Laser diffraction analysis
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Laser diffraction analysis, also known as laser diffraction spectroscopy, is a technology that utilizes
diffraction Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
patterns of a
laser beam A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
passed through any object ranging from nanometers to millimeters in size to quickly measure geometrical dimensions of a particle. This
particle size analysis Particle size analysis, particle size measurement, or simply particle sizing, is the collective name of the technical procedures, or laboratory techniques which determines the size range, and/or the average, or mean size of the particles in a p ...
process does not depend on
volumetric flow rate In physics and engineering, in particular fluid dynamics, the volumetric flow rate (also known as volume flow rate, or volume velocity) is the volume of fluid which passes per unit time; usually it is represented by the symbol (sometimes ). I ...
, the amount of particles that passes through a surface over time.


Fraunhofer vs. Mie Theory

Laser diffraction analysis is originally based on the
Fraunhofer diffraction In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance (a distance satisfying Fraunhofer ...
theory, stating that the intensity of light scattered by a particle is directly proportional to the particle size. The angle of the laser beam and particle size have an inversely proportional relationship, where the laser beam angle increases as particle size decreases and vice versa. The
Mie scattering The Mie solution to Maxwell's equations (also known as the Lorenz–Mie solution, the Lorenz–Mie–Debye solution or Mie scattering) describes the scattering of an electromagnetic plane wave by a homogeneous sphere. The solution takes the f ...
model, or Mie theory, is used as alternative to the Fraunhofer theory since the 1990s. Commercial laser diffraction analyzers leave to the user the choice of using either Fraunhofer or Mie theory for data analysis, hence the importance of understanding the strengths and limitations of both models. Fraunhofer theory only takes into account the diffraction phenomena occurring at the contour of the particle. Its main advantage is that it does not require any knowledge of the optical properties (
complex refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
) of the particle’s material. Hence is it typically applied to samples of unknown optical properties, or to mixtures of different materials. For samples of known optical properties, Fraunhofer theory should only be applied for particles of an expected diameter at least 10 times larger than the light source’s wavelength, and/or to opaque particles. The Mie theory is based on measuring the scattering of electromagnetic waves on spherical particles. Hence, it is taking into account not only the diffraction at the particle’s contour, but also the refraction, reflection and absorption phenomena within the particle and at its surface. Thus, this theory is better suited than the Fraunhofer theory for particles that are not significantly larger than the wavelength of the light source, and to transparent particles. The model’s main limitation is that it requires precise knowledge of the
complex refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
(including the absorption coefficient) of the particle’s material. The lower theoretical detection limit of laser diffraction, using the Mie theory, is generally thought to lie around 10 nm.


Optical setup

Laser diffraction analysis is typically accomplished via a red He-Ne laser or
laser diode file:Laser diode chip.jpg, The laser diode chip removed and placed on the eye of a needle for scale A laser diode (LD, also injection laser diode or ILD, or diode laser) is a semiconductor device similar to a light-emitting diode in which a di ...
, a
high-voltage High voltage electricity refers to electrical potential large enough to cause injury or damage. In certain industries, ''high voltage'' refers to voltage above a certain threshold. Equipment and Electrical conductor, conductors that carry high ...
power supply, and structural packaging. Alternatively, blue laser diodes or LEDs of shorter wavelength may be used. The light source affects the detection limits, with lasers of shorter wavelengths better suited for the detection of submicron particles. Angling of the
light energy Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 terahe ...
produced by the laser is detected by having a beam of light go through a flow of dispersed particles and then onto a
sensor A sensor is a device that produces an output signal for the purpose of sensing a physical phenomenon. In the broadest definition, a sensor is a device, module, machine, or subsystem that detects events or changes in its environment and sends ...
. A
lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
is placed between the object being analyzed and the detector's focal point, causing only the surrounding laser diffraction to appear. The sizes the laser can analyze depend on the lens'
focal length The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative foca ...
, the distance from the lens to its point of focus. As the focal length increases, the area the laser can detect increases as well, displaying a proportional relationship. Multiple light detectors are used to collect the diffracted light, which are placed at fixed angles relative to the laser beam. More detector elements extend sensitivity and size limits. A computer can then be used to detect the object's particle sizes from the light energy produced and its layout, which the computer derives from the data collected on the particle
frequencies Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
and
wavelengths In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
. In practical terms, laser diffraction instruments can measure particles in liquid suspension, using a carrier solvent, or as dry powders, using compressed air or simply gravity to mobilize the particles. Sprays and aerosols generally require a specific setup.


