Self-mixing interferometry

Abstract

A self-mixing interferometer for detecting particles within a monitored region of space comprises a laser cavity (1A) and an optical assembly (1B) configured to bathe the monitored region with laser light possessing optical wavefronts (10) configured by the optical assembly such that at separate locations within the monitored region the optical wavefronts comprise different respective orientations relative to the optical assembly. A laser monitoring unit (1C) acquires an interferometric signal generated by the interferometer in response to light returned to the laser cavity assembly from the wavefronts by the particles. A processing module (1D) detects the presence of particles within the monitored region on condition that a frequency of the interferometric signal waveform is less than a pre-set threshold frequency value and subsequently to determine a property of the particles according to changes in the waveform frequency conditional that the frequency exceeds the pre-set threshold frequency value.

Description

[0001]SELF-MIXING INTERFEROMETRY BACKGROUND The self-mixing effect is a form of laser feedback interferometry. It occurs within a laser resonator cavity due to the deliberate mixing of the intracavity electromagnetic wave with an electromagnetic wave that has been emitted from the resonator cavity and subsequently reinjected into the resonator cavity after interaction in an “external cavity”. The external cavity is simply the region of space through which the outward-and-return path of the emitted electromagnetic wave passes before re-entering the resonator cavity. The laser resonator cavity plus the external cavity collectively define an interferometer, and the external cavity serves as an interferometer arm of the interferometer. Changes in the optical path length of this interferometer arm reveal themselves as modulations in the optical power within the laser resonator cavity, or as modulations in the voltage across the drive terminals of the laser cavity. This phenomenon is typically referred to as self-mixing interferometry (SMI), but is also referred to by other names, such as: laser feedback interferometry, back-scatter-modulation, induced- modulation, self-coupling, optical feedback, external feedback, and auto-dyning. Here we refer to the phenomenon as self-mixing interferometry (SMI), and it is to be understood that this includes a reference to the other names given to this phenomenon as identified above. This phenomenon may occur in lasers regardless of their type, and may be implemented using gas lasers, in-plane semiconductor diode lasers, vertical-cavity surface-emitting lasers (VCSEL), mid-infrared and terahertz quantum cascade lasers (QCLs), inter-band cascade lasers, fibre lasers and fibre ring lasers, solid-state lasers, micro-ring lasers, and quantum dot lasers, for example. The effect is observable when typically as little as 0.1%, or less, of emitted radiation is reflected back into a laser resonator cavity from an external object some distance from the laser resonator cavity. Using a photosensitive detector to collect radiation emitted from one partially transmissive mirror of the laser resonator cavity, displacement of the object in the external cavity may be sensed using radiation reinjected into the laser resonator cavity through the partially transmissive second mirror (i.e., the laser output mirror) after reflection from the object. The phenomenon has also been proposed for use in measuring physical parameters that are capable of altering an optical path length in the external cavity of the self-mixing interferometer. These parameters include physical size and velocity measurement of reflecting objects within the external cavity. The present invention has been devised in light of the above considerations. P004737-GB01 2 SUMMARY An SMI system operates on the following principle schematically illustrated in Fig.1A and Fig. 1B. Laser light 2 is emitted from the laser resonator cavity of a laser 1 and is transmitted as an electromagnetic wave 3 to an external target object 4 from which it is partially reflected, or back- scattered. A portion of the reflected or back-scattered light is transmitted back to the laser as a returned electromagnetic wave (5A or 5B) where a portion of it 6 re-enters the resonator cavity of the laser 1. Inside the resonator cavity of the laser, the re-entered light mixes with resident light of the resonator cavity that exists in one or more of the resonant modes of the laser resonator cavity (see Mixing Modulation 7A, 7B). As a result of the mixing of light within the laser resonator cavity, the re-entered light perturbs the electromagnetic field within the resonator cavity. This perturbation becomes measurable as consequential perturbations (7A, 7B) to the operating parameters of the laser. Consequently, the branch of the laser light path extending from the laser resonator cavity to the target object may be regarded as a first arm (an external arm) of an interferometer for light output from (and returned to) the cavity, and the laser resonator cavity may be regarded as a second arm (an internal arm) of the interferometer for light remaining within the cavity. Light waves (3, 5A, 5B) propagating along these two arms of the interferometer are brought together within the laser resonator cavity where they mix and cause constructive or destructive interferences generating perturbations (e.g., mixing modulations 7A, 7B) in operating parameters of the laser. Perturbations in operating parameters influencing the gain of the laser result in measurable perturbations in the optical power of the laser and the voltage at the drive terminals of the resonator cavity. Variations in optical power may be monitored using a photodetector (‘PD’; Fig.1C) to indirectly measure the optical power of light sampled from the optical resonator cavity of the laser, or variations in the voltage of drive terminals of the resonator cavity can be monitored directly. Indirect measurement of optical power may be achieved either by use of a laser having an optical resonator cavity in which both mirrors of the cavity are partially transmissive thereby to release, from each end of the resonator cavity, a defined proportion of the light within resonator cavity. Of course, the output laser beam, 2, is the result of the front mirror of the optical cavity releasing a defined first proportion of the light from within resonator cavity. In addition, the back mirror of P004737-GB01 3 the resonator cavity may also release a defined second proportion of the light from within resonator cavity resulting in a second output of laser light (2B; Fig.1C) which is received and monitored by the photodetector. Referring to Fig.1C, in a so-called “three-mirror model” of SMI, the laser resonator cavity 1A is represented as the “internal” cavity with length Lint, refractive index nint. Light 2A within this internal cavity has a round-trip propagation time ^^^^௧. Light 2 leaves the internal cavity through the partially transmissive front mirror M2, of reflectivity R2, and traverses the external cavity of length Lextwhere it reflects from the external mirror M3, of reflectivity R. This external light has a round-trip propagation time ^^^௫௧. A portion 6 of this light re-enters the laser resonator cavity 1A through the front mirror M2 and mixes with the electromagnetic field inside the laser resonator cavity. A small portion 2B of the intra-cavity light exits the laser resonator cavity 1A through the back mirror M1and is detected by a monitoring photodetector (PD). When a single reflection from M3 is considered, the rate at which re-injected light 6 is coupled into the laser cavity 1A given by: The “feedback level” (^^) within the resonator cavity is given by: Here, the term ^^ is known in the art as the “linewidth enhancement factor”. It is known in the art that the optical coupling within the resonator cavity of the laser results in the so-called “excess phase equation”: The term ^^ி^represents the phase accumulated by the electromagnetic field of the laser on feed- back (FB) transmission through the external cavity. The term ^^^corresponds to the phase accumulated by transmission through the external cavity if the laser were not experiencing optical feedback. The feedback level ^^ determines the degree of nonlinear coupling within the laser resonator cavity. In the following discussions, we will consider the “weak feedback” P004737-GB01 4regime in which ^^ → 0 such that no nonlinear coupling exist. The observable quantities areeither a variation in laser power or a variation in voltage across the laser terminals. The dependence of these quantities on the phase term ^^ி^can be found as follows. ^^ ൌ ^^ ^ ^^ cos ି^^^^^^ ^^^^ ^ ^^ sin^^^ி^ ^ tan ^^^^However, when there is only a weak feedback intensity in the light returned to the laser cavity from the mirror M3 the coefficient ^^ becomes negligible, and one may write: ^^^^^^^ ≅ ^^ ^ ^^ cos^^^Here, the amplitude of the modulation ^^ ∝ ^^, and the resulting SMI signal, for a given laserresonator cavity, depends the reflectivity of the external mirror M3 and the nature of the accumulated phase ^^^. Returning to Fig.1A, there is schematically shown a situation where the wavelength of the laser light is ^^ and the accumulated phase ^^^within the returned light wave 5A corresponds to an even integer multiple, ^^, of half-wavelengths, and for simplicity we haveset ^^ ൌ ^^, such that constructive interference modulates the laser power signal 7A, such that:^^^^^^^ ≅ ^^ ^ ^^ cos^^^^^^ ൌ ^^ ^ ^^ ൌ 2^^Returning to Fig.1B, there is schematically shown a situation where the scattering target object 4 has moved away from the laser resonator cavity 1 so as to increase the length of the external arm of the interferometer by ^^ / 4 corresponding to one quarter of one wavelength of the laser light, noting that the wavelength of the laser light is ^^. As a result of this movement, the accumulatedphase ^^^ within the returned light wave 5B corresponds to an odd-multiple, ^^ ^ 1, of these half-wavelengths, such that destructive interference modulates the laser power signal 7B, such that: ^^^^^^^ ≅ ^^ ^ ^^ cos^^^^^^ ^ 1^^ ൌ ^^ െ ^^ ൌ 0It is to be understood that the schematic representations shown in Fig.1A and Fig.1B are simplified representations provided to aid understanding of the principles of self-mixing interferometry. The invention employs self-mixing interferometry for detecting particles (particulate material) and properties thereof. P004737-GB01 5 In the following, several aspects of the invention are disclosed, and many desirable or preferred features are described. However, it is to be understood that the invention includes the combination of any one or more of the desirable or preferred features described below with any one or more of the aspects of the invention described below, except where such a combination is clearly impermissible or expressly avoided. In one aspect the invention proposes a particulate matter detector based on the principle of self- mixing interferometry employing an interferometric laser providing electromagnetic wavefronts defined by an optical wave comprising different respective orientations / directions within the monitored region. The inventors have realised that this wavefront geometry permits creation of self-mixing interferometry signals having a property that is indicative of the presence of a particle amongst the electromagnetic wavefronts, and that the application of signal processing steps to a self-mixing interferometry signal to determine a property of a detected particle may be done selectively when the interferometry signal has that property. This saves power usage by applying power-intensive signal processing steps only when appropriate (e.g., when a particle is present amongst the wavefronts), and not when inappropriate (e.g., when a particle is not present amongst the wavefronts). In any aspect of the invention, the wavelength (^^) of laser light of the self-mixing interferometer may be in the visible light range or in the near-infrared (NIR) range. For example, thewavelength (^^) of laser