Adaptive Optics Definitions

Most definitions were taken in part from Wikipedia.

Aperture

The aperature is the hole or opening through which light travels, typically into an optical system such as a telescope or camera.


Large and small apertures in a Minolta camera lens. Image source: http://en.wikipedia.org/wiki/File:16_minolta_50mm.jpg

Airy Disk


3D view of an Airy disk of a telescope. Image Source: http://en.wikipedia.org/wiki/Airy_disc
In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light.

The angle at which the first diffraction minimum occurs at:

sin θ ≈ 1.22 λ/d

where d is the diameter of a telescope.

 

 

Bend Radius

The minimum radius to which a material can bend without kinking or going outside its elastic limits.

Bimorph & Unimorph

Directly from the Wikipedia entry:


A bimorph moving a track. Image Source: http://en.wikipedia.org/wiki/Bimorph
A bimorph is a cantilever that consists of two active layers: piezoelectric and metal. These layers produce a displacement via:

  • thermal activation (a temperature change causes one layer to expand more than the other).
  • electrical activation as in a piezoelectric bimorph (electric field causes one layer to extend and the other layer to contract).

A piezoelectric unimorph has one active (i.e. piezoelectric) layer and one inactive (i.e. non-piezoelectric) layer.

Curvature Deformable Mirror

A curvature deformable mirror has the ability to be deformed into the shape of incoming wavefronts that have been distorted by the atmosphere. Generally, in a curvature-correcting AO system, wavefront curvature is measured and then the curvature deformable mirror is adjusted to match that wavefront curvature.


Deformable Mirror Adjusted to Curvature of Incoming Wavefronts.
Image Source: http://en.wikipedia.org/wiki/Adaptive_optics

The curvature deformable mirror in UH's Hokupa'a-85 system is made with a thin sheet of piezoelectric material that is deformed by variable current levels input at the mirror's edges.

Cyanoacrylate

Cyanoacrylate is a tenacious adhesive, aka super glue! Cyanoacrylate is a fast-acting adhesive with low shear strength. In electronics, the adhesive is used to assemble prototype electronics. Interestingly, it also adheres to skin and has been used for suture-free surgery.

Diffraction Limit

The diffraction limit of a telescope is the theoretical maximum resolution the telescope can achieve if the optical system is free of all aberrations and imperfections. In space, it is said that the telescope is diffraction limited - i.e. the resolution it can achieve is only limited by the system itself. On Earth, telescopes are often seeing limited - i.e the resolution is limited by the turbulence of the atmosphere. In the diffraction limit, the smallest size that can be resolved is the Airy disk.

Electrostriction / Electrostrictors

All dielectric materials experience electrostriction. When an electric field is applied to a dielectric, material thickness is reduced in the direction of the electric field. The thickness is not restored when the electric field polarity is reversed.

Electrostriction can be used to mobilize actuators on a small scale. Electrostrictors are materials that experience electrostriction and can be used as actuators in AO systems to control the shape of the surface of deformable mirrors.

Fried Parameter

The Fried (pronounced freed) parameter is the smallest possible radius at visible wavelengths that can be resolved due to turbulence in the atmosphere. Telescopes with resolutions smaller than the Fried parameter are inherently limited by the Friend parameter. Because the parameter depends on the conditions in the atmosphere, it generally varies between 5 - 20 cm. This is the length scale over which turbulence becomes significant and, in adaptive optics, defines the lenth scale over which corrections must be made.

Hysteresis

Hysteresis is a lag or delay in response to a force applied to or removed from a system. Electric hysteresis refers to a lag in response to a varying electric field. Lag does not necessarily mean time lag, rather the key behavior in a system with hysteresis is that the system displays rate-independent irreversible behavior.

Hysteresis can also mean that a system has a "memory" of the forces that have been placed upon it. For example, If iron is placed in a magnetic field, some part of the metal becomes permanently magnetized, even when the external magnetic field is removed.

