Deformable mirror
Encyclopedia
Deformable mirror represents the most convenient tool for wavefront
control and correction of optical aberration
s. Deformable mirrors are used in combination with wavefront sensor
s and real-time control systems in adaptive optics
. They are also finding a new use in femtosecond pulse shaping
http://www.adaptiveoptics.org/News_0106_2.html.
The shape of the DM can be controlled with a speed that is appropriate for compensation of dynamic aberrations present in the optical system. In practice the DM shape should be changed much faster than the process to be corrected, as the correction process, even for a static aberration, may take several iterations.
A DM usually has many degrees of freedom. Typically, these degrees of freedom are associated with the mechanical actuators and it can be roughly taken that one actuator corresponds to one degree of freedom.
) the mirror can correct. It is very common to compare an arbitrary DM to an ideal device that can perfectly reproduce wavefront modes in the form of Zernike polynomials
. For predefined statistics of aberrations a deformable mirror with M actuators can be equivalent to an ideal Zernike corrector with N (usually N < M) degrees of freedom. For correction of the atmospheric turbulence, elimination of low-order Zernike terms usually results in significant improvement of the image quality, while further correction of the higher-order terms introduces less significant improvements. For strong and rapid wavefront error fluctuations such as shocks and wake turbulence typically encountered in high-speed aerodynamic flowfields, the number of actuators, actuator pitch and stroke determine the maximum wavefront gradients that can be compensated for.
Actuator pitch is the distance between actuator centers. Deformable mirrors with large actuator pitch and large number of actuators are bulky and expensive.
Actuator stroke is the maximum possible actuator displacement, typically in positive or negative excursions from some central null position. Stroke typically ranges from ±1 to ±10 micrometres. Free actuator stroke limits the maximum amplitude of the corrected wavefront, while the inter-actuator stroke limits the maximum amplitude and gradients of correctable higher-order aberrations.
Influence function is the characteristic shape corresponding to the mirror response to the action of a single actuator. Different types of deformable mirrors have different influence functions, moreover the influence functions can be different for different actuators of the same mirror. Influence function that covers the whole mirror surface is called a "modal" function, while localized response is called "zonal".
Actuator coupling shows how much the movement of one actuator will displace its neighbors. All "modal" mirrors have large cross-coupling, which in fact is good as it secures the high quality of correction of smooth low-order optical aberrations that usually have the highest statistical weight.
Response time shows how quickly the mirror will react to the control signal. Can vary from microseconds (MEMS mirrors) to tens of seconds for thermally controlled DM's.
Hysteresis and creep are nonlinear actuation effects that decrease the precision of the response of the deformable mirror. For different concepts, the hysteresis can vary from zero (electrostatically-actuated mirrors) to tens of percent for mirrors with piezoelectric actuators. Hysteresis is a residual positional error from previous actuator position commands, and limits the mirror ability to work in a feedforward mode, outside of a feedback loop.
.
Continuous faceplate concept mirrors with discrete actuators are formed by the front surface of a thin deformable membrane. The shape of the plate is controlled by a number of discrete actuators that are fixed to its back side. The shape of the mirror depends on the combination of forces applied to the faceplate, boundary conditions (the way the plate is fixed to the mirror) and the geometry and the material of the plate. These mirrors are often the most desirable implementation, as they allow smooth wavefront control with very large - up to several thousands - degrees of freedom.
MEMS
concept mirrors are fabricated using bulk and surface micromachining technologies. MEMS mirrors have a great potential to be cheap. They can break the high price threshold of conventional adaptive optics
. MEMS mirrors typically have high response rates, high precision and have no hysteresis, unlike other types of deformable mirrors.
Membrane concept mirrors are formed by a thin conductive and reflective membrane stretched over a solid flat frame. The membrane can be deformed electrostatically by applying control voltages to electrostatic electrode actuators that can be positioned under or over the membrane. If there are any electrodes positioned over the membrane, they are transparent. It is possible to operate the mirror with only one group of electrodes positioned under the mirror. In this case a bias voltage is applied to all electrodes, to make the membrane initially spherical. The membrane can move back and forth with respect to the reference sphere.
Bimorph concept mirrors are formed by two or more layers of different materials. One or more of (active) layers are fabricated from a piezoelectric or electrostrictive material. Electrode structure is patterned on the active layer to facilitate local response. The mirror is deformed when a voltage is applied to one or more of its electrodes, causing them to extend laterally, which results in local mirror curvature. Bimorph mirrors are rarely made with more than 100 electrodes.
Ferrofluid
concept mirrors are liquid deformable mirrors
made with a suspension of small (about 10 nm in diameter) ferromagnetic nanoparticles dispersed in a liquid carrier. In the presence of an external magnetic field, the ferromagnetic particles align with the field, the liquid becomes magnetized and its surface acquires a shape governed by the equilibrium between the magnetic, gravitational and surface tension forces. Using proper magnetic field geometries, any desired shape can be produced at the surface of the ferrofluid. This new concept offers a potential alternative for low-cost, high stroke and large number of actuators deformable mirrors.
