Patent Publication Number: US-2022234066-A1

Title: Method and apparatus for controlling cold spraying

Description:
FIELD 
     The aspects of the disclosed embodiments relates to controlling cold spray coating. 
     BACKGROUND 
     Objects may be coated by gas dynamic cold spraying. The cold spraying may comprise accelerating coating particles with a supersonic gas jet, and causing the particles to impact on a target object such that the particles undergo plastic deformation and adhere to the target. The size of the particles may be e.g. in the range of 1 to 50 μm, and the velocities of the particles may be e.g. in the range of 400 to 1200 m/s. The temperatures of the sprayed particles typically remain substantially below the melting temperature of said particles. 
     The properties of the formed coating may be measured e.g. by destructive or nondestructive testing. An effect of an operating parameter of the cold spraying on the properties of the coating may be determined e.g. by forming coatings by varying one or more operating parameters, by measuring the properties of the formed coatings, and by plotting the measured properties as a function of an operating parameter. 
     SUMMARY 
     Some versions may relate to a method for controlling cold spraying. Some versions may relate to an apparatus for forming a coating by cold spraying. Some versions may relate to a method for controlling operation of a cold spraying apparatus. Some versions may relate to a method for verifying operation of a cold spraying apparatus. 
     According to an aspect, there is provided a method for controlling gas dynamic cold spraying, the method comprising:
         providing a particle jet (JET 0 ) by using an accelerating nozzle (NOZ 1 ), according to a first set of operating parameters (PAR 1 ),   illuminating the particle jet (JET 0 ) with illuminating light pulses (LB 0 ),   capturing one or more images (IMG 2 ) of the particle jet (JET 0 ) by using an imaging unit ( 200 ), and   determining one or more velocity values (v AVE , v(x)) by analyzing the captured images (IMG 2 ),       

     wherein the method comprises providing two or more sequences (SEQ 1 , SEQ 2 )) of illuminating light pulses (LB 0 ) during an exposure time period (T ex ) of a single captured image (IMG 2 ). 
     Further aspects are defined in the claims and/or in the examples. 
     The scope of protection sought for various embodiments of the present disclosure is set out by the independent claims. The embodiments and features, if any, described in this specification that do not fall under the scope of the independent claims are to be interpreted as examples useful for understanding various embodiments of the present disclosure. 
     A cold spraying apparatus may comprise the accelerating nozzle to provide a particle jet. The particle jet may be directed to a target object in order to form a coating by cold spraying. The particles of the particle jet may impact on a target object such that the particles undergo plastic deformation and adhere to the target object. A cold spraying operation may need to be verified e.g. when forming a coating on a critical part. A cold spraying operation may need to be verified e.g. when producing critical parts of an airplane. 
     The particle jet may be monitored by using a monitoring device, which comprises an imaging unit. The imaging unit may be arranged to capture images of a measuring region of the particle jet. One or more captured images may be analyzed in order to count the number of detected particles and/or in order to determine velocities of detected particles. The monitoring device may be arranged to determine one or more velocity values by analyzing the captured images. The monitoring device may be arranged to determine one or more velocity distributions, wherein a velocity distribution may indicate velocity as a function of position. 
     The monitoring device may be arranged to provide several sequences of illuminating light pulses during a single exposure time period to increase the number of the detected particles. The illuminating unit may be arranged to provide several sequences during the single exposure time period e.g. in order to increase the number of detected particles in a situation where a number of particles detected in captured images is lower than a predetermined limit. 
     Increasing the number of the detected particles may improve accuracy and/or statistical reliability of the measurement of average velocity values. Increasing the number of the detected particles may allow obtaining the average velocity values during a shorter measurement time period. 
     Image capturing may take time, and also image analysis may take time. Using an extended exposure time together with several pulse sequences may facilitate image analysis. Increasing the number of particles detectable in a single image may facilitate the image analysis such that the total number of detected particles may be increased also in a situation where total number of captured images would be lower due to a longer exposure time period. 
     The monitoring device may be arranged to determine one or more number density values by analyzing the captured images. The monitoring device may be arranged to determine one or more number density distributions, wherein a number density distribution may indicate number density as a function of position. The monitoring device may also be arranged to calculate a mass flux value from a determined velocity value and from a determined number density value. The mass flux value may be indicative of a local deposition rate for forming a coating with the spraying apparatus. 
     A cold spraying operation may be controlled and/or verified based on one or more values measured by the monitoring device. For example, one or more measured velocity values may be compared with reference data. A control operation for controlling the cold spraying may be carried out based on a result of the comparison. The control operation may comprise e.g. adjusting one or more operating parameters of the cold spraying. The control operation may comprise e.g. verifying a performed cold spraying operation to be valid or invalid, e.g. to accept or reject a coating formed on a target object. 
     The operation of the cold spraying apparatus may be verified by using an optical measuring device, which comprises an imaging unit. The imaging unit may be arranged to detect particles, which are moving within a measurement region. The measurement region may comprise an object plane. The imaging unit may be arranged to capture substantially sharp images of particles, which are moving in the vicinity of the object plane. The monitoring device may be arranged to determine e.g. one or more velocity values by analyzing the captured images. The monitoring device may be arranged to determine e.g. one or more velocity distributions. The monitoring device may be arranged to determine e.g. one or more number density values. The monitoring device may be arranged to determine e.g. one or more particle number density distributions. The monitoring device may be arranged to calculate e.g. a mass flux value from a determined velocity value and from a particle number density value. 
     Capturing a plurality of images by varying the position of the object plane, and by analyzing the captured images may allow determining accurate data based on a high number of detected particles, while also providing a sufficient spatial resolution in a transverse direction. 
     The monitoring of the particle jet may facilitate determining optimum operating parameters of the coating apparatus. The monitoring of the particle jet may improve quality and/or reliability of a coating formed a target object. Monitoring the particle jet may reduce costs spent on a target object, which might be rejected due to an invalid coating. 
     One or more operating parameters of the coating process may be adjusted based on information obtained from the monitoring device. 
     A coating operation may be performed such that the particle jet is not continuously monitored during the actual coating operation. The spraying gun may be driven to a measurement position close to the optical monitoring device, so as to measure one or more distributions of the particle jet in a situation where the particle jet does not impinge on a first target object. 
     The nozzle may be moved by an actuator during the monitoring, in a situation where the imaging unit and the illuminating unit of the monitoring device may be kept immobile. Moving the nozzle may change the position of the object plane with respect to the nozzle such that monitoring device may gather image data from several transverse planes of the particle jet. Several lateral distributions may be determined by analyzing the images captured by the imaging unit. The apparatus may be arranged to form one or more transverse distributions from the determined lateral distributions. The apparatus may be arranged to form a three-dimensional distribution from the determined lateral distributions. A coating may be formed on the first target object before or after said monitoring. 
     The central axis of the particle jet may sometimes be displaced with respect to an axis of symmetry of the accelerating nozzle of the spraying gun. Information about the position of the accelerating nozzle of the spraying gun may sometimes even be erroneous. In an embodiment, the method may comprise determining an actual position of the central axis of the particle jet based on one or more determined distributions. The method may comprise determining a center position of the particle jet e.g. by calculating a center of gravity of one or more determined distributions. The method may comprise determining an actual center position of the particle jet e.g. by fitting a function to one or more determined distributions. 
     The method may comprise communicating information about the determined position of the central axis of the particle jet to a control system of the cold spraying apparatus. The control system of the cold spraying apparatus may be arranged to use the information about the determined position of the central axis of the particle jet to adjust and/or correct the position of the particle jet with respect to the target object. Information about the actual center of the particle jet may facilitate more accurate control of local thickness of the coating formed on a target object. 
     In an embodiment, the positions of the object plane of the optical measuring device may be optimized so as to gather a maximum amount of relevant information during a measuring time period. The operation of the monitoring device may be controlled based on analysis of the captured images. The monitoring device may be arranged to adjust one or more operating parameters of said monitoring device based on analysis of the captured images. For example, the method may comprise setting the object plane of the measuring device to one or more measurement positions, which are determined based on analysis of the captured images. For example, the object plane may be set to a position where an abnormal region is detected. For example, the object plane may be set to a position where the number density of particles is close to a maximum value, so as to minimize time needed to gather statistically meaningful information. In an embodiment, the object plane may be set to two or more positions which allow determining the position of the axis of the particle jet at a high accuracy. For example, an exposure time period for capturing a single image may be selected based on a number of particles detected in one or more previous images. 
     The method may comprise determining a first lateral distribution by analyzing the one or more first images, and the method may comprise determining a second lateral distribution by analyzing the one or more second images. The method may comprise determining a transverse distribution from the first lateral distribution and from the second lateral distribution. The method may comprise determining a transverse distribution from two or more lateral distributions. The method may comprise capturing images from two or more viewing directions, determining two or more lateral distributions by analyzing the captured images, and determining one or more transverse distributions from the lateral distributions. 