Another example of hysteresis: Stretch a rubber band and then release the tension. The rubber band does not quite return to its original length. Instead, it is slightly longer due to energy lost to thermal exchange with the environment.

Interdigitated

To interlock like the fingers of folded hands. In electronics, comb-like electrode structures can interlock in such a way.

Kolmogorov Spectrum

airplane turbulence
Image Source: Wikipedia - Turbulence
When a fluid becomes turbulent, the turbulence is generally thought of as a series of eddies. The large eddies break into smaller eddies which then break into smaller eddies and so on until, finally, the eddies are so small that the viscosity of the fluid can effectively dissipate the kinetic energy as internal energy. In this way, energy flows from large to small scales through turbulence. In 1941, Andrey Kolmogorov developed a theory describing this turbulent flow. He postulated that turbulent flows are statistically isotropic and that the statistics of the flow are the same for all scales (for very high Reynolds numbers). Secondly, he hypothesized that the statistics at small scales depended only on the viscosity of the fluid (ν) and the rate of energy dissipation (ε). This theory then yields the Kolmogorov length scale:

η = (ν 3/ε)1/4

and the Kolmogorov energy spectrum that follows a 5/3 power law:

E(k) ∝ k-5/3

where k is 2π/r. This theory isn't a completely correct description of turbulence, but it is a good estimate of turbulent length and energy scales.

Lenselet

In an adaptive optics system, the incoming wavefronts are measured in different areas of the pupil plane. This is done by breaking up the pupil plane into sections using a lenselet array. Each lenselet focuses part of the pupil plane onto a detector, which then compares the light from the lenselets to determine characteristics of the incoming wavefronts across the pupil plane.

In the case of Hokupa'a-85, the lenselet array (pictured) samples 85 portions of the pupil plane.

 
LEFT: Array of 85 lenselets - a part of Hokupa'a-85's AO sytem.
RIGHT: Diagram of light passing through lenselets which are then imaged on to a CCD.
Image Source: http://www.cvs.rochester.edu/williamslab/r_shackhartmann.html

Photodiode

A photodiode converts light into voltage or current. When a photon strikes a photodiode, it liberates an electron which results in the detection of the photon. UH's AO systems currently use avalanche photodiodes, which have an internal gain that raises the responsiveness of the device. Avalanche photodiodes can effectively count each every photon the strikes them (compared to other diodes that have lower levels of detection efficiencies).

Piezoelectric

Piezoelectric materials respond to electric current by changing shape. The word "piezoelectricity" means electricity generated from pressure. Piezoelectric materials generate internal electrical charge under the influence of mechanical force. Conversely, these materials will generate mechanical force when an electrical current is applied. Piezoelectric materials are crystalline and occur in nature. Examples of piezoelectric materials include tourmaline, quartz, topaz, and cane sugar. In optics, applying current to a piezoelectric crystal can cause deformation that leads to a change in polarization, making them useful for the creation of polarimeters. In adaptive optics, the application of electric current to a piezoelectric crystal can cause deformation, making it a useful material for controlling the shape of AO deformable mirrors.


Voltage applied to piezoelectric mater causes it to change shape. Image Source: http://archives.sensorsmag.com/articles/0203/33/main.shtml

Direct Piezoelectric Effect

The application of compression or tension stress on a piezoelectric material creates a voltage. This is called the direct piezoelectric effect. The two types of stress create opposite polarity voltages inside the material.

Indirect/Inverse Piezoelectric Effect

The indirect or inverse piezoelectric effect occurs by exactly the opposite mechanism. A voltage difference across the surface of the material causes the material to deform.

Poled / Unpoled Piezoelectric

A potentially piezoelectric material can be forced to be piezoelectric through a process called poling. Poling forces dipoles within the material (under special conditions) to align.

Unpoled piezoelectrics are materials that naturally display piezoelectric behaviors.

