1. A microencapsulation system, comprising:
a microcapsule production unit;
a fluidized passage for washing and harvesting microcapsules dispensed from the microcapsule production unit;
a flow sensor for sizing and counting the microcapsules; and
a controller configured to simultaneously operate the microcapsule production unit, fluidized passage and flow sensor to process the microcapsules in a continuous manner.
2. The microencapsulation system of claim 1, wherein the controller is further configured to provide feedback control for the microcapsule production unit, fluidized passage and flow sensor.
3. The microencapsulation system of claim 1, wherein the microcapsule production unit comprises:
a dual-dispenser system configured to form co-axial multi-lamellar microspheres; and
a bath of solution configured to receive and form a membrane about the co-axial multi-lamellar microspheres to form microcapsules.
4. The microencapsulation system of claim 1, wherein the microcapsule production unit comprises a dual-dispenser system configured to form substantially uniform co-axial multi-lamellar microspheres.
5. The microencapsulation system of claim 3, further comprising a separation baffle system arranged down stream from the microcapsule production unit, wherein the separation baffle system is configured to separate residual amounts of one or more fluids used to form the co-axial multi-lamellar microspheres from the solution used to form the membrane about the co-axial multi-lamellar microspheres.
6. The microencapsulation system of claim 5, further comprising a recirculation conduit configured to recycle the one or more fluids back to the dual-dispenser system.
7. The microencapsulation system of claim 5, further comprising a recirculation conduit configured to recycle the solution back to the bath.
8. The microencapsulation system of claim 1, wherein the flow sensor comprises:
an imaging system configured to acquire images of the microcapsules; and
a photometer configured to measure intensity of light transmitted through the microcapsules.
9. A microencapsulation system, comprising:
a microcapsule production unit comprising:
a dual-dispenser system configured to form co-axial multi-lamellar microspheres; and
a bath of solution configured to receive and form a membrane about the co-axial multi-lamellar microspheres to form microcapsules;
a separation baffle system arranged down stream from the microcapsule production unit, wherein the separation baffle system is configured to separate residual amounts of one or more fluids used to form the co-axial multi-lamellar microspheres from the solution used to form the membrane about the co-axial multi-lamellar microspheres;
a fluidized passage for washing and harvesting microcapsules dispensed from the microcapsule production unit;
a flow sensor for sizing and counting the microcapsules comprising:
an imaging system configured to acquire images of the microcapsules; and
a photometer configured to measure intensity of light transmitted through the microcapsules; and
a controller configured to simultaneously operate the microcapsule production unit, fluidized passage and flow sensor to process the microcapsules in a continuous manner.
10. The microencapsulation system of claim 9, wherein the controller is further configured to provide feedback control for the microcapsule production unit, fluidized passage and flow sensor.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A method for computing an approximation of a natural logarithm function comprising the steps of:
partitioning an interval between 1 and 2 into N equally spaced sub-regions;
precomputing a reference point ai of each of the N equally spaced sub-regions, where i=0, . . . ,N\u22121;
selecting N sufficiently large so that, for each sub-region, a first degree polynomial in m computes log(m) to within a preselected degree of accuracy for any m within the sub-region, where m is a binary mantissa of a binary floating point representation of a variable x;
computing a value of log(x) for a binary floating point representation of x stored in a memory of a computing device utilizing the first degree polynomial in the binary mantissa m, wherein log(x) is a function of a distance between the reference point ai and the binary mantissa m; and
generating an image by using the computed value of log(x), wherein x has a binary exponent e in addition to the binary mantissa m;
and further wherein computing a value of log(x) for the binary floating point representation of x comprises the steps of:
partitioning the binary mantissa m of a binary representation of x in a memory, the representation of x including a binary exponent e and the binary mantissa m, wherein a first, most significant part of the partition corresponds to a region i and a second, less significant part of the partition corresponds to a region \u0394x, where \u0394x is a distance from the binary mantissa m to the reference point
a
i
=
1
+
i
+
0.5
N
;
computing an approximation to log(x), using the first degree polynomial in the binary mantissa m and a precomputed value of log(ai), wherein computing an approximation to log(x) comprises the step of computing an approximation written as:
y=\u2212log(x)\u2248bi+ci\u0394x+e\xd7log(2)
for i=0, . . . ,N\u22121
where:
b
i
=
–
log
\u2061
(
a
i
)
+
(
1
4
\u2062
a
i
\u2062
N
)
2
–
(
1
+
1
2
\u2062
N
)
\u2062
1
a
i
;
\u2062
and
ci=\u22121ai;
precomputing a value for log(2); and
for each i, precomputing each value of bi and ci.