light of the self-mixing interferometer may be in the range: 380^^^^ ^^^ ^ 2.0^^^^. In other examples, the wavelength (^^) of laser light of the self-mixing interferometermay outside of this range. The wavelength of the laser light of the self-mixing interferometer may be selected in preference to the range of particle that the apparatus is intended to preferentially detect. This is because the mechanism for the scattering of light from a particle is influenced by the ratio (^^ / ^^) of the wavelength (^^) of scattering light and the radius (^^) of the particle from which the light scatters. For example, if this ratio is much smaller than one (1) then Rayleigh scattering mechanisms dominate. "Mie scattering" mechanisms dominate in situations where the size of the scattering particles is comparable to the wavelength of the light, such that the ratio is comparable to one (1), rather than much smaller or much larger. However, geometrical optical mechanisms (GO) dominate when the ratio is much larger than one (1). By an appropriate choice of laser light wavelength, the user may select the most appropriate scattering mechanism to take place in respect of the particle size range to be sensed. The invention disclosed herein may be configured to monitor particulate material according to a ratio P004737-GB01 6 (^^ / ^^) of the wavelength (^^) of the self-mixing interferometer and the radius (^^) of the particlesto be monitored which is, for example and without limitation, in the range: 0.1 ^ ^^ / ^^ ^ 100.In a first aspect, the invention may provide a self-mixing interferometer configured to monitor particulate material within a monitored region of space comprising: a laser cavity assembly; an optical assembly configured to bathe the monitored region with laser light of the interferometer possessing one or more optical wavefront(s) defined by an optical wave configured by the optical assembly such that at separate locations within the monitored region the one or more optical wavefront(s) comprises different respective orientations relative to the optical assembly; a laser monitoring unit configured to acquire an interferometric signal generated by the interferometer in response to light returned to the laser cavity assembly from the one or more optical wavefronts by the particulate material; a processing module configured to detect the presence of particulate material within the monitored region on condition that a frequency of a waveform of the interferometric signal is less than a pre-set threshold frequency value and subsequently to determine a property of the detected particulate material according to changes in the frequency of the waveform of the interferometric signal on condition that the frequency is greater than the pre-set threshold frequency value. The processing module may comprise a signal processor unit configured to process the interferometric signal according to a first processor clock speed to detect the presence of particulate material, and to process the interferometric signal according to a second processor clock speed subsequently to determine said property of the detected particulate material, wherein the second processor clock speed exceeds the first processor clock speed. The processing module may be configured, in response to detection of the presence of particulate material within the monitored region, to cease processing the interferometric signal according to the first processor clock speed, and to commence processing the interferometric signal according to the second processor clock speed. The processing module may be configured, in response to a cessation of the waveform in the interferometric signal, to cease processing the interferometric signal according to the second P004737-GB01 7 processor clock speed and to revert to processing the interferometric signal according to the first processor clock speed. The processing module may be configured to determine a frequency bandwidth corresponding to the changes in the frequency of the waveform of the interferometric signal, to determine an average frequency of the waveform of the interferometric signal, and to determine an estimated speed of the detected particulate material as the property of the detected particulate material, according to a ratio of the average frequency and the frequency bandwidth. The frequency bandwidth may comprise a fractional bandwidth corresponding to the changes in the frequency of the waveform of the interferometric signal. The term “fractional bandwidth” may include a reference to the absolute bandwidth, ∆^^, divided by the bandwidth centre frequency, ^^^^^௧^^. A bandwidth of a signal may be expressed as the standard deviation, ^^^^^^, of the distribution of frequencies in the signal. A centre frequency may be defined as the mean (arithmetic or geometric) of the uppermost, ^^ு, and lowermost, ^^^, frequencies of a bandwidth of frequencies. Examples include, but are not limited to, the following: ^^^^^^ ൌ ∆^^ / ^^^^^௧^^∆^^ ൌ ^^ு െ ^^^; ∆^^ ൌ ^^^^^^ The processing module may be configured to determine a concentration of the particulate material according to the value of the estimated speed of the detected particulate material within the monitored region, a cross sectional area of the monitored region, and a rate of detection of the presence of particulate material within the monitored region. A concentration (C) may be defined as: ^^ ൌ ^^ / ^^^^^^Here, the quantity ^^ is a rate of detections, per second, the quantity ^^ is a detection area transverse to a particle flow direction, and the quantity ^^ is the particle speed. The processing module may be configured to determine a plurality of successive time points at which a signal polarity in the waveform of the interferometric signal changes, and to determine a P004737-GB01 8 frequency of the waveform of the interferometric signal according to the plurality of successive time points so determined. A term “polarity” in the context of a signal may include a reference to the signal's position or voltage above or below a median line, which may be the ‘zero’ line, but need not be. An aforementioned time point may correspond to a zero-crossing of the waveform of the interferometric signal coincident with a sign-change of a value of the waveform of the interferometric signal. The processing module may be configured to determine a zero-crossing rate (ZCR) and therewith to determine a frequency of the waveform of the interferometric signal. In a second aspect, the invention may provide a method for self-mixing interferometry for monitoring particulate material within a monitored region of space comprising: providing a self-mixing interferometer comprising a laser cavity assembly and an optical assembly; bathing the monitored region with laser light of the interferometer possessing one or more optical wavefront(s) defined by an optical wave configured by the optical assembly such that at separate locations within the monitored region the one or more optical wavefront(s) comprises different respective orientations relative to the optical assembly; acquiring an interferometric signal generated by the interferometer in response to light returned to the laser cavity assembly from the one or more optical wavefronts by said particulate material; by a processing module, detecting the presence of particulate material within the monitored region on condition that a frequency of a waveform of the interferometric signal is less than a pre-set threshold frequency value and subsequently to determining a property of the detected particulate material according to changes in the frequency of the waveform of the interferometric signal on condition that the frequency is greater than the pre-set threshold frequency value. The method may comprise, by a signal processor unit of the processing module, processing the interferometric signal according to a first processor clock speed to detect the presence of particulate material, and processing the interferometric signal according to a second processor clock speed subsequently to determine said property of the detected particulate material, wherein the second processor clock speed exceeds the first processor clock speed. P004737-GB01 9 The method may comprise, in response to detection of the presence of particulate material within the monitored region, ceasing the processing of the interferometric signal according to the first processor clock speed, and commencing the processing the interferometric signal according to the second processor clock speed. The method may comprise, in response to a cessation of the waveform in the interferometric signal, ceasing the processing of the interferometric signal according to the second processor clock speed and reverting to the processing the interferometric signal according to the first processor clock speed. The method may comprise determining a frequency bandwidth corresponding to the changes in the frequency of the waveform of the interferometric signal, determining an average frequency of the waveform of the interferometric signal, and determining an estimated speed of the detected particulate material as said property of the detected particulate material, according to a ratio of the average frequency and the frequency bandwidth. The frequency bandwidth may comprise a fractional bandwidth corresponding to the changes in the frequency of the waveform of the interferometric signal. The method may comprise determining a concentration of the particulate material according to the value of the estimated speed of the detected particulate material within the monitored region, a cross sectional area of the monitored region, and a rate of detection of the presence of particulate material within the monitored region. The method may comprise determining a plurality of successive time points at which a signal polarity in the waveform of the interferometric signal changes, and determining a frequency of the waveform of the interferometric signal according to the plurality of successive time points so determined. Each aforesaid time point may correspond to a zero-crossing of the waveform of the interferometric signal coincident with a sign-change of a value of the waveform of the interferometric signal. The method may comprise determining a zero-crossing rate (ZCR) and therewith determining a frequency of the waveform of the interferometric signal. P004737-GB01 10 BRIEF DESCRIPTION OF THE DRAWINGS Figures 1A and 1B show schematic representations of a self-mixing interferometer. Figure 1C shows a schematic representation of a self-mixing interferometer. Figures 2A, 2B and 2C each show a schematic representation of a self-mixing interferometer. Figure 3 shows a schematic representation a self-mixing interferometer laser beam in relation to a particle path through the beam. Figure 4 shows a schematic representation a self-mixing interferometer laser beam in relation to a particle path through the beam. Figures 5A and 5B show two self-mixing interferometer signal waveforms. Figure 6A shows a schematic representation a self-mixing interferometer laser beam in relation to two particle paths through the beam. Figures 6B shows two self-mixing interferometer signal waveforms. Figures 7 shows a laser cavity assembly of a self-mixing interferometer. Figures 8A, 8B and 8C show, respectively, (8A) a particle path through a self-mixing interferometer laser beam, (8B) a resulting self-mixing interferometer signal waveform, and (8C) a signal processing step applied to the self-mixing interferometer signal waveform. P004737-GB01 11 Figures 9A, 9B and 9C show, respectively, (9A) a particle path through a self-mixing interferometer laser beam, (9B) a resulting self-mixing interferometer signal waveform, and (9C) a signal processing step applied to the self-mixing interferometer signal waveform. Figures 10A, 10B and 10C show, respectively, (10A) a particle path through a self-mixing interferometer laser beam, (10B) a resulting self-mixing interferometer signal waveform, and (10C) a signal processing step applied to the self-mixing interferometer signal waveform. Figures 11 and 12 each show a graph of fractional frequency bandwidth of