Optics: measuring and testing – For size of particles – By particle light scattering
Reexamination Certificate
2002-02-21
2002-10-29
Stafira, Michael P. (Department: 2877)
Optics: measuring and testing
For size of particles
By particle light scattering
C356S338000
Reexamination Certificate
active
06473178
ABSTRACT:
BACKGROUND OF THE INVENTION AND RELATED ART STATEMENT
The invention relates to a particle size analyzer based on a laser diffraction method, more particularly, a particle size analyzer capable of accurately measuring a wide range of particles having a fine diameter of the order of 0.1 &mgr;m to a large diameter of the order of several thousands &mgr;m.
In a particle size analyzer based on the laser diffraction method, generally, a particle size distribution of particles to be measured can be calculated through measuring a space intensity distribution of diffracted/scattered light obtained by irradiating laser light to the particles to be measured in a dispersing/flying state; and calculating the measured results based on a Mie's scattering theory and a Fraunhofer's diffraction theory.
More specifically, in a basic structure of a measuring portion of the measuring apparatus of this type as diagrammatically shown in
FIG. 6
, when laser beam from a laser light source
41
is irradiated to a particle group P to be measured through a collimating lens
42
to be parallel beam, the laser beam is diffracted or scattered by the particle group P to be measured to thereby form a spacial light intensity distribution pattern. Among the diffracted/scattered light (hereinafter simply referred to as “scattered light”), the forward scattered light is converged by a lens
53
a
to form ring-shape scattered images on a detection plane disposed at a focal distance position. The forward scattered light intensity distribution pattern is detected by a ring detector (forward scattered light sensor)
53
b
formed of a plurality of light sensor elements having ring-shape light receiving surfaces of different radii arranged concentrically. Also, the sideward and backward scattered light is detected by sideward scattered light sensors
54
and backward scattered light sensors
55
.
The space intensity distribution pattern of the scattered light measured at the measuring portion by the plural light sensors is digitized by the A/D converter and inputted to a computer as the scattered light intensity distribution data.
The scattered light intensity distribution data are varied depending on the size of the particles. Since different size particles are mixed in the actual particle group P to be measured, the intensity distribution data of the scattered light by the particle group P are formed by laying one scattered light on top of the other, respectively. When this situation is expressed by a matrix, Equation (1) can be obtained:
s=Aq
(1)
wherein,
s
=
(
s
1
s
2
⋮
s
m
)
,
q
=
(
q
1
q
2
⋮
q
n
)
(
2
)
A
=
(
a
1
,
1
a
1
,
2
⋯
⋯
a
1
,
n
a
2
,
1
⋮
a
i
,
j
⋮
a
m
,
1
⋯
⋯
⋯
a
m
,
n
)
(
3
)
s (vector) is intensity distribution data (vector) of the scattered light. Their elements s
i
(i=1, 2, . . . m) are incident light quantities detected by the respective elements of the ring detector
53
b,
and sideward and backward scattered light sensors
54
,
55
.
q (vector) is particle size distribution data (vector) expressed as a frequency distribution %. A region of diameters of the particle group to be measured (maximum particle diameter: X
1
, minimum particle diameter: X
n+1
) are divided into n, and the respective particle diameter intervals are represented by (X
j
, X
j+1
) (j=1, 2, . . . n). The elements q
j
(j=1, 2, . . . n) of the q (vector) are the particle quantities corresponding to the particle diameter intervals (X
j
, X
j+1
). Normally, it is normalized to be the following Equation (4).
∑
j
=
1
n
q
j
=
100
%
(
4
)
A (matrix) is a coefficient matrix for converting the particle size distribution data (vector) q to light intensity distribution data (vector) s. The physical meaning of elements a
i,j
(i=1, 2, . . . m, j=1, 2, . . . n) of A (matrix) is an incident light quantity with respect to the i-th element of light scattered by the particles of a unit particle quantity belonging to the particle diameter interval (X
j
, X
j+1
).
A numeral value of a
i,j
can be theoretically calculated beforehand. In case the diameter of the particle is sufficiently large when compared with a wavelength of the laser beam as the light source, Fraunhofer's diffraction theory is used. However, in a region where the diameter of the particle is shorter than or the same as the wavelength of the laser beam, i.e. sub-micron region, it is necessary to use Mie's scattering theory. The Fraunhofer's diffraction theory can be considered to be an excellent approximate of the Mie's scatting theory effective in case the particle diameter is sufficiently large when compared with the wavelength in a forward fine-angle scattering.
In order to calculate the elements of a constant matrix A by using the Mie's scatting theory, it is necessary to set the absolute refractive indexes, i.e. complex numbers, of particles and a medium, i.e. medium liquid, in which the particles are dispersed. There may be a case where a relative refractive index, i.e. complex number, of the particles and the medium is set, instead of setting the respective refractive indexes.
As an equation for obtaining the least square integral of the particle size distribution data (vector) q based on the above equation (1), the following equation is obtained:
q
=(
A
T
A
)
−1
A
T
S
(5)
wherein, A
T
is a transpose of A, and ( )
−1
is an inverse matrix.
The respective elements of the light intensity distribution data (vector) s in the right side of Equation (5) are numeral values detected by the ring detector
53
b,
sideward scattered light sensors
54
and backward scattered light sensors
55
. Also, the coefficient matrix A can be obtained beforehand by using the Fraunhofer's diffraction theory or the Mie's scattering theory. Therefore, when the calculation of Equation (5) is carried out by using the known data, it is apparent that the particle size distribution data (vector) q can be obtained.
The above explanation is a basic measuring theory of the particle size distribution measurement based on the laser diffraction method. Incidentally, the above-explained method is one example of methods for calculating the particle size distribution, and there are many other variations in measuring methods and kinds and arrangements of the sensors and detectors.
Here, in the conventional particle size analyzer based on the laser diffraction method, a laser beam source having a wavelength of 600 to 800 nm is used as a laser beam source
41
, as shown in FIG.
6
. With the laser beam having such a wavelength, a particle size distribution in a particle diameter region of the order of sub-sub-micron less than 0.1 &mgr;m can not be measured.
A specific structure of a conventional particle size analyzer based on the laser diffraction method is shown as a block diagram in FIG.
7
. The particle size analyzer in this example comprises an irradiation optical system
51
including a semiconductor laser
51
a
and a collimating lens
51
b
to allow output beam therefrom to become parallel beam; and a measurement optical system
56
including a flow cell
52
wherein a suspension in which a sample P to be measured is dispersed in a medium liquid flows, a forward scattered light sensor formed of a converging lens
53
a
for detecting only the light diffracted/scattered in a predetermined front angle region among the diffracted/scattered light by the particle group P to be measured and a ring detector
53
b,
sideward scattered light sensors
54
and backward scattered light sensors
55
for detecting the light diffracted/scattered sideward and backward among the light diffracted/scattered by the particle group P to be measured, respectively. Then, outputs from the respective light sensors are amplified and digitized at a data sampling circuit
57
including amplifiers and A/D converters co
Kanesaka & Takeuchi
Shimadzu Corporation
Stafira Michael P.
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