Abstract:
The present invention relates to a compact and inexpensive optical displacement sensor that does not require accurate control of the distance to the object. A repetitive optical structure is utilized for formation of a repetitive optical signal emitted by an illuminated moving object. The repetitive optical structure is illuminated by the light source for formation of a fringe pattern (similar to Laser Doppler Anemometry), and/or, an object is illuminated by the light source and the repetitive optical structure diverts light from the illuminated object onto light sensors. A speckle pattern is formed on the object by the illumination. The speckle pattern moves with movement of the object, and speckle pattern movement is determined without a need for imaging the object onto the repetitive optical structure. Since the speckle pattern is not imaged onto the optical member, the distance and possible distance changes between the object and the optical member substantially do not affect system performance.

Description:
FIELD OF THE INVENTION  
       [0001]     The present invention relates to a compact and inexpensive optical displacement sensor for determination of displacement of an object, such as linear displacement, angular displacement, vibration, etc.  
       BACKGROUND OF THE INVENTION  
       [0002]     Provision of compact and inexpensive sensors for determination of movement of an object has been pursued for some time.  
         [0003]     In Detection of movement with laser speckle patterns: statistical properties, Schnell et al., Vol. 15, No. 1, January 1998, J. Opt. Soc. Am., a sensor for determination of in-plane movement of a diffusing object is disclosed. The object is illuminated with coherent light and a speckle pattern is formed by interaction of the light with the surface of the object. Two interlaced differential comb photo detector arrays act as a periodic filter to the spatial-frequency spectrum of the speckle pattern intensity. The detector produces a zero-offset, periodic output signal versus displacement that permits measurement of the movement at arbitrarily low speed. The direction of the movement can be detected with a quadrature signal produced by a second pair of interlaced comb photo detector arrays.  
         [0004]     In WO 98/53271, a sensor for determination of angular displacement of one or more parts of an object is disclosed. The determination is also based on speckle patterns and is independent of the distance to the object, any longitudinal and transversal movements, the shape of the object, and the radius of angular displacement.  
         [0005]     In T. Ushizaka, Y. Aizu, and T. Asakura: “Measurements of Velocity Using a Lenticular Grating”, Appl. Phys. B 39, 97-106 (1986), and Y. Aizu: “Principles and Development of spatial Filtering Velocimetry”, Appl. Phys. B 43, 209-224 (1987), discloses utilization of a so-called lenticular grating for deflection of light scattered from a particle onto photo detectors. A particle traversing a measurement volume is illuminated by diffuse light from a He—Ne laser (5 mW) illuminating a ground glass placed at the measurement volume. It is a fundamental characteristic of the measurement system disclosed that the moving particle is imaged onto the lenticular grating. Thus, the distance between the lenticular grating and the moving particle has to be accurately controlled. Furthermore, a set of lenses is placed behind the lens array in order to adequately collect light onto the detectors. This eliminates the possibility for realizing a compact one-element optical system.  
       SUMMARY OF THE INVENTION  
       [0006]     Thus, there is a need for a more compact and inexpensive displacement sensor, and a sensor that does not require accurate control of the distance to the object.  
         [0007]     According to the present invention the above-mentioned and other objects are fulfilled by an optical displacement sensor system for detection of displacement of an object, comprising a coherent light source for illumination of at least part of the object with spatially coherent light, an optical member with at least three optical elements for mapping of different specific first areas in space onto substantially the same second area in space thereby generating an oscillating optical signal caused by phase variations of light emanating from the object moving in the first areas.  
         [0008]     It is a fundamental aspect of the present invention that a repetitive optical structure, i.e. the optical member, is utilized for formation of a repetitive optical signal emitted by an illuminated moving object by 
    1) Illuminating the repetitive optical structure by the light source for formation of a fringe pattern (similar to Laser Doppler Anemometry), and/or,     2) Illuminating an object by the light source and diverting light from the illuminated object onto light sensors by the repetitive optical structure.    
 
         [0011]     The light source illuminates the object whereby a speckle pattern is formed on the object. The speckle pattern moves with movement of the object, and speckle pattern movement is determined without a need for imaging the object onto the repetitive optical structure, i.e. the optical member.  
         [0012]     Since the speckle pattern is not imaged onto the optical member, the distance and possible distance changes between the object and the optical member substantially do not affect system performance.  