     In an embodiment, the method may comprise causing a change of transverse position of the optical measuring device with respect to the spraying gun and/or causing a change of angular orientation of the optical measuring device with respect to the spraying gun, so as to capture images from different viewpoints with respect to the particle jet. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the following examples, several variations will be described in more detail with reference to the appended drawings, in which 
         FIG. 1 a    shows, by way of example, in a cross-sectional view, forming a coating on an object by gas dynamic cold spraying, 
         FIG. 1 b    shows, by way of example, minimum and maximum velocities for forming a coating with coating particles of different sizes, 
         FIG. 1 c    shows, by way of example, a coating apparatus, which comprises an optical monitoring device, 
         FIG. 1 d    shows, by way of example, an axis of the nozzle and an axis of the particle jet, 
         FIG. 1 e    shows, by way of example, lateral distribution of mass flux of a particle jet, 
         FIG. 2 a    shows, by way of example, in a three-dimensional view, forming a coating on a target object by cold spraying, 
         FIG. 2 b    shows, by way of example, in a three-dimensional view, detecting particles which pass through a reference area, 
         FIG. 2 c    shows, by way of example, in a three-dimensional view, capturing images of a measuring region of the particle jet, 
         FIG. 3  shows, by way of example, in a three-dimensional view, units of the monitoring device, 
         FIG. 4 a    shows, by way of example, timing of illuminating light pulses, 
         FIG. 4 b    shows, by way of example, an image captured by the image sensor of the measuring device, 
         FIG. 4 c    shows, by way of example, an image captured by the image sensor of the measuring device, 
         FIG. 4 d    shows an annotated version of the digital image of  FIG. 4   c,    
         FIG. 4 e    shows, by way of example, particle velocity vectors determined by analyzing a captured image, 
         FIG. 4 f    shows, by way of example, timing of illuminating light pulses when providing several pulse sequences during a single exposure time period, 
         FIG. 5  shows, by way of example, a probability distribution function at a given position of the particle jet, 
         FIG. 6  shows, by way of example, determining one or more distributions by analyzing captured images, 
         FIG. 7 a    shows, by way of example, lateral velocity distributions determined by analyzing captured images, 
         FIG. 7 b    shows, by way of example, comparing a lateral velocity distribution with a reference distribution, 
         FIG. 7 c    shows, by way of example, comparing a transverse distribution with a reference distribution, 
         FIG. 8 a    shows, by way of example, measured particle velocity of the particle jet as a function of two position coordinates, 
         FIG. 8 b    shows, by way of example, measured particle number density of the particle jet as a function of two position coordinates, 
         FIG. 9 a    shows, by way of example, in a three-dimensional view, a first angular orientation of the object plane, 
         FIG. 9 b    shows, by way of example, in a three-dimensional view, a second angular orientation of the object plane, 
         FIG. 10  shows, by way of example, method steps for determining one or more distributions by analyzing captured images, and for controlling operation of the cold spraying apparatus based on the determined distributions, 
     
    
    
     DETAILED DESCRIPTION 
     Referring to  FIG. 1 a   , a coating particle P 0   k  of a particle jet JET 0  may move at a velocity v k . The particle P 0   k  may be deformed when it impinges on the surface of a target object TARG 1 . The particles P 0  of the jet JET 0  may be converted into deformed coating particles CP 1 . A plurality of coating particles CP 1  may be adhered to the target object TARG 1 . A plurality of coating particles CP 1  may together constitute a coating COAT 1 . The target object TARG 1  may be e.g. a component of an engine, a component of a gas turbine, and/or a component of an aircraft. 
     Referring to  FIG. 1 b   , a suitable velocity range for forming a coating may depend on the particle size D P0 . The lower curve CRV 1  may represent a minimum velocity limit, and the higher curve CRV 2  may represent a maximum velocity limit. A suitable velocity range for forming a coating may reside between the upper curve CRV 2  and the lower curve CRV 1 . Velocities lower than the limit CRV 1  and velocities higher than the limit CRV 2  may cause erosion of the target object TARG 1  and/or erosion of a previously formed coating COAT 1 . 
     A coating process may have an optimum region OR 1 . A coating having desired properties may be formed by providing the particle jet such that the particle velocity and the particle size reside within the optimum region OR 1 . The optimum region may depend e.g. on the material of the particles and on the material of the target object. 
     A cold spray coating operation may be determined to be valid e.g. if at least a predetermined percentage of the particles of the particle jet reside within the optimum region OR 1 . 
     The cold spray coating operation may be determined to be invalid e.g. if less than a predetermined percentage of the particles of the particle jet reside within the optimum region OR 1 . 
     Referring to  FIG. 1 c   , a coating apparatus  1000  may comprise an optical measuring device  500  for measuring one or more velocity values of the particle jet JET 0 . One or more measured values may be compared with reference data, and a spraying operation may be controlled based on a result of the comparison. In particular, the optical measuring device  500  may measure velocity distributions of the particle jet JET 0 . A measured distribution may be compared with a reference distribution, and a spraying operation may be controlled based on a result of the comparison. 
     The apparatus  1000  may provide a particle jet JET 0  by accelerating particles P 0  to a high velocity. The apparatus  1000  may comprise an accelerating nozzle NOZ 1  to accelerate working gas GAS 0  to a high velocity. The accelerating nozzle NOZ 1  may be e.g. a diverging nozzle, which may be arranged to accelerate the working gas to supersonic velocities, i.e. to velocities higher than the speed of sound. The diverging nozzle may be e.g. a de Laval nozzle. The particles P 0  may be guided to the working gas GAS 0  via a feeding nozzle NOZ 1 . The accelerated working gas GAS 0  may, in turn, accelerate the particles P 0  to a high velocity. The accelerated particles P 0  may together constitute a particle jet JET 0 . The accelerating nozzle NOZ 1  may provide a particle jet JET 0 , which comprises a plurality of particles P 0   k , P 0   k+1 , P 0   k+2 , . . . moving at high velocities v k , v k+1 , v k+2 , . . . . The nozzle NOZ 1  may have a central axis AX 0  of symmetry. 
     The particles P 0  of the particle jet JET 0  may impinge on a target object TARG 1 , so as to form a coating COAT 1 . The apparatus  100  may comprise an actuator ACU 1  to cause a relative movement between the nozzle NOZ 1  and the target object TARG 1 , e.g. in order to form a coating on a large area of a target object TARG 1 . In particular, the actuator ACU 1  may be arranged to move the nozzle NOZ 1 . 
     The working gas GAS 0  may be provided e.g. from a gas cylinder CYL 1 . The working gas GAS 0  may be e.g. helium or nitrogen. The apparatus  1000  may comprise a valve VAL 1  for controlling flow rate and/or pressure of the working gas GAS 0 . The apparatus  1000  may comprise a heater to heat the working gas GAS 0 . The working gas GAS 0  may be guided to the nozzle NOZ 1  via a plenum chamber CHA 1 . The apparatus  1000  may comprise a particle feeding unit FEED 1  to feed coating particles P 0  to the particle jet JET 0  at a controlled flow rate. The apparatus  1000  may comprise a container SILO 1  to provide particles P 0  to the feeding unit FEED 1 . 
     The apparatus  1000  may comprise one or more sensors G 1 , G 2  to monitor the pressure and/or temperature of the heated working gas GAS 0 . The apparatus  1000  may comprise a feeding nozzle NOZ 2  to guide particles P 0  received from the feeding unit FEED 1  into the particle jet JET 0 . The particles may be carried from the feeding unit FEED 1  to the nozzle NOZ 2  by using carrier gas GAS 0 ′. For example, a partial flow of the working gas GAS 0  may be used as the carrier gas GAS 0 ′ to carry the particles from the feeding unit FEED 1  into the particle jet JET 0 . The apparatus  1000  may comprise a valve VAL 2  to control flow rate and/or pressure of the carrier gas flow. The particles P 0  and the carrier gas may be guided from the feeding unit to the feeding nozzle NOZ 2  via a duct TUB 1 . 
     The accelerating nozzle NOZ 1 , the plenum chamber CHA 1 , and the feeding nozzle NOZ 2  may together constitute a unit GUN 1 , which may be called e.g. as a spraying gun. 
     The apparatus  1000  may comprise a control unit CNT 2  to control operation of the spraying gun GUN 1 . For example, the control unit CNT 2  may be arranged to control operation of the apparatus  1000  according to selected operating parameters PAR 1 . The operating parameters PAR 1  may be e.g. flow rate of working gas, pressure of working gas, temperature of working gas, flow rate of particles, and/or a trajectory for moving the nozzle NOZ 1 . The operating parameters PAR 1  may be stored e.g. in a memory MEM 20 . 
     The apparatus  1000  may comprise a user interface UIF 2  for providing information to a user and/or for receiving user input. 
     The apparatus  1000  may provide position information POS 1  indicative of the position of the nozzle NOZ 1  with respect to the target TARG 1 . The position information POS 1  may indicate the position of the nozzle NOZ 1  e.g. in a situation where the actuator ACU 1  moves the nozzle NOZ 1  with respect to the imaging unit  200  of the monitoring device  500 . 