self-mixing interferometer signal waveforms plotted against a cosine of an angle subtended by a particle path relative to a beam axis of a self-mixing interferometer laser beam. Figure 13 shows a self-mixing interferometer apparatus. Figure 14 shows steps in a method of calculating a particle concentration within a volume of space monitored by a self-mixing interferometer laser beam. DETAILED DESCRIPTION Aspects and embodiments of the present invention will now be discussed with reference to the accompanying figures. Further aspects and embodiments will be apparent to those skilled in the art. All documents mentioned in this text are incorporated herein by reference. Figure 2A schematically illustrates a self-mixing interferometer device 1 for detecting particulate material, according to an embodiment of the invention. The device is configured to monitor particulate material, such as a particle of material 4, within a monitored region of space. It comprises a laser cavity assembly 1A and an optical assembly 1B configured to bathe the monitored region with laser light 2 of the interferometer possessing wavefronts 10 having different directions at different respective locations within the monitored region. The laser light 2 forms a cone of light having a cone angle ^^ as measured from an edge 8a of the light cone to a central cone axis 8b. Light 2 output by the self-mixing interferometer P004737-GB01 12 device 1 may be scattered from a particle of material 4 within the cone of light such that some of the scattered light 6 is returned to the laser cavity assembly 1A of the self-mixing interferometer device to interact therewith and form an interferometric signal. The motion of the particle 4 along a trajectory or path 7 passing through the light cone, causes detectable changes in the interferometric signal, as is discussed in more detail below. In Fig.2A, one particle 4 is shown in three successive positions along its path through the cone of the laser beam 2. The self-mixing interferometer includes a laser monitoring unit 1C configured to acquire an interferometric signal generated by the interferometer in response to light returned to the laser cavity assembly 1A from the wavefronts by the particulate material. The self-mixing interferometer also includes a processing module 1D configured to determine a property of the particulate material within the monitored region according to changes in the frequency of a waveform within at least a part of the interferometric signal. In particular, Fig.2B, and Fig.2C show arrangements consistent with aspects of the invention. The schematic diagram of Fig.2B corresponds to the arrangement shown in Fig.2A. Here it can be seen that the optical assembly is configured to structure the laser beam such that it possesses curved wavefronts 10. The optical path length between the optical resonator cavity 1A and any point on a wavefront 10 is constant. This means that any spacing Δ, in a direction perpendicular to a given wavefront 10, between a point on that wavefront and a position of the particle at a particular instant of time along its part 7 through the laser beam, is equivalent to an optical path difference between light at the optical wavefront and light having reached the particle and about to be reflected from it back to the laser resonator cavity. Because the speed of light is so very much greater than the speed of the particle, the position of a given wavefront 10 when the particle enters the laser beam may be used as a reference wavefront with which to determine how the value of the spacing, Δ, changes as the particle progresses along its path. In other words, a wavefront corresponding to a particular phase of the electromagnetic wave of the laser light can be considered to be always present at the position of the reference wavefront. As shown in Fig.2B, the value of the spacing, Δ, changes continuously (Δ → Δ1→ Δ2→ Δ3… etc.) as the linear path of the particle 7 first coincides with a reference wavefront upon entering the laser beam, then moves further away from the reference wavefront as the particle approaches the central axis of the laser beam, due to the outward curvature of the reference wavefront. Subsequently, the linear path of the particle 7 moves towards the reference wavefront as the P004737-GB01 13 particle moves away from the central axis of the laser beam until it finally coincides with the reference wavefront upon exiting the laser beam. In addition, the spacing, Δ, between the path 7 of the particle and a reference wavefront changes continuously over time as the particle progresses through the laser beam. As will be discussed below, a consequence of this is that the frequency of a waveform in the interferometric signal of the self-mixing interferometer 1 is caused to change over time in at least a part of the interferometric signal, often appearing in the form of a ‘chirp’ or the like, in the signal. This changing frequency of waveform in the interferometric signal can be used to provide information about properties of the particle causing the signal. In order to better illustrate the causes of a ‘chirp’ signal, consider the circumstances illustrated schematically in Fig.2C. Here, a self-mixing interferometer 100 is configured to provide a collimated laser beam 8a of laser light 2 possessing substantially flat wavefronts 10. Consider a particle 4 passing through the laser beam along a linear path 7a within the laser beam with linear velocity ^^. This linear velocity has a direction subtending an angle ^^ relative to the axis of the laser beam. Both the subtended angle ^^ and the linear velocity ^^ may be determined as follows. The angular frequency, ^^^, of the interferometric signal corresponds to the rate of change of the accumulated phase ^^^within the light wave of the laser light (6, Fig.1A) re-injected into the optical cavity of the laser of the self-mixing interferometer by reflection or back-scattering from the particle 4. Noting that a change ^^^^^in the accumulated phase ^^^arises because of a change ^^^^ in the difference between the position of the particle 4 and a reference wavefront of the laser beam, we may write: Given that the duration Δ^^ of the transit of the particle 4 across the laser beam of width ^^ is: ^^ Δ^^ ൌ^^ sin ^^One may combine these two equations to yield: P004737-GB01 14 The quantities ^^ and ^^ are properties of the laser system and are known. The quantities Δ^^ and ^^^may be accurately estimated by applying a wavelet transformation to the interferometric signal. As an example of the invention, consider the same analysis as applied to the circumstances illustrated schematically in Fig.2A, or Fig.2B. The processing module of the self-mixing interferometer is configured to detect particulate material and the optical assembly 1B of the self-mixing interferometer 1 is configured to provide a laser beam 8a possessing wavefronts 10 having different directions at different respective locations within the monitored region. Fig.3 shows a diverging cone 8a of laser light emanating from the self-mixing interferometer 1. The cone of light is centred upon a cone axis 8b. The angle of divergence of the laser beam relative to the cone axis is ^^. Consider a particle 4 following a linear path 7 passing through the cone of laser light at speed ^^ the direction of which subtends an angle ^^ relative to the cone axis 8b. One can see that the following relations exist in relation to a change ^^^^ in the distance between the particle 4 and a reference wavefront 10 of the laser beam (8a, 8b), measured in a direction perpendicular to the reference wavefront, as determined from two different points on the path 7 of the particle 4 separated by a linear distance ^^^^. Given that the speed of the particle 4 is ^^, one may write: ^^^^ ൌ ^^^^^^ Referring to Fig.4, the following relations exist between the geometry of the conical laser beam of divergence angle ^^, the angle ^^ subtended by the path 7 of the particle relative to the central axis 8b of the conical laser beam, the times ^^^and ^^ଷof entering and exiting, respectively, the conical laser beam, the intermediate time ^^ଶof reaching a tangential position (“X”) at which the part of 7 of the particle is instantaneously parallel to the reference wavefront such that the rate of change ^^^^ / ^^^^ of the distance between the particle 4 and a reference wavefront 10 of the laser beam momentarily vanishes: P004737-GB01 15 Here, ^^′ is the part of the path 7 of the particle 4 extending between the point of entry of the particle into the conical laser beam, when at a distance ^^^from the laser resonator cavity 1A, and the tangential position. The quantity ^^′′, illustrated in Fig.4, is the part of the path 7 of the particle 4 extending between the point of exit of the particle from the conical laser beam, when at a distance ^^ଷfrom the laser resonator cavity 1A, and the tangential position. Consequently, the quantity ^^ is the full linear path length of the particle within the conical laser beam, such that: ^^ ൌ ^^′ ^ ^^′′One can see that: More generally, for a given instant in time, ^^, we may identify the angular position of the particle, relative to the central beam axis 8b as: Consequently, we may conclude that the rate of change of the distance between the particle 4 and a reference wavefront 10 of the laser beam (8a, 8b), measured in a direction perpendicular to the reference wavefront, is: Using the following known trigonometric relation: sin^^^ And defining Gives P004737-GB01 16 ^^ ^^ ^^ൌ tan^2െ ^^^ ൌ ^^Therefore ^^^^ ^^ ^^^^ ^^ ^^^^ൌ ^^ sin ^tanି^^^^^ ^ ି^2െ ^^^ ൌ ^ ^ି^^ ^^1 ^ ^^ଶ cos^ tan ^^ ^ ^^1 ^ ^^ଶ sin^tan ^^ ^Here Given the known trigonometric relation: ^sin^tanି^^^ cos ^^^^^ ൌ^1 ^ ^^ଶ We may write that: As discussed above, the response of the laser cavity of the interferometer can be expressed in the following terms: ^^^^^^^ ൌ ^^ ^ ^^ cos^^ி^ ^^ ^ ൌ ^^ ^ ^^ cos^^^^ ^ ^^ ି^^^^^ sin^^^ி^ ^ tan ^^^^However, when there is only a weak intensity in the light returned to the laser cavity from the particle the coefficient ^^ becomes negligible, and one may write: We may also define the phase ^^^as: Therefore, the laser interferometric signal becomes: P004737-GB01 17 In other words, the rate of change of the phase ^^^is equivalent to an instantaneous value of the frequency of the laser interferometric signal: It can be seen that this frequency, ^^^, is proportional to the speed, ^^, of the particle, as well as aspects of the geometry, ^^, of the laser beam and the orientation, ^^, of the path of the particle relative to the axis of the laser beam. Noting again that: we may use the above known trigonometric relation to express the term in square brackets as follows: Consequently, the signal frequency may be alternatively expressed succinctly as follows: Here: For conciseness, we may write the term ^^ as a simple algebraic function of time, ^^, as follows: ^^^ ^ ^^ ^^^^ ൌ ଶ^^ଷ ^ ^^ସ^^In this way, the term ^^ is a simple polynomial function of time. Here, the terms ^^^, ^^ଶ, ^^ଷ and ^^ସtake the following form: ^^^ ൌ ^^ ; ^^ ൌ ଶ െ ^^^ ^^ ଶ ଶ െ1 ; ^^ଷ ൌtan ^^ ^ ^^^^^ ; ^^ସ ൌ െ^^In the situation where the particle crosses the laser beam axis in a direction perpendicular to theaxis, then ^^ ൌ ^^ / 2 and ^^ ൌ 0, such that ^^ → ^^^ ൌ ^^^^ ^ ^^ଶ^^^ / ^^ଷ, and: P004737-GB01 18 ^^ ^^^^ ൌ4^^^^ ^^^ ; ^ ^^ଶ െ ^^^^ ^^ଶ ^ ^^ ൌ ^^^ ൨ tan ^^^1 ^ ^^ ଶ െ ^^^In the situation where the particle crosses the laser beam in a direction which forms a tangent toa wavefront of the laser beam at a point in time ^^ ൌ ^^ଶ whilst within the laser beam, then at thatpoint ^^^ ൌ 0, and ^^^^^^ ൌ ^^ଶ^ ൌ 0.In the situation where the particle progresses directly along the laser beam axis in a directionparallel to the axis, then ^^ ൌ 0 such that ^^ ൌ 0, and: Particles crossing the laser beam axis in directions between these two extremes will produce instantaneous values of the frequency of the laser interferometric signal between these two extremes: 0^ ^^4^^^^ ^^^^^ ^^^ Fig.5A shows an example of this waveform in the interferometric signal, ^^^^^^^, of the laser: ^^^^^^^ ൌ ^^ ^ ^^ cos^^^^^^ ^ ^^^^Here, Thus, Here, ^^, ^^, and ^^ are