         [0013]     In an embodiment of the invention well suited for Laser Doppler Anemometry applications, a collimated light source is provided for illuminating the optical member, and an imaging system is provided for imaging the optical member onto a measurement volume thereby forming a fringe pattern in the measurement volume.  
         [0014]     In another embodiment of the invention light emanating from the object are received at an input plane. The optical member directs light emanating from different parts of the input plane in substantially the same direction by corresponding elements of the optical member.  
         [0015]     In yet another embodiment of the invention, the above-mentioned embodiments are combined, i.e. the optical member is utilized both for transmission of coherent light towards the object and for reception of light emanating from the object.  
         [0016]     Dividing the light beam from the light source into a plurality of light beams by illumination of the optical member increases safety, since the power of an individual light beam that accidentally may enter a human eye is lowered.  
         [0017]     Further the signal to noise ratio is increased, since the projection of a fringe-like pattern onto the object will make the speckle spectrum correspond to the optimum for the optical member.  
         [0018]     The individual optical elements may interact with light by reflection, refraction, scattering, diffraction, etc, either alone or in any combination, of light incident upon them. Thus, the individual optical elements may be lenses, such as cylindrical lenses, spherical lenses, Fresnel lenses, ball lenses, etc, prisms, prism stubs, mirrors, liquid crystals, etc.  
         [0019]     Alternatively, the optical member may be formed by a diffractive optical element, such as holographically produced lenses, etc.  
         [0020]     Further, the optical member may comprise a linear phase grating with a sinusoidal modulation of the film thickness, e.g. in a photo resist film.  
         [0021]     After interaction with the individual optical elements, the light may be transmitted through the elements or be reflected from the elements, e.g. appropriately coated for reflection. The system also comprises a detector with at least one optical detector element for conversion of light incident upon it into a corresponding electronic signal.  
         [0022]     The detector is positioned in the propagation path of the light emanating from the optical member. The invention is most easily understood considering an embodiment wherein the optical member is a repetitive optical member constituted by a linear array of cylindrical lenses. The focal length of the lenses may be positive or negative. For simplicity only positive lenses are depicted in the appended figures. The input plane is located in front of the array of lenses at a distance equal to the focal length of the lenses and perpendicular to the direction of propagation of the incoming light emanating from the object.  
         [0023]     The object has a surface of a size that allows formation of a speckle pattern. Surface roughness of the object causes formation of the speckle pattern since surface deviations modify the phase of various parts of the incident light differently. Preferably, at least a part of the surface is illuminated by a laser, and a speckle pattern could be detected at the input plane, e.g. by intensity measurements, caused by variations of the electromagnetic field along the input plane. In the following, such electromagnetic intensity variations are termed “speckle variations”. When the object is displaced, the speckle variations move along the input plane with a velocity proportional to the surface velocity or the rotational speed. The individual optical elements direct the light towards an optical detector of the embodiment. When a speckle variation at the input plane has moved a distance that is equal to the width of an individual optical element, the corresponding light emanating from the individual optical element sweep across the area of the optical detector. This is repeated for the next optical element, and it is seen that when a speckle variation has traversed a distance equal to the length of the linear array, the optical detector is swept repetitively a number of times equal to the number of individual optical elements of the linear array. It is seen that for a regular speckle variation pattern at the input plane with a speckle size that is substantially equal to the size of an individual optical element, the intensity of the electromagnetic field at a detector element varies between a high intensity when light areas of the speckle variations are aligned with the optical elements and a low intensity when dark areas of the speckle variations are aligned with the optical elements, and that the frequency of the oscillations corresponds to the velocity of displacement of the speckle variations in the direction of the longitudinal extension of the linear array divided by the array pitch, i.e. the distance between individual neighboring optical elements.  
         [0024]     This principle of operation applies in general to other embodiments of the present invention regardless of the type of optical member utilized and regardless of whether or not an image of the object is formed at the input plane. For example, a point source positioned substantially at the input plane and emitting a diverging beam of light may illuminate the object. The radiation is diffusely reflected by the object and received at the input plane. It is well known in the art that speckle variation displacements at the input plane is twice the corresponding displacements at the surface of the object regardless of the distance between the object and the input plane.  