Source: http://www.chm.bris.ac.uk/webprojects2004/phillips/PZ/pz-poling.html

Pupil

Light first enters an optical system through an aperture stop, such as the end of a telescope. The pupil is the image of that aperture stop throughout the optical system. The image of the aperture stop just before it enters the optical system is called the entrance pupil. The image of the pupil after it has passed through the optical path is called the exit pupil.

PZT Sandwich

PZT stands for piezoelectric transducer. PZTs convert electric signals into mechanical vibrations, often used in acoustic situations. Combining PZTs or sandwiching a PZT between other types of material is done to enhance the vibrations or response to applied voltage.

Resonant Frequency

A resonant frequency is close to (depending on damping) the natural frequency at which an object vibrates. When a system is driven at a resonant frequency, the amplitude of the oscillations rapidly increases and energy is easily transferred between two or more storage modes (such as kinetic and potential energy). In adaptive optics, a deformable mirror has a specific resonant frequency/set of resonant frequencies.

Pushing a person on a swing at the resonant frequency makes the swing go higher and higher after every impulse.

 

 

Shack-Hartmann wavefront sensor

A Shack-Hartmann wavefront sensor is a type of adaptive optics system. It uses an array of lenselets, all of which have the same focal length, which are focused on a detector, typically a CCD. The lenselets are able to measure the phase aberration across the image and approximate this aberration with a set of tilts. The wavefront can then be approximated. However, this system cannot measure the curvature of or discontinuities in the wavefront, making it inherently limited.

Shot Noise

Shot noise is an electronic noise that becomes important when a detector has a very low signal. In astronomy, when a detector recieves a low number of photons, random electronic fluctuations in the detector become important and measureable. Because one or small numbers of electrons are released when a photon hits a detector, random fluctuations in these small number of electrons is detectable. This electronic noise is shot noise.

Strehl Ratio

The Strehl ratio is a measure of how sharply an optical system brings a point-source into focus compared to the theoretical diffraction limit of the system. The Strehl ratio is the ratio of the peak focal intensities of the aberrated and ideal point spread functions.


The Strehl ratio as a telescope is defocused.
Image Source: Click here.

Silicon Carbide

Silicon carbide's chemical formula is SiC. It has been used since the late 1800's as an abrasive. It is widely used in car brakes, ceramic plates, and bullet-proof vests. SiC is widely used in high-temperature, high-voltage semiconductor electronics. In astronomy, SiC's high rigidity and thermal conductivity make it a desirable material to create optics in telescopes.

Tilt

Tilt is a deviation in the direction a beam of light travels as it passes through the atmosphere. A variation in tilt causes the image of an object to jump around on the pupil plane in both X and Y. Tip-tilt correction is the first order correction in an adaptive optics system.

Wavefront

A wavefront is the line or locus of points in a series of waves that have the same phase.


Wavefronts in water waves. Image Source: Click here.

Wavefront / Phase Curvature

When an incoming wavefront is curved, the wavefront is distorted such that parts of the wavefront arrive sooner than other parts of the wavefront (see diagram associated with "curvature deformable mirror" above). This variation in phase results in a variation in focus aross the focal plane. One portion of the wavefront may come into focus in front of the focal plane while another portion of the same wavefront reaches a focus behind the focal plane. A curvature-sensing adaptive optics system measures this variation of focus across the focal plane and then employs a deformable mirror to correct this aberration.

Wavefront Sensor

A wavefront sensor measures aberrations in optical wavefronts. The aberrations are measured as outlined in the "Wavefront Curvature" entry above.

Zernike Component

Zernike polynomials are a series of polynomials that are orthogonal on a unit disk. One use of the Zernike polynomials is to characterize high order aberrations in optics. In the case of adaptive optics, aberrations caused by the atmosphere can be modeled with specific Zernike terms. The control system uses these terms to automatically adjust the mirrors and counteract the atmospheric disturbance.

Adaptive Optics Laboratory
University of Hawaii Institute for Astronomy
2680 Woodlawn Dr. Honolulu, HI 96813
(808) 956-7434

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