2. A method in accordance with claim 1 further comprising the step of storing the precomputed values of bi and ci in a look-up table.
3. A method for computing an approximation of a natural logarithm function comprising the steps of:
partitioning an interval between 1 and 2 into N equally spaced sub-regions;
precomputing a reference point ai of each of the N equally spaced sub-regions, where i=0, . . . , N\u22121;
selecting N sufficiently large so that, for each sub-region, a first degree polynomial in m computes log(m) to within a preselected degree of accuracy for any m within the sub-region, where m is a binary mantissa of a binary floating point representation of a variable x;
computing a value of log(x) for a binary floating point representation of x stored in a memory of a computing device utilizing the first degree polynomial in the binary mantissa m, wherein log(x) is a function of a distance between the reference point ai and the binary mantissa m;
generating an image by using the computed value of log(x), wherein x has a binary exponent e in addition to the binary mantissa m;
and further wherein computing a value of log(x) for the binary floating point representation of x comprises the steps of:
partitioning the binary mantissa m of a binary representation of x in a memory, the representation of x including a binary exponent e and the binary mantissa m, wherein a first, most significant part of the partition corresponds to a region i and a second, less significant part of the partition corresponds to a region \u0394x, where \u0394x is a distance from the binary mantissa m to the reference point
a
i
=
1
+
i
+
0.5
N
;
\u2062
and
computing an approximation to log(x), using the first degree polynomial in the binary mantissa m and a precomputed value of log(ai);
and further wherein computing an approximation to log(x) comprises the step of computing an approximation written as:
y=\u2212log(x)\u2248bi+ci\u0394x+e\xd7log(2)
for i=0, . . . ,N\u22121
where:
b
i
=
–
log
\u2061
(
a
i
)
+
(
1
4
\u2062
a
i
\u2062
N
)
2
–
(
1
+
1
2
\u2062
N
)
\u2062
1
a
i
;
\u2062
and
c1=\u22121ai;
precomputing a value for log(2); and
for each i, precomputing each value of bi and ci; and
said method utilized in a computed tomography (CT) scanner configured to generate an image of an object from acquired projection data of the object.
4. A method in accordance with claim 3 further comprising the step of storing the precomputed values of bi and ci in a look-up table.
5. A computing device comprising a memory in which binary floating point representations of particular numbers are stored, said device being configured to:
partition an interval between 1 and 2 into N equally spaced sub-regions;
precompute a reference point ai of each of the N equally spaced sub-regions, where i=0, . . . ,N\u22121, wherein N is sufficiently large so that, within each sub-region, a first degree polynomial in m computes log(m) to within a preselected degree of accuracy for any m within the sub-region, where m is a mantissa of a binary floating point representation of a variable x;
compute a value of log(x) for a binary floating point representation of x stored in said memory utilizing the first degree polynomial in the binary mantissa m, wherein log(x) is a function of a distance between the reference point ai and the binary mantissa m;
generate an image by using the computed value of log(x);
wherein x has a binary exponent e in addition to the binary mantissa m and wherein said device being configured to compute a value of log(x) for the binary floating point representation of x comprises said device being configured to:
partition the binary mantissa m of a binary representation of x in a memory of said device, the representation of x including a binary exponent e and the binary mantissa m, wherein a first, most significant part of the partition corresponds to a region i and a second, less significant part of the partition corresponds to a region \u0394x, where \u0394x is a distance from the binary mantissa m to the reference point
a
i
=
1
+
i
+
0.5
N
;
\u2062
and
compute an approximation to log(x), using a polynomial of first degree in m and a precomputed value of log(ai);
and further wherein said device being configured to compute the approximation to log(x) comprises said device being configured to compute an approximation written as:
log
\u2061
(
m
)
\u2248
log
\u2061
(
a
i
)
+
(
m
–
a
i
)
a
i
;
where the reference point ai is a closest reference point to the binary mantissa m; and
1\u2266ai<2.
