# 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. |  |
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| **The Raw sensor** coordinate system starts from upper left and extends rightwards and downwards.
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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:
* adjust sweep frequency or scanning speed to avoid non-square pixels.
* adjust optical alignment to minimize perspective effect. The field of view should be parallel to the sensor plane.
* use long focal distances and good quality lenses to minimize Optical distortion.
* use appropriate scale factor based on lens magnification, observation distance and focusing.
* 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. |  |
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| **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. |  |