constants for a given particle trajectory within a given laser beam cone. In aspects of the invention, the processing module of the self-mixing interferometer may be configured to detect particulate material using an interferometric signal of this form, e.g., as disclosed herein. In this example, we have expanded the term ^^ as a polynomial function,assuming ^^ଶ ≪ 1, of time variable, ^^, including terms of order no higher than the second order.Fig. 5A shows this waveform in which ^^ ൌ 3, ^^ ൌ 1.5, ^^ ൌ െ1, ^^ ൌ 0 and ^^ ൌ 2. Fig. 5Bshows this waveform in which ^^ ൌ 3, ^^ ൌ 1.5, ^^ ൌ 4, ^^ ൌ െ6 and ^^ ൌ 2. P004737-GB01 19In Fig. 5A and Fig, 5B, the waveform is shown with the parameters ^^ ൌ 3 and ^^ ൌ 1.5. In thisway, the value of ^^ represents an amplitude of a modulation of the interferometric signal, ^^^^^^^,of the laser. The different values of ^^, ^^ and ^^ represent differences in the terms ^^^, ^^ଶ, ^^ଷ and ^^ସdefined above which, in turn are determined by the known divergence angle ^^ of the laser beam,the measurable times ^^^, ^^^ of the entry of the particle into the laser beam and the time at whichthe tangential position is momentarily achieved, and the angle ^^ of the particle path 7 relative to the central axis of the laser beam. As described above, the time at which the tangential position is momentarily achieved corresponds to a moment at which the frequency of the interferometric signal, ^^^^^^^, becomes zero. This is indicated by the turning point 21 of the waveform 20 of Fig. 5A and by the turning point 23 of the waveform 22 of Fig.5B.Because the values of ^^, ^^ and ^^ for Fig. 5B differ from the values of ^^, ^^ and ^^ for Fig. 5A, thenso do the respective positions of the turning points in the associates waveforms (20, 22). Similarly, the frequency each waveform changes continuously, and the frequency of the waveform in Fig.5B changes more rapidly than does the frequency of the waveform in Fig.5A.The shape and structure of the waveform is the result of the values of ^^, ^^ and ^^ which, in turnare the result of differences in the speed ^^ of the particle 4 within the laser beam and the angle ^^ its path 7 subtends to the central axis 8b of the laser beam.Note that the two different values of ^^ (i.e., ^^ ൌ െ1, and ^^ ൌ 4) may be considered tocorrespond to the interferometric signals associated with the particle trajectory crossing the optical wave 2 at a different axial location as shown schematically in Fig.6A. This is because the parameter ^^ is a constant phase term (i.e., time-independent) and instantaneous changes in its value correspond to instantaneous changes in phase of the interferometric signal waveform. Forexample, the value ^^ ൌ െ1 may be associated with a first optical phase and the value ^^ ൌ 4 maybe associated with a different optical phase. These differences, and other differences, in theshape and structure of the waveform, are the result of differences in the values of ^^, ^^ and ^^which, in turn are the result of differences in the speed ^^ of the particle 4 within the laser beam and the angle ^^ its path 7 subtends to the central axis 6b of the laser beam. Fig.6A and Fig.6B show, schematically two different but parallel paths of a particle through a laser beam (Fig.6A), and the resulting self-mixing interferometric signals (Fig.6B). The angle(^^ ൌ ^^ െ ^^ െ ^^) at which that the linear path of a particle (7 or 7’) approaches, and enters, theconical edge of the diverging beam 8a of laser light determines the frequency of the waveform ofthe interferometric signal generated by the laser interferometer 1 at that moment (^^ ൌ ^^^) in time.Similarly, the angle (^^ ൌ ^^ െ ^^) that the same path of a particle approaches, and exits, the P004737-GB01 20 opposite conical edge of the diverging beam 8a of laser light determines the frequency of the waveform of the interferometric signal generated by the laser interferometer at that subsequentmoment (^^ ൌ ^^ଷ) in time. The entry and exit angles are independent of the distance of thedistance of the particle from the laser interferometer at those times. Consequently, the frequency of the waveform of the interferometric signal at its beginning and at its end, corresponding to the moments of entry and exit, respectively, of the particle into the conical laser beam, are also independent of the distance of the distance of the particle from the laser interferometer. The frequencies present within the interferometric signal waveform (24, 25) shown in Fig.6B are determined by the rate at which a particle traverses successive wavefronts of the laser light that intersect the path (7, 7’) of the particle through the laser beam. One full wave cycle within the interferometric signal waveform is achieved upon the particle passing through two successive wavefronts of the laser light (i.e., two wavefronts separated by one wavelength of the laser light). Wavefronts, by definition, extend in a direction perpendicular to the direction of forward travel (i.e., the light ray direction) of the light wave. Consequently, a particle path subtending a given angle, ^^, of incidence to the light rays defining the bounding edges of the laser beam also subtend a related angle, ^^, relative to the wavefronts of the laser light at the bounding light ray(i.e., Fig. 6A: ^^ ൌ ^^ െ ^^). This related angle determines that initial rate at which the particle, ofa given speed, can traverses successive wavefronts of the laser light that intersect the path and, therefore, determined the initial frequency of the interferometric waveform. The same holds true for the exit angle subtended by the particle path relative to the bounding ray of the laser light beam. However, a closer particle 4’ traverses a shorter path 7’ through the conical beam, whereas a more distant particle 4 traverses a longer path within the conical beam. For a given speed ^^ of particle, the time taken to traverse the conical beam increases in proportion to an increase in the distance of the distance of the particle from the laser interferometer. For a given speed ^^ ofparticle, a more distant particle 4 has a path 7 that enters the cone of the laser beam at time: ^^ ൌ^^^, and exits the cone of the laser beam at time: ^^ ൌ ^^ଷ. At the intermediate time: ^^ ൌ ^^ଶ, the path7 become tangential to the wavefronts of the laser light signifying the closest approach of the particle to the laser resonator cavity of the interferometer. For the same given speed ^^ of particle,a nearer particle 4’ has a path 7’ that enters the cone of the laser beam at time: ^^ ൌ ^^′^, and exitsthe cone of the laser beam at time: ^^ ൌ ^^′ଷ. At the intermediate time: ^^ ൌ ^^′ଶ, the path 7’ become P004737-GB01 21 tangential to the wavefronts of the laser light signifying the closest approach of the particle to the laser resonator cavity of the interferometer. Each particle path crosses a number of curved wavefronts 10 of the laser light as that path (7, 7’) crosses the laser beam. Each wavefront crossing corresponds to a full wave cycle in the waveform (24, 25) of the interferometric signal generated by the laser interferometer. A particle path 7 twice as far from the laser cavity of the interferometer may generate twice as many wave cycles within the interferometric waveform as are produced in the interferometric waveform generated by the same laser interferometer by a particle following a parallel path at half the distance from the laser. For example, in the schematic diagram of Fig.6A, the more distant path 7 of the particle 4 is approximately (but not exactly) twice as far from the laser resonator cavity 1 as is the less distant path 7’ of the particle 4’. For this reason, the number of wave cycles in the waveform of the interferometric signal 24 corresponding to the more distant path 7 is approximately twice the number of cycles in the interferometric signal 25 corresponding to theless distant path 7’. Each waveform of these two interferometric signals starts (at ^^ ൌ or ^^ ൌ^^′^) with the same initial low frequency ^^^when the particle enters the conical laser beam,reduces in frequency to an intermediate minimum value ^^ ^ 0 (at ^^ ൌ ^^ଶ or ^^ ൌ ^^′ଶ) andsubsequently ends (at ^^ ൌ ^^ଷ or ^^ ൌ with some final high frequency ^^ଶ when the particleexits the beam. Thus, the interferometric signal waveform ‘chirps’ through a range offrequencies extending from ^^ ^ 0 to ^^ ൌ ^^ଶ, corresponding to a frequency bandwidth of ∆^^ ൌ^^ଶ. Notably, however, the modulation amplitude of the waveform corresponding to the amplitude term ^^ in the analytical expression: ^^^^^^^ ൌ ^^ ^ ^^ cos^^^^^^ ^ ^^^^in practice shows a systematic rise from a value ^^ ൌ 0 at time ^^ ൌ when the particle enters thelaser beam, to a peak value before subsequently decaying again to a value ^^ ൌ 0 at time ^^ ൌ ^^ଷ,when the particle exits the laser beam. In between these two time points, the particle reaches atangential position at time ^^ ൌ ^^ଶ when the frequency of the interferometric signal momentarilyfalls to zero: ^^^^^^ ൌ ^^ଶ^ ൌ 0. The rise and fall of the modulation amplitude ^^ is the result of thedistribution of laser light intensity across the laser beam, in which the greater intensity is within the central regions of the laser beam, and the light intensity of the laser beam falls to zero at the edge of the laser beam in a smooth fashion rather than in an instantaneous or abrupt ‘edge’ as has been assumed in the analytical expression shown in Fig.5A and Fig.5B. When in regions of greater light intensity, the optical coupling between the light within the laser resonator cavity and P004737-GB01 22 the light re-injected into the laser resonator cavity as reflected / scattered from the particle, is greater and this results in a greater modulation amplitude ^^. This enables one to identify thetimes ^^ ൌ ^^^, and ^^ ൌ ^^ଷ as those times when the interferometric signal 34 begins and ends. Thetime ^^ ൌ ^^ଶ can also be identified as the time when the frequency of the interferometric signalmomentarily falls to zero: ^^^^^^ ൌ ^^ଶ^ ൌ 0.Figure 7 shows a cross sectional view of an example of a part of a self-mixing interferometer assembly 150 comprising a laser cavity 1A in optical communication with and an optical assembly 1B, together forming a part of the self-mixing interferometer schematically illustrated in Figure 2A, and configured to generate a beam of laser light comprising curved optical wavefronts for bathing a monitored region 37 of space. The optical assembly comprises a spherical lens 32, and the laser cavity comprises a solid-state laser 30 (e.g., a laser diode). Each is housed within a common housing in optical communication such that laser light output by the laser 30 is formed, by the spherical lens, into a focussed beam of laser light 34 configured to converge to, and subsequently diverge from, an optical focal point 36 within the monitored region of space 37. The focal region of the laser beam comprises a convergent cone of light 40 immediately before the optical focal point and forms a divergent cone of light 42 immediately after the optical focal point. Each cone of light has a divergence angle of ^^ relative to the laser beam axis 8b and each is an example of (or equivalent to) the divergent laser beam described herein with reference to figures 2A, 2B, 3, 4 and 6A. Figure 8A shows a schematic diagram of the focal region of the laser beam when the angle, ^^, subtended between the axis of the laser beam 8b and the path 7 of the particle crossing the beam is ^^ = 75 degrees. The resulting self-mixing interferometer signal 44 generated by the self- mixing interferometer is shown in Figure 8B. This illustrates a waveform of the nature described herein with reference to figures 5A, 5B and 6B, which follows the form: ^^^^^^^ ൌ ^^ ^ ^^ cos^^^^^^ ^ ^^^^The waveform shown in Figure 8B displays a ‘chirp’ of the type discussed in relation to figures 5A, 5B and 6B and additionally displays an amplitude modulation (i.e., a modulation of the amplitude term ^^ in the above expression). This amplitude modulation is Gaussian-like in nature and follows the Gaussian-like shape of the cross-sectional intensity profile of the laser beam as experienced by the particle