IEEE - Aerospace and Electronic Systems - January 2020 - 16

Calibration Method of Laser Detection System With Position Sensitive Detector

SEMIPHYSICAL SIMULATION TEST
In order to verify the feasibility of the LDS calibration
method, a semiphysical simulation test has been carried
out, and the test site is shown in Figure 7. The laser source
frequency is 650 nm, the focal length of optical lens is
43 mm, and the PSD number is S5991-01. To avoid the
influence of the ambient light on the test, a 650 nm filter
is added to the LDS. During the test, the LDS is fixed
on the three-axis turntable A; the laser source is fixed on
the three-axis turntable B; the three-axis turntable A simulates the flying attitude of projectile; and the three-axis
turntable B and the laser source simulate the diffuse reflection echo information L . Reference data in this experiment are provided by the turntable A and the measured
data are obtained by the LDS and computers. The Turntable B is only used as a fixture, which can be replaced by
something else that can fix the laser source. So, the turntable A is of great necessity in this experiment.

Figure 7.
Semiphysical simulation test site.

CALIBRATION METHOD OF INSTALLATION ANGLE
ERRORS Iu and Ic
An assumption that installation angle errors Iu and Ic are
approximately equal to zero is used in the previous section. Although the installation error angles Iu and Ic are
small, they also affect the output value of the PSD. This
section will study the calibration method of installation
angle errors Iu and Ic . If those variables, which are the
installation roll error angle Ig , the installation displacement errors Dy3 and Dz3 , the imaging point p, the projectile roll angle g, and the focal length f, are known, the
matrix M can be calculated by (9). At the same time, (8)
can be rewritten as
A ¼ XL

(17)

where A ¼ ðR
Rg RIg ÞT M , X ¼ R Ic RIu . If the laser
unit vector L takes different values, the imaging point of
the PSD correspond to different output values. The output
equation can be obtained from (17) as
c ¼ Xd

(18)
2

where

A 11
c ¼ 4 A 21
A 31

A 12
A 22
A 32

L11
Á Á Á A 1m
Á Á Á A 2m 5, d ¼ 4 L21
Á Á Á A 3m
L31

L 12
L 22
L 32

3
Á Á Á L 1m
Á Á Á L 2m 5,
Á Á Á L 3m

m is the number of measurements. Based on the matrix
operation, (18) can be written as
À
ÁÀ1
:
X ¼ c dT d dT

(19)

The installation angle errors Iu and Ic can be written
as follows:
(

À
Á
Ic ¼ arcsinðX 13 Þ; Ic 2 À p2 ; p2
À p pÁ
X 11 Þ; Iu 2 À 2 ; 2
Iu ¼ arctanðX 12 =X

(20)

where X ij is the element of column j in row i of matrix X .
16

CALIBRATION PROCESS OF INSTALLATION
DISPLACEMENT ERRORS
The calibration method of installation displacement errors
has been introduced in "CALIBRATION METHOD OF
INSTALLATION DISPLACEMENT ERRORS," but a
condition that the laser unit vector L is collinear with the
x3 -axis of the frame o1 x3 y3 z3 should be ensured. With
the condition of the laser unit vector L 6¼ ½ 1 0 0 T , the
trajectory of the imaging point will be a circle after one
roll of the projectile. As the angle ax approaches 0 rad,
the trajectory of the imaging point will converge from a
circle to a point. And if the angle ax is equal to 0 rad, the
output values of the PSD are the installation displacement
errors Dy3 and Dz3 of the LDS.
In order to make the trajectory of the imaging point
converges from a circle to a point, the three-axis turntable
B and the laser source are fixed, and the angle ax changes
with the adjustment of the three-axis turntable A. By comparing the size of the imaging point trajectory, we can
make the circle contract to a point. To display the process
of finding convergence point, several imaging point trajectories are shown in Figure 8. In fact, the imaging point trajectory cannot converge to a theoretical point at last. Due
to several facts, such as the random measurement error of
the PSD and the minimum adjustment angle of the threeaxis turntable A. We can regard the mean value of the minimum circle as the installation displacement error of the
LDS, and the installation displacement errors of the LDS
are Dy3 ¼ À0:3404 mm,Dz3 ¼ 1:0173 mmin Figure 8.
The minimum circle in the figure is taken as a standard
where the laser angles u and c are equal to zero. The
laser angles u and c can be changed to an arbitrary value
by adjusting the laser unit vector L .

IEEE A&E SYSTEMS MAGAZINE

JANUARY 2020

IEEE - Aerospace and Electronic Systems - January 2020

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