Results


Volume-weighted particle size distribution

Because the light energy recorded by the detector array is proportional to the volume of the particles, laser diffraction results are intrinsically volume-weighted. This means that the
particle size distribution The particle-size distribution (PSD) of a powder, or granular material, or particles dispersed in fluid, is a list of values or a mathematical function that defines the relative amount, typically by mass, of particles present according to size. Sig ...
represents the ''volume'' of particle material in the different size classes. This is in contrast to counting-based optical methods such as microspcopy or dynamic image analysis, which report the ''number'' of particles in the different size classes. That the diffracted light is proportional to the particle’s volume also implies that results are assuming particle sphericity, i.e. that the particle size result is an
equivalent spherical diameter The equivalent spherical diameter of an irregularly shaped object is the diameter of a sphere of equivalent geometric, optical, electrical, aerodynamic or hydrodynamic behavior to that of the particle under investigation. The particle size of a pe ...
. Hence particle shape cannot be determined by the technique. The main graphical representation of laser diffraction results is the volume-weighted particle size distribution, either represented as density distribution (which highlights the different modes) or as cumulative undersize distribution.


Numerical results

The most widely used numerical laser diffraction results are: * The median volume-weighted diameter, or D50. Derived from the cumulative curve, it represents the particle diameter separating the upper 50 % of the data from the lower 50 %. * The D10 and D90 values, also derived from the cumulative curve. * The mean volume-weighted diameter, also termed D ,3or
De Brouckere mean diameter The De Brouckere mean diameter is the mean of a particle size distribution weighted by the volume (also called volume-weighted mean diameter, volume moment mean diameter. or volume-weighted mean size). It is the mean diameter, which is directly obt ...
. * The span, which gives a measure of the width of the particle size distribution, and is calculated as span = 90 – D10D50.


Result quality and instrument validation

Harmonized standards for the accuracy and precision of laser diffraction measurements have been defined both by
ISO ISO is the most common abbreviation for the International Organization for Standardization. ISO or Iso may also refer to: Business and finance * Iso (supermarket), a chain of Danish supermarkets incorporated into the SuperBest chain in 2007 * Iso ...
, in standard ISO 13320:2020, and by the
United States Pharmacopoeia The ''United States Pharmacopeia'' (''USP'') is a pharmacopeia (compendium of drug information) for the United States published annually by the United States Pharmacopeial Convention (usually also called the USP), a nonprofit organization that ...
, in chapter USP <429>.


Uses

Laser diffraction analysis has been used to measure particle-size objects in situations such as: *  observing distribution of
soil texture Soil texture is a classification instrument used both in the field and laboratory to determine soil classes based on their physical texture. Soil texture can be determined using qualitative methods such as texture by feel, and quantitative methods ...
and
sediments Sediment is a naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of wind, water, or ice or by the force of gravity acting on the particles. For example, sand a ...
such as
clay Clay is a type of fine-grained natural soil material containing clay minerals (hydrous aluminium phyllosilicates, e.g. kaolin, Al2 Si2 O5( OH)4). Clays develop plasticity when wet, due to a molecular film of water surrounding the clay par ...
and
mud A MUD (; originally multi-user dungeon, with later variants multi-user dimension and multi-user domain) is a Multiplayer video game, multiplayer Time-keeping systems in games#Real-time, real-time virtual world, usually Text-based game, text-bas ...
, with an emphasis on
silt Silt is granular material of a size between sand and clay and composed mostly of broken grains of quartz. Silt may occur as a soil (often mixed with sand or clay) or as sediment mixed in suspension with water. Silt usually has a floury feel when ...
and the sizes of bigger samples of clay. *  determining
in situ ''In situ'' (; often not italicized in English) is a Latin phrase that translates literally to "on site" or "in position." It can mean "locally", "on site", "on the premises", or "in place" to describe where an event takes place and is used in ...
measurements of particles in
estuaries An estuary is a partially enclosed coastal body of brackish water with one or more rivers or streams flowing into it, and with a free connection to the open sea. Estuaries form a transition zone between river environments and maritime environment ...
. Particles in estuaries are important as they allow for natural or pollutant chemical species to move around with ease. The size, density, and stability of particles in estuaries are important for their transportation. Laser diffraction analysis is used here to compare particle size distributions to support this claim as well as find cycles of change in estuaries that occur because of different particles. *  
soil Soil, also commonly referred to as earth or dirt, is a mixture of organic matter, minerals, gases, liquids, and organisms that together support life. Some scientific definitions distinguish ''dirt'' from ''soil'' by restricting the former te ...
and its stability when wet. The stability of soil aggregation (clumps held together by moist clay) and clay dispersion (clay separating in moist soil), the two different states of soil in the
Cerrado The ''Cerrado'' (, ) is a vast ecoregion of tropical savanna in eastern Brazil, particularly in the states of Goiás, Mato Grosso do Sul, Mato Grosso, Tocantins, Minas Gerais, and the Federal District. The core areas of the Cerrado biome are t ...
savanna region, were compared with laser diffraction analysis to determine if plowing had an effect on the two. Measurements were made before
plowing A plough or plow (Differences between American and British spellings, US; both ) is a farm tool for loosening or turning the soil before sowing seed or planting. Ploughs were traditionally drawn by oxen and horses, but in modern farms are draw ...
and after plowing for different intervals of time. Clay dispersion turned out to not be affected by plowing while soil aggregation did. *  
erythrocyte deformability Erythrocyte deformability refers to the ability of erythrocytes (red blood cells, RBC) to change shape under a given level of applied stress, without hemolysing (rupturing). This is an important property because erythrocytes must change their shape ...
under shear. Due to a special phenomenon called ''tank treading'', the membrane of the
erythrocyte Red blood cells (RBCs), also referred to as red cells, red blood corpuscles (in humans or other animals not having nucleus in red blood cells), haematids, erythroid cells or erythrocytes (from Greek ''erythros'' for "red" and ''kytos'' for "holl ...
(red blood cell, RBC) rotates relative to the shear force and the cell's
cytoplasm In cell biology, the cytoplasm is all of the material within a eukaryotic cell, enclosed by the cell membrane, except for the cell nucleus. The material inside the nucleus and contained within the nuclear membrane is termed the nucleoplasm. The ...
causing RBCs to orient themselves. Oriented and stretched red blood cells have a diffraction pattern representing the apparent particle size in each direction, making it possible to measure the
erythrocyte deformability Erythrocyte deformability refers to the ability of erythrocytes (red blood cells, RBC) to change shape under a given level of applied stress, without hemolysing (rupturing). This is an important property because erythrocytes must change their shape ...
and the orientability of the cells. In an ''ektacytometer'' erythrocyte deformability can be measured under changing
osmotic stress Osmotic shock or osmotic stress is physiologic dysfunction caused by a sudden change in the solute concentration around a cell, which causes a rapid change in the movement of water across its cell membrane. Under hypertonic conditions - conditio ...
or
oxygen tension Blood gas tension refers to the partial pressure of gases in blood. There are several significant purposes for measuring gas tension. The most common gas tensions measured are oxygen tension (PxO2), carbon dioxide tension (PxCO2) and carbon monox ...
and is used in the diagnosis and follow up of congenital hemolytic anemias.