along its path 7 through the beam. Figure 8C illustrates the application of a signal processing step applied to a section of the self-mixing interferometer signal 44 of about 430µs duration extending from a section start time 46 (see Figure 8B) preceding the Gaussian-like amplitude peak of the signal 44, to an end time 48 succeeding the P004737-GB01 23 Gaussian amplitude peak of the signal. The signal processing step comprises identifying successive time-points 52 at which amplitude modulation term ^^ of the self-mixinginterferometer signal ^^^^^^^ (item 44) vanishes (^^ ൌ 0) as it transitions from a positive value to anegative value, or as it transitions from a negative value to a positive value. In this sense, the time-points 52 each correspond to a “zero-crossing” point of the self-mixing interferometer signal. In the example shown in Figure 8C, purely for ease of illustration, the self-mixing interferometer signal ^^^^^^^follows the following expression, which is discussed in detailelsewhere herein, with the term ^^ set to a value ^^ ൌ 0:^^^^^^^ ൌ ^^ ^ ^^ cos^^^^^^ ^ ^^^^Thus each “zero-crossing” point of the self-mixing interferometer signal also coincides with atime-point at which the interferometer signal as a whole vanishes, such that ^^^^^^^ ൌ 0 as ittransitions from a positive value to a negative value, or as it transitions from a negative value to apositive value. It is to be understood that the value of the term ^^ need not be set to a value ^^ ൌ0, and may be non-zero (finite) in value. Figure 9A shows a schematic diagram of the focal region of the laser beam when the angle, ^^, subtended between the axis of the laser beam 8b and the path 7 of the particle crossing the beam is ^^ = 60 degrees. The resulting self-mixing interferometer signal 54 generated by the self- mixing interferometer is shown in Figure 9B. This again illustrates a waveform of the nature described herein with reference to figures 5A, 5B and 6B, which follows the form: ^^^^^^^ ൌ ^^ ^ ^^ cos^^^^^^ ^ ^^^^The waveform shown in Figure 9B also displays a ‘chirp’ of the type discussed in relation to figures 5A, 5B and 6B and once more displays the Gaussian-like amplitude modulation (i.e., a modulation of the amplitude term ^^ in the above expression) corresponding to the shape of the cross-sectional intensity profile of the diverging cone region 42 of the laser beam 34 as experienced by the particle along its path 7 through the beam. Figure 9C illustrates the application of the aforementioned signal processing step applied to a section of the self-mixing interferometer signal 54 of about 400µs duration extending from a section start time 56 (see Figure 9B) preceding the Gaussian-like amplitude peak of the signal 54, to an end time 58 succeeding the Gaussian-like amplitude peak of the signal. As discussed above, the signal processing step comprises identifying successive time-points 62 at which amplitude modulationterm ^^ of the self-mixing interferometer signal ^^^^^^^ (item 54) vanishes (^^ ൌ 0) as it transitionsfrom a positive value to a negative value, or as it transitions from a negative value to a positive value. In this sense, the time-points 62 once more each correspond to a “zero-crossing” point of P004737-GB01 24 the self-mixing interferometer signal. In the example shown in Figure 9C, as in Figure 8C and purely for ease of illustration, the self-mixing interferometer signal ^^^^^^^follows the followingexpression with the term ^^ set to a value ^^ ൌ 0:^^^^^^^ ൌ ^^ ^ ^^ cos^^^^^^ ^ ^^^^Thus each “zero-crossing” point of the self-mixing interferometer signal 54 also coincides with atime-point at which the interferometer signal as a whole vanishes, such that ^^^^^^^ ൌ 0 as ittransitions from a positive value to a negative value, or as it transitions from a negative value to a positive value. Again, as noted before, it is to be understood that the value of the term ^^ need notbe set to a value ^^ ൌ 0, and may be non-zero (finite) in value.Comparing the interferometer signal waveform 54 of Figure 9B to the interferometer signal waveform 44 of Figure 8B, one can see a clear increase in the oscillation frequency ^^^of the waveform which, as noted above, has the form: Here, as noted above, the parameter ^^ is a function of ^^, the angle subtended between the axis of the laser beam 8b and the path 7 of the particle crossing the beam. In the scenario of figures 8A,8B and 8C, ^^ ൌ 75 degrees, whereas in the scenario of figures 9A, 9B and 9C, ^^ ൌ 60 degrees.Figure 10A shows another schematic diagram of the focal region of the laser beam when the angle, ^^, subtended between the axis of the laser beam 8b and the path 7 of the particle crossing the beam is ^^ = 41 degrees. The resulting self-mixing interferometer signal 64 generated by the self-mixing interferometer is shown in Figure 10B. This once more illustrates a waveform of the nature described herein with reference to figures 5A, 5B and 6B, which follows the form: ^^^^^^^ ൌ ^^ ^ ^^ cos^^^^^^ ^ ^^^^The waveform shown in Figure 10B also displays a ‘chirp’ of the type discussed in relation to figures 5A, 5B and 6B and once more displays the Gaussian-like amplitude modulation (i.e., a modulation of the amplitude term ^^ in the above expression) corresponding to the shape of the cross-sectional intensity profile of the diverging cone region 42 of the laser beam 34 as experienced by the particle along its path 7 through the beam. Figure 10C illustrates the application of the aforementioned signal processing step applied to a section of the self-mixing interferometer signal 64 of about 560µs duration extending from a section start time 66 (see Figure 10B) preceding the Gaussian-like amplitude peak of the signal 64, to an end time 68 succeeding the Gaussian-like amplitude peak of the signal. As discussed above, the signal P004737-GB01 25 processing step comprises identifying successive time-points 70 at which amplitude modulationterm ^^ of the self-mixing interferometer signal ^^^^^^^ (item 64) vanishes (^^ ൌ 0) as it transitionsfrom a positive value to a negative value, or as it transitions from a negative value to a positive value. In this sense, the time-points 62 once more each correspond to a “zero-crossing” point of the self-mixing interferometer signal. In the example shown in Figure 10C, as in figures 9C and 8C and purely for ease of illustration, the self-mixing interferometer signal ^^^^^^^follows thefollowing expression with the term ^^ set to a value ^^ ൌ 0:^^^^^^^ ൌ ^^ ^ ^^ cos^^^^^^ ^ ^^^^Thus each “zero-crossing” point of the self-mixing interferometer signal 64 also coincides with atime-point at which the interferometer signal as a whole vanishes, such that ^^^^^^^ ൌ 0 as ittransitions from a positive value to a negative value, or as it transitions from a negative value to a positive value. Again, as noted before, it is to be understood that the value of the term ^^ need notbe set to a value ^^ ൌ 0, and may be non-zero (finite) in value.Comparing the interferometer signal waveform 64 of Figure 10B to the interferometer signal waveform 54 of Figure 9B, one can see a clear increase in the oscillation frequency ^^^of the waveform which, as noted above, has the form: Here, as noted above, the parameter ^^ is a function of ^^, the angle subtended between the axis of the laser beam 8b and the path 7 of the particle crossing the beam. In the scenario of figures 9A,9B and 9C, ^^ ൌ 60 degrees, whereas in the scenario of figures 10A, 10B and 10C, ^^ ൌ 41degrees. It is to be noted that in the scenarios discussed above with reference to figures 8A, 9A and 10A, the divergence angle ^^ of the laser beam cone 42 through which the particle path 7 passes remains unchanged in each scenario. Furthermore, consider reversing the direction of the particle path 7 so that it is directed anti-parallel (i.e., parallel but in the opposite direction) to the path 7 shown in figures 8A, 9A and 10A, and consider axially shifting the reversed particle path towards and below the focal point 36 of the beam such that the shifted, reversed particle path now enters the laser beam at the converging cone 40 of the beam at an entry point that is the same distance from the focal point 36 as the entry point at which the original particle path 7 (illustrated) enters the diverging cone 42 of the laser beam. Due to the symmetry of the laser beam either side of the focal point 36 of the beam, the corresponding self-mixing interferometer signal ^^^^^^^, in each scenario, will be the same as shown in figures 8B, 9B and 10B. Thus, both P004737-GB01 26 the diverging cone 42 and the converging cone 40 act to detect particles within the region of space where they reside. In the situation where the particle path 7 passes directly along the laser beam axis 8b in a direction parallel to the axis, such that the path crosses all optical wavefronts 10 at a right-angle,then ^^ ൌ 0 and ^^ ൌ 0, then: Conversely, in the situation where the particle path 7 crosses the laser beam axis 8b in a directionwhich forms a tangent to a wavefront of the laser beam momentarily at a point in time ^^ ൌ ^^ଶ,such that the path is parallel to the wavefront 10 at that point, then momentarily at that point intime ^^ ൌ ^^ଶ: ^^ ൌ 0, and ^^^^^^ ൌ ^^ଶ^ ൌ 0. Particles crossing the laser beam axis, i.e., in directionsother than parallel to the laser beam axis, will produce instantaneous values of the frequency of the laser interferometric signal between these two extremes: 4^^^^ 0^ ^^^^^^^ ^^^ The inventors have discovered that the fractional bandwidth, of the range instantaneous frequencies contained within the ‘chirped’ interferometric signal is closely correlated to the cosine of the of ^^, the angle subtended between the axis of the laser beam 8b and the path 7 of the particle crossing the beam, such that: ^^^^^^^^^^^^^^^^^^^^^ ൌ ^^ ∙ cos^^^^ ^ ^^Here, ^^ is a constant of proportionality and ^^ is a constant. The fractional bandwidth is defined as: Here, is the highest frequency component present within the self-mixing signal, and^is the lowest frequency component present within the self-mixing interferometer signal. Figure 11 shows this relationship as revealed from computer simulations performed by the inventors. Here, simulation results are shown in which the value of the cosine, cos^^^^, of the angle, ^^, subtended between the axis of a simulated laser beam 8b and the simulated path 7 of the particle crossing the beam. This is identified in the horizontal graph axis as “cosine (angle)”, P004737-GB01 27 and is plotted against the logarithm (base 10) of the values of the fractional frequency bandwidth, ^^^^^^^^^^^, of the resulting simulated self-mixing interferometer signal ^^^^^^^for twovalues of particle rectilinear velocity, ^^, which are: ^^ ൌ 0.1^^ / ^^ and ^^ ൌ 0.3^^ / ^^.Figure 12 also shows experimental results including the value of the cosine, cos^^^^, of the angle, ^^, subtended between the axis of a real laser beam 8b and the real path 7 of the particle crossing the beam. Particles were entrained within a flow of air directed along the longitudinal axis of a linear air flow duct, such that the particle paths were parallel to the longitudinal axis of a linear air flow duct. The axis of a laser beam 8b from a self-mixing interferometer was directed across the longitudinal axis of a linear air flow duct, and the particle paths, 7, therein. The orientation of the laser beam axis was varied to vary the angle, ^^, subtended between the axis of a laser beam 8b and the paths 7 of the particles crossing the beam. The value of the cosine, cos^^^^, of the angle, ^^, was calculated. This is, again, identified in the horizontal graph axis as “cosine (angle)”, and is plotted against the logarithm (base 10) of the values of the fractional frequency bandwidth, ^^^^^^^^^^^, of the measured self-mixing interferometer signal ^^^^^^^caused by laser light scattered, and returned, by the particles for one common value of particle rectilinear velocity, ^^, which was controlled in the experiment by maintaining a fixed flow velocity of air within which particles were entrained. The experimental results show a high degree of linearity as between the fractional