Wavefront
In physics, a wavefront is the locus of points having the same phase. Since infrared, optical, x-ray and gamma-ray frequencies are so high, the temporal component of electromagnetic waves is usually ignored at these wavelengths, and it is only the phase of the spatial oscillation that is described...
control and correction of optical aberration
Aberration
An aberration is something that deviates from the normal way.Aberration may refer to:In optics and physics:*Optical aberration, an imperfection in image formation by an optical system...
s. Deformable mirrors are used in combination with wavefront sensor
Wavefront sensor
A wavefront sensor is a device for measuring the aberrations of an optical wavefront. Although an amplitude splitting interferometer such as the Michelson interferometer could be called a wavefront sensor, the term is normally applied to instruments that do not require an unaberrated reference...
s and real-time control systems in adaptive optics
Adaptive optics
Adaptive optics is a technology used to improve the performance of optical systems by reducing the effect of wavefront distortions. It is used in astronomical telescopes and laser communication systems to remove the effects of atmospheric distortion, and in retinal imaging systems to reduce the...
. They are also finding a new use in femtosecond pulse shaping
Femtosecond pulse shaping
In optics, femtosecond pulse shaping is a technique that modifies the temporal profile of an ultrashort pulse from a laser. Pulse shaping can be used to shorten/elongate the duration of optical pulse, or to generate more complex pulses.-Introduction:...
http://www.adaptiveoptics.org/News_0106_2.html.
The shape of the DM can be controlled with a speed that is appropriate for compensation of dynamic aberrations present in the optical system. In practice the DM shape should be changed much faster than the process to be corrected, as the correction process, even for a static aberration, may take several iterations.
A DM usually has many degrees of freedom. Typically, these degrees of freedom are associated with the mechanical actuators and it can be roughly taken that one actuator corresponds to one degree of freedom.
Deformable mirror parameters
Number of actuators determines the number of degrees of freedom (wavefront inflectionsInflection point
In differential calculus, an inflection point, point of inflection, or inflection is a point on a curve at which the curvature or concavity changes sign. The curve changes from being concave upwards to concave downwards , or vice versa...
) the mirror can correct. It is very common to compare an arbitrary DM to an ideal device that can perfectly reproduce wavefront modes in the form of Zernike polynomials
Zernike polynomials
In mathematics, the Zernike polynomials are a sequence of polynomials that are orthogonal on the unit disk. Named after Frits Zernike, they play an important role in beam optics.-Definitions:There are even and odd Zernike polynomials...
. For predefined statistics of aberrations a deformable mirror with M actuators can be equivalent to an ideal Zernike corrector with N (usually N < M) degrees of freedom. For correction of the atmospheric turbulence, elimination of low-order Zernike terms usually results in significant improvement of the image quality, while further correction of the higher-order terms introduces less significant improvements. For strong and rapid wavefront error fluctuations such as shocks and wake turbulence typically encountered in high-speed aerodynamic flowfields, the number of actuators, actuator pitch and stroke determine the maximum wavefront gradients that can be compensated for.
Actuator pitch is the distance between actuator centers. Deformable mirrors with large actuator pitch and large number of actuators are bulky and expensive.
Actuator stroke is the maximum possible actuator displacement, typically in positive or negative excursions from some central null position. Stroke typically ranges from ±1 to ±10 micrometres. Free actuator stroke limits the maximum amplitude of the corrected wavefront, while the inter-actuator stroke limits the maximum amplitude and gradients of correctable higher-order aberrations.
Influence function is the characteristic shape corresponding to the mirror response to the action of a single actuator. Different types of deformable mirrors have different influence functions, moreover the influence functions can be different for different actuators of the same mirror. Influence function that covers the whole mirror surface is called a "modal" function, while localized response is called "zonal".
Actuator coupling shows how much the movement of one actuator will displace its neighbors. All "modal" mirrors have large cross-coupling, which in fact is good as it secures the high quality of correction of smooth low-order optical aberrations that usually have the highest statistical weight.
Response time shows how quickly the mirror will react to the control signal. Can vary from microseconds (MEMS mirrors) to tens of seconds for thermally controlled DM's.
Hysteresis and creep are nonlinear actuation effects that decrease the precision of the response of the deformable mirror. For different concepts, the hysteresis can vary from zero (electrostatically-actuated mirrors) to tens of percent for mirrors with piezoelectric actuators. Hysteresis is a residual positional error from previous actuator position commands, and limits the mirror ability to work in a feedforward mode, outside of a feedback loop.
