{
  "annotation_id": "3deb1788-f0ea-429b-8690-ee83cae189b3",
  "date_created": "2026-03-02T18:00:32.727000Z",
  "date_modified": "2026-03-02T18:00:32.727000Z",
  "file_hash": "31a7033d623559f32bce4eedce5e00c3481999bbc9cdfe0ecb8f27e6258cbbda",
  "private": false,
  "record": {
    "abstract": "The ABCD matrix is one of the essential mathematical instruments in optics.\nIt is the two-by-two representation of the group Sp(2), which is applicable to\nmany branches of physics, including squeezed states of light, special\nrelativity and coupled oscillators. It is pointed out that the shear\nrepresentation is oriented to binary logic which may be friendly to computer\napplications. While this is a future possibility, it is known that para-axial\nlens optics is based on the shear representation of the Sp(2) group. It is\npointed out that the most general form of the ABCD matrix can be written in\nterms of six shear matrices, which correspond to lens and translation matrices.\nThe parameter for each shear matrix is computed in terms of the three\nindependent parameters of the ABCD matrix.",
    "arxiv_id": "physics/0008220",
    "authors": [
      "S. Baskal",
      "Y. S. Kim"
    ],
    "categories": [
      "physics.optics",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1103/PhysRevE.63.056606",
    "journal_ref": "Phys. Rev. E 63 (2001) 56606",
    "title": "Binary Representations of ABCD Matrices",
    "url": "https://arxiv.org/abs/physics/0008220"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "71e23669-ddc8-417d-aeb2-09502d22ddfe",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}