frequency bandwidth, ^^^^^^^^^^^, and the value of the cosine, cos^^^^, of the angle, ^^, subtended verifying the above relation. The relationship is revealed from direct experimental measurements performed by the inventors. The inventors have also found that the component, ^^∥, of the velocity resolved in a direction parallel to the laser beam axis 8b of a particle passing through a divergent (or convergent) cone of a laser beam of a self-mixing interferometer may be estimated accurately according to the following relation: ^^∥ ൌ ^^ ∙ 〈^^〉Here, the quantity〈^^^〉is the mean frequency of the amongst of the frequencies present within a ‘chirped’ self-mixing interferometer signal. Here, ^^ is a constant of proportionality. The component, ^^∥, of the velocity of a particle crossing the laser beam 8b on a path 7 subtending an angle ^^ with the axis of the laser beam, is related to the particle velocity ^^ according to the relation: ^^∥ ൌ ^^ ∙ cos^^^^ P004737-GB01 28 Thus, the inventors have discovered that it is possible to calculate an accurate estimate of the particle velocity using the mean frequency, 〈^^^〉, and the fractional bandwidth ^^ఠ^^^^^^^^^ of the frequency components present within the ‘chirped’ self-mixing interferometer signal, as follows: Particle Concentration Having obtained an estimate of the speed ^^ of a particle, according to any technique disclosed herein, it is possible to generate an estimate of the concentration of detected particles within the region bathed by the laser light of the self-mixing interferometer(s) in question. Consider volume^^ ൌ ^^^^ of space defined by a plane area ^^ swept through a linear distance ^^. If this volume ofspace contains ^^ particles then the particle concentration, ^^, is defined as: Now consider that the plane area ^^ is swept through the linear distance ^^ due to a uniform flow of a gas at an average speed〈^^〉within which the particles are entrained and possess the sameaverage speed such that 〈^^〉 ൌ ^^. If the average separation, in the direction of the flow of gas,between successive particles within this gas flow is ∆^^, then: In other words, for a segment of the volume ^^ defined as ∆^^ ൌ ^^∆^^, one particle is present onaverage. This means that a self-mixing interferometer configured to detect the presence of a particle in the region of volume ∆^^ will detect one particle. Thus, over an interval of time Δ^^, theself-mixing interferometer may detect ൌ ^^Δ^^⁄ ∆^^ separate particles, successively.Substituting for ∆^^ reveals that the particle concentration may be determined from the averagerate, ^^ ൌ ^^^௧⁄ Δ^^ , of particle detection events as follows: Here, is the number of particle detection events occurring at the self-mixing laser interferometer device over a period of time Δ^^, ^^ is the projected area of the effective detection region of the laser beam of the interferometer in a direction perpendicular to the average direction of flow of gas within which the detected particles were entrained, and ^^ is the speed (e.g., averaged across the measured speeds of the detected population of particles) of detected P004737-GB01 29 particles within that flow. In aspects of the invention, the processing module of the self-mixing interferometer may be configured to determine a value of particle concentration accordingly, e.g., as disclosed herein. As expected, for a given particle concentration ^^, an increase in the average speed of detected particles results in a proportional increase in the number of detected particles within the period of time Δ^^. The average direction of gas flow may be determined according to a technique disclosed herein. The cross-sectional area ^^ of the volume ^^ of the region of space that the self-mixing interferometer configured to detect particles, may be determined from the known geometry and configuration of the laser beam of the interferometer. The average rate, ^^, of particle detectionmay be determined by calculating the quantity: ^^ ൌ ^^^௧⁄ Δ^^ . This may be done in a continuouslyupdating manner such that: ^^ ൌ ^^^^^^⁄ ^^^ െ ^^^^Here, ^^^^^^ is the cumulative number of particles detected, or the cumulative number of individual particle detection events, at a time ^^ measured continuously from a starting time of^^ ൌ ^^^. In aspects of the invention, the processing module of the self-mixing interferometer maybe configured to determine a value of particle detection rate accordingly, e.g., as disclosed herein. Figure 13 shows a self-mixing interferometer apparatus configured to monitor particulate material within a monitored region of space for determining a velocity, ^^, and a concentration, ^^, of particles detected within the monitored volume of space. The apparatus comprises an SMI module 80 including a laser cavity assembly (laser diode 88) and associated optical assembly 81 configured to bathe the monitored region with laser light of the interferometer possessing one or more optical wavefront(s) defined by an optical wave configured by the optical assembly such that at separate locations within the monitored region the one or more optical wavefront(s) comprises different respective orientations relative to the optical assembly. A laser monitoring unit (photodiode 90) is configured to acquire an interferometric signal of theform: ^^^^^^^ ൌ ^^ ^ ^^ cos^^^^^^ ^ ^^^^ as generated by the interferometer in response to lightreturned to the laser cavity assembly from the one or more optical wavefronts by particles within the monitored region. The acquired signal is initially received by a trans-impedance amplifier 82 P004737-GB01 30 configured to amplify the raw self-mixing interferometer signal to provide an amplified signal 84 in which background signals are suppressed. For example, this has the effect of setting the term^^ ൌ 0 in the signal to provide:^^^^^^^ ൌ ^^ cos^^^^^^ ^ ^^^^A processing module is configured to detect the presence of particles within the monitored region on condition that a frequency, ^^^, of the chirped waveform of the interferometric signal is less than a pre-set threshold frequency value. If a particle is detected, in this lower-frequency regime, then processing module subsequently determines a velocity, ^^, and a concentration, ^^, of particles detected within the monitored volume of space, according to changes in the frequency of the chirped waveform of the interferometric signal on condition that the frequency, ^^^, of the chirped waveform is greater than the pre-set threshold frequency value. The processing module comprises a signal processor unit 86 configured to process the interferometric signal according to a first processor clock speed to detect the presence of particles, and to process the interferometric signal according to a second processor clock speed subsequently to determine a velocity, ^^, and a concentration, ^^, of particles detected within the monitored volume of space. Notably, the second processor clock speed exceeds the first processor clock speed. In other words, the processing module monitors the self-mixing interferometer output signal to look for the low-frequency part of the signal ‘chirp’ as a flag to indicate that a particle has entered the optical field. It operates at a slower processor clock speed during this phase. Once particle detection happens, the processor operates at a higher processor clock speed and processes the high-frequency part of the signal ‘chirp’ to calculate particle speed and, from that, estimate particle concentration in the monitored region. This saves energy, using power-hungry high clock speed only when needed. The processing module is configured, in response to a cessation of the waveform in the interferometric signal, to cease processing the interferometric signal according to the second processor clock speed and to revert to processing the interferometric signal according to the first processor clock speed. The processing module determines a fractional frequency bandwidth, of the spectrum of frequencies present in the “chirped” waveform 84 of the interferometric signal, and also determines an average frequency, 〈^^〉, of the waveform of the interferometric signal. Using P004737-GB01 31 these quantities, as disclosed above, the processing module determines an estimated speed, ^^, of the detected particles, according to a ratio of the average frequency and the fractional frequency bandwidth according to the following relation: The fractional frequency bandwidth is defined as: In order to determine a frequency component of the chirped interferometric signal waveform, theprocessing module determines a plurality of successive time points, ^^^ ∶ ^^ ൌ 1, 2, 3, …, (e.g.,Fig.8C, items 52) at which a signal polarity in the waveform of the interferometric signal changes. The processing module determines a frequency of the waveform of the interferometric signal according to the plurality of successive time points so determined, by calculating adifference, Δ^^^ ൌ ^^^ା^ െ ∶ ^^^^^^ ^^, between any two successive such time-points, and invertingthe result to give a value for the ithfrequency component so calculated, and from that calculating the ithfrequency component as: The time points, ^^^, each correspond to a zero-crossing of the waveform of the interferometric signal coincident with a sign-change of a value of the waveform of the interferometric signal. Because a full wave cycle will consist of two successive zero-crossings, the differenceΔ^^^ ൌ ^^^ା^ െ ^^^ represents the time interval to complete one half-cycle of the waveform and so afrequency calculated by inverting this value approximates twice the value of the ithfrequency component. In alternative examples, the processing module may determine a frequency of the waveform of the interferometric signal according to the plurality of successive time points sodetermined, by calculating a difference, Δ^^^ప ൌ ^^^ାଶ െ ∶ ^^^^^^ ^^, between any time-point and thesecond successive time point following it, corresponding to completion of one cycle of the waveform, and inverting the result to give a value for the ithfrequency component so calculated, and from that calculating the ithfrequency component as: Figure 14 shows a flow diagram of signal processing steps performed by the processing module as it determines a velocity, ^^, and a concentration, ^^, of particles detected within the monitored volume of space. P004737-GB01 32 In a first step, S1, the processing module determines the shortest time difference, Δ^^^ௌ, and the longest time difference, Δ^^^^, and from the result calculates the fractional frequency bandwidth,^^ఠ^^^^^^^^^, according to: In alternative examples, as noted above: In a second step S2, the processing module uses the calibration function: ^^^^^^^^^^^^^^^^^^^^^ ൌ ^^ ∙ cos^^^^ ^ ^^to obtain an estimate of the cosine of the angle, cos^^^^, between the axis of the laser and the airflow carrying the particles. In a third step S3, the processing module calculates the average, 〈Δ^^^〉, of the time difference values, Δ^^^, and calculates from the inverse of that average the mean frequency,〈^^〉, of the chirp signal, then calculates the speed, ^^, of the flow detected particles from the cosine angle, cos^^^^,and the average,〈^^〉, of the mean frequency as follows: In alternative examples, as noted above: In a fourth step, S4, the processing module uses the speed of the flow, ^^, and a rate of detection of particles, ^^, to calculate the particle concentration, ^^, over the monitoring time interval passing through an area ^^ of the monitored volume: ^^ ൌ^^ ^^^^ Turning to Figure 13 again in more detail, this shows a self-mixing interferometer 1 configured to monitor particulate material within a monitored region of space, and includes a transducer portion comprising a self-mixing interferometry (SMI) module 80 containing an optical assembly 81, a laser diode 88 comprising a laser resonator cavity assembly and containing a photodiode 90 configured to measure the optical power of a small portion of light sampled from the laser resonator cavity and therefrom to produce an electrical signal which is input to a transimpedance amplifier 82 configured to amplify the electrical signal so as to produce a