6. A computing device in accordance with claim 5 wherein x is represented by a 32-bit representation having a sign bit, an 8-bit exponent, and a 23-bit binary mantissa having bits b22 to b0 in order of significance with b22 being a bit of greatest significance; and wherein said device being configured to partition the binary mantissa m comprises said device being configured to select a first group of bits b22 through b16 as index i and bits b15 through b0 as \u0394x.
7. A computing device in accordance with claim 5 in a computed tomography (CT) scanner and utilized by said CT scanner for calculating logarithms when said CT scanner generates an image of an object from acquired projection data of the object.
8. A computing device in accordance with claim 7 wherein said CT scanner utilizes said computing device to calculate natural logarithm in an image reconstructor to generate the image of the object.
9. A computing device in accordance with claim 5, said computing device further configured to use the value of log(x) to process at least one image of an object of interest.
10. A computing device in accordance with claim 5 wherein the reference point ai is a centerpoint of each of the N equally spaced sub-regions.
11. A computing device in a computed tomography (CT) scanner and utilized by said CT scanner for calculating logarithms when said CT scanner generates an image of an object from acquired projection data of the object, said computing device comprising a memory in which binary floating point representations of particular numbers are stored, said device being configured to:
partition an interval between 1 and 2 into N equally spaced sub-regions;
precompute a reference point ai of each of the N equally spaced sub-regions, where i=0, . . . ,N\u22121, wherein N is sufficiently large so that, within each sub-region, a first degree polynomial in m computes log(m) to within a preselected degree of accuracy for any m within the sub-region, where m is a mantissa of a binary floating point representation of a variable x;
compute a value of log(x) for a binary floating point representation of x stored in said memory utilizing the first degree polynomial in the binary mantissa m, wherein log(x) is a function of a distance between the reference point ai and the binary mantissa m; and
generate an image by using the computed value of log(x);
wherein x is stored with a binary exponent e in addition to the binary mantissa m;
and further wherein said device being configured to compute a value of log(x) for the binary floating point representation of x comprises said device being configured to:
partition the binary mantissa m of a binary representation of x in a memory, the representation of x including a binary exponent e and the binary mantissa m, wherein a first, most significant part of the partition corresponds to a region i and a second, less significant part of the partition corresponds to a region \u0394x, where \u0394x is a distance from mantissa m to reference point
a
i
=
1
+
i
+
0.5
N
;
\u2062
and
compute an approximation to log(x), using a polynomial of first degree in m and a precomputed value of log(ai);
and further wherein said device being configured to compute an approximation to log(x) comprises said device being configured to compute an approximation written as:
y=\u2212log(x)\u2248bi+ci\u0394x+e\xd7log(2)
for i=0, . . . ,N\u22121
where:
b
i
=
–
log
\u2061
(
a
i
)
+
(
1
4
\u2062
a
i
\u2062
N
)
2
–
(
1
+
1
2
\u2062
N
)
\u2062
1
a
i
;
\u2062
and
ci=\u22121ai;
and said device is further configured to precompute a value for log(2); and
for each i, to precompute each value of bi and ci.
12. A computing device in accordance with claim 11 further configured to store the precomputed values of bi and ci in a look-up table.