         [0025]     Alternatively, the object may be illuminated by a collimated beam of light in which case, the displacement of speckle variations at the input plane is equal to corresponding displacements at the surface of the object independent of the distance between the object and the input plane.  
         [0026]     In still another embodiment of the present invention, a Fourier transforming lens is positioned between the object and the input plane in such a way that the input plane is positioned at the Fourier plane of the Fourier transforming lens, i.e. at the back focal plane of the lens, whereby rotational displacement of the object can be determined independent of the distance between the object and the input plane. Furthermore, the detected frequency will be independent of the radius of curvature of the rotating object and independent of the wavelength. Besides, a transverse displacement of the object will only give rise to speckle de-correlation and not give rise to speckle displacement.  
         [0027]     The optical member provides a spatial filtering of the electromagnetic field at the input plane in such a way that moving speckle variations of a size comparable to the size of the individual optical elements leads to an oscillating detector signal. Speed of movement can e.g. be measured by zero-crossing detection of this signal.  
         [0028]     It is seen that two-dimensional speckle displacement may be determined with an embodiment of the present invention having a two-dimensional array of optical elements.  
         [0029]     In a preferred embodiment of the present invention, the system further comprises an imaging system for imaging part of the input plane onto the at least one detector element whereby each of the individual optical elements in combination with the imaging system images specific parts of the input plane onto the same specific area of an output plane so that points at the input plane that are positioned at the same relative positions in relation to adjacent respective optical elements are imaged onto the same point at the optical detector. As further explained below, without the imaging system, there is a small distance between imaged points at the detector for corresponding points at the input plane having the same relative position in relation to respective optical elements. However, the accuracy of the system may still be sufficient and will depend on the actual size of the system.  
         [0030]     The optical member and the above-mentioned imaging system may be merged into a single physical component, such as a molded plastic component, in order to obtain a further compact system suited for mass production.  
         [0031]     The displacement sensor with the optical member facilitates determination of speckle variation movement at the input plane in a direction of the optical member. An optical system positioned between the object and the input plane determines the type of object movement that is determined by converting the speckle variations arising from the specified object movement into a linear speckle translation in the system input plane. The object movement could be in-plane or out-of-plane rotation and/or displacement, such as one- or two-dimensional displacement, one- or two-dimensional velocity, angular displacement, angular velocity, etc.  
         [0032]     The number, size, and position of the detector elements together with the processing of the signals obtained from the elements, such as subtraction, addition, etc, determine the suppression of harmonics in the output signal. Specifically, the direction of movement of speckle variations can be probed in case a quadrature (or close to quadrature) signal is obtained.  
         [0033]     It is an important advantage of the present invention that the displacement sensor only comprises a few optical detector elements, such as one, two, four, six or seven, etc, elements.  
         [0034]     Occurrence of velocity signal drop out may be reduced by provision of a second set of optical detector elements that is displaced in relation to the existing set of detector elements so that a signal that is statistically independent of the other signal may be available from one set of detector elements during absence of a signal from the other set of detector elements. Thus by proper processing of the two signals, e.g. switching to a set of detector elements generating a velocity signal, occurrence of signal drop out is minimized. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0035]     For a better understanding of the present invention reference will now be made, by way of example, to the accompanying drawings, in which:  
         [0036]      FIG. 1  schematically illustrates a preferred embodiment of a displacement sensor according to the present invention,  
         [0037]      FIG. 2  illustrates the operating principle of the displacement sensor of  FIG. 1 ,  
         [0038]      FIG. 3  schematically illustrates another preferred embodiment of a displacement sensor according to the present invention,  
         [0039]      FIG. 4  illustrates the operating principle of the displacement sensor of  FIG. 3 ,  
         [0040]      FIG. 5  schematically illustrates electromagnetic wave propagation in the displacement sensor of  FIG. 1 ,  
         [0041]      FIG. 6  schematically illustrates a displacement sensor with a Fresnel lens array,  
         [0042]      FIG. 7  schematically illustrates a displacement sensor with a linear phase grating having a sinusoidal modulation in the film thickness,  
         [0043]      FIG. 8  schematically illustrates a displacement sensor with a prism array,  