self- P004737-GB01 33 mixing interferometer signal 84 for output. The self-mixing interferometer signal 84 thereby gives a measure of variations in optical power in the laser resonator cavity are thereby monitored using the photodiode 90. The self-mixing interferometry (SMI) module 80 also comprises an optical assembly 81 configured to bathe the monitored region with laser light of the interferometer possessing one or more optical wavefront(s) defined by an optical wave configured by the optical assembly, as is described in detail above, such that at separate locations within the monitored region the one or more optical wavefront(s) comprises different respective orientations relative to the optical assembly. The self-mixing interferometer 1 further comprises a laser monitoring unit comprising an analogue front-end portion (denoted “AFE” in Fig.13) and analogue-to-digital converter portion (denoted “A / D Conversion” in Fig.13) configured to acquire the interferometric signal 84 generated by the self-mixing interferometry (SMI) module 80 in response to light returned to the laser cavity assembly of the laser diode 88 from the one or more optical wavefronts by the particulate material. A signal processor module 86 (denoted “Digital interface” in Fig.13) is configured to detect the presence of particulate material within the monitored region on condition that a frequency of a waveform of the interferometric signal 84 is less than a pre-set threshold frequency value 103 and subsequently to determine a velocity and concentration of the detected particulate material according to changes in the frequency of the waveform of the interferometric signal 84 on condition that the frequency is greater than the pre-set threshold frequency value 103. The signal processor module 86 is configured to process the interferometric signal 84 according to a slower processor clock speed to detect the presence of particulate material, and to process the interferometric signal according to a faster second processor clock speed subsequently to determine a velocity and concentration of the detected particulate material. The faster processor clock speed exceeds the slower processor clock speed. In response to detection of the presence of particulate material within the monitored region, the signal processor module 86 is configured to cease processing the interferometric signal according to the slower processor clock speed, and to commence processing the interferometric signal according to the faster processor clock speed. In addition, in response to a cessation of the waveform in the interferometric signal, the signal processor module 86 is configured to cease processing the interferometric signal according to the faster processor clock speed and to revert to processing the interferometric signal according to the slower processor clock speed. P004737-GB01 34 Referring to Fig.13 in more detail, the interferometric signal immediately output by the photodiode 90 of the self-mixing interferometry (SMI) module 80 is feed to the Analogue Front- End (AFE) which is subdivided into the following parts: (a) The transimpedance amplifier (TIA) stage, 82, operating at an operating frequency lying within a bandwidth (e.g., a frequency a bandwidth of between about 1kHz and about 20MHz) that is matched to the frequency of the interferometric signal from the SMI optical unit 80. (b) A “slower” signal processing branch 87 of the analogue signal output of the transimpedance amplifier 82 configured to input the amplified interferometric signal 84 output by the transimpedance amplifier (TIA) stage, 82, as an input to a signal processor stage (98, 100, 109) configured to process the received signal at a relatively slower processor clock speed. The “slower” signal processor stage is comprised of a signal rectification unit 98 configured to rectify the received interferometric signal 84, followed by a low pass filter unit, 100, configured to receive the rectified signal and low-pass filter it. The low pass filter unit, 100, is configured to transmit frequency components of the received rectified signal that have a frequency, ^^, below a pre-set threshold frequency 103. The resulting transmitted signal defines an envelope signal 104. (c) The “slower” signal processor stage also includes a “slower” comparator unit 109 configured to receive the envelope signal 104 output by the low pass filter unit, 100, and to compare the envelope signal to a pre-set event threshold value 111 and to output the result of the comparison to a polarity detection unit 113. If the comparator finds that the value of the envelope signal exceeds the event threshold value 111, then it outputs a digital value of “1” (one). Otherwise, if the comparator finds that the value of the envelope signal does not exceed the event threshold value 111, then it outputs a digital value of “0” (zero). In this way, the “slow” comparator provides a digital output of an event detection circuit, whereby a particle detection “event” is heralded by the output of a digital value of “1” (one). As noted above, low frequency components are present in a self-mixing interferometry signal when a particle initially enters a divergent laser beam in a direction crossing the beam axis, and these components are replaced by ever-higher frequency components as the particle progresses through the laser beam and the “chirp” of the self-mixing interferometry signal rises in frequency. (d) A “faster” branch 85 of the analogue signal output of the transimpedance amplifier 82 configured to input the amplified interferometric signal 84 output by the transimpedance amplifier (TIA) stage, 82, as an input to a high pass filter unit 96 with a pre-set cut-off frequency 103 which is larger than the lowest frequency components within the waveform of the interferometric signal 84 (e.g., a cut-off frequency exceeding about 1kHz and optionally not exceeding about 20MHz). P004737-GB01 35 (e) The “faster” signal processor branch also includes a “faster” comparator unit 106 configured to receive the signal 102 output by the high-pass filter unit, 96, and to compare the signal to a pre-set threshold value of zero (0) and to output a digital value of “1” (one) if the result of the comparison indicates that the value of the signal exceeds the pre-set threshold (i.e., it is positive in value). Otherwise, if the comparator finds that the result of the comparison indicates that the value of the signal is less than the pre-set threshold (i.e., it is negative in value), then it outputs a digital value of “0” (zero). In this way, the “faster” comparator provides a digital output signal 112 that alternates between a value of “0” (zero) and “1” (one) with a frequency according to the frequency of the “chirp” in the interferometric signal 84. Both the two comparator signals (from the “slower” comparator 109 and from the “faster” comparator 106) are each passed to the following stages for the Digital Interface 86. In the Digital Interface the following units are provided: (f) A polarity detection unit 113, which is configured to receive the signal output by the “slower” comparator 109 and to complete the event detection process by producing one of the following two signal types, namely: a. a “wake-up” signal 114 for input to an activation unit 120 if the signal received from the “slower” comparator 109 comprises a digital value of “1” (one). The activation unit is responsive to the “wake-up” signal 114 by activating a “faster” clock speed for the signal processing operations by a “faster” processing unit 126 configured to determine a plurality of successive time points, ^^^ ∶ ^^ ൌ 1, 2, 3, …,for each “zero-crossing” time in the sequence of “zero-crossing” times, and to calculate a value of a particle velocity, ^^, and of particle concentration, ^^, using those time points, as described above; or, b. a “stop” signal 116 if the signal received from the “slower” comparator 109 comprises a digital value of “0” (zero). The “faster” processing unit 126 is responsive to the “stop” signal 114 by ceasing its signal processing operations These two signal types are used by a Finite State Machine (FSM) to toggle between a “sleep” state and an “active” state. The “sleep” state is running in a “slower” clock speed for the signal processing operations while the “active” state is running in a “faster” clock speed for the signal processing operations. In this example, the operation performed in the “faster” clock speed is the creation of the “zero- crossing” signal 112 by the “faster” comparator 106, and the subsequent processing of that signalto determine a plurality of successive time points, ∶ ^^ ൌ 1, 2, 3, …, for each “zero-crossing”time in the sequence of “zero-crossing” times, and the storage of those time points in a “fast storage” memory unit 128. P004737-GB01 36 A cross clock unit 122 provides access to the “fast storage” memory unit 128 across the two clock-speed domains and permits to transmit the “zero-crossing” time records, acquired during the active state, during the sleep state. The statistical distribution of time points contains information related to the frequency of crossing wavefronts oriented in different directions in different points of the paths of particles inside the laser beam. As described above, this information enables one to determine velocities and concentrations of the particles. However, such extraction of information is resource intense. Hence, there is a switch between a fast processor clock speeds (upon a particle detection event) and a slower clock (when in sleep mode) so that resources are not overly drained when not determining a sequence of “zero-crossing” times. This is particularly useful for low-powered devices such as wearables devices, watches, headphones, etc. It is to be noted that the power consumption of digital electronic devices is proportional to the clock frequency, the number of gates (capacitance) that the clock controls and the technology node used in the fabrication. The invention includes the combination of the aspects and preferred features described except where such a combination is clearly impermissible or expressly avoided. The features disclosed in the foregoing description, or in the following claims, or in the accompanying drawings, expressed in their specific forms or in terms of a means for performing the disclosed function, or a method or process for obtaining the disclosed results, as appropriate, may, separately, or in any combination of such features, be utilised for realising the invention in diverse forms thereof. While the invention has been described in conjunction with the exemplary embodiments described above, many equivalent modifications and variations will be apparent to those skilled in the art when given this disclosure. Accordingly, the exemplary embodiments of the invention set forth above are considered to be illustrative and not limiting. Various changes to the described embodiments may be made without departing from the spirit and scope of the invention. For the avoidance of any doubt, any theoretical explanations provided herein are provided for the purposes of improving the understanding of a reader. The inventors do not wish to be bound by any of these theoretical explanations. Any section headings used herein are for organizational purposes only and are not to be construed as limiting the subject matter described. Throughout this specification, including the claims which follow, unless the context requires otherwise, the word “comprise” and “include”, and variations such as “comprises”, “comprising”, and “including” will be understood to imply the inclusion of a stated integer or P004737-GB01 37 step or group of integers or steps but not the exclusion of any other integer or step or group of integers or steps. It must be noted that, as used in the specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another embodiment includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by the use of the antecedent “about,” it will be understood that the particular value forms another embodiment. The term “about” in relation to a numerical value is optional and means for example + / - 10%.

