Table 1 Parameters of a GOBO projection-based 3D sensor that affect the accuracy and completeness of the 3D result
From: GOBO projection for 3D measurements at highest frame rates: a performance analysis
Parameter | Description | Typ. value | Sim. value |
|---|---|---|---|
N ≥ 3, \(N \in {\Bbb N}\) | Number of patterns per sequence | 8…12 | 10 |
ntot = 2k, \(k \in {\Bbb N}\) | Number of strips + number of slits in the GOBO wheel | 1200…2000 | 250…5000 |
\(\phi _{{\rm{avg}}} = \frac{{360^\circ }}{{n_{{\rm{tot}}}}}\) | Average angle that is covered by one strip or slit | 0.18°…0.3° | 0.1°…1.5° |
\(c = \frac{{\phi _{{\rm{max}}}}}{{\phi _{{\rm{min}}}}} \ge 1\) | Ratio of the maximum and minimum angles that are covered by one strip or slit | 2 | 1…10 |
P(φ) | Probability distribution of the strip or slit angle φ | Uniform dist. | Uniform dist. |
r > 0 | Distance of illuminated square’s centre from the GOBO wheel’s centre | 20…200 mm | 25 mm |
a > 0 | Width (= height) of the illuminated square on the GOBO wheel | 10…100 mm | 10 mm |
\(\delta = 2\,\arctan \frac{{a/2}}{{r - a/2}}\) | Maximum angle that is covered by the illuminated square | 15°…30° | 28.1° |
0 < n < ntot | Number of illuminated strips + number of illuminated slits | 50…150 | 20…400 |
σblur ≥ 0 | Projector defocusing, which is approximated by Gaussian blur with std. dev. σblur | \(0.2r\tan \frac{{\phi _{{\rm{avg}}}}}{2}\) | 0…50 µm |
s > 0 | Width (= height) of the measurement volume | 0.2…2 m | 0.3 m |
d > 0 | Depth of the measurement volume | 0.2…1 m | 0.3 m |
\(v = \frac{s}{d} > 0\) | Ratio of the width s and depth d of the measurement volume | 0.5…2 | 1 |
\(M = \frac{s}{a} > 0\) | Magnification of the GOBO pattern | 10…50 | 30 |
w > 0 | Working distance (projection centre to measurement volume’s centre) | 0.5…4 m | 1 m |
\(\omega = \frac{\varphi }{T} > 0\) | Rotational speed of the GOBO wheel, which is given by the covered angle ϕ between two images from cameras at frame rate f = T−1 | \(0.5\frac{{\phi _{{\rm{avg}}}}}{T} \ldots \frac{{\phi _{{\rm{avg}}}}}{T}\) | \(\frac{{0.001^\circ }}{T} \ldots \frac{{2.5^\circ }}{T}\) |
\(0 < e = \frac{{t_{{\rm{exp}}}}}{T} \le 1\) | Ratio of the camera exposure time texp and period T = f−1 | 0.6…0.95 | 0.5…1 |
l > 0 | Distance between the two camera centres | 0.1…1 m | 0.2 m |
\(\gamma = 2\,\arctan \frac{{l/2}}{w}\) | Triangulation angle between the optical axes of the cameras | 10°…30° | 11.42° |
α | Horizontal (= vertical) field of view of the cameras | 15°…40° | 16.2° |
A | Camera resolution | 0.25…4 Mpx | 1 Mpx |
b | Camera bit depth | 8 bit, 12 bit | 8 bit |
\(\sigma _e^2\), \(\sigma _d^2\), \(\sigma _q^2\) | Camera noise (shot noise, dark noise, analogue-to-digital conversion)28 | – | 0 |
