Home Blog
Previous | Next

Laser Radar
Operational Problems

Contents -- Acceleration Limits | Scanning or Sweeping Error | Aiming and Alignment Errors | Speed Error Due to Range Error | Range Resolution
Acceleration Limits

Laser radars, like microwave radars, are designed to measure vehicles traveling at a relatively constant speed. Vehicles changing speed greater than the accuracy during one sample period cannot be measured, speed is changing too fast. Laser radars typically have longer sample times making the acceleration limits more narrow.

Acceleration Limit = accuracy / sample period

amax = ± vacc / ti

amax = Maximum Acceleration
± vacc = Speed Accuracy
ti = Sample Time

Common sample periods, varies with model, 300, 333, 400, 500, 700 milliseconds - 0.25, 0.3, and 1/3 seconds

Acceleration Limits
Sample Period Maximum
Change in Speed
seconds milliseconds
1/3 333 ms ± 3.3 mph / second
0.3 300 ms ± 3.0 mph / second
1/2 500 ms ± 2.0 mph / second
0.7 700 ms ± 1.4 mph / second
1 1000 ms ± 1.0 mph / second

Sponsored links

Scanning or Sweeping Error

Scanning or sweeping the lidar beam across the ground such that range increases, or decreases, in a steady manner will produce a speed reading. The measured speed is a function of the change in range over sweep time. Increasing range short to long produces a receding speed, sweeping long to short range produces an approaching speed.

vm = Rd / ( n ti )
Rd = vm n ti
vm = measured speed
Rd = distance lidar scanned
ti = lidar sample time
n = number of sample periods

Range versus Speed for 1 Sample Period

Fig 5.3-1

Speed in mph and Range in feet
vm = (15/22) Rd / (n ti)
Rd = 22 vm n ti / 15

Sponsored links

Aiming and Alignment Errors

The narrow laser beam and aim crosshairs must be closely aligned to very tight tolerances. Any misalignment introduces aiming errors. For the crosshairs to fall in the beam the alignment error must be less than half of the beamwidth. An alignment error that is greater than half the beamwidth will place the crosshairs outside the beam.

Beam Divergence: 3.0 mR
3.5 mR
4.0 mR
Half Beamwidth: 1.5 mR
1.25 mR
2.0 mR

The greater the alignment error and the greater the target range, the greater the distance error between the beam center and crosshairs.

derr = R tan ßerr
derr = distance off beam center
R = Range
ßerr = alignment angle error

Distance in feet (') or inches (in) Off Beam Center
given Range and Alignment Angle Error

Angle Error = 0.086° 0.100° 0.115° 0.5°
Range Distance Beam Off Center
100' 3.6 in 4.2 in 4.8 in 10.5 in 1.8'
200' 7.2 in 8.4 in 9.6 in 1.8' 3.5'
300' 10.8 in 1.1' 1.2' 2.6' 5.2'
400' 1.2' 1.4' 1.6' 3.5' 7.0'
500' 1.5' 1.8' 2.0' 4.4' 8.7'
600' 1.8' 2.1' 2.4' 5.2' 10.5'
700' 2.1' 2.5' 2.8' 6.1' 12.2'
800' 2.4' 2.8' 3.2' 7.0' 14.0'
900' 2.7' 3.2' 3.6' 7.9' 15.7'
1000' 3.0' 3.5' 4.0' 8.7' 17.5'

Distance Off Beam Center versus Range
for Alignment Angle Errors

Fig 5.3-2

Calculate Distance Error
R = Range:
ßerr = Angle Error:

Distance Off Beam Center

A 3 milliradian beamwidth edge occurs 0.086° off center, a 4 milliradian beamwidth edge occurs 0.115° from beam center.

The operator must aim the beam to an accuracy of within tenths of a degree, the aperture must be aligned within hundredths of a degree to the optical aiming device. A two-aperture system must align both apertures to thousandths of a degree, and this combination must then be aligned to the optical aiming device.

Windshield and other Interference
Operating a lidar through a windshield will diffract the infrared beam introducing an angle alignment error. All vehicles use safety glass that consist of glass covered with a thin plastic coating to reduce shattering. The coating also introduces another angle error in addition to the glass. The diffraction error is a function of material thickness and index of refraction, and the beam angle to the windshield.

Bright lights, such as halogens, beaming directly into the aperture will desensitize or entirely mask reflections. The degree of interference depends on the intensity and wavelengths of the light. The brighter and closer the light source, the greater the chance of interference.

If for any reason signal echoes are interrupted the lidar may not be able to determine target speed for that sample time. A vehicle passing between the intended target and lidar, or the lidar beam striking a tree, branches, leafs, sign, utility pole or tower, some or all returns could be missed or from other objects.

Sponsored links

Speed Error Due to Range Error

Reflection from Different Vehicle Parts and Sections
Laser radars are designed to track flat surfaces on a target vehicle. Manufactures suggest aiming at the license plate. Reflections that do not come from the same section, range, of the vehicle will cause range errors. Tracking from the back to front of a vehicle causes a high measured speed. Tracking from the front to back of a vehicle causes a low measured speed.

Range and Speed Error

Fig 5.3-3

Measured speed given range and distance error, and sample time.
vm = ( R ± derr ) / ti
vm = measured speed
derr = distance error (vehicle length)
R = actual change in range
ti = sample time

Speed error for range error and sample time.
verr = ± derr / ti
verr = speed error
derr = distance error ti = sample time

Distance Error versus Speed Error

Fig 5.3-4

Range Resolution

Range Resolution Lidar pulse width determines range resolution, the ability to separate closely spaced objects in the range dimension. The more narrow the pulse the higher the resolution. A high resolution narrow pulse could reflect from different parts of a target vehicle introducing range and speed errors.

To resolve two objects in range they must be separated by over half a pulse width. Pulse widths vary from 5 to 35 nanoseconds.

ds > c tpw / 2
ds = object separation
tpw = lidar pulse width
c = speed of light

ds > 0.5 tpw
ds = object separation in feet
tpw = pulse width in nanoseconds

Distance Between Objects
Pulse Width
5 ns 2.5 feet
10 ns 5.0 feet
15 ns 7.5 feet
20 ns 10.0 feet
25 ns 12.5 feet
30 ns 15.0 feet
35 ns 17.5 feet

Police Radar Information Center

Laser Radar Operational Problems
Previous | Top | Next