     The measuring device  500  may receive position information POS 1  from the apparatus  1000 . The position information POS 1  may be indicative of a transverse position of the axis AX 0 . The position information POS 1  may be received e.g. from the actuator ACU 1 , from a position sensor of the actuator ACU 1 , and/or from a control unit CNT 2  of apparatus  1000 . The position information POS 1  may also be indicative of a relative position of the object plane O 1  of the monitoring device  500  with respect to the axis AX 0  of the nozzle NOZ 1 . 
     The apparatus  1000  may comprise an optical measuring device  500  for measuring one or more distributions of the particle jet JET 0 . The measuring device  500  may be arranged to detect particles which are moving in the vicinity of an object plane O 1  of the optical measuring device  500 . 
     The symbol d 1  may denote the distance between the object plane O 1  and the axis AX 0  of the nozzle NOZ 1 . SX, SY and SZ may denote orthogonal directions. The direction SY may be parallel with the direction of the axis AX 0  of the nozzle NOZ 1 . The direction SX may be called e.g. as a lateral direction. The direction SZ may be called e.g. as a transverse direction. 
     The device  500  may comprise a user interface UIF 1  e.g. for displaying measured velocity values to a user and/or for receiving user input from a user. The user interface UIF 1  may display e.g. a determined distribution to a user. 
     Referring to  FIG. 1 d   , the central axis AXJ 0  of the particle jet JET 0  may sometimes be displaced with respect to the central axis AX 0  of the accelerating nozzle NOZ 1 . d AXJ0  may denote a distance between the axis AX 0  and the axis AXJ 0 , e.g. at the center of the object plane O 1  of the measuring device  500 . The displacement d AXJ0  may be caused e.g. due to one or more asymmetric flows of the spraying gun GUN 1 . For example, the feeding nozzle NOZ 2  may be displaced with respect to the axis AX 0  of accelerating nozzle NOZ 1 . For example, one or more gas flows may be introduced asymmetrically to a plenum chamber CHA 1  of the spraying gun GUN 1 . 
     The axis AX 0  of the accelerating nozzle NOZ 1  may be defined to be e.g. an axis of symmetry of the accelerating nozzle NOZ 1 . 
     The method may comprise measuring the lateral and/or transverse position of the central axis AXJ 0  of the particle jet JET 0 , e.g. in order to accurately control the deposition rate at different lateral and transverse positions of the target TARG 1 . 
     The method may comprise determining a position of a central axis AXJ 0  of the particle jet JET 0  based on one or more determined distributions (v(x),v(z)). The method may comprise controlling moving the particle jet (JET 0 ) with respect to a target object (TARG 1 ) according to the determined position of the central axis (AXJ 0 ) of the particle jet (JET 0 ). 
     The axis AXJ 0  of the jet JET 0  may be defined to be e.g. at a center of gravity of the spatial mass flux distribution of the particle jet JET 0 . 
     The accelerating nozzle NOZ 1  may have an inner diameter d NOZ1  at the outlet. 
       FIG. 1 e    shows, by way of example, relative mass flux J(x)/JMAX of the particle jet JET 0  as a function of lateral position coordinate x. The unit of mass flux J(x) may be e.g. mass per unit area per unit time (g/m 2 /s). JMAX may denote the maximum value of the mass flux J(x). Relative mass flux may mean the mass flux J(x) divided by the maximum value JMAX. To the first approximation, the mass flux J(x,y,z) at a position (x,y,z) may be proportional to the particle number density n(x,y,z) multiplied by the particle mean velocity v(x,y,z). To the first approximation, the deposition rate for forming the coating COAT 1  at a position (x,z) may be substantially proportional to the mass flux J(x,y,z) at the position (x,y,z). The number density means the number or particles per unit volume. 
     The symbol x AX0  may denote the lateral position of the axis AX 0  of the nozzle NOZ 1 . The symbol x AXJ0  may denote the lateral position of the axis AXJ 0  of the particle jet JET 0 . 
     The symbol x BND1  may denote a first lateral position where mass flux is equal to 50% of the maximum value JMAX. x BND2  may denote a second lateral position where mass flux is equal to 50% of the maximum value JMAX. d JET0  may denote a width of the particle jet JET 0  in the lateral direction SX. The width d JET0  of the particle jet JET 0  may be e.g. equal to the distance x BND2 −x BND1 . The width d JET0  of the particle jet JET 0  may mean e.g. a (maximum) distance between points where the mass flux distribution reaches 50% of the maximum value JMAX. The width d JET0  may mean e.g. the full-width-at-half-maximum width (FWHM width) of the mass flux distribution J(x,y,z). 
     Referring to  FIG. 2 a   , moving particles P 0  of the jet JET 0  may be deformed when they impact on the target object TARG 1 . The deformed particles CP 1  may form a deposited layer COAT 1  on the surface SRF 2  of the target object TARG 1 . The symbol L 2  may denote a distance between the accelerating nozzle NOZ 1  and the surface SRF 2  of the target object TARG 1 . 
     Referring to  FIG. 2 b   , the nozzle NOZ 1  may provide a particle flux through a reference area AREA 0 . L 0  may denote the distance between the accelerating nozzle NOZ 1  and the reference area AREA 0 . The jet may have a diameter (d JET0 ) at the position of the reference area AREA 0 . The measuring device  500  may be arranged to measure velocity, number density and/or size of particles which pass through the reference area AREA 0  during a measurement time period. The measuring device  500  may be arranged to capture images of particles which pass through the reference area AREA 0 . The measuring device  500  may be arranged to monitor the particle jet in the vicinity of the reference area AREA 0 . In an embodiment, the reference area AREA 0  may be positioned e.g. such that the distance L 0  is substantially equal to the distance L 2 . For example, the nozzle NOZ 1  may be moved away from the target object TARG 1  to a monitoring position, so that the device  500  may detect and monitor particles which are moving at the distance L 2  from the nozzle NOZ 1 . 
     The optical measuring device  500  may be arranged to measure one or more properties of particles P 0  passing through the reference area AREA 0 . The optical measuring device  500  may be arranged to determine e.g. one or more velocity values of particles P 0  passing through the reference area AREA 0 . The optical measuring device  500  may be arranged to determine e.g. one or more velocity distributions in the reference area AREA 0 , e.g. as a function of position coordinate x and/or as a function of position coordinate z. The optical measuring device  500  may be arranged to determine e.g. one or more number density distributions in the reference area AREA 0 , e.g. as a function of position coordinate x and/or as a function of position coordinate z. 
     Referring to  FIGS. 2 c    and  3 , the measuring device  500  may comprise an imaging unit  200 , and a data processing unit  400 . The imaging unit  200  may be arranged to capture digital images IMG 2  of particles located within a measurement region RG 0  of the particle jet JET 0 . The imaging unit  200  may be arranged to capture a plurality of images at a high frame rate. The imaging unit  200  may be a video camera. 
     The measuring device  500  may be arranged to measure one or more velocity values by analyzing the captured images. The measuring device  500  may be arranged to measure one or more spatial distributions F 1   1 ( x ), F 1   2 ( x ) by analyzing the captured images ( FIG. 4 e   ). The device  500  may be arranged to detect images of particles in a captured image. The device  500  may be arranged to count images of detectable particles in a captured image. The device  500  may be arranged to determine a velocity of a particle from a displacement between a first sub-image and a second sub-image of the same particle. The device  500  may be arranged to determine a mean velocity value (v AVE ) from velocities (v k , v k+1 ) of several particles. 
     For example, the device  500  may be arranged to measure a spatial particle velocity distribution. The measuring device  500  may be arranged to measure a lateral velocity distribution by analyzing the captured images. The velocity distribution v AVE (x) may provide e.g. mean particle velocity as a function of a lateral position (x) with respect to the axis AX 0  of the nozzle NOZ 1 . The lateral position may be specified e.g. by x-coordinate in the direction SX. 
     The measuring device  500  may be arranged to measure a spatial velocity distribution by analyzing the captured images. A particle P 0  may have a large axial velocity component v y  in the direction of the axis AX 0  (i.e. in the direction SY). The particle P 0  may also have a lateral velocity component v X  in the direction SX and/or a transverse velocity component v Z  in the direction SZ. The measuring device  500  may be arranged to measure e.g. the velocity components v Y  and v X  for each particle located in the measurement region RG 0 . The measuring device  500  may be arranged to measure a spatial velocity distribution for the axial velocity components v Y  as a function of the lateral position x. 
     The measuring device  500  may be arranged to measure a local velocity probability distribution (p v (v)) by analyzing the captured images ( FIG. 5 ). 
     The measuring device  500  may be arranged to measure a spatial distribution of mass flow by analyzing the captured images. A mass flux value at a position x may be determined e.g. by multiplying measured velocity v AVE (x) with measured particle number density n(x) and with a constant m P0 . The constant m P0  may represent e.g. an average mass of a single particle P 0 . 
     The one or more spatial distributions may provide information e.g. about an effective width (d JET0 ) of the particle jet. 
     The particles P 0  may reflect, refract and/or scatter light LB 1  towards the illuminating unit  100 . The particles P 0  may provide reflected light LB 1  by reflecting, refracting and/or scattering illuminating light LB 0  ( FIG. 3 ). 