13. A computing device comprising a memory in which binary floating point representations of particular numbers are stored, said device being configured to:
partition an interval between 1 and 2 into N equally spaced sub-regions;
precompute a reference point ai of each of the N equally spaced sub-regions, where i=0, . . . ,N\u22121, wherein N is sufficiently large so that, within each sub-region, a first degree polynomial in m computes log(m) to within a preselected degree of accuracy for any m within the sub-region, where m is a mantissa of a binary floating point representation of a variable x;
compute a value of log(x) for a binary floating point representation of x stored in said memory utilizing the first degree polynomial in the binary mantissa m, wherein log(x) is a function of a distance between the reference point ai and the binary mantissa m; and
generate an image by using the computed value of log(x), wherein x has a binary exponent e in addition to the binary mantissa m;
and wherein said device being configured to compute a value of log(x) for the binary floating point representation of x comprises said device being configured to:
partition the binary mantissa m of a binary representation of x in a memory of said device, the representation of x including a binary exponent e and the binary mantissa m, wherein a first, most significant part of the partition corresponds to a region i and a second, less significant part of the partition corresponds to a region \u0394x, where \u0394x is a distance from the binary mantissa m to the reference point
a
i
=
1
+
i
+
0.5
N
;
\u2062
and
compute an approximation to log(x), using a polynomial of first degree in m and a precomputed value of log(ai);
and further wherein said device being configured to compute an approximation to log(x) comprises said device being configured to compute an approximation written as:
y=\u2212log(x)\u2248bi+ci\u0394x+e\xd7log(2)
for i=0, . . . ,N\u22121
where:
b
i
=
–
log
\u2061
(
a
i
)
+
(
1
4
\u2062
a
i
\u2062
N
)
2
–
(
1
+
1
2
\u2062
N
)
\u2062
1
a
i
;
\u2062
and
ci=\u22121ai;
and said device further configured to precompute a value for log(2); and
for each i, to precompute each value of bi and ci.
14. A computing device in accordance with claim 13 further configured to store the precomputed values of bi and ci in a look-up table.
15. A method for computing an approximation of a natural logarithm function comprising the steps of:
partitioning an interval between 1 and 2 into N equally spaced sub-regions;
precomputing a reference point ai of each of the N equally spaced sub-regions, where i=0, . . . ,N\u22121;
selecting N sufficiently large so that, for each sub-region, a first degree polynomial in m computes log(m) to within a preselected degree of accuracy for any m within the sub-region, where m is a binary mantissa of a binary floating point representation of a variable x;
computing a value of log(x) for a binary floating point representation of x stored in a memory of a computing device utilizing the first degree polynomial in the binary mantissa m, wherein log(x) is a function of a distance between the reference point ai and the binary mantissa m;
generating an image by using the computed value of log(x);
wherein x has a binary exponent e in addition to the binary mantissa m;
and further wherein computing a value of log(x) for the binary floating point representation of x comprises the steps of:
partitioning the binary mantissa m of a binary representation of x in a memory, the representation of x including a binary exponent e and the binary mantissa m, wherein a first, most significant part of the partition corresponds to a region i and a second, less significant part of the partition corresponds to a region \u0394x, where \u0394x is a distance from the binary mantissa m to the reference point
a
i
=
1
+
i
+
0.5
N
;
\u2062
and
computing an approximation to log(x), using the first degree polynomial in the binary mantissa m and a precomputed value of log(ai);
wherein computing the approximation to log(x) comprises the step of computing an approximation written as:
log
\u2061
(
m
)
\u2248
log
\u2061
(
a
i
)
+
(
m
–
a
i
)
a
i
;
where the reference point ai is a closest reference point to the binary mantissa m of x; and
1\u2266ai<2.
16. A method in accordance with claim 15 wherein x is represented by a 32-bit representation having a sign bit, an 8-bit exponent, and a 23-bit binary mantissa having bits b22 to b0 in order of significance with b22 being a bit of greatest significance; and the step of partitioning the binary mantissa m comprises the step of selecting a first group of bits b22 through b16 as index i and bits b15 through b0 as \u0394x.
17. A method in accordance with claim 15 utilized in a computed tomography (CT) scanner for generating an image of an object from acquired projection data of the object.
