIVE OPTICS

What is Adaptive Optics?
Which are the applications of Adaptive Optics?
What is a wavefront?
How can I deform a wavefront?
How can I measure a wavefront?
Which kind of deformable mirrors do exist?
Which is the most common setup for Adaptive Optics?
What is the Influence matrix?

What is Adaptive Optics?

Adaptive Optics (AO) is a technology that allows the enhancement of the quality of optical systems by acting actively on the wavefront of the optical beam. AO can correct for disturbances created by an optical system itself such as misalignment or non perfect optical elements and for external disturbance such as heat effects, atmospheric effects. AO was first proposed in the 1953 and then developed principally in astronomy for compensating the atmosphere effects, nowadays AO is used in many fields, from industrial machines, to medical equipments.

Which are the applications of Adaptive Optics?

AO devices are presently employed in a very broad range of applications, involving both imaging and non imaging applications.

1) Imaging applications may use AO for a better image quality and can be divided into several sectors:

• Biomedical applications such as ophthalmology for overcoming the aberration of the eye. In this way high resolution retinal images can be acquired, allowing more precise medical inferences.
• Microscopy, which can benefits of AO for static lens correction,
• Wide filed microscopy, strong reduction of the cost of high quality optical objectives is achieved by the use of AO
• Optical Coherence Tomography (OCT) the depth of scanning can be increased by AO.
• Robotic Vision AO allows real time optical accommodation for robotics vision
• Surveillance Correction of atmospheric turbulence could be exploited for real time optical corrections of surveillance cameras
• Astronomy applications such as rejection of atmospheric effects
• Vision Application such as environment surveillance in which AO can be a unique tool for long distance imaging and hyper-vision.
• In 3D imaging the use of AO allows increasing the instrumental depth range.

2) The non imaging applications spans from enhancing and controlling laser systems (intra-cavity AO systems for mode selection or extra-cavity AO for beam shaping) to free space classical and quantum communication for noise rejection and precise pointing as well as measuring and probing laser systems where AO can increase the precision of the measurement. Some example are:

• Laser materials processing. The quality of the process is improved using AO devices to control the LASER beam size and shape.
• Free-space optical high speed communications will benefit from using AO for increasing the signal to noise ration.

What is a wavefront?

The wavefront of a two dimensional (or three dimensional) wave is the line (surface) in which the points have the same phase. Another way of seeing it is the perpendicular in every point to the propagating direction so for example the wavefront of a plane bi dimensional (3D) wave is a strait line (a plane) perpendicular to the propagating direction (Figures A & B). The easiest way to modify a wavefront is to place a lens to create a spherical wavefront (Figure C).

How can I deform a wavefront?

Any wavefront can be modified by optical elements such as lenses or mirrors. In general a wavefront is modified every time the optical path length (OPL) i.e. the travelled length times the index of refraction is not the same along the wavefront domain. If one uses elements that can introduce differences in OPL the wavefront can be modified. Adaptive Optics elements such as deformable mirrors do exactly this with the plus that one can choose the deformation to give to the wavefront.

How can I measure a wavefront?

The wave-front sensor is used to measure the deformation of a wave-front. There are several techniques that can be used in order to get this information. The most common is the Shack Hartmann approach: it consist on a spatial sampling of the wave-front by means of a lenslet (array of micro lenses), the position of the spots produced by the lenses on a CCD reveal the local phase information on the wave-front. The latter can then be reconstructed using this local information or by a modal decomposition. Other techniques are Wave-front Curvature Sensor, Common Path Interferometer, pyramid wave-front sensor.

Example of Shack Hartmann Wave-front Sensor principle.

Which kind of deformable mirrors do exist?

There are a number of different types of deformable mirrors (DMs), some are on the market some other are still inside research labs. The paramenter that characterize a deformable mirror are:

1. Actuation technology: mechanical, piezoelectric, electrostatic (membrane), magnetic, bimorph, MEMS
2. Quality of Surface:
   a)segmented, made of small pieces of mirror each moves separately
   b)continuous, made by a single reflective surface which can be moved in different points. In any case the optical quality must guarantee the desired correction effectiveness.
   
3. Number of Actuators: the number of actuators defines the quality and the number of different shapes that the mirror can reproduce
4. Size: there are DMs from some millimeters to secondary deformable mirrors for telescope of tens of centimetres.

Every combination has advantages and drawbacks regarding costs, power consuption, optical load, hysteresis and repeatability.
In particular membrane electrostatic mirrors specs are: low cost, large dynamic behaviour, achromaticity, no hysteresis, relatively high optical load, good performance in aberrations generation, low power consumption. The drawback of these devices is the limited amount of maximum stroke (maximum deformation ...) and the high correlation within the electrodes. In this sense other solutions can be thought such as to place actuator on the top on structure so being able to either to pull or push the membrane.

Which is the most common setup for Adaptive Optics?

The most common setup for Adaptive Optics is the close loop correction in which a portion of the light is taken after the deformable mirror and sent to a wavefront sensor in order to monitor the error in the wavefront and keep it as close as possible to zero.

What is the Influence matrix?

The influence matrix is the matrix that has on its columns the influence function of the mirror actuators i.e. the deformation that one single actuator produces. In more detailed terms consider a mirror with N actuators and a wavefront domain of M=nxny where the grid nx x ny is the bi dimensional domain of the wavefront. The influence matrix A (MxN) is obtained activating the j-th actuator j=1:N and measuring the corresponding wavefront wj (M x 1), called influence function, and then placing all the influence function in a row: A=[w1 w2 . . . wN]. At this point it easy to write any mirror deformation as linear combination of influence functions as w=Av where w (M x 1) is the wavefront, A (M x N) is the influence matrix and v (N x 1) is the voltage vector squared. The inverse problem can also be addressed if one wants to know the voltages that give a specified deformation; the matrix A can be pseudo inverted or alternative iterative solution can be used in order to obtain a relation similar to: v=(A^-1)w where the squared voltages are obtained from the desired deformation.

What is a close loop system?

A closed loop system is a setup in which a portion of the light is taken after the deformable mirror and sent to a wavefront sensor in order to monitor the error in the wavefront and keep it as close as possible to zero.