     The imaging unit  200  may comprise focusing optics  210  and an image sensor SEN 1 . The focusing optics  210  may be arranged to form an optical image IMG 1  on an image sensor SEN 1 , by focusing the light LB 1  received from the particles. The image sensor SEN 1  may convert one or more optical images IMG 1  into a digital image IMG 2 . The data processing unit  400  may be configured to analyze one or more digital images IMG 2  obtained from the image sensor SEN 1 . The data processing unit  400  may comprise one or more data processors. The data processing unit  400  may be configured to perform one or more data processing operations e.g. for determining one or more distributions. The data processing unit  400  may be configured to verify operation of cold spraying apparatus, to control operation of the cold spraying apparatus, and/or to provide an indication if a determined distribution comprises an abnormal region. 
     The image sensor SEN 1  may be e.g. a CMOS sensor or a CCD sensor. CMOS means Complementary Metal Oxide Semiconductor. CCD means Charge Coupled Device. The image sensor SEN 1  may comprise a plurality of light detector pixels arranged in a two-dimensional array. 
     The digital image IMG 2  may have a width ξ IMG  and a height υ IMG  in the image space defined by directions Sξ and Sυ. The image of the axis AX 0  may be e.g. substantially parallel with the direction Sξ. The direction Sυ may be perpendicular to the direction Sξ ( FIG. 4 b   ). 
     SX, SY and SZ may denote orthogonal directions. The axis AX 0  of the nozzle NOZ 1  may be parallel with the direction SY. The direction SX may be called as a lateral direction. The direction SZ may be called as a transverse direction. The imaging unit  200  may have an optical axis AX 2 . The optical axis AX 2  of the imaging unit  200  may be e.g. transverse with respect to the axis AX 0  of the nozzle NOZ 1 . 
     The measuring region RG 0  of the measuring device  500  may be a substantially planar volume, which comprises the object plane O 1  in the middle of the measuring region RG 0 . The thickness of the measuring region RG 0  may be equal to the depth-of-field d 12  in a transverse direction SZ. The measuring region RG 0  may extend by a distance of 50% of the depth-of-field d 12  from the object plane O 1  in the direction SZ and also in the opposite direction −SZ. 
     The depth-of-field d 12  of the imaging unit  200  may be e.g. smaller than or equal to 2 mm, advantageously in the range of 0.1 mm to 1.0 mm. 
     The depth-of-field d 12  may be e.g. in the range of 2% to 40% of a width d JET0  of the particle jet JET 0  at the outlet end of the nozzle NOZ 1 . 
     A distance a 1  between the object plane O 1  and the imaging optics  210  may be in e.g. the range of 5 to 50 times the transverse width d JET0  of the particle jet JET 0  at the outlet end of the nozzle NOZ 1 . 
     The imaging unit  200  may form a substantially sharp image of a particle on the image sensor SEN 1  when the particle is within the measuring region RG 0 . The imaging unit  200  may form a substantially sharp image of a particle on the image sensor SEN 1  when the particle is within 50% of the depth-of-field d 12  from the object plane O 1 . The imaging unit  200  may form a blurred image of a particle on the image sensor SEN 1  when the particle is outside the measurement region RG 0  but close to the measurement region RG 0 . Yet, some particles may be so far away from the measurement region RG 0  that the imaging unit  200  does not form a detectable image of those particles. 
     Each optical image IMG 1  formed on the image sensor SEN 1  may be an image of the measurement region RG 0 . The image IMG 1  may comprise one or more sub-images P 1  of the moving particles P 0  of the particle jet JET 0 . The measurement region RG 0  may have a central plane O 1 , which may be called e.g. as the object plane of the imaging unit  200 . The imaging optics  210  may have a limited depth of field d 12 . Consequently, the imaging unit  200  may form a sharp sub-image P 1  of a particle P 0  on the image sensor SEN 1  only when said particle P 0  is located on the object plane O 1 . The sub-image P 1  of a particle P 0  may be less sharp, i.e. slightly blurred when the distance between said particle P 0  and the object plane O 1  is greater than zero. The measurement region RG 0  may be located between a first boundary E 1  and a second boundary E 2 . The object plane O 1  may be located between the boundaries E 1 , E 2 . The distance between the boundaries E 1 , E 2  may be equal to the depth of field d 12  of the imaging unit  200 . The measurement region RG 0  may have a thickness d 12  in the transverse direction SZ. 
     The apparatus  1000  may be arranged to change the transverse position z of the object plane O 1 , with respect to the axis AX 0  of the nozzle NOZ 1 . The transverse position z of the object plane O 1  may be changed e.g. using the actuator ACU 1  to move the nozzle NOZ 1  with respect to the imaging unit  200 . The actuator ACU 1  to move the nozzle NOZ 1  e.g. in the direction SZ. The actuator ACU 1  may comprise e.g. a translation stage, which is moved by one or more stepper motors. The actuator ACU 1  may be e.g. an industrial robot. 
     The method may comprise changing the relative position of the object plane O 1  from a first position (e.g. z=z 1 ) to a second position (e.g. z=z 2 ) by using the actuator ACU 1  to cause a translational movement the nozzle NOZ 1  with respect to the imaging unit  200 . 
     Each moving particle P 0   k  of the particle jet JET 0  may have an instantaneous lateral position x k  with respect to the axis AX 0  of the nozzle NOZ 1 . 
     A particle P 0  which is outside the measurement region RG 0  may have a blurred sub-image on the image sensor SEN 1 . The device  500  may be arranged to operate such that excessively blurred sub-images are not used as a basis for determining a velocity of a particle. 
     The imaging unit  200  may form a substantially sharp image P 1  of each particle P 0 , which is located in the measurement region RG 0  during an exposure time T ex  of the image sensor SEN 1 . The imaging unit  200  may form a substantially sharp image P 1  of each particle P 0 , which is located in the measurement region RG 0  during triggering of an illuminating light pulse LB 0 . The optical image IMG 1  formed on the active area of the image sensor SEN 1  may comprise a plurality of sub-images P 1 . Each sub-image P 1  may be an image of a particle P 0 . The image sensor SEN 1  may convert an optical image IMG 1  into a digital (captured) image IMG 2 . The active area may mean the active light-detecting area of the image sensor. 
     The image IMG 2  captured by the imaging unit  200  may represent a common overlapping portion of the measurement region RG 0  and the particle jet JET 0 . An average number of particles appearing in a single captured image may be e.g. in the range of 2 to 1000. An average number of particles appearing in a single captured image may be e.g. in the range of 10 to 100. The sub-images P 1  of the particles P 0  may be detected by an image analysis algorithm. The particles P 0  may be moving at a high velocity during capturing of an image IMG 2 . The velocity of each particle appearing in a captured image may be determined from the displacement value Δu and from the timing of the exposure and/or illumination. The optical image P 1  of each particle P 0  may move during capturing of the image IMG 2 . The movement of the optical image may define a displacement value Δu, which may be determined from the captured image IMG 2  by image analysis. Each substantially sharp image P 1  of a particle P 0  may be associated with a displacement value Δu. The velocity v k  of a particle P 0   k  may be determined from the displacement value Δu k  and from the duration (T F ) of illumination and/or from the exposure time period T ex . 
     The measuring device  500  may comprise a data processor  400  to determine one or more velocity values by analyzing the captured digital images IMG 2 . The determined velocity values may be stored e.g. in a memory MEM 1 . The measuring device  500  may comprise a data processor  400  to form one or more lateral distributions F 1   1 ( x ), F 1   2 ( x ) by analyzing captured digital images IMG 2 . The determined distributions F 1   1 ( x ), F 1   2 ( x ) may be stored e.g. in a memory MEM 1 . 
     The measuring device  500  may capture a first image IMG 2   z1  of the particle jet JET 0  when the object plane O 1  is at a first transverse position z 1  with respect to the axis AX 0  (e.g. d 1 =z 1 ). The measuring device  500  may capture a second image IMG 2   z2  of the particle jet JET 0  when the object plane O 1  is at a second different transverse position z 2  with respect to the axis AX 0  (e.g. d 1 =z 2 ). The measuring device  500  may determine a first lateral distribution F 1   1 ( x ) by analyzing the first captured image. The measuring device  500  may determine a second lateral distribution F 1   2 ( x ) by analyzing the second captured image IMG 2 . The measuring device  500  may be arranged to determine one or more transverse distributions from the lateral distributions. The measuring device  500  may be arranged to determine one or more transverse distributions F 2 ( z ) from the lateral distributions F 1   1 ( x ), F 1   2 ( x ) by using the position information POS 1 . 