18. A method in accordance with claim 17 wherein said natural logarithm is used in an image reconstructor to generate the image of the object.
19. A method in accordance with claim 15 further comprising using the approximation to process at least one image of an object of interest.
20. A method in accordance with claim 15 wherein precomputing a reference point ai of each of the N equally spaced sub-regions comprising precomputing a centerpoint of each of the N equally spaced sub-regions.
21. A method for computing an approximation of a natural logarithm function comprising the steps of:
partitioning an interval between 1 and 2 into N equally spaced sub-regions;
precomputing a reference point ai of each of the N equally spaced sub-regions, where i=0, . . . ,N\u22121;
selecting N sufficiently large so that, for each sub-region, a first degree polynomial in m computes log(m) to within a preselected degree of accuracy for any m within the sub-region, where m is a binary mantissa of a binary floating point representation of a variable x;
computing a value of log(x) for a binary floating point representation of x stored in a memory of a computing device utilizing the first degree polynomial in the binary mantissa m, wherein log(x) is a function of a distance between the reference point ai and the binary mantissa m; and
generating an image by using the computed value of log(x), wherein x has a binary exponent e in addition to the binary mantissa m;
and further wherein computing a value of log(x) for the binary floating point representation of x comprises the steps of:
partitioning the binary mantissa m of a binary representation of x in a memory, the representation of x including a binary exponent e and the binary mantissa m, wherein a first, most significant part of the partition corresponds to a region i and a second, less significant part of the partition corresponds to a region \u0394x, where \u0394x is a distance from the binary mantissa m to the reference point
a
i
=
1
+
i
+
0.5
N
;
\u2062
and
computing an approximation to log(x), using the first degree polynomial in the binary mantissa m and a precomputed value of log(ai);
wherein computing an approximation to log(x) comprises the step of computing an approximation written as:
y=\u2212log(x)\u2248bi+ci\u0394x+e\xd7log(2)
for i=0, . . . ,N\u22121
where:
b
i
=
–
log
\u2061
(
a
i
)
+
(
1
4
\u2062
a
i
\u2062
N
)
2
–
(
1
+
1
2
\u2062
N
)
\u2062
1
a
i
;
\u2062
and
ci=\u22121ai.
22. A method for computing an approximation of a natural logarithm function comprising the steps of:
partitioning an interval between 1 and 2 into N equally spaced sub-regions;
precomputing a reference point ai of each of the N equally spaced sub-regions, where i=0, . . . ,N\u22121;
selecting N sufficiently large so that, for each sub-region, a first degree polynomial in m computes log(m) to within a preselected degree of accuracy for any m within the sub-region, where m is a binary mantissa of a binary floating point representation of a variable x;
computing a value of log(x) for a binary floating point representation of x stored in a memory of a computing device utilizing the first degree polynomial in the binary mantissa m, wherein log(x) is a function of a distance between the reference point ai and the binary mantissa m; and
generating an image by using the computed value of log(x), wherein x has a binary exponent e in addition to the binary mantissa m;
wherein said method is utilized in a computed tomography (CT) scanner for generating an image of an object from acquired projection data of the object;
and further wherein computing a value of log(x) for the binary floating point representation of x comprises the steps of:
partitioning the binary mantissa m of a binary representation of x in a memory, the representation of x including a binary exponent e and the binary mantissa m, wherein a first, most significant part of the partition corresponds to a region i and a second, less significant part of the partition corresponds to a region \u0394x, where \u0394x is a distance from the binary mantissa m to the reference point
a
i
=
1
+
i
+
0.5
N
;
\u2062
and
computing an approximation to log(x), using the first degree polynomial in the binary mantissa m and a precomputed value of log(ai);
and further wherein computing an approximation to log(x) comprises the step of computing an approximation written as:
y=\u2212log(x)\u2248bi+ci\u0394x+e\xd7log(2)
for i=0, . . . ,N\u22121
where:
b
i
=
–
log
\u2061
(
a
i
)
+
(
1
4
\u2062
a
i
\u2062
N
)
2
–
(
1
+
1
2
\u2062
N
)
\u2062
1
a
i
;
\u2062
and
ci=\u22121ai.
