Particle size analyzer based on the laser diffraction method

Details Particle size analyzer based on the laser diffraction method Particle size analyzer based on the laser diffraction method

2001-07-26

2002-10-22

Epps, Georgia (Department: 2873)

Optics: measuring and testing

For size of particles

By particle light scattering

C356S338000, C356S343000, C356S340000

Reexamination Certificate

active

06469786

ABSTRACT:

BACKGROUND OF THE INVENTION AND RELATED ART STATEMENT
The invention relates to a particle size analyzer based on the laser diffraction method, more specifically, a particle size analyzer based on the laser diffraction method wherein a particle size in a submicron area can be measured with a high resolution.
In a conventional particle size analyzer based on the laser diffraction method, generally, a spatial intensity distribution of scattered light generated by irradiating laser beam to particles to be measured in a dispersion state, is measured. Since the light intensity distribution conforms to a Mie's scattering theory or Fraunhofer's diffraction theory, a particle size distribution of the particles to be measured is calculated from the measured results of the spatial intensity distribution of the scattered light through a calculation based on the Mie's scattering theory or the Fraunhofer's diffraction theory.
In the conventional particle size analyzer of this type, as an optical system for measuring the spatial intensity of the scattered light by the particles to be measured, an apparatus shown in
FIG. 2
(Japanese Patent No.2139485) has been widely used.
More specifically, laser beam as parallel beam is irradiated to a flow cell
21
, in which a suspension S prepared by dispersing particles P to be measured in a medium liquid flows, by an irradiation optical system
22
formed of a laser beam source
22
a
, condenser lens
22
b
, spatial filter
22
c
and collimator lens
22
d
. The laser beam is scattered by the particles P to be measured in the suspension S to thereby produce a spatial light intensity distribution pattern. In the scattered light, light in a scattering angle smaller than 35° at the most in a predetermined forward angle are condensed by a condenser lens
23
to form a scattering image on a ring detector
24
positioned at a focal point of the lens. The ring detector
24
is structured such that several tens of light receiving elements, each having a light receiving surface with a ring shape, a semi-ring shape or a quarter ring shape, of different radii are coaxially arranged around an optical axis of the irradiation laser beam, so that the intensity of the scattered light condensed by the condenser lens
23
can be continuously measured in every small angle. Also, the light scattered forwardly in the large angle and laterally and rearwardly, which are not condensed by the condenser lens
23
, are detected by forward large angle scattered light sensors
25
, sideward scattered light sensors
26
and rearward scattered light sensors
27
, formed of independent light sensors, respectively.
The spatial intensity distribution pattern of the scattered light measured as described above is digitized by an A-D converter; then taken into a computer as scattered light intensity distribution data; and converted into the particle size distribution of the particles P to be measured according to a theory explained below.
The intensity distribution data of the light scattered by the particles P to be measured vary according to the sizes of the particles. Since the actual particles P to be measured contain particles with different sizes, the intensity distribution data of the scattered light generated by the particles P to be measured become a superposition of the lights scattered from the respective particles. When this is expressed by a matrix,
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
)
In the above respective formulas, s (vector) is intensity distribution data (vector) of the scattered light. Elements s
i
(i=1, 2, . . . m) are incident light quantities detected by the respective elements of the ring detector
24
and the forward large angle, sideward and rearward scattered light sensors
25
,
26
,
27
.
q (vector) is particle size distribution data (vector) expressed as a frequency distribution percentage. A diameter range of the particles to be measured (largest particle diameter: X
1
, the smallest particle diameter: X
n+1
) is divided into n, and an interval between the respective particle diameters is expressed by [X
j
, X
j+1
] (j=1, 2, . . . n). The elements q
j
(j=1, 2, . . . n) of q (vector) are particle quantities corresponding to the particle diameter intervals [X
j
, X
j+1
].
Generally, a normalization is carried out to obtain
∑
j
=
1
n
⁢
q
j
=
100
⁢
%
(
4
)
A (matrix) is a coefficient matrix for converting the particle distribution data (vector) q to the light intensity distribution data (vector) s. The physical meaning of elements ai, (i=1, 2, . . . m, j=1, 2, . . . n) of A (matrix) is an incident light quantity with respect to the i-th element of the light scattered by the particles of a unit particle quantity belonging to the particle diameter interval [X
j
, X
j+1
].
The numeral value of a
i,j
can be theoretically calculated in advance. For this purpose, in case the particle diameter is sufficiently large when compared with a wavelength of the laser beam as a light source, the Fraunhofer's diffraction theory is used. However, in a submicron area where the particle diameter is the same size as the wavelength of the laser beam or smaller than that, the Mie's scattering theory must be used. The Fraunhofer's diffraction theory seems to extremely approximate to the Mie's scattering theory which is effective in case the particle diameter is sufficiently large when compared with the wavelength in the forward small angle scattering.
In order to calculate the elements of the coefficient matrix A based on the Mie's scattering theory, it is necessary to establish absolute refractive indices (complex numbers) of the particles and the medium (medium liquid) into which the particles are dispersed. Instead of the respective refractive indices, a relative refractive index (complex number) of the particles and the medium may be established.
Based on Equation (1), when a formula for obtaining the least square solution of the particle size distribution data (vector) q is found, Equation (5) can be obtained.
q
=(
A
T
A
)
−1
A
T
s
  (5)
wherein A
T
is a transposed matrix of A, and ( )
−1
is an inverse matrix.
The respective elements of the light intensity distribution data (vector) s in the right-hand side of Equation (5) are numeral values detected by the ring detector
24
, forward large angle scattered light sensors
25
, sideward scattered light sensors
26
and rearward scattered light sensors
27
as described before. Also, the coefficient matrix A can be obtained in advance by using the Fraunhofer's diffraction theory or Mie's scattering theory. Therefore, when calculation of Equation (5) is carried out by using these already known data, 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, although only one example for calculating the particle size distribution has been shown, there are various other methods. Also, with respect to the optical system for measuring scattered light, there are many other variations. For example, a measuring optical system using an reverse Fourier optical system as shown in
FIG. 3
has been known.
In the measuring optical system using the reverse Fourier optical system shown in
FIG. 3
, instead of irradiating the parallel laser beam to the particles to be measured as in the optical system shown in
FIG. 2
, the laser beam set to be parallel by a laser beam source
32
a
, condenser lens
32
b
, spatial filter
32
c
and collimator lens
32
d
are condensed by a condenser lens
32
e
positioned on the side of a flow cell
31
, and t

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