System and method of measuring field-of-view of an optical sensor
View Patent ↗A method of measuring a field-of-view (FOV) of an optical sensor includes the steps of: (a) uniformly illuminating a FOV of the optical sensor; (b) moving, at an angle of motion, a slit across the FOV and illuminating the optical sensor through the slit; (c) measuring an optical response of the sensor through the slit, at evenly spaced positions of the moving slit; (d) changing the angle of motion and repeating steps (b) and (c); (e) repeating step (d) for equally spaced angles of motion; and (f) constructing a two-dimensional map of the FOV of the optical sensor, after completing step (e). Constructing the two-dimensional map of the FOV includes filtering the measured data using a filtered backprojection algorithm, and interpolating among the filtered measured data to form the two-dimensional map.
1. A method of measuring a field-of-view (FOV) of an optical sensor comprising the steps of:
(a) uniformly illuminating a FOV of the optical sensor;
(b) moving, at an angle of motion, a slit across the FOV and illuminating the optical sensor through the slit;
(c) measuring an optical response of the sensor through the slit, at evenly spaced positions of the moving slit;
(d) changing the angle of motion and repeating steps (b) and (c);
(e) repeating step (d) for equally spaced angles of motion; and
(f) constructing a two-dimensional map of the FOV of the optical sensor, after completing step (e);
wherein the slit includes a longitudinal dimension greater than a span length across the FOV of the optical sensor.
2. The method of claim 1 wherein constructing the two-dimensional map of the FOV includes filtering measured data obtained in step (e) using a filtered backprojection algorithm, and
interpolating among the filtered measured data to form the two-dimensional map of the FOV.
3. The method of claim 1 wherein constructing the two-dimensional map of the FOV includes
forming a grid of values corresponding to the measured optical response of the sensor at the evenly spaced positions of the moving slit and the equally spaced angles of motion, and
interpolating on the grid to find a value of the FOV at a point on the optical sensor.
4. The method of claim 3 wherein interpolating on the grid includes
estimating the value of the FOV at the point given by coordinates x, y using adjacent values formed on the grid.
5. The method of claim 3 wherein interpolating on the grid includes
estimating the value of the FOV at the point given by coordinates x, y, using adjacent values formed on the grid, as a function of evenly spaced angles between zero radians and pi radians.
6. The method of claim 1 wherein
moving the slit across the FOV includes positioning the slit in an X,Y plane of the FOV of the optical sensor, wherein a center of the slit is disposed at a distance t k along a t direction from an origin of an X,Y,Z coordinate system, and the t direction is oriented at an angle θ j with respect to the X-axis of the coordinate system;
measuring the optical response of the sensor includes measuring a detected signal of the sensor as a value of P j,k where a j'th angle is θ j and a k'th value of the t direction is t k ; and
constructing the two-dimensional map of the FOV includes filtering the optical response of the sensor by multiplying a weighting function h k with the value of P j,k to form a quantity of Q j,k .
7. The method of claim 6 wherein filtering the optical response of the sensor includes
forming a grid of values at different integer values of j and k, wherein each grid value is
Q
j
,
k
=
Δ
t
w
∑
i
=
0
N
k
-
1
P
j
,
i
h
k
-
i
where:
Δt is a distance along the t direction between adjacent slit positions,
w is a width of the slit,
N j is an evenly spaced angle between zero radians and pi radians, the j'th angle is θ j , and θ j+1 =θ j +Δθ, where Δθ is the separation of adjacent angles,
N k is an evenly spaced value of t, where t is a distance of the slit from the origin of the coordinate system, and
the k'th value of t is t k and t k+1 =t k +Δt, where Δt is the distance between adjacent slot positions.
8. The method of claim 7 wherein the weighting function h k is
h
k
=
{
0
when
k
=
±
2
,
±
4
,
±
6
,
…
-
1
/
(
k
πΔ
t
)
2
when
k
=
±
1
,
±
3
,
±
5
,
…
1
/
(
2
Δ
t
)
2
when
k
=
0.
