Shack–Hartmann wavefront sensor
The Hartmann- Shack sensor (including Shack- Hartmann sensor ) is a wavefront sensor for measuring an optical wavefront.
Construction
The Hartmann-Shack - sensor comprises a two-dimensional lens array and a 2D optical detector. Each of the lenses produced in the focal plane of an image which is shifted in accordance with the local slope of the wavefront relative to the reference position. The respective displacement can be measured with position sensitive detectors or a CMOS or CCD camera chip.
The Hartmann test was developed as a perforated plate test by Johannes Hartmann in 1900 and refined by Shack. The principle is based on the geometric- optical determination of the local wavefront tilt.
Function
An incident wavefront produces a characteristic pattern of spots on the camera chip. Each lens will produce a light spot on the chip. In a plane and perpendicularly incident wave front, the distances of the points of light agree with each other with those of the lenses agree with each other. By analyzing the local deflections of the points from their ideal positions statements about the local slope behavior of the incident wavefront can be made. The mathematical description of the wave front can eg effected by means of Zernike polynomials. On an optical wave, the direct measurement of the phase is not possible. The Shack- Hartmann sensor is a process to convert this phase information into a measurable intensity distribution.
Dynamic range and sensitivity
The disadvantage of a Shack- Hartmann sensor, the sizes measurement accuracy and dynamic range are not independent.
If a wave front portion at an angle on a single lens, then the smallest still to be released tilting of the local wavefront component is obtained by:
At the same time the largest detectable tilt of the wavefront portion is by
Given. In this case, and the focal length and the diameter of the lens and the smallest resolvable by the detector used in displacement of the focal point.
If you now wish to increase the measurement accuracy for the same detector, so it must be increased, the focal length of the lenses. An increase in the focal length at the same time leads to a reduction of the dynamic range. Measurement accuracy and dynamic range are not independent of each other but need to be adjusted together on the application.
Area of application
- In quality testing of optical components for the assessment of surface and transmission qualities.
- In the laser technology for the characterization of the optical properties of a laser beam.
- In astronomy, to measure the deviation of the beam front of the light of distant stars on the way through the earth's atmosphere. Adaptive optics telescopes can be corrected accordingly.
- In ophthalmology for accurate measurement of the aberrations of the human eye, especially for accurate planning of interventions in refractive surgery.
History
The design of this sensor was published by Johannes Hartmann in 1900. A good 70 years later Shack and Platt built a functioning device. In the U.S. space Shack is therefore given priority, whereas otherwise mostly the course of history will be used for naming (as well as of Shack even suggested).
However, the fundamental principle was about 400 years earlier, even before Huygens documented by the Jesuits Christoph Scheiner in Austria to its explanation, however, not the model of wave optics, but the ray optics was used. Scheiner the disc is used in ophthalmology to measure aberrations in the human eye and provides a simple form of a two-beam aberrometer is, which is related on the Hartmann mask with the Hartmann -Shack sensor. However, the Hartmann- Shack sensor is capable of distortion over the entire field of view to determine parallel and in 1994 was first used for the measurement of aberrations in the human eye.