23. A computing device comprising a memory in which binary floating point representations of particular numbers are stored, said device being configured to:
partition an interval between 1 and 2 into N equally spaced sub-regions;
precompute a reference point ai of each of the N equally spaced sub-regions, where i=0, . . . ,N\u22121, wherein N is sufficiently large so that, within each sub-region, a first degree polynomial in m computes log(m) to within a preselected degree of accuracy for any m within the sub-region, where m is a mantissa of a binary floating point representation of a variable x;
compute a value of log(x) for a binary floating point representation of x stored in said memory utilizing the first degree polynomial in the binary mantissa m, wherein log(x) is a function of a distance between the reference point ai and the binary mantissa m; and
generate an image by using the computed value of log(x), wherein x has a binary exponent e in addition to the binary mantissa m;
and wherein said device being configured to compute a value of log(x) for the binary floating point representation of x comprises said device being configured to:
partition the binary mantissa m of a binary representation of x in a memory of said device, the representation of x including a binary exponent e and the binary mantissa m, wherein a first, most significant part of the partition corresponds to a region i and a second, less significant part of the partition corresponds to a region \u0394x, where \u0394x is a distance from the binary mantissa m to the reference point
a
i
=
1
+
i
+
0.5
N
;
\u2062
and
compute an approximation to log(x), using a polynomial of first degree in m and a precomputed value of log(ai);
and further wherein said device being configured to compute an approximation to log(x) comprises said device being configured to compute an approximation written as:
y=\u2212log(x)\u2248bi+ci\u0394x+e\xd7log(2)
for i=0, . . . ,N\u22121
where:
b
i
=
–
log
\u2061
(
a
i
)
+
(
1
4
\u2062
a
i
\u2062
N
)
2
–
(
1
+
1
2
\u2062
N
)
\u2062
1
a
i
;
\u2062
and
ci=\u22121ai.
24. A computing device comprising a memory in which binary floating point representations of particular numbers are stored, said device being configured to:
partition an interval between 1 and 2 into N equally spaced sub-regions;
precompute a reference point ai of each of the N equally spaced sub-regions, where i=0, . . . ,N\u22121, wherein N is sufficiently large so that, within each sub-region, a first degree polynomial in m computes log(m) to within a preselected degree of accuracy for any m within the sub-region, where m is a mantissa of a binary floating point representation of a variable x;
compute a value of log(x) for a binary floating point representation of x stored in said memory utilizing the first degree polynomial in the binary mantissa m, wherein log(x) is a function of a distance between the reference point ai and the binary mantissa m; and
generate an image by using the computed value of log(x), wherein x is stored with a binary exponent e in addition to the binary mantissa m; said device in a computed tomography (CT) scanner and utilized by said CT scanner for calculating logarithms when said CT scanner generates an image of an object from acquired projection data of the object;
and further wherein said device being configured to compute a value of log(x) for the binary floating point representation of x comprises said device being configured to:
partition the binary mantissa m of a binary representation of x in a memory, the representation of x including a binary exponent e and the binary mantissa m, wherein a first, most significant part of the partition corresponds to a region i and a second, less significant part of the partition corresponds to a region \u0394x, where \u0394x is a distance from mantissa m to reference point
a
i
=
1
+
i
+
0.5
N
;
\u2062
and
compute an approximation to log(x), using a polynomial of first degree in m and a precomputed value of log(ai);
and further wherein said device being configured to compute an approximation to log(x) comprises said device being configured to compute an approximation written as:
y=\u2212log(x)\u2248bi+ci\u0394x+e\xd7log(2)
for i=0, . . . ,N\u22121
where:
b
i
=
–
log
\u2061
(
a
i
)
+
(
1
4
\u2062
a
i
\u2062
N
)
2
–
(
1
+
1
2
\u2062
N
)
\u2062
1
a
i
;
\u2062
and
ci=\u22121ai.