Comparisons

Since laser diffraction analysis is not the sole way of measuring particles it has been compared to the sieve-pipette method, which is a traditional technique for grain size analysis. When compared, results showed that laser diffraction analysis made fast calculations that were easy to recreate after a one-time analysis, did not need large sample sizes, and produced large amounts of data. Results can easily be manipulated because the data is on a digital surface. Both the sieve-pipette method and laser diffraction analysis are able to analyze minuscule objects, but laser diffraction analysis resulted in having better precision than its counterpart method of particle measurement.


Criticism

Laser diffraction analysis has been questioned in validity in the following areas: *  assumptions including particles having random configurations and volume values. In some dispersion units, particles have been shown to align themselves together rather than have a
turbulent flow In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between ...
, causing them to lead themselves in an orderly direction. *
algorithms In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing c ...
used in laser diffraction analysis are not thoroughly validated. Different algorithms are used at times to have collected data match assumptions made by users as an attempt to avoid data that looks incorrect. * measurement inaccuracies due to sharp edges on objects. Laser diffraction analysis has the chance of detecting imaginary particles at sharp edges because of the large angles the lasers make upon them. * when compared to the data collecting of
optical imaging Medical optical imaging is the use of light as an investigational :wikt:imaging, imaging technique for medical applications. Examples include optical microscopy, spectroscopy, endoscopy, scanning laser ophthalmoscopy, laser Doppler imaging, and opti ...
, another particle-sizing technique, correlation between the two was poor for non-spherical particles. This is due to the fact that the underlying Fraunhofer and Mie theories only cover spherical particles. Non-spherical particles cause more diffuse scatter patterns and are more difficult to interpret. Some manufacturers have included algorithms in their software, which can partly compensate for non-spherical particles.


See also

*
Diffraction tomography Diffraction tomography is an inverse scattering technique used to find the shape of a scattering object by illuminating it with probing waves and recording the reflections. It is based on the diffraction slice theorem and assumes that the scatte ...
*
List of laser articles This is a list of laser topics. A * 3D printing, additive manufacturing * Abnormal reflection * Above-threshold ionization * Absorption spectroscopy * Accelerator physics * Acoustic microscopy * Acousto-optic deflector * Acousto-optic modul ...
*
Particle size distribution The particle-size distribution (PSD) of a powder, or granular material, or particles dispersed in fluid, is a list of values or a mathematical function that defines the relative amount, typically by mass, of particles present according to size. Sig ...


References

{{Lasers Spectroscopy