Imaging inspection apparatus incorporating a device for solving cubic polynomials
An imaging inspection machine for inspecting objects located within articles, with the imaging inspection machine having an inspection location for articles having a quantity of objects located along a path of travel through an inspection location located within the imaging inspection machine. Imaging inspection devices are positioned on the frame and adapted for directing beams through articles as articles move through the inspection location within the imaging inspection machine. As a result of inspecting the articles, output signals are applied to a processing and analysis assembly which performs only simple table lookups into an appropriately formed table and one multiplication for each pixel to correct nonlinearities matched by a cubic polynomial.
1. An imaging apparatus for inspecting objects located within moving articles, said imaging inspection apparatus comprising:
a plurality of at least one imaging inspection device positioned on said frame and adapted for directing beams onto said articles as said articles through said inspection location substantially within said imaging apparatus to thereby inspect said articles, and for providing output signals as a result of said inspecting; and
a processing and analysis assembly for receiving said output signals from said plurality of imaging inspection devices and for performing table lookups and simple multiplication, said table having a particular form adequate to correct nonlinearities matching a cubic polynomial; and including:
a) an offset X for said lookup, stored for each pixel having the nonlinearity shape parameter ξ where
if
ξ
>
0.05
,
i
=
int
(
150.5
+
100
log
ξ
log
400
)
;
if i≧200, set i=200, Then X=401i;
if
ξ
<
-
0.05
,
i
=
int
(
50.5
-
100
log
(
-
ξ
)
log
400
)
;
if i≦0, set i=0, Then X=401i; otherwise, X=40100;
b) the parameter τ also stored for each pixel; and
c) a count of N is collected in a dwell of duration D, then the correction factor is stored at location X+n in said table where
n
=
int
{
200
N
τ
D
+
300.5
}
where:
X is an integer value,
i is an integer,
τ is a scale factor with units of time per count or time per pulse, and
n is an integer.
2. The imaging apparatus of claim 1 , wherein said plurality of imaging inspection devices each comprises an X-ray computer tomography (XCT) scanning device and said beams are X-rays.
3. The imaging apparatus of claim 2 , wherein said XCT scanning devices are positioned on said frame in at least three groupings, each grouping of said XCT scanning devices being positioned relative to said inspection location and adapted for directing said X-rays along a different plane onto only said main portion within said inspection location substantially within said imaging apparatus, each of said planes being substantially perpendicular to said inspection location.
4. The imaging apparatus of claim 3 , further including at least one X-ray detector positioned on said frame relative to said main portion of said inspection location and adapted for receiving said X-rays from selected ones of said XCT scanning devices as said X-rays pass through said articles at said inspection location.
5. In an imaging apparatus for inspecting objects located within moving articles, said imaging inspection apparatus having at least one imaging inspection device positioned on said frame and adapted for directing beams onto said articles as said articles pass through said inspection location substantially within said imaging apparatus to thereby inspect said articles, and for providing output signals as a result of said inspecting, the improvement comprising:
a processing and analysis assembly adapted for receiving said output signals from said plurality of imaging inspection devices and for accessing correction factors, said processing and analysis assembly performing steps comprising:
a) storing
τ
=
Q
A
2
and the row offset X(ξ):
b) storing the table T; and
c) accessing the correction factor T(n+X); if a count of N is collected in a dwell of duration D,
n
=
int
{
200
N
τ
D
+
300.5
}
where:
τ is a scale factor with units of time per count or time per pulse,
Q is a unit of time,
A is a dimension of a pixel receiving photons,
ξ is a dimensionless parameter,
n is an integer,
Nτ is a product of a number of photon counts and a scale factor, and
X is an integer value.
6. The imaging apparatus of claim 5 , wherein said imaging inspection devices each comprises an X-ray computer tomography (XCT) scanning device and said beams are X-rays.
7. The imaging apparatus of claim 6 , wherein said XCT scanning devices are positioned on said frame in at least three groupings, each grouping of said XCT scanning devices being positioned relative to said inspection location and adapted for directing said X-rays along a different plane onto only said main portion within said inspection location located substantially within said imaging apparatus, each of said planes being substantially perpendicular to said inspection location.
8. The imaging apparatus of claim 7 , further including at least one X-ray detector positioned on said frame relative to said main portion of said inspection location for receiving said X-rays from selected ones of said XCT scanning devices as said X-rays pass through said articles at said inspection location.
9. In an imaging apparatus for inspecting objects located within moving articles, said imaging inspection apparatus having at least one imaging inspection device positioned on said frame and adapted for directing beams onto said articles as said articles pass through said inspection location substantially within said imaging apparatus to thereby inspect said articles, and for providing output signals as a result of said inspecting, the improvement comprising a process of inspecting objects, the steps comprising providing a processing and analysis assembly adapted for receiving said output signals from said plurality of imaging inspection devices and for retrieving correction factors derived by matching the nonlinearities of the imaging apparatus pixels to cubic equations, the steps comprising correcting N counts, collected in time D, to NT(X+n), the substeps comprising:
i) accessing τ and the row offset X(ξ);
ii) computing the index
n
=
int
{
200
N
τ
D
+
300.5
}
;
and
iii) accessing T(X+n) where:
τ is a scale factor with units of time per count or time per pulse,
ξ is a dimensionless parameter,
Nτ is a product of a number of photon counts and a scale factor,
n is an integer,
X is an integer value, and
T is a two-dimensional table containing correction factors.
10. The imaging apparatus of claim 9 , wherein said imaging inspection devices each comprises an X-ray computer tomography (XCT) scanning device and said beams are X-rays.
11. The imaging apparatus of claim 10 , wherein said XCT scanning devices are positioned on said frame in at least three groupings, each grouping of said XCT scanning devices being positioned relative to said inspection location and adapted for directing said X-rays along a different plane onto only said main portion within said inspection location located substantially within said imaging apparatus, each of said planes being substantially perpendicular to said inspection location.
12. The imaging apparatus of claim 11 , further including at least one X-ray detector positioned on said frame relative to said main portion of said inspection location and adapted for receiving said X-rays from selected ones of said XCT scanning devices as said X-rays pass through said articles at said inspection location.