9. The method of claim 7 wherein
after forming the grid of values, the method includes the following step:
interpolating among adjacent values of the grid of values to determine a value of the FOV at a point given by coordinates x,y and defined by f(x,y), as follows:
f
(
x
,
y
)
=
π
N
ϕ
-
1
∑
i
=
1
N
ϕ
-
2
q
(
ϕ
i
,
x
cos
(
ϕ
i
)
+
y
sin
(
ϕ
i
)
)
+
1
2
π
N
ϕ
-
1
[
q
(
ϕ
0
,
x
cos
(
ϕ
0
)
+
y
sin
(
ϕ
0
)
)
+
q
(
ϕ
N
ϕ
-
1
,
x
cos
(
ϕ
N
ϕ
-
1
)
+
y
sin
(
ϕ
N
ϕ
-
1
)
)
]
where:
Δφ=π/(N φ −1) in radians
N φ is an angle in radians specified by φi=iΔφ for i=0,1,2, . . . N φ −1
t k ≦t<t k+1
θ j ≦φ<θj+1
q(φ,t)=(1−v)(1−u)Q j,k +v(1−u)Q j+1,k +vuQ j+1,k+1 +(1−v)uQ j,k+1
v
=
ϕ
-
θ
j
θ
j
+
1
-
θ
j
=
ϕ
-
θ
j
Δθ
and
u
=
t
-
t
k
t
k
+
1
-
t
k
=
t
-
t
k
Δ
t
.
10. The method of claim 1 wherein the slit includes a width dimension of approximately equal to one percent of a span length across the FOV of the optical sensor.
11. A method of measuring a field-of-view (FOV) of an optical sensor having circular symmetry, the method comprising the steps of:
(a) uniformly illuminating a FOV of the optical sensor;
(b) moving a slit across the FOV and illuminating the optical sensor through the slit;
(c) measuring an optical response of the sensor through the slit, at evenly spaced positions across the FOV; and
(d) constructing a two-dimensional map of the FOV of the optical sensor, after completing step (c);
wherein the slit includes a longitudinal dimension greater than a span length across the FOV of the optical sensor.
12. The method of claim 11 wherein
step (b) includes moving the slit across the FOV in a single direction only.
13. The method of claim 12 wherein constructing the two-dimensional map of the FOV includes
forming a grid of values corresponding to the measured optical response of the sensor at the evenly spaced positions along the single direction, and
interpolating on the grid to find a value of the FOV at a point on the optical sensor.
14. The method of claim 13 wherein interpolating on the grid includes
estimating the value of the FOV at the point given by coordinates x, y using adjacent values formed on the grid.
15. The method of claim 13 wherein interpolating on the grid includes
estimating the value of the FOV at the point given by a distance r from the origin of coordinates x, y, using adjacent values formed on the grid, as a function of evenly spaced angles between zero radians and pi radians.
16. The method of claim 11 wherein
moving the slit across the FOV includes positioning the slit in an X,Y plane of the FOV of the optical sensor, wherein a center of the slit is disposed at a distance t k along a t direction from an origin of an X,Y,Z coordinate system;
measuring the optical response of the sensor includes measuring a detected signal of the sensor as a value of P k , where a k'th value of the t direction is t k ; and
constructing the two-dimensional map of the FOV includes filtering the optical response of the sensor by multiplying a weighting function h k with the value of P k to form a quantity of Q k .
17. The method of claim 16 wherein filtering the optical response of the sensor includes
forming a grid of values at different integer values of k, wherein each grid value is
Q
k
=
Δ
t
w
∑
i
=
0
N
k
-
1
P
i
h
k
-
i
where:
Δt is a distance along the t direction between adjacent slit positions,
w is a width of the slit,
N k is an evenly spaced value of t, where t is a distance of the slit from the origin of the coordinate system, and
the k'th value of t is t k and t k+1 =t k +Δt, where Δt is the distance between adjacent slot positions.
18. The method of claim 16 wherein the weighting function h k is
h
k
=
{
0
when
k
=
±
2
,
±
4
,
±
6
,
…
-
1
/
(
k
πΔ
t
)
2
when
k
=
±
1
,
±
3
,
±
5
,
…
1
/
(
2
Δ
t
)
2
when
k
=
0.