Claims

P004737-GB01 38 CLAIMS 1. A self-mixing interferometer configured to monitor particulate material within a monitored region of space comprising: a laser cavity assembly; an optical assembly configured to bathe the monitored region with laser light of the interferometer possessing one or more optical wavefront(s) defined by an optical wave configured by the optical assembly such that at separate locations within the monitored region the one or more optical wavefront(s) comprises different respective orientations relative to the optical assembly; a laser monitoring unit configured to acquire an interferometric signal generated by the interferometer in response to light returned to the laser cavity assembly from said one or more optical wavefronts by said particulate material; a processing module configured to detect the presence of particulate material within the monitored region on condition that a frequency of a waveform of the interferometric signal is less than a pre-set threshold frequency value and subsequently to determine a property of the detected particulate material according to changes in the frequency of the waveform of the interferometric signal on condition that the frequency is greater than the pre-set threshold frequency value.

2. The self-mixing interferometer according to any preceding claim wherein the processing module comprises a signal processor unit configured to process the interferometric signal according to a first processor clock speed to detect the presence of particulate material, and to process the interferometric signal according to a second processor clock speed subsequently to determine said property of the detected particulate material, wherein the second processor clock speed exceeds the first processor clock speed.

3. The self-mixing interferometer according to claim 2 wherein the processing module is configured, in response to detection of the presence of particulate material within the monitored region, to cease processing the interferometric signal according to the firstP004737-GB01 39 processor clock speed, and to commence processing the interferometric signal according to the second processor clock speed.

4. The self-mixing interferometer according to claim 2 or claim 3 wherein the processing module is configured, in response to a cessation of the waveform in the interferometric signal, to cease processing the interferometric signal according to the second processor clock speed and to revert to processing the interferometric signal according to the first processor clock speed.

5. The self-mixing interferometer according to any preceding claim wherein the processing module is configured to determine a frequency bandwidth corresponding to said changes in the frequency of the waveform of the interferometric signal, to determine an average frequency of the waveform of the interferometric signal, and to determine an estimated speed of the detected particulate material as said property of the detected particulate material, according to a ratio of the average frequency and the frequency bandwidth.

6. The self-mixing interferometer according to claim 5 wherein the frequency bandwidth comprises a fractional bandwidth corresponding to said changes in the frequency of the waveform of the interferometric signal.

7. The self-mixing interferometer according to any of claims 5 or 6 wherein the processing module is configured to determine a concentration of the particulate material according to the value of the estimated speed of the detected particulate material within the monitored region, a cross sectional area of the monitored region, and a rate of detection of the presence of particulate material within the monitored region.

8. The self-mixing interferometer according to any preceding claim wherein the processing module is configured to determine a plurality of successive time points at which a signal polarity in the waveform of the interferometric signal changes, and to determine a frequency of the waveform of the interferometric signal according to the plurality of successive time points so determined.

9. The self-mixing interferometer according to claim 8 wherein each said time point corresponds to a zero-crossing of the waveform of the interferometric signal coincident withP004737-GB01 40 a sign-change of a value of the waveform of the interferometric signal, and the processing module is configured to determine a zero-crossing rate (ZCR) and therewith to determine a frequency of the waveform of the interferometric signal.

10. A method for self-mixing interferometry for monitoring particulate material within a monitored region of space comprising: providing a self-mixing interferometer comprising a laser cavity assembly and an optical assembly; bathing the monitored region with laser light of the interferometer possessing one or more optical wavefront(s) defined by an optical wave configured by the optical assembly such that at separate locations within the monitored region the one or more optical wavefront(s) comprises different respective orientations relative to the optical assembly; acquiring an interferometric signal generated by the interferometer in response to light returned to the laser cavity assembly from said one or more optical wavefronts by said particulate material; by a processing module, detecting the presence of particulate material within the monitored region on condition that a frequency of a waveform of the interferometric signal is less than a pre-set threshold frequency value and subsequently to determining a property of the detected particulate material according to changes in the frequency of the waveform of the interferometric signal on condition that the frequency is greater than the pre-set threshold frequency value.

11. The method according to claim 10 comprising, by a signal processor unit of the processing module, processing the interferometric signal according to a first processor clock speed to detect the presence of particulate material, and processing the interferometric signal according to a second processor clock speed subsequently to determine said property of the detected particulate material, wherein the second processor clock speed exceeds the first processor clock speed.P004737-GB01 41 12. The method according to claim 11 comprising, in response to detection of the presence of particulate material within the monitored region, ceasing the processing of the interferometric signal according to the first processor clock speed, and commencing the processing the interferometric signal according to the second processor clock speed.

13. The method according to claim 11 or claim 12 comprising, in response to a cessation of the waveform in the interferometric signal, ceasing the processing of the interferometric signal according to the second processor clock speed and reverting to the processing the interferometric signal according to the first processor clock speed.

14. The method according to any of claims 10 to 13 comprising determining a frequency bandwidth corresponding to said changes in the frequency of the waveform of the interferometric signal, determining an average frequency of the waveform of the interferometric signal, and determining an estimated speed of the detected particulate material as said property of the detected particulate material, according to a ratio of the average frequency and the frequency bandwidth.

15. The method according to claim 14 wherein the frequency bandwidth comprises a fractional bandwidth corresponding to said changes in the frequency of the waveform of the interferometric signal.

16. The method according to any of claims 14 of 15 comprising determining a concentration of the particulate material according to the value of the estimated speed of the detected particulate material within the monitored region, a cross sectional area of the monitored region, and a rate of detection of the presence of particulate material within the monitored region.

17. The method according to any of claims 10 to 16 comprising determining a plurality of successive time points at which a signal polarity in the waveform of the interferometric signal changes, and determining a frequency of the waveform of the interferometric signal according to the plurality of successive time points so determined.

18. The method according to claim 17 wherein each said time point corresponds to a zero- crossing of the waveform of the interferometric signal coincident with a sign-change of aP004737-GB01 42 value of the waveform of the interferometric signal, and the method comprises determining a zero-crossing rate (ZCR) and therewith determining a frequency of the waveform of the interferometric signal.

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