{
  "annotation_id": "cf67228d-1878-4ee1-bc96-3cf3339888a2",
  "date_created": "2026-03-02T18:01:07.827000Z",
  "date_modified": "2026-03-02T18:01:07.827000Z",
  "file_hash": "f228722a3cbfa859043bd612d35d23deade97fdc73471b608844fbe103af2135",
  "private": false,
  "record": {
    "abstract": "Phase steps are an important type of wavefront aberrations generated by large\ntelescopes with segmented mirrors. In a closed-loop correction cycle these\nphase steps have to be measured with the highest possible precision using\nnatural reference stars, that is with a small number of photons. In this paper\nthe classical Fisher information of statistics is used for calculating the\nCramer-Rao bound, which determines the limit to the precision with which the\nheight of the steps can be estimated in an unbiased fashion with a given number\nof photons and a given measuring device. Four types of measurement devices are\ndiscussed: a Shack-Hartmann sensor with one small cylindrical lenslet covering\na sub-aperture centred over a border, a modified Mach-Zehnder interferometer, a\nFoucault test, and a curvature sensor. The Cramer-Rao bound is calculated for\nall sensors under ideal conditions, that is narrowband measurements without\nadditional noise or disturbances apart from the photon shot noise. This limit\nis compared with the ultimate quantum statistical limit for the estimate of\nsuch a step which is independent of the measuring device. For the\nShack-Hartmann sensor, the effects on the Cramer-Rao bound of broadband\nmeasurements, finite sampling, and disturbances such as atmospheric seeing and\ndetector readout noise are also investigated. The methods presented here can be\nused to compare the precision limits of various devices for measuring phase\nsteps and for optimising the parameters of the devices. Under ideal conditions\nthe Shack-Hartmann and the Foucault devices nearly attain the ultimate quantum\nstatistical limits, whereas the Mach-Zehnder and the curvature devices each\nrequire approximately twenty times as many photons in order to reach the same\nprecision.",
    "arxiv_id": "physics/0604056",
    "authors": [
      "L. Noethe",
      "H. M. Adorf"
    ],
    "categories": [
      "physics.optics"
    ],
    "doi": "10.1080/09500340600842252",
    "title": "Optical measurements of phase steps in segmented mirrors - fundamental   precision limits",
    "url": "https://arxiv.org/abs/physics/0604056"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8fc2f62c-d9c3-433e-820e-2b4240a04073",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}