         [0044]      FIG. 9  illustrates the operating principle of the displacement sensor of  FIG. 8 ,  
         [0045]      FIG. 10  schematically illustrates a displacement sensor with an array of prism stubs,  
         [0046]      FIG. 11  illustrates the operating principle of the displacement sensor of  FIG. 10 ,  
         [0047]      FIG. 12  illustrates an embodiment operating like a Laser Doppler Anemometer,  
         [0048]      FIG. 13  illustrates another embodiment operating like a Laser Doppler Anemometer,  
         [0049]      FIG. 14  illustrates an embodiment suited for determination of the velocity of a particle, where direction for particle velocity can be determined.,  
         [0050]      FIG. 15  is a plot of a detector element signal from an embodiment shown in  FIG. 12  or  13 ,  
         [0051]      FIG. 16  is a plot of a signal from a displaced optical detector element having a phase lag in relation to the signal shown in  FIG. 14 ,  
         [0052]      FIG. 17  is a plot of the difference between the signals shown in  FIGS. 14 and 15 ,  
         [0053]      FIG. 18  illustrates the definition of the input plane for an embodiment of the invention,  
         [0054]      FIG. 19  illustrates the definition of the input plane for another embodiment of the invention,  
         [0055]      FIG. 20  illustrates the definition of the input plane for yet another embodiment of the invention,  
         [0056]      FIG. 21  illustrates combining of optical components of a displacement sensor according to the present invention,  
         [0057]      FIG. 22  illustrates another way of combining of optical components of a displacement sensor according to the present invention,  
         [0058]      FIG. 23  illustrates combining of optical components of a displacement sensor with a prism array according to the present invention,  
         [0059]      FIG. 24  schematically illustrates a displacement sensor according to the present invention with optical components combined with a prism,  
         [0060]      FIG. 25  schematically illustrates another displacement sensor according to the present invention with optical components combined with a prism,  
         [0061]      FIG. 26  schematically illustrates a two-dimensional array of prism stubs,  
         [0062]      FIG. 27  illustrates electromagnetic wave propagation of waves to the detector plane having been refracted by a prism stub,  
         [0063]      FIG. 28  schematically illustrates the operation of a linear displacement sensor system according to the present invention,  
         [0064]      FIG. 29  schematically illustrates the operation of another linear displacement sensor system according to the present invention,  
         [0065]      FIG. 30  schematically illustrates the operation of a displacement sensor system for determination of rotational displacement according to the present invention,  
         [0066]      FIG. 31  schematically illustrates a reflection configuration of the present invention for determination of linear displacement,  
         [0067]      FIG. 32  schematically illustrates a reflection configuration of the present invention for determination of rotational displacement,  
         [0068]      FIG. 33  schematically illustrates a reflection configuration of the present invention for determination of 2D rotational displacement,  
         [0069]      FIG. 34  schematically illustrates a reflection configuration of the present invention for determination of 2D linear displacement,  
         [0070]      FIG. 35  schematically illustrates an embodiment with three lenticular arrays,  
         [0071]      FIG. 36  schematically illustrates an embodiment with four lenticular arrays,  
         [0072]      FIG. 37  schematically illustrates a simple detector configuration,  
         [0073]      FIG. 38  is a plot of a signal provided by the detector illustrated in  FIG. 37 ,  
         [0074]      FIG. 39  is a plot of the power spectrum of the signal shown in  FIG. 38 ,  
         [0075]      FIG. 40  schematically illustrates another detector configuration,  
         [0076]      FIG. 41  is a plot of a signal provided by the detector illustrated in  FIG. 34 ,  
         [0077]      FIG. 42  is a plot of the power spectrum of the signal shown in  FIG. 41 ,  
         [0078]      FIG. 43  schematically illustrates yet another detector configuration,  
         [0079]      FIG. 44  is a plot of a signal provided by the detector configuration illustrated in  FIG. 43 ,  
         [0080]      FIG. 45  is a phase plot of the signal shown in  FIG. 44 ,  
         [0081]      FIG. 46  schematically illustrates still another detector configuration,  
         [0082]      FIG. 47  is a plot of a signal provided by the detector illustrated in  FIG. 46 ,  
         [0083]      FIG. 48  is a phase plot of the signal shown in  FIG. 47 ,  
         [0084]      FIG. 49  schematically illustrates a miniaturized embodiment of the invention,  
         [0085]      FIG. 50  schematically illustrates another miniaturized embodiment of the invention,  
         [0086]      FIG. 51  schematically illustrates an embodiment with common transmitting and receiving optics,  
         [0087]      FIG. 52  schematically illustrates the operating principle of the embodiment shown in  FIG. 51 ,  
         [0088]      FIG. 53  illustrates the intensity distribution at the surface of an object illuminated by the embodiment shown in  FIG. 51 , and  
         [0089]      FIG. 54  illustrates (unintentional) illumination of the human eye by the embodiment shown in  FIG. 51 . 
