Hartmann Shack sensor

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The Hartmann-Shack-Sensor (also Shack-Hartmann-Sensor) is a wavefront sensor for the measurement of an optical wavefront .


Functional principle of the Hartmann Shack sensor

The Hartmann-Shack sensor consists of a lens mask, for example a glass plate with microlenses regularly arranged on it, and a 2D detector. If a collimated light beam from a point source falls on the lens mask, each lens generates a point image in the focal plane , i.e. where the 2D detector is located, which can be shifted from its nominal position according to the local inclination of the wavefront above the respective microlens. The respective position of the point spreadsheets can be measured with location-sensitive detectors, usually a CMOS or CCD camera chip. If, for example, 8x8 pixels of a CCD detector are located in the focal plane behind each microlens, one expects, with perfect alignment and optics, that the center of each point image falls exactly between the 4th and 5th pixel in both directions of the 8x8 pixels. If, on the other hand, the collimated light beam is optically disturbed, for example somewhat defocused, the point spreads of each microlens shift. By measuring the distance between the point spreads with an illumination once without and once with optical interference, the tilting of the wavefront in two directions is obtained via the respective microlens. For example, the imaging errors of an objective can then be determined from all tilts together.

The Hartmann test was developed in 1900/1904 as a perforated disc test by Johannes Hartmann and refined by Roland Shack and Ben Platt in the late 1960s / early 1970s. The principle is based on the geometrical-optical determination of the local wavefront inclination.


An incident wave front creates a characteristic spot pattern on the camera chip. Each lens will create a point of light on the chip. In the case of a plane and perpendicularly incident wave front, the distances between the light points and those of the lenses correspond to one another. By analyzing the local deflections of the points from their ideal positions, statements can be made about the local slope behavior of the incident wave front. The mathematical description of the wavefront can e.g. B. be done with the help of Zernike polynomials . Direct measurement of the phase is not possible with an optical wave . The Shack-Hartmann sensor is a method for converting this phase information into a measurable intensity distribution.

Dynamic range and sensitivity

Single lenslet from a Shack-Hartmann sensor

A disadvantage of a Shack-Hartmann sensor is that the quantities of measurement accuracy and dynamic range are not independent of one another.

If a wavefront component falls on a single lens at an angle , the smallest tilt of the local wavefront component that can still be resolved results from:


At the same time, the greatest detectable tilting of the wavefront component is through

given. Here and are the focal length and the diameter of the lens and the smallest shift of the focal point that can be resolved by the detector used.

If you want to increase the measurement accuracy for the same detector , the focal length of the lenses must be increased. However, an increase in the focal length leads to a reduction in the dynamic range . Measurement accuracy and dynamic range are therefore not independent of each other, but must be adapted to the application together.

operation area


The design of this sensor was published by Johannes Hartmann as early as 1900. A good 70 years later, Shack and Platt built a functional device. In the US, Shack is therefore given priority, whereas otherwise the historical process is usually used for the naming (as suggested by Shack himself).

The fundamental principle, however, was documented around 400 years earlier, even before Huygens, by the Jesuit Christoph Scheiner in Austria , although not the model of wave optics but that of ray optics was used to explain it. The Scheiner disk is used in ophthalmology to measure aberrations in the human eye and represents a simple form of a two-beam aberrometer that is related to the Hartmann-Shack sensor via the Hartmann mask . The Hartmann-Shack sensor can, however, determine distortions over the entire field of view in parallel and was first used in 1994 to measure aberrations in the human eye.


  1. a b J. Hartmann, remarks on the construction and adjustment of spectrographs, Zeitschrift für Instrumentenkunde 20, September 1900, pages 17ff and 47ff, online version
  2. ^ J. Hartmann, About a new camera lens for spectrographs, Zeitschrift für Instrumentenkunde 24, September 1904, pages 257–263, online version
  3. Platt, BC & Shack, R. “History and Principles of Shack-Hartmann Wavefront Sensing”, Journal of Refractive Surgery, Sept./Oct. 2001, Vol. 17., online version
  4. Jae Won Cha, Jerome Ballesta, Peter TC So: Shack-Hartmann wavefront-sensor-based adaptive optics system for multiphoton microscopy . In: Journal of Biomedical Optics . tape 15 , no. 4 , 2010, ISSN  1083-3668 , p. 046022 , doi : 10.1117 / 1.3475954 .
  5. ^ Shack, Platt: Production and Use of a Lenticular Hartmann Screen . (Oral presentation) JOSA 61: 656 (1971). Program booklet
  6. C. Scheiner: Oculus, Sive Fundamentum Opticum, Innsbruck (1619).
  7. Klaus Biedermann: The Eye, Hartmann, Shack, and Scheiner ( PDF )
  8. David R. Williams: History of Ophthalmic Wavefront Sensing (2003) ( PDF )
  9. ^ Liang, Grimm, Gölz, Bille: Objective Measurement of Wave Aberrations of the Human Eye with the Use of a Hartmann-Shack Wave-front Sensor . JOSA-A 11: 1949-57 (1994). Online version

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