     Referring to  FIG. 3 , the monitoring device  500  may comprise an illuminating unit  100  to provide illuminating light LB 0 . The illuminating unit  100  may provide a sheet of illuminating light LB 0 . The illuminating unit  100  may be arranged to provide a sheet of illuminating light LB 0  to illuminate the measuring region RG 0 . The sheet of illuminating light LB 0  may overlap the measuring region RG 0 . The sheet of illuminating light LB 0  may comprise the object plane O 1 . The sheet of illuminating light LB 0  may be substantially parallel with the object plane O 1 . The illuminating unit  100  may comprise e.g. one or more laser emitters to provide illuminating light LB 0 . The illuminating unit  100  may comprise e.g. one or more light emitting diodes (LED) to provide illuminating light LB 0 . 
     The position of the illuminating unit  100  may be e.g. mechanically coupled to the position of the imaging unit  200  so as to ensure that the illuminating light LB 0  may overlap the measuring region RG 0  and/or in order to ensure that the illuminating light LB 0  may be substantially parallel with the object plane O 1 . The illuminating unit  100  may be attached to the imaging unit  200  e.g. by one or more supporting structures  291 . 
     The illuminating unit  100  may be arranged to provide a sheet of illuminating light pulses LB 0 . The sheet may have a thickness d 0 . The thickness d 0  of the illuminating sheet may be e.g. smaller than the depth-of-field d 12  (d 0 &gt;d 12 ), substantially equal to the depth-of-field d 12  (d 0 =d 12 ), or greater than the depth-of-field d 12  (d 0 &gt;d 12 ). Using a thickness d 0  smaller than or equal to the depth-of-field d 12  may facilitate analysis of the captured images by eliminating blurred sub-images from the captured images. 
     The illuminating light beam LB 0  may have e.g. a thickness d 0  in the direction of the optical axis AX 2 . The illuminating unit  100  may be arranged to provide e.g. a substantially planar light beam. Illuminating the jet by the light sheet may allow defining the thickness d 0  and/or position of the measurement region RG 0  accurately. 
     The illuminating unit  100  may be arranged to modulate the illuminating light beam LB 0 . The illuminating unit  100  may be arranged to modulate the optical intensity of the illuminating light beam LB 0  according to control signal S 100 . The measuring device  500  may be arranged to provide a control signal S 100  for modulating the illuminating light beam LB 0 . The control signal S 100  may comprise e.g. timing pulses for controlling timing of operation of the illuminating unit  100 . The illuminating unit  100  may be arranged to provide one or more illuminating light pulses LB 0 . 
     The image sensor SEN 1  may convert one or more optical images IMG 1  into a digital image IMG 2 . The data processing unit  400  may be configured to analyze one or more digital images IMG 2  obtained from the image sensor SEN 1 . The data processing unit  400  may be configured to perform one or more data processing operations e.g. for determining one or more velocity values, for determining a distribution, for comparing a determined distribution with reference data, and/or for performing a control operation based on a result of the comparison. The data processing unit  400  may be configured to verify operation of cold spraying apparatus, to control operation of the cold spraying apparatus, and/or to provide an indication if a determined distribution comprises an abnormal region. 
     The device  500  may comprise a memory MEM 1  for storing one or more distributions F 1   1 ( x ), F 1   2 ( x ). For example, a first lateral distribution F 1   1 ( x ) may be determined e.g. from images IMG 2  captured when the object plane O 1  is at a first position z=z 1 , and a second lateral distribution F 1   2 ( x ) may be determined e.g. from images IMG 2  captured when the object plane O 1  is at a second different position z=z 2 . 
     The data processor  400  may be arranged to form one or more transverse distributions F 2 ( z ) from the lateral distributions F 1   1 ( x ), F 1   2 ( x ). The transverse distributions F 2 ( z ) may be stored e.g. in a memory MEM 2 . 
     The device  500  may comprise a memory MEM 3  for storing one or more reference distributions REF 1 , REF 2 . For example, an abnormal condition may be detected by comparing a determined distribution F 1   1 ( x ) with a reference distribution REF 1  (see e.g.  FIG. 7 b    and  FIG. 7 c   ). 
     The device  500  may comprise a user interface UIF 1  for receiving user input from a user and/or for providing information to a user. The user interface UIF 1  may comprise e.g. a keypad or a touch screen for receiving user input. The user interface UIF 1  may comprise e.g. a display for displaying visual information. The user interface UIF 1  may comprise e.g. a display for displaying one or more measured values determined by analyzing the images. The user interface UIF 1  may be arranged to display one or more determined distributions. The user interface UIF 1  may comprise e.g. a display for displaying an indication when one or more values measured by the device are outside an acceptable range. The user interface UIF 1  may comprise e.g. an audio output device for providing an indication if one or more velocity values measured by the device are outside an acceptable range. The user interface UIF 1  may be configured to provide a visual alarm and/or an alarm sound if one or more velocity values measured by the device are outside an acceptable range. 
     The device  500  may comprise a communication unit RXTX 1  for receiving and/or transmitting data. The device  500  may be arranged to communicate e.g. with a control unit CNT 2  of a cold spraying apparatus  1000  via the communication unit RXTX 1 . The device  500  may receive e.g. position information POS 1  via the communication unit RXTX 1 . The position information POS 1  indicate e.g. the position of the nozzle NOZ 1 . The device  500  may send process control data via the communication unit RXTX 1 . The process control data may comprise e.g. data for adjusting one or more process parameters PAR 1  of the cold spraying apparatus  1000 . The device  500  may send one or more measured values via the communication unit RXTX 1 . The device  500  may send one or more measured values e.g. to an Internet server. 
     The device  500  may comprise a memory MEM 4  for storing computer program code PROG 1 . For example, the code PROG 1  may, when executed by one or more data processors, cause a system or the device  500  to determine one or more velocity values by analyzing captured images, to compared one or more velocity values with reference data, and to control operation of the spraying apparatus based on the result of the comparison. The code PROG 1  may, when executed by one or more data processors, cause a system or the device  500  to form a transverse distribution F 2 ( z ) from the lateral distributions F 1 ( x ), F 1   2 ( x ). For example, the code PROG 1  may, when executed by one or more data processors, cause a system or the device  500  to determine one or more distributions F 1   1 ( x ) by analyzing captured images, to compare one or more distributions F 1   1 ( x ) with reference data REF 1 , and to control operation of the spraying apparatus based on the result of the comparison. 
     One or more determined values may be provided to a user and/or to a system. For example, one or more determined distributions may be displayed on a display of a user interface UIF 1 . 
     For example, one or more determined distributions may be associated with an identifier and stored in a database. The determined data may be stored e.g. in a protected data archive. The stored data may be subsequently retrieved from the database (archive) based on the identifier. The target object may be e.g. a part of an airplane, wherein it may be useful to have a possibility to study the archived manufacturing data at a later stage. The database may be subsequently accessed e.g. via an internet server. 
     The monitoring device  500  may be arranged to provide one or more velocity values by analyzing the captured images. The monitoring device  500  may be arranged to provide e.g. a velocity distribution v AVE (x) and/or a particle number density distribution n(x). 
     Referring to  FIGS. 4 a  and 4 b   , the imaging unit  200  may form an image P 1  of each particle P 0 , which is located in the measurement region RG 0  during an exposure time T ex  of the image sensor SEN 1 . The optical image IMG 1  formed on the active area of the image sensor SEN 1  may comprise a plurality of sub-images P 1 . Each sub-image P 1  may be an image of a particle P 0 . The image sensor SEN 1  may convert an optical image IMG 1  into a digital (captured) image IMG 2 . A (single) captured digital image IMG 2  may represent all optical images IMG 1  formed on the image sensor SEN 1  during the exposure time period T ex . 
     The image IMG 2  captured by the imaging unit  200  may represent a region RG 0  of the particle jet JET 0 . An average number of particles appearing in a single captured image may be e.g. in the range of 2 to 1000. An average number of particles appearing in a single captured image may be e.g. in the range of 10 to 100. The sub-images P 1  of the particles P 0  may be detected by an image analysis algorithm. The particles P 0  may be moving at a high velocity during capturing of an image IMG 2 . The velocity of each particle appearing in a captured image may be determined from the displacement value Δu and from the timing of the exposure and/or illumination. The optical image P 1  of each particle P 0  may move during capturing of the image IMG 2 . The movement of the optical image may define a displacement value Δu, which may be determined from the captured image IMG 2  by image analysis. Each substantially sharp image P 1  of a particle P 0  may be associated with a displacement value Δu. The velocity v k  of a particle P 0   k  may be determined from the displacement value Δu k  and from the duration (T F ) of illumination and/or from the exposure time period T ex . 
     When using illuminating pulse sequences SEQ 1 , SEQ 2 , the velocity v k  of a particle P 0   k  may be determined from the displacement value Δu k  and from the timing (e.g. t 3 −t 1 ) of illuminating light pulses LB 0 . In particular, the axial velocity of a particle may be substantially proportional to Δu k /T F . 
       FIG. 4 a    shows, by way of example, temporal evolution of optical intensity of illuminating light LB 0  in the measurement region RG 0 . 
     The illuminating unit  100  may be arranged to provide pulse sequences SEQ 1 , SEQ 2 , e.g. in order to facilitate detection of the sub-images P 1  by an image analysis algorithm. A pulse sequence SEQ 1  may comprise e.g. two or more pulses. A first pulse sequence may comprise e.g. pulses starting at times t 1 , t 2 , t 3 . A second pulse SEQ 2  sequence may comprise e.g. pulses starting at times t 1 ′, t 2 ′, t 3 ′. 