     
    
     DESCRIPTION OF PREFERRED EMBODIMENTS  
       [0090]      FIG. 1  schematically shows a displacement sensor  10  according to the present invention with a linear array  12  of cylindrical lenses  18 . f 1  is the focal length of the cylindrical lenses  18 . The input plane  14  is located at a distance equal to the focal length f 1  of the lenses  18  and perpendicular to the direction  16  of propagation of the incoming light emanating from the object (not shown). In this embodiment  10 , a part of the surface of the object (not shown) scatters light onto the input plane  14 . Preferably, a laser illuminates the part of the surface, and a speckle variation is generated at the input plane. When the object is displaced, the speckle variations move correspondingly along the input plane  14 . The individual cylindrical lenses  18  direct the light  16 ,  20  towards a refractive lens  22  having a focal length f 2  and being positioned a distance equal to f 1 +f 2  from the linear array  12 . The lens  22  further refracts the light  20  into waves  24  propagating towards optical detector elements  26 ,  28 , and  30  positioned at the focal plane of lens  22 . In this way, the input plane  14  is repeatedly imaged onto an output plane  15 . The detector elements  26 ,  28 ,  30  are positioned so that their individual surfaces for reception of light coincide with the output plane  15 . It is seen that an area  32  of the input plane is imaged onto an area  34  of a detector element  28  and that corresponding areas  36  that are located at the same relative positions in relation to adjacent respective cylindrical lenses  18  are imaged onto the same area  34  of the optical detector constituted by the detector elements  26 ,  28 ,  30 .  
         [0091]     It should be noted that the distance between the linear array  12  and the lens  22  is chosen to be equal to f 1 +f 2  in the present example for ease of explanation of the operation of the displacement sensor  10 . However, the displacement sensor  10  operates with any distance between the linear array  12  and the lens  22 . For compactness it may be preferred to set the distance to zero.  
         [0092]     It should also be noted that in an imaging system as the one shown in  FIG. 28 , a rotational displacement of the object does not lead to translation of speckle variations in the input plane. However, rotational displacement of the object will typically lead to speckle boiling.  
         [0093]     The operating principle of the displacement sensor of  FIG. 1  is further illustrated in  FIG. 2 . When a speckle variation  16  at the input plane  14  has moved a distance  38  that is equal to the width Λ 0 , i.e. the pitch, of an individual optical element  18 , the corresponding image formed by the combination of lens  22  and the respective cylindrical lens  18  sweeps across the area  40  of the optical detector elements  26 ,  28 , and  30 . This is repeated for the other optical elements  18 , and it is seen that when a speckle variation has traversed a distance equal to the length of the linear array  12 , the optical detector  26 ,  28 ,  30  is swept repetitively a number of times equal to the number of individual optical elements  18  of the linear array  12 . It is seen that for a regular speckle variation pattern at the input plane with an average speckle size that is comparable with the size  38  of an individual optical element  18 , the intensity of the electromagnetic field at a detector element  26 ,  28 ,  30  varies between a high intensity when bright areas of the speckle variations are aligned with the sensor elements  26 ,  28 ,  30  and a low intensity when dark areas of the speckle variations are aligned with the optical elements  26 ,  28 ,  30 , and that the frequency of the oscillations corresponds to the velocity of displacement of the speckle variations in the direction Δx of the longitudinal extension of the linear array  12  divided by the array pitch, i.e. the distance between individual neighboring optical elements.  
         [0094]     As previously mentioned, the same principle of operation applies in general to other embodiments of the present invention regardless of the type of optical member utilized and regardless of whether or not an image of the object is formed at the input plane  14 .  
