Someone correct any mistakes I make or any assumptions that I may have incorrect. Perhaps this will start some good discussion.
FOV of Natal:
Horizontal FOV = tan(x) = a/b
a = 1/2 of the width. This is because we are measuring 4 meters from the center point of the lens to the mid point of the slice of space at that distance. The width of the image at 4 meters distance is 4 meters. So a = 2 meters.
b = distance from camera to center of image.
tan(x) = 2/4
arctan(0.5) = 26.56 degrees. We need to double this
Horizontal FOV = 53.12 degrees
Vertical FOV = tan(x) = a/b
a = 1.35 meters.
b = 4 meters
tan(x) = 1.35/4
arctan(0.3375) = 18.649 degrees. We need to double this:
Vertical FOV = 37.298 degrees
XY Accuracy at 4 meters:
Based on the article, at a distance of 4 meters, the dimensions of the detected image is 4000mm x 2700mm.
Given that the sensor in Natal is 640x480, we can determine the distance that 1 pixel represents.
On the X axis, 1mm = 0.16 pixel. So 1 pixel = 6.25mm.
On the Y axis, 1mm = 0.17mm. So 1 pixel = 5.88mm.
XY Accuracy at 2 meters:
Since the dimensions will be linear, we can just divide everything by two.
Dimensions of image = 2000mm x 1350mm
X axis = 1 pixel = 3.125mm
Y axis = 1 pixel = 2.94mm
I do not know how the Z accuracy can be determined since that is based on light intensity of reflected IR, but the only thing we can go by at this point is some specs from a similar product called PrimeSense, which I have listed below.
http://www.primesense.com/category/reference_design
Specification
Property |
Spec |
Field of View (Horizontal, Vertical, Diagonal) |
58° H, 45° V, 70° D |
Depth image size |
VGA (640x480) |
Spatial x/y resolution (@ 2m distance from sensor) |
3mm |
Depth z resolution (@ 2m distance from sensor) |
1cm |
Maximum image throughput (frame rate) |
60fps |
Operation range |
0.8m - 3.5m |
Several things we can use from the specs to make assumptions about Natal. The Z accuracy at 2 meters is 1cm, so at 4 meters perhaps we can assume it will be 2 cm. That is with the assumption that it follows a linear function. The XY accuracy is similar to my calculations. A maximum distance of 3.5 meters is similar to the stated 4 meter max from the article. The only big surprise here is that the Vertical field of view is largely different than what I calculated. Is there an issue with my methods? Been a while since I have used any trig stuff.