     The particles P 0  may be illuminated by a sequence SEQ 1  of light pulses LB 0  during an exposure time period T ex . A first exposure time for capturing a first image IMG 2   t0  may start at a time t 0 . A first illuminating light pulse LB 0  may start at a time t 1 . T F  may denote the duration of the illuminating light pulses LB 0 . A second exposure time for capturing a second image IMG 2   t0 , may start at a time t 0 ′. A second sequence SEQ 2  of illuminating light pulses LB 0  may start at a time t 0 ′. 
     Referring to  FIG. 4 b   , the digital image IMG 2  may comprise e.g. sub-images P 1   k,t1 , P 1   k,t2 , P 1   k,t3 . Each sub-image P 1   k  may be an image of a particle P 0   k . The sub-image P 1   k+1  may be an image of a particle P 0   k+1 . The sub-image P 1   k+2  may be an image of a particle P 0   k+2 . The dimension Δu of each sub-image P 1  may be substantially proportional to the velocity of the corresponding particle P 0 . One or more sub-images P 1   k  may have a dimension Δu k  in the direction Sξ. One or more sub-images P 1   k+1  may have a dimension Δu k+1 . One or more sub-images P 1   k+2  may have a dimension Δu k+2 . 
     The exposure time T ex  may temporally overlap several light pulses so that each particle P 0  may be represented by a group GRP, which is formed of two or more sub-images P 1  appearing in the digital image IMG 2 . For example, the particle P 0   k  may be represented by a first group GRP k  of sub-images P 1   k,t1 , P 1   k,t2 , P 1   k,t3 . The distance between adjacent sub-images P 1   k,t1 , P 1   k,t2  may depend on the velocity v k  of the particle P 0   k  and on the timing of the light pulses. 
     The first group GRP k  of sub-images P 1   k,t1 , P 1   k,t2 , P 1   k,t3  may have a dimension Δu k  in the direction Sξ. A second group GRP k+1  may have a dimension Δu k+1 . A third group GRP k+2  may have a dimension Δu k+2 . 
     The sub-images may be detected e.g. by an image analysis algorithm. The device  500  may be configured to detect the sub-images by using an image analysis algorithm. The device  500  may be configured to determine the dimensions Δu k , Δu k+1 , Δu k+2  from one or more captured images IMG 2  by using an image analysis algorithm. 
     The velocity of each individual particle P 1  may be calculated from the dimension Δu of the corresponding sub-image P 1 , and from the timing or duration T F  of the illuminating light pulses LB 0 . For example, the velocity v k  of the particle P 0   k  may be substantially proportional to the value Δu k /T F . 
     The digital image IMG 2  may have a width ξ IMG  and a height υ IMG  in the image space defined by directions Sξ and Sυ. The image of the axis AX 0  may be parallel with the direction Sξ. The direction Sυ may be perpendicular to the direction Sξ. 
     The width ξ IMG  may be e.g. equal to 1024 pixels, and the height υ IMG  may be e.g. equal to 512 pixels. 
     The velocity of the particles may also be measured by using continuous illuminating light, i.e. light, which is not pulsed. In that case the velocity v k  of the particle P 0   k  may be substantially proportional to the value Δu k /T ex . 
     The use of pulsed illumination may allow high instantaneous intensity and/or may allow precise timing for forming the sub-images. 
     Consequently, the velocity of each particle appearing in the image IMG 2  may be determined by analyzing the image IMG 2 . The sub-images P 1   k,t1 , P 1   k,t2 , P 1   k,t3  may together form a combined shape, which may facilitate reliable detection of the sub-images P 1   k,t1 , P 1   k,t2 , P 1   k,t3 , when analyzing the captured image IMG 2 . A second particle P 0   k+1  may be represented by a second group GRP k+1  formed of sub-images P 1   k+1,t1 , P 1   k+1,t2 , P 1   k+1,t3 . 
       FIGS. 4 c  and 4 d    show, by way of example, a (digital) image IMG 2 , which was captured by using the illuminating pulse sequence.  FIGS. 4 c  and 4 d    show the same captured image IMG 2 . When using three or more illuminating pulses, the captured image IMG 2  may comprise easily discernible substantially linear groups GRP of sub-images (e.g. P 1   k,t1 , P 1   k,t2 , P 1   k,t3 ), wherein each group GRP may represent a single moving particle (e.g. P 0   k ) which was illuminated by the pulse sequence during the exposure time period T ex  of the captured image IMG 2 . The position of the first sub-image P 1   k,t1  of the first group GRP k  may be specified e.g. by image coordinates (ξ k,υk ). The position (ξ k,υk ) may indicate the position of the particle P 0   k  when the image IMG 2  was captured. The position (ξ k,υk ) may indicate the position of the particle P 0   k  when the first pulse of an illuminating pulse sequence was triggered. 
     The velocity of the particles may be determined by analyzing the captured images. For example, the velocity of a first particle P 0   k  may be determined from the dimension Δu k  of a first group GRP k  formed of the sub-images P 1   k,t1 , P 1   k,t2 , P 1   k,t3 . For example, the velocity of a second particle P 0   k+1  may be determined from the dimension Δu k+1  of a second group GRP k+1  formed of the sub-images P 1   k+1,t1 , P 1   k+1,t2 , P 1   k+1,t3 . 
     The method may comprise counting the number of particles appearing in a single captured image. The method may comprise counting the number of particles appearing in the captured images. The particle density may be determined from the counted number of particles. Thus, the particle density may be determined by analyzing the captured images. 
     The imaging unit  200  may have a certain depth of field (d 12 ) such that particles which are within the depth of field may have substantially sharp sub-images on the image sensor SEN 1 , and particles which are outside the depth of field may have blurred sub-images on the image sensor SEN 1 . 
     Some of the sub-images (P 1 ) shown in  FIG. 4 d    are sharp, and some of the sub-images (P 1 ) shown in  FIG. 4 d    are blurred. 
     The groups (e.g. GRP k ) formed of the sub-images (e.g. P 1   k,t1 , P 1   k,t2 , P 1   k,t3 ) may be detected by using a pattern recognition algorithm. Each particle P 0  may be assumed to have a substantially constant velocity during the pulse sequence SEQ 1 . 
     A candidate group representing a particle may be accepted if the sub-images of said group are aligned in a substantially linear manner and if the distance between adjacent sub-images of said candidate group match with the timing (t 1 ,t 2 ,t 3 ) of the illuminating light pulses LB 0 . 
     A candidate group may be e.g. discarded if the sub-images of said group are not aligned in a linear manner and/or if the distance between adjacent sub-images of said candidate group do not match with the timing (t 1 ,t 2 ,t 3 ) of the illuminating light pulses LB 0 . 
     AX 0 ′ may indicate the position of the axis AX 0  of the nozzle NOZ 1 . AREA 0 ′ may indicate the position of a reference area AREA 0 . The position of the projection of the reference area AREA 0  may be indicated by a line AREA 0 ′, which may be superposed on the captured image IMG 2 . The position of the projection of the axis AX 0  may be indicated by a line AX 0 ′, which may be superposed on the captured image IMG 2 . 
       FIG. 4 e    shows, by way of example, a plurality of arrow symbols, which indicate velocity vectors v k , v k+1  of particles. The velocity vectors may be determined by analyzing the captured image of  FIG. 4 c   . The method may comprise determining the direction movement of a particle by analyzing one or more captured images. The length of each arrow symbol may be proportional to the speed of a particle, and the direction of the arrow symbol may indicate the direction of movement of the particle. 
     The velocity of a particle may have significant transverse component, i.e. the velocity is not always parallel with the axis AX 0  of the jet. The velocity v k  of a particle may have an axial component v k,y , a lateral component v k,x , and a transverse component v k,z . The axial component v k,z  is parallel with the axis AX 0 . The lateral component v k,x  and the transverse component v k,y  are perpendicular to the axis AX 0 . To the first approximation, the kinetic energy of each particle may be calculated from the axial component, by omitting the lateral and transverse components. To the first approximation, the capability of a particle P 0   k  to adhere to the target object TARG 1  may depend on the axial velocity component of said particle. Velocity values (v RMS , v AVE ) may be determined from the axial velocity values of the individual particles P 0 . The axial velocity values of the individual particles P 0  may be determined from the captured images. 
     v AVE  denotes the average velocity of particles which pass through a reference area (AREA 0 ) during a measurement time period. To the first approximation, the number density of particles in the jet may be inversely proportional to the average velocity v AVE  of the particles, in a situation where the mass flow rate of the particles is substantially constant. The average velocity v AVE  may be determined by analyzing the images captured by the measuring device during the measurement time period. A determined velocity distribution may indicate e.g. the average velocity v AVE  as a function of lateral position x or as a function of transverse position z. 
     Also a RMS velocity v RMS  may be determined by analyzing the captured images IMG 2 . RMS means root mean square. The RMS velocity value v RMS  may be indicative of a mean kinetic energy of the particles. 
