Calibration and Transformation

Field-of-view calibration

Calibration establishes the relationship between real-world point coordinates and image pixels. A simple calibration model computes faster, a repeatable part position is easier to locate.
The Raw sensor coordinate system starts from upper left and extends rightwards and downwards. The range of abscissas is 0 to width-1 and the range of ordinates is 0 to height-1 where integer coordinate values correspond to pixel centers.
The Centered sensor coordinate system starts at the center ([width-1]/2, [height-1]/2 in the Raw system) and extends rightwards and upwards.
The real world 3D coordinates are defined in a 2D reference frame tied to a reference plane. The origin and direction of the axis are normally aligned with major features of the inspected parts.

Before World-to-Sensor Transform

Before converting from world to sensor coordinates, sources of distortion should be eliminated:

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adjust sweep frequency or scanning speed to avoid non-square pixels.

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adjust optical alignment to minimize perspective effect. The field of view should be parallel to the sensor plane.

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use long focal distances and good quality lenses to minimize Optical distortion.

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use appropriate scale factor based on lens magnification, observation distance and focusing.

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minimize skew and translation effects by secure fixtures, and part-movement / acquisition-triggering synchronization.

Effects of World-to-Sensor Transform

● No calibration. World and sensor coordinates are identical.
● Translated calibration: The coordinate origin can be moved. World coordinates correspond to pixel units.
● Isotropic scaling (square pixels). A scale factor converts pixel values to physical measurements.
● Anisotropic scaling (non-square pixels). Uses two scale factors with pixel aspect ratio (X /Y ) in the range [-4/3, -3/4] (or [3/4, 4/3]). Pixels are always displayed as square, so the image appears stretched.
● Scaled and skewed (square pixels). Real-world axis aligns with rotated inspected part using translation, rotation and scaling.
● Scaled and skewed (non-square pixels). Distortion is apparent. Occurs when camera scan speed does not match pixel spacing.
● Perspective distortion causes further away objects to look smaller; lines remain straight but angles are not preserved.
● Optical distortion causes cushion or barrel appearance of rectangles.
● Combined distortions result in a complex, non linear, transform from real-world to sensor spaces.