Geometry
Approximate range resolution
Specular
ΔZ ≈ ΔX ⋅ cos(β) / sin(α+β), If α = β: ΔZ ≈ ΔX / 2 ⋅ sin(α)
Look-away
ΔZ ≈ ΔX ⋅ cos(β) / sin(|α–β|)
where:
ΔZ = Height resolution (mm/pixel)
ΔX = Width resolution (mm/pixel)
α = Angle between camera and vertical axis (see the figures above)
β = Angle between laser and vertical axis (see the figures above)
Note that these approximations give the resolution for whole pixels. If the measurement
is made with sub-pixel resolution, the resolution in the measurement is the approxi‐
mated resolution divided by the sub-pixel factor. For example, if the measurement is
made with the Hi3D component that has a resolution of 1/16
th
pixel, the approximate
resolution is ΔZ/16.
15.1.5
Sensor coordinate system
Typically, the camera views the object and the laser line from above, with a certain
angle between the camera and the laser, as described in this document. The sensor
image has its origo in the top left corner when you view the image on screen, see the
figure below. This means that the v-coordinate of a point that is close to the bottom of
the screen (v
1
) is greater than the v-coordinate of a point that is higher up on the screen
(v
2
).
(0,0)
u
v
(u
1
,v
1
)
(u
2
,v
2
)
Figure 61: Sensor image and coordinate system
When the coordinates from the sensor image are used as 3D data, a high value of the
v-coordinate will give a high range value.
In the coordinate system above, parts of the object that are far away from the camera
will get a high range value, and parts that are close to the camera will get a low range
value. That is, the range value represents distance from the camera. If you view the 3D
image in a coordinate system that has its origo in the lower left corner, the 3D image
will appear upside down.
NOTE
If you want the range value to represent height from a surface, rather than distance
from the camera, you set the
RangeAxis
parameter to
Reverse
.
. Then parts of the object that are close to the camera will get a high range
value and parts that are far away from the camera will get a low range value.
15
ANNEX
82
O P E R A T I N G I N S T R U C T I O N S | Ranger3
8020774/14IM/2019-07 | SICK
Subject to change without notice