         [0095]     With reference again to  FIGS. 1 and 2  wherein Λ 0  denotes the pitch  38  of the optical member  12  and f 1  is the focal length of the individual optical elements  18  of the optical member  12  and f 2  is the focal length of the lens  22 , the distance D 0  in the detector plane  26  and  30 , repetitively swept by a speckle traversing the input plane is given by  
         D   0     =       Λ   0     ⁢         f   2       f   1       .           
 
         [0096]     In the detected electrical signal D 0  corresponds to the period of the signal, i.e. a 360° phase shift. This equation is valid for any distance between the optical member  12  and the lens  22 .  
         [0097]     For the aperture of the system D, e.g. in  FIG. 1D  is equal to the diameter of the lens  22 , the following equation should preferably be fulfilled:  
         D     f   2       ≥         Λ   0       f   1       .         
 
         [0098]     Further, it is preferred that the effect of the individual optical elements is governed by the lens effect and not by diffraction, i.e.:  
           f   1       k   ⁢           ⁢     Λ   0   2         ⁢     &lt;&lt;   1.         
 
         [0099]     Where k is the optical wavenumber.  FIG. 3  schematically shows another displacement sensor  11  according to the present invention without the lens  22 , i.e. without an imaging system that images the input plane  14  onto the output plane  15 . In this embodiment, the receiving areas of the detector elements  26 ,  28 ,  30  define the output plane  15 . As more clearly illustrated in  FIG. 4 , without the imaging system, there is a small distance between imaged points  34  at the detector  26 ,  28 ,  30  for corresponding points  32  at the input plane  14  having the same relative position in relation to respective optical elements  18 . However, the accuracy of the system  11  may still be sufficient and will depend on the actual size of the system  11 .  
         [0100]     In  FIG. 5 , the image forming of the displacement sensor shown in  FIG. 1  is further illustrated, and it is seen that the position of the intersection  34  between the optical detector element  28  and incident light  24  is independent of the slope of the electromagnetic wave  16  incident on the input plane  14 . It only depends on the relative position of the intersection  32  between the input plane  14  and the input wave  16  in relation to the adjacent optical element  18 .  
         [0101]      FIG. 6  schematically illustrates a displacement sensor similar to the sensor shown in  FIG. 1 , wherein the linear array of cylindrical lenses has been substituted with a Fresnel lens array  42 . The linear array of cylindrical lenses may alternatively be substituted by a diffractive optical element  42 .  
         [0102]     Likewise  FIG. 7  schematically illustrates a displacement sensor similar to the sensor shown in  FIG. 1 , wherein the linear array of cylindrical lenses has been substituted with a linear phase grating  43  with a sinusoidal modulation of the film thickness, e.g. in a photo resist film. The phase grating can be made by exposing a (thick) photo resist plate with an interference pattern made by crossing two laser beams. Incident light will primarily be diffracted in the “plus first” and “minus fist” order. Besides, non-diffracted light will pass directly through the phase grating.  
         [0103]     In  FIG. 8 , an alternative embodiment of the displacement sensor shown in  FIG. 3  is illustrated, wherein the linear array of cylindrical lenses has been substituted by a linear array  44  of prisms. The two sides of each prism refract incoming rays of light towards two respective detector elements  26 ,  30 .  
         [0104]     The operating principle of the displacement sensor of  FIG. 8  is more clearly illustrated in  FIG. 9  showing that a speckle variation is alternatingly directed toward the two respective detector elements  26 ,  30  when the speckle variation traverses the linear prism array  44  along its longitudinal extension.  
         [0105]     In  FIG. 10 , a similar embodiment of the displacement sensor is illustrated, wherein the linear array of cylindrical lenses has been substituted by a linear array  44  of prism stubs. As before, the two sides of each prism refract incoming rays of light towards two respective detector elements  26 ,  30  while the top surface transmits or refracts incoming rays toward a third detector element  28 .  
         [0106]     The operating principle of the displacement sensor of  FIG. 10  is more clearly illustrated in  FIG. 11  showing that a speckle variation is alternatingly directed toward the three respective detector elements  26 ,  28 ,  30  when the speckle variation traverses the linear prism stub array  44  along its longitudinal extension.  
         [0107]     It should be noted that the direction of propagation of waves refracted by the prisms depends on the slope of the direction of propagation of the incoming light. It should also be noted that the phase difference between detector signals is fixed. It is an important advantage of these embodiments of the invention that the phase difference is determined by the geometry of the optical member and independent on the detector element positions. It is another advantage that utilization of prisms facilitates utilization of small detectors.  