     The method may comprise determining an angular divergence of the particle jet JET 0  by analyzing the captured images IMG 1 . 
     The method may comprise determining a width and/or a radial dimension of the particle jet JET 0  by analyzing the captured images IMG 1 . 
     One or more operating parameters of the monitoring device  500  itself may be adjusted and/or optimized, based on the analysis of the images. For example, the temporal width T F  of a pulse sequence SEQ 1  may be adjusted based on an average velocity of detected particles. For example, the intensity of illuminating light LB 0  may be increased or reduced based on brightness of the sub-images P 1  of a captured image IMG 1 . For example, the temporal width of each illuminating pulse may be increased or reduced based on brightness of the sub-images P 1  of a captured image IMG 1 . For example, a step size for moving the object plane O 1  with respect to the nozzle NOZ 1  may be selected based on a number of detected particles appearing in a captured image. The step size for a movement may also be determined e.g. by analyzing one or more determined distributions (F 1 ( x ), F 2 ( z )). The position of the object plane O 1  may be changed according to the determined step size. For example, the step size may be determined so as to gather data related to an abnormal region of a distribution. 
     Referring to  FIG. 4 f   , the device  500  may be arranged to provide two or more pulse sequences SEQ 1 , SEQ 2  during the exposure time period T ex  of a single image IMG 2 . Each sequence SEQ 1 , SEQ 2 , . . . may comprise e.g. three or more illuminating light pulses. Consecutive sequences may be separated by a blanking time period T BLANK . For example, a first sequence SEQ 1  may comprise illuminating light pulses LB 0  emitted at times t 1 , t 2 , t 3 , and a second sequence SEQ 2  may comprise illuminating light pulses LB 0  emitted at times t 4 , t 5 , t 6 . 
     The method may comprise:
         capturing images IMG 2  by providing only two or more pulse sequences SEQ 1 , SEQ 2  during an exposure time period T ex  of each single image IMG 2 , and   determining one or more distributions by analyzing the second images IMG 2 .       

     The device  500  may be arranged to provide several sequences SEQ 1 , SEQ 2  during a single exposure time period T ex  e.g. in order to increase the number of detected particles. The illuminating unit  100  may be arranged to provide several sequences SEQ 1 , SEQ 2  during the single exposure time period T ex  e.g. in order to increase the number of detected particles in a situation where a number of particles detected in captured images IMG 2  is lower than a predetermined limit. The exposure time period T ex  may be increased e.g. in order to increase the number of detectable particles. 
     Image capturing may take time, and also image analysis may take time. Increasing the number of detectable particles in a single image may facilitate image analysis. Increasing the number of particles detectable in a single image may facilitate the image analysis such that the total number of detected particles may be increased even in a situation where total number of captured images would be lower due to a longer exposure time period T ex . 
     The method may comprise:
         capturing first images IMG 2  by providing only one pulse sequence SEQ 1  during an exposure time period T ex  of each single image IMG 2 ,   counting a first number NUM 1  of detected particles in the first images IMG 2 ,   comparing the first number with a first limit value LIM 1 ,   capturing second images IMG 2  by providing only two or more pulse sequences SEQ 1 , SEQ 2  during an exposure time period T ex  of each single image IMG 2  if the first number NUM 1  of detected particles is lower than the first limit value LIM 1 , and   determining one or more distributions by analyzing the second images IMG 2 .       

     The blanking time period T BLANK  between consecutive sequences SEQ 1 , SEQ 2  may be selected to be long enough such that each moving particle P 0  may provide only one group GRP of sub-images P 1  appearing in the digital image IMG 2 , so as to facilitate image analysis. 
     The blanking time period T BLANK  between consecutive sequences SEQ 1 , SEQ 2  may be selected to be long enough such that the slowest moving particle appearing in the image IMG 2  may provide only one group GRP of sub-images P 1  appearing in the digital image IMG 2 . 
     The blanking time period T BLANK  between consecutive sequences SEQ 1 , SEQ 2  may be selected to be long enough such that even the slowest moving particle illuminated by the first sequence SEQ 1  in the measuring region RG 0  may have sufficient time to move out of the measuring region RG 0  before start of the second sequence SEQ 2 . The ratio T ex /T F  may be selected to be greater than or equal to the ratio ξ IMG /Δu MIN . 
     Illuminating a (slow) particle P 0  with the first sequence SEQ 1  may provide a group GRP of sub-images P 1  appearing in the image IMG 2 . The symbol T F  may denote the temporal width of the first pulse sequence SEQ 1 . The symbol Δu MIN  may denote the displacement value of the group GRP of sub-images P 1  of the (slow) particle P 0 . The symbol ξ IMG  may denote the width of the image IMG 2 . 
       FIG. 5  shows, by way of example, a probability density function p v (v) obtained by fitting a regression function to velocity values determined from captured images. The method may comprise fitting a regression function to the measured data. The probability density function p v (v) may be optionally normalized such that the integral of the probability density function p v (v) over all possible velocities is equal to one. The probability density function p v (v) may represent a measured velocity distribution of the particles at a given point of the jet JET 0 . The probability density function p v (v) may have a peak value p MAX  associated with a velocity v PEAK . The velocity v PEAK  may denote the most probable velocity of the particles P 0 . The velocity distribution p v (v) may have a width Δv FWHM , which may be defined by a first velocity v L  and a second velocity v H . The velocities v L , v H  may be selected such that the velocity distribution p v (v) is equal to 50% of the maximum value p MAX  at the velocities v L  and v H . 
     Referring to  FIG. 6 , the method may comprise capturing and analyzing a plurality of images at each transverse position (e.g. z=z 1 ), so as to determine a lateral distribution based on a sufficient number of detected particles. 
     A first lateral distribution F 1   1 ( x ) may be determined by analyzing a first group of images IMG 2   z1,t11 , IMG 2   z1,t12 , IMG 2   z1,t13 , IMG 2   z1,t14  captured when the object plane O 1  is at a first transverse position z=z 1  with respect to the axis AX 0  of the nozzle NOZ 1 . 
     A second lateral distribution F 1   2 ( x ) may be determined by analyzing a second group of images IMG 2   z2,t21 , IMG 2   z2,t22 , IMG 2   z2,t23 , IMG 2   z2,t24  captured when the object plane O 1  is at a second transverse position z=z 2  with respect to the axis AX 0 . 
     A third lateral distribution F 1   3 ( x ) may be determined by analyzing a third group of images IMG 2   z3,t31 , IMG 2   z3,t32 , IMG 2   z3,t33 , IMG 2   z3,t34  captured when the object plane O 1  is at a third transverse position z=z 2  with respect to the axis AX 0 . 
     Referring to  FIG. 7 a   , the determined lateral distributions F 1   1 ( x ), F 1   2 ( x ), F 1   3 ( x ) may be e.g. lateral velocity distributions. Each distribution F 1   1 ( x ), F 1   2 ( x ), F 1   3 ( x ) may represent e.g. mean particle velocity as a function of lateral position coordinate x. 
     Referring to  FIG. 7 b   , the method may comprise comparing a determined lateral distribution F 1 ( x ) with a reference distribution REF 1 . The reference distribution may be e.g. velocity distribution v REF (x), which indicates a mean velocity as a function of lateral position x. For example, comparison of the distribution F 1 ( x ) with a reference distribution REF 1  may indicate that average particle velocity in a portion of the particle jet JET 0  is abnormally high. The symbol AR 2  may denote an abnormal region of the distribution, and the symbol NR 1  may denote a normal region of the distribution. The abnormal region AR 2  may be e.g. a region where the determined distribution substantially deviates from a reference distribution REF 1 . 
     Referring to  FIG. 7 c   , the method may comprise determining one or more transverse distributions F 2 ( z ) from several lateral distributions F 1 ( x ). The method may comprise comparing a determined transverse distribution F 2 ( z ) with a reference distribution REF 2 . For example, comparison of the transverse distribution F 2 ( z ) with a reference distribution REF 2  may indicate that average particle velocity in a peripheral portion of the particle jet JET 0  is abnormally high. The symbol AR 2  may denote an abnormal region of the determined transverse distribution, and the symbol NR 1  may denote a normal region of the distribution. The abnormal region AR 2  may be e.g. a region where the determined transverse distribution substantially deviates from a reference distribution REF 2 . 
     Determining the transverse distribution F 2 ( z ) may facilitate detecting certain types of abnormal conditions. For example, detecting an abnormal region AR 2  based on the transverse distribution F 2 ( z ) of  FIG. 7 c    may be easier than detecting an abnormal region AR 2  only from the uppermost lateral distribution of  FIG. 7   a.    
     The method may comprise adjusting one or more operating parameters PAR 1  of the cold spraying process based on the result of the comparison. For example, a relative position of the feeding nozzle NOZ 2  with respect to the accelerating nozzle NOZ 1  may be adjusted so as to provide a desired distribution F 1 ( x ) and/or F 2 ( z ). For example, one or more flow rates of the spraying apparatus may be adjusted so as to provide a desired transverse distribution F 2 ( z ). 