Deformable mirror concepts
Segmented concept mirrors are formed by independent flat mirror segments. Each segment can move a small distance back and forth to approximate the average value of the wavefront over the patch area. Normally these mirrors have little or zero cross-talk between actuators. Stepwise approximation works poorly for smooth continuous wavefronts. Sharp edges of the segments and gaps between the segments contribute to light scattering, limiting the applications to those not sensitive to scattered light. Considerable improvement of the performance of the segmented mirror can be achieved by introduction of three degrees of freedom per segment: piston, tip and tilt. These mirrors require three times more actuators than piston segmented mirrors and they suffer from diffraction on the segment edges. This concept was used for fabrication of large segmented primary mirrors for the Keck telescopesKeck telescopes
The W. M. Keck Observatory is a two-telescope astronomical observatory at an elevation of near the summit of Mauna Kea in Hawai'i. The primary mirrors of each of the two telescopes are in diameter, making them the second largest optical telescopes in the world, slightly behind the Gran Telescopio...
.
Continuous faceplate concept mirrors with discrete actuators are formed by the front surface of a thin deformable membrane. The shape of the plate is controlled by a number of discrete actuators that are fixed to its back side. The shape of the mirror depends on the combination of forces applied to the faceplate, boundary conditions (the way the plate is fixed to the mirror) and the geometry and the material of the plate. These mirrors are often the most desirable implementation, as they allow smooth wavefront control with very large - up to several thousands - degrees of freedom.
MEMS
Microelectromechanical systems
Microelectromechanical systems is the technology of very small mechanical devices driven by electricity; it merges at the nano-scale into nanoelectromechanical systems and nanotechnology...
concept mirrors are fabricated using bulk and surface micromachining technologies. MEMS mirrors have a great potential to be cheap. They can break the high price threshold of conventional adaptive optics
Adaptive optics
Adaptive optics is a technology used to improve the performance of optical systems by reducing the effect of wavefront distortions. It is used in astronomical telescopes and laser communication systems to remove the effects of atmospheric distortion, and in retinal imaging systems to reduce the...
. MEMS mirrors typically have high response rates, high precision and have no hysteresis, unlike other types of deformable mirrors.
Membrane concept mirrors are formed by a thin conductive and reflective membrane stretched over a solid flat frame. The membrane can be deformed electrostatically by applying control voltages to electrostatic electrode actuators that can be positioned under or over the membrane. If there are any electrodes positioned over the membrane, they are transparent. It is possible to operate the mirror with only one group of electrodes positioned under the mirror. In this case a bias voltage is applied to all electrodes, to make the membrane initially spherical. The membrane can move back and forth with respect to the reference sphere.
Bimorph concept mirrors are formed by two or more layers of different materials. One or more of (active) layers are fabricated from a piezoelectric or electrostrictive material. Electrode structure is patterned on the active layer to facilitate local response. The mirror is deformed when a voltage is applied to one or more of its electrodes, causing them to extend laterally, which results in local mirror curvature. Bimorph mirrors are rarely made with more than 100 electrodes.
Ferrofluid
Ferrofluid
A ferrofluid is a liquid which becomes strongly magnetized in the presence of a magnetic field.Ferrofluids are colloidal liquids made of nanoscale ferromagnetic, or ferrimagnetic, particles suspended in a carrier fluid . Each tiny particle is thoroughly coated with a surfactant to inhibit clumping...
concept mirrors are liquid deformable mirrors
Ferrofluid mirror
Ferrofluid mirrors are commonly used in adaptive optics as a deformable mirror. They are made of a ferrofluid that uses electromagnets to change its shape....
made with a suspension of small (about 10 nm in diameter) ferromagnetic nanoparticles dispersed in a liquid carrier. In the presence of an external magnetic field, the ferromagnetic particles align with the field, the liquid becomes magnetized and its surface acquires a shape governed by the equilibrium between the magnetic, gravitational and surface tension forces. Using proper magnetic field geometries, any desired shape can be produced at the surface of the ferrofluid. This new concept offers a potential alternative for low-cost, high stroke and large number of actuators deformable mirrors.
See also
- Wavefront sensorWavefront sensorA wavefront sensor is a device for measuring the aberrations of an optical wavefront. Although an amplitude splitting interferometer such as the Michelson interferometer could be called a wavefront sensor, the term is normally applied to instruments that do not require an unaberrated reference...
- Adaptive opticsAdaptive opticsAdaptive optics is a technology used to improve the performance of optical systems by reducing the effect of wavefront distortions. It is used in astronomical telescopes and laser communication systems to remove the effects of atmospheric distortion, and in retinal imaging systems to reduce the...
- Microelectromechanical systemsMicroelectromechanical systemsMicroelectromechanical systems is the technology of very small mechanical devices driven by electricity; it merges at the nano-scale into nanoelectromechanical systems and nanotechnology...
- Ferrofluid mirrorFerrofluid mirrorFerrofluid mirrors are commonly used in adaptive optics as a deformable mirror. They are made of a ferrofluid that uses electromagnets to change its shape....