         [0108]      FIG. 12  illustrates an embodiment  80  of the invention that operates like a Laser Doppler Anemometer. Light  82  emitted from a point source laser  84  is collimated by lens  86  and the collimated light illuminates an array  12  of cylindrical lenses. Lenses  88  and  90  form a telescope that images the focal spots of the cylindrical lenses  12  in the measuring volume  92  whereby a set of straight and equidistant fringe planes  94  are formed in the measurement volume  92 . It is seen that the first areas occupied by the fringes  94  are mapped into the same second area  96  at the laser source  84 .  
         [0109]      FIG. 13  illustrates another embodiment  100  of the invention that is similar to the embodiment  80  shown in  FIG. 12 , however, in this embodiment an array  12  of spherical lenses has substituted the array of cylinder lenses in  FIG. 12 . This leads to equidistant and straight cylindrical focal lines  94 .  
         [0110]     Particles or a solid surface passing the fringes created in the measuring volume will scatter light. A detector place at an arbitrary position will give rise to a modulated signal, the frequency of which is given by the velocity component perpendicular to the fringes divided by the fringe distance.  
         [0111]      FIG. 14  illustrates the embodiment  102  also shown in  FIG. 1  for measurement of particle velocity  106 . A laser beam  104  is focused onto a measurement volume  108  that is imaged onto the input plane  15  of the system with lens f 1 . When a particle  110  traverses the measurement volume  108 , its image  112  will traverse the array  12  of cylindrical lenses, and each of the detectors  26 ,  28 ,  30  receives an oscillating optical signal similar to the signal created by fringes in a Laser Doppler Anemometer. Thus, each detector element  26 ,  28 ,  30  receives light from the particle  110  as if the particle  110  traverses a set of fringes, in the following denoted virtual fringes.  FIG. 15  is a plot of the output signal  114  from one of the detector elements generated in response to the oscillating optical signal. A corresponding signal  116  from an adjacent detector element is shown in  FIG. 16 . This signal  116  is phase shifted in relation to the signal  114  shown in  FIG. 15  because of the physical displacement of the detector elements.  
         [0112]     Since the low frequency pedestals of the two signals are substantially identical, the difference between the two signals  114 ,  116  is an AC-signal  118  as shown in  FIG. 17 . It is preferred that the phase shift between the two detector elements  26 ,  28 ;  28 ,  30  is substantially equal to 90° so that the direction of the particle velocity can be deduced whereby the requirement of a costly Bragg-cell is eliminated. The angle of the incident laser beam is not critical. A forward scattering system provides the largest signals, however, a back scattering system may be preferred for other reasons.  
         [0113]     In this embodiment  102  of the invention, it is seen that first areas of the measurement volume  108 , i.e. corresponding to the virtual fringes, are mapped into the same second area at a detector element.  
         [0114]      FIG. 18  illustrates the definition of the input plane  14  of the system. In the embodiment  10  shown in  FIG. 1 , the output plane  15 , defined by the detector element  26 ,  28 ,  30  surfaces, is imaged onto the input plane  14  by the combination of the lens array  12  and the lens  22 . Thus, rays  120  emitted from the output plane  15  would be focused onto the input plane  14  by an element  18  of the optical member  12 .  
         [0115]      FIG. 19  illustrates the definition of the input plane  14  for the embodiment  11  shown in  FIG. 3 . There is no imaging system in this embodiment  11 , however still, rays  120  emitted from the output plane  15  would be focused onto the input plane  14  by an element  18  of the optical member.  
         [0116]      FIG. 20  illustrates the definition of the input plane for the embodiment shown in  FIG. 8 . Also in this embodiment, there is no imaging system, however still, rays  120  emitted from the output plane  15  would be focused onto the input plane  14  by an element of the optical member  44 .  
         [0117]      FIGS. 21-23  illustrates various ways of combining the optical components of the previously illustrated displacement sensors in order to provide a further compact system suited for mass production.  
         [0118]     In  FIGS. 24 and 38 , the optical components have been combined with a prism to limit the linear extension of the system. In  FIG. 25 , the lens  22  shown in  FIG. 13  has been substituted by a concave mirror  23 .  