     The method may comprise classifying a cold spraying operation as valid or invalid by checking whether a determined distribution substantially matches with a reference distribution or not. 
     Referring to  FIGS. 8 a  and 8 b   , the method may comprise determining a plurality of lateral distributions, and determining a plurality of transverse distributions from the lateral distributions by plotting each lateral distribution at a transverse position, which corresponds to an object plane position associated with said lateral distribution. Referring to  FIG. 8 a   , the transverse distributions may be represented e.g. by a particle velocity map, which may indicate e.g. mean particle velocity as a function of position coordinates (x,z). Referring to  FIG. 8 b   , the transverse distributions may be represented e.g. by a particle number density map, which may indicate e.g. particle number density as a function of position coordinates (x,z). 
     In an embodiment, the determined distributions may also be functions of the axial position (i.e. functions of coordinate y). For example, the captured images may be partitioned into two or more regions to determine particle velocities at a first distance (axial position y 1 ) from the nozzle NOZ 1  and at a second different distance (axial position y 2 ) from the nozzle NOZ 2 . The method may comprise forming a three-dimensional distribution F(x,y,z) from the determined distributions (F 1   1 ( x,y,z =z 1 ), F 1   2 ( x,y,z =z 2 ), F 2   1 ( x =x 1 ,y,z,), F 2   2 ( x =x 2 ,y,z,)). 
     Referring to  FIGS. 9 a  and 9 b   , the method may also comprise changing angular orientation of the object plane O 1  of the optical measuring device  500  with respect to the nozzle NOZ 1 . The angular orientation of the object plane O 1  may be specified e.g. by an angle θ between the normal of the object plane O 1  and a vertical direction SG. The vertical direction may be defined e.g. by the direction of gravity. 
       FIG. 9 a    shows a situation where the object plane O 1  is substantially horizontal, and  FIG. 9 b    shows a situation where the object plane O 1  is substantially vertical. The method may comprise rotating the object plane O 1  from a first angular position θ 1  to a second angular position θ 2 . The method may comprise capturing images at two or more angular positions (θ) of the object plane O 1 . 
     The method may comprise rotating the object plane O 1  to change an angular position of the object plane O 1  from a first angular position (θ 1 ) to a second angular position (θ 2 ). One or more images (IMG 2 ) may be captured when the object plane (O 1 ) is at the first angular position (θ 1 ). One or more images (IMG 2 ) may be captured when the object plane (O 1 ) is at the second angular position (θ 2 ). 
     The device  500  may comprise e.g. an actuator, which may be arranged to rotate the imaging unit  200  around the axis AX 0  of the nozzle NOZ 1 , so as to capture images of the jet JET 0  from different directions. The actuator may be e.g. an industrial robot. 
     The method may comprise capturing one or more first images of the particle jet when the object plane has a first angular orientation with respect to the nozzle, and capturing one or more second images of the particle jet when the object plane has a second different angular orientation with respect to the nozzle. For example, the method may comprise capturing one or more first images of the particle jet when the object plane O 1  is substantially vertical, and the method may comprise capturing one or more second images of the particle jet when the object plane O 1  is substantially horizontal. Analysis of said first images may provide e.g. one or more distributions F 1   1 ( x,z =z 1 ), F 1   2 ( x,z =z 2 ). Analysis of said second images may provide e.g. one or more distributions F 2   1 ( z,x =x 1 ), F 2   2 ( z,x =x 2 ). The method may comprise forming a two-dimensional distribution F(x,z) from the determined distributions (F 1   1 ( x,z =z 1 ), F 1   2 ( x,z =z 2 ), F 2   1 ( z,x =x 1 ), F 2   2 ( z,x =x 2 )). 
     The method may also comprise using a combination of translational and rotational movements. The method may comprise causing translational movements of the object plane O 1  with respect to the nozzle NOZ 1 , causing rotational movements of the object plane O 1  with respect to the nozzle NOZ 1 , capturing images when the object plane is located at the different positions, and determining one or more distributions by analyzing the captured images. 
     In an embodiment, the actuator ACU 1  may also rotate the spraying gun GUN 1  with respect to a stationary imaging unit  200 , so as to capture images of the jet JET 0  from different directions. Analysis of the captured images (IMG 2 ) may provide one or more distributions. 
     The method may comprise forming a two-dimensional distribution from the determined distributions. 
       FIG. 10  shows, by way of example, method steps for controlling cold spraying. 
     The spraying apparatus  1000  may be arranged to provide a particle jet JET 0  according a first set of operating parameters (PAR 1 ) in step  1110 . 
     One or more images IMG 2  of the measuring region RG 0  may be captured when the measuring region RG 0  is illuminated with illuminating light pulses LB 0  (step  1120 ). 
     One or more velocity values (e.g. average velocity v AVE ) may be determined by analyzing the captured images IMG 2  (step  1130 ). One or more velocity distributions v(x) may be determined from the captured images IMG 2 . 
     The position of the accelerating nozzle NOZ 1  may be changed with respect to the illuminating unit  200  in step  1140 . For example, the spraying gun GUN 1  may be moved by the actuator ACU 1  in a situation where the illuminating unit  200  is stationary. 
     The imaging unit may capture one or more images IMG 2  when the object plane O 1  is at a first position (e.g. z=z 1 ) with respect to the accelerating nozzle NOZ 1 . The position of the object plane O 1  may be changed to a next different position (e.g. z=z 2 ), and images IMG 2  may be captured at the next position. 
     The steps  1120 ,  1130 ,  1140  may be repeated in order to gather image data from different transverse planes of the particle jet JET 0 . 
     One or more transverse distributions v(z) may be determined from the measured velocity values v(x,z=z 1 ), v(x,z=z 2 ) in step  1150 . 
     One or more determined distributions may be compared with reference data REF 1 , REF 2  in step  1160 . 
     One or more operating parameters PAR 1  of the cold spraying may be adjusted based on a result of the comparison in step  1170 . 
     A modified set of operating parameters (PAR 1 ) may be determined based on the result of the comparison. The cold spraying apparatus may be subsequently arranged to provide a particle jet JET 0  according to the modified set of operating parameters (PAR 1 ). 
     The method may comprise comparing one or more determined distributions with a reference distribution (REF), and validating or rejecting a cold spraying operation based on the result of the comparison. 
     Gas dynamic cold spraying may mean forming a coating on a target by a method, which comprises accelerating coating material particles e.g. with a gas jet, and which comprises causing the particles to impact on the target object such that the particles undergo plastic deformation and adhere to the target. The velocity of the particles may be e.g. greater than 400 m/s. The velocity of the particles may be e.g. in the range of 400 m/s to 1200 m/s. 
     The kinetic energy of a coating particle may cause deformation of the particle and/or local deformation of the surface of the target when the coating particle impacts on the target. The maximum temperature of the particles, when moving in the particle jet, may remain substantially below melting temperature of the material of the particles. The diameter of the particles may be e.g. in the range of 1 to 100 m. The suitable size range of the particles may depend on the material of the particles and/or on the material of the target. A large target may be coated e.g. by moving the central axis of the particle jet with respect to the target. The material of the coating particles may be e.g. a metal, polymer, ceramic. composite material. The material of the particles may be polycrystalline. 
     The particles may be accelerated by introducing the particles into a high velocity gas jet. The gas jet may be provided e.g. by guiding pressurized and heated gas into a diverging nozzle, in order to accelerate the gas and the particles to supersonic velocities. Supersonic velocity means a velocity which is higher than the speed of sound. In particular, the diverging nozzle may be a de Laval nozzle. The gas of the accelerating gas jet may be e.g. helium or nitrogen. The speed of sound in nitrogen at 20° C. is 349 m/s. The speed of sound in helium at 20° C. is 1007 m/s. Using helium as the accelerating gas may provide higher particle velocities. The temperature of the gas may be e.g. in the range of 500° C. to 900° C. The parameters of the coating process may be selected so as to provide plastic deformation of the particles at the impact, wherein the maximum temperature of the particles, when moving in the particle jet, may remain below the melting temperature of the material of the particles. 
     The temperature of the particles P 0  may be so low that thermal radiation emitted from the particles does not significantly contribute to the images captured by the image sensor SEN 1 . The imaging unit  200  may optionally comprise an optical filter to reject thermal radiation emitted from the particles P 0 . 
     The method may comprise selecting one or more operating parameters of the coating process. The operating parameters may include e.g. gas pressure, gas temperature, particle size, material of the particles, dimensions of the nozzle, material of the target, distance between the nozzle and/or the target, transverse speed of the nozzle with respect to the target. 
     Cold spraying may also be used for producing an object by additive manufacturing. The produced object may comprise or consist essentially of the material of the coating particles. 
     For the person skilled in the art, it will be clear that modifications and variations of the devices and the methods according to the present disclosure are perceivable. The figures are schematic. The particular embodiments described above with reference to the accompanying drawings are illustrative only and not meant to limit the scope of the disclosed embodiments, which is defined by the appended claims.