Dimensional Measurement using Vision Systems - NPL Publications ...

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Measurement Good Practice Guide No. 39 Figure 28: Intensity profile of a dark line on a bright background. For high power microscopy, the true edge of a feature will be located at some point between the 25% - 50% intensity level, as the illumination will be partially coherent (see section 2.8). Under these conditions, the correct threshold may be found experimentally, by measuring the dimensions of a calibrated feature at varying thresholds within the 25% - 50% range. The formula for calculating the true edge threshold is given in equation 15. t = i (b + (a – b)) …..(15) Where ; t = Grey scale intensity threshold of the camera i = True edge intensity threshold, expressed as a decimal fraction, i.e. 30% = 0.3 b = Mean dark level intensity a = Mean bright level intensity It is worth noting that the intensity profile in Figure 28 is of a straight edge and is the average profile over 500 pixel rows on the y-axis. Figure 29 shows the comparison of an averaged intensity profile and the profile of an edge along a single row of pixels. The difference between the two calculated 50% thresholds is only 4 grey scale values, and for most applications, is negligible. However, where possible, straight edges and averaging should be used, as the noise level on the profile is reduced and the dynamic grey scale range is more accurate. 51
Measurement Good Practice Guide No. 39 255 Grey scale value 0 Average Single 0 100 200 300 400 500 Pixels Average profile 50% threshold Single profile 50% threshold Figure 29: Comparison of average intensity profile with a single pixel line intensity profile. 7.5 QUANTIFYING THE EFFECTS OF DISTORTION AND MAGNIFICATION ERRORS Now that the camera has been calibrated and the correct threshold determined, the useable measurement area must be identified. Localised magnification errors are quite common and knowledge of where and by how much the scaling breaks down, allows the determination of the usable measuring area of the image. This is done by imaging an array of calibrated spots, or other suitable standard, over the entire image, as shown in Figure 30. The diameters of the spots are then measured and any deviation in the sizes of the spots can be seen by comparison with the calibrated values. Measurements must be made rather than direct visual observations because screen distortions may affect judgment. Errors due to distortion are usually found at the edge of the field of view. These may be quantified by measuring the diameters, or centre-to-centre pitches, of the array of spots and comparing them to the calibrated values. It is also possible to perform the pixel calibration using this method and this can provide a more accurate and reliable calibration value for the system, as the centroids of the spots are determined with sub-pixel accuracy. Both axes may be calibrated at the same time and an error map produced very quickly for the entire image area. Once the useable area of the screen has been determined, the pixel calibration should be repeated within that area to minimise errors. 52
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