Distortion changes where image content appears. A camera maps object positions to sensor coordinates; a display or projector maps commanded coordinates to visible positions. Either path can bend lines or change local scale without necessarily blurring a small feature. Measurement requires an explicit ideal mapping, because magnification, perspective, and optical distortion describe different departures from geometry.
Define the position error
For a rotationally symmetric mapping, compare measured image height with ideal image height :
At nonzero field radius, negative radial distortion corresponds to barrel distortion and positive to pincushion distortion under this convention. A simple radial model is:
The coefficient units depend on the coordinate normalization. Complex lenses can combine barrel and pincushion behavior across the field, so one corner percentage may conceal a change of sign. Decentering effects require additional terms beyond a radial model.
Imaging: calibrate object-to-sensor geometry
Image a dimensionally characterized grid or dot target at the intended working distance. Estimate feature centers, account for target pose, and fit the camera mapping. Perspective from a tilted target should not be mistaken for lens distortion. Target flatness, feature localization, and calibration coverage influence the recovered parameters.
Report displacement vectors and residual errors across the usable field, ideally in pixels and application units. A low fitting residual on the calibration data does not establish independent measurement accuracy. Validate with separate positions or reference dimensions. Lens focus changes, mechanical movement, and temperature can require renewed calibration.
Display: calibrate commanded-to-viewed geometry
Display a grid and measure its visible coordinates using a calibrated camera or other suitable metrology. Projection optics, screen shape, alignment, and viewing position can all contribute. For near-eye systems, eye position and the specified angular coordinate system are part of the measurement geometry.
Remove or model the measuring camera’s own distortion before attributing all observed bending to the display. Prewarping can correct a stable mapping, but resampling consumes spatial resolution and cannot create missing field coverage. Validate the corrected grid, local scale, and usable image boundary at representative viewing positions.
Keep TV distortion separate from radial distortion
TV distortion summarizes bending near the picture boundary; it is not the maximum radial position error. For the SMIA-style full-height convention shown here:
and are the picture’s full vertical heights at its left and right edges; is its full height at horizontal center. Barrel bending gives and a negative value. State the convention with the number: a traditional single-edge displacement divided by full picture height has half the magnitude for a vertically symmetric pattern.
Neither TV nor radial distortion alone captures keystone, local warping, or all asymmetric errors. Preserve the coordinate map and measurement setup alongside the summary metric. The calculator illustrates declared radial and TV definitions; a production calibration needs spatial data and independent verification.
Iris Optics can develop camera and display mapping calibrations, separate device geometry from measurement-system error, and verify whether the corrected system meets dimensional or visual requirements.