page_title: Scheimpflug principle
section_title: Angle of the PoF with the image plane
hierarchical_section_title: Scheimpflug principle / Derivation of the formulas / Angle of the PoF with the image plane
caption_attribution_description: English: Diagram of camera with tilted lens plane, for showing derivations of plane-of-focus angle formulas and proof of the "hinge rule".
context_page_description: The Scheimpflug principle is the geometric rule that describes the orientation of the plane of focus, the lens plane, and the image plane of an optical system when the lens plane is not parallel to the image plane. It is applicable to the use of some camera movements on a view camera. It is also the principle used in corneal pachymetry, the mapping of corneal topography, done prior to refractive eye surgery such as LASIK, and used for early detection of keratoconus. The principle is named after Austrian army Captain Theodor Scheimpflug, who used it in devising a systematic method and apparatus for correcting perspective distortion in aerial photographs; even though Captain Scheimpflug himself credits Jules Carpentier with the rule, thus making it an example of Stigler's law of eponymy.
context_section_description: From Figure 7,
  where u′ and v′ are the object and image distances along the line of sight and S is the distance from the line of sight to the Scheimpflug intersection at S. Again from Figure 7,
  combining the previous two equations gives
  From the thin-lens equation,
  Solving for u′ gives
  substituting this result into the equation for tan ψ gives
  or
  Similarly, the thin-lens equation can be solved for v′, and the result substituted into the equation for tan ψ to give the object-side relationship
  Noting that
  the relationship between ψ and θ can be expressed in terms of the magnification m of the object in the line of sight:
caption: Figure 7. Angle of the PoF with the image plane
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