# Theory of operation

Aug. 1, 1998
The light source of the laser range finder is a collimated diode laser with an output beam of divergence less than 1 mrad. It produces a spot A on the first obstacle located at the distance D from the source (see figure). The triangle IAC is formed by the reference base B perpendicular to distance D and the retrodiffused ray AC, which forms angle a with a line parallel to D. A lens L of focal length f is located with its optical center at point C. The retrodiffused light from A is collected by

Theory of operation

The light source of the laser range finder is a collimated diode laser with an output beam of divergence less than 1 mrad. It produces a spot A on the first obstacle located at the distance D from the source (see figure). The triangle IAC is formed by the reference base B perpendicular to distance D and the retrodiffused ray AC, which forms angle a with a line parallel to D. A lens L of focal length f is located with its optical center at point C. The retrodiffused light from A is collected by the lens via an interference filter (IF) and focused in at A` on a charge-coupled device (CCD).

For A at infinity, A` is at the focus F` of the lens. To reduce loss of focus at short distances, the CCD line is not perpendicular to the optical lens axis; it forms an angle q with D. The q angle inclination is given by tan q = B/f and the position of the image center A` is x` = F`A`, which is given by

x`/sin a = f/sin (q - a)

with tan a = B/D

The CCD has 2048 pixels, each 11 µm wide, and the x` maximum value is 2048 ¥ 1.1 ¥ 10-5 m = 2.25 ¥ 10-2 m or 22.5 mm. With the numerical value of B = 60 mm and f = 30 mm, the minimal measurable distance is D = 30 [1+(4500)1/2]/22.5 100 mm and, in this case, the angle a is given by arctan 60/100 31°.

As the laser beam divergence a` is about 0.8 mrad, at a long distance it can be considered that the A` image at the focal point is at least equal to fa` = 24 µm, which is at least two pixels. The interference filter, which reduces natural light perturbations, is tilted about 15° against the lens plane to match incidences on the filter. In fact the lens is not a simple one but a large-field optical system.

R. R.

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