         [0119]      FIG. 26  schematically illustrates a repetitive optical member in the form of a two-dimensional array  46  of prism stubs for determination of speckle displacement in two dimensions.  FIG. 27  illustrates electromagnetic wave propagation of waves  50  having been refracted by a prism stub. It is seen that a flat top prism refracts incoming beams of light into five directions towards five different respective detector elements. The phase difference between detector element output signals depends solely on the geometry of the flat top prism array. It does not depend on detector element position. A prism array  44 ,  46 ,  48  facilitates the use of small detector elements.  
         [0120]      FIG. 28  schematically illustrates a displacement sensor system  52  according to the present invention, comprising an imaging system  54  that images a part  56  of the surface of a moving object  58  onto the input plane  14  of a displacement sensor  10  also shown in  FIG. 1 . The object  58  is illuminated with a collimated laser beam  60  so that the velocity component along the intersection of the input plane  14  and the plane of  FIG. 28  determined at the input plane  14  is the magnification ratio of the imaging system  54  times the corresponding velocity component of the surface  56 .  
         [0121]      FIG. 29  schematically illustrates a displacement sensor system  62  that differs from the displacement sensor system shown in  FIG. 28  in that the system  62  does not have an imaging system  54  and that the object  58  is illuminated with a divergent laser beam  64  emanating from a point source, e.g. a VCSEL, positioned at the input plane  14 . It is well known in the art that speckle variation displacements at the input plane is twice the corresponding displacements at the surface of the object regardless of the distance between the object and the input plane. Thus, the velocity component along the intersection of the input plane  14  and the plane of  FIG. 29  determined at the input plane  14  is two times the corresponding velocity component of the surface  56 .  
         [0122]      FIG. 30  schematically illustrates yet another displacement sensor system  66  according to the present invention, comprising a Fourier transforming lens  70  positioned so that its Fourier plane, i.e. the back focal plane of lens  70 , coincides with the input plane  14  of a displacement sensor  10  also shown in  FIG. 1 . The object  68  is illuminated with a collimated laser beam  60  and the velocity component of the speckles in the input plane along the intersection of the input plane  14  and the plane of  FIG. 18  corresponds to the angular velocity of the object  68 .  
         [0123]     It should be noted that translational displacement of the object  68  does not lead to translation of speckle variations in the input plane. However, translational displacement of the object  68  will typically lead to speckle boiling.  
         [0124]      FIG. 31  schematically illustrates a displacement sensor system  75  for determination of linear displacement with a reflecting member  12  comprising a linear array of cylindrical concave mirrors  18  performing an optical function similar to the optical function of the cylindrical lenses shown in e.g.  FIG. 1 . The displacement sensor operates similar to the operation of the sensor shown in  FIG. 3  apart from the fact that the optical member  12  shown in  FIG. 21  reflects light while the corresponding optical member  12  shown in  FIG. 3  refracts light.  
         [0125]      FIG. 32  schematically illustrates another reflection configuration  76  of the present invention for determination of rotational displacement also having a reflecting member  12  comprising a linear array of cylindrical concave mirrors  18 . The system illustrated operates similar to the system illustrated in  FIG. 30 , however, it should be noted that in the system  76 , the functions of lenses  22  and  70  of the system illustrated in  FIG. 30  are combined into one lens  22 .  
         [0126]      FIG. 33  schematically illustrates a displacement sensor system  77  for determination of rotation in two dimensions. The system  77  is similar to the one-dimensional system  76  illustrated in  FIG. 32 , however, the linear array of cylindrical concave mirrors has been replaced by a two-dimensional array  12  of spherical concave mirrors  18 , and two optical detector elements  27 ,  29  have been added facilitating detection, in combination with detector element  28 , of speckle movement in a direction substantially perpendicular to the direction of movement detected by the combination of optical detector elements  26 ,  28 ,  30 .  
         [0127]     Likewise,  FIG. 34  schematically illustrates a displacement sensor system  78  for determination of displacement in two dimensions. The system  77  is similar to the one-dimensional system  75  illustrated in  FIG. 31 , however, the linear array of cylindrical concave mirrors has been replaced by a two-dimensional array  12  of spherical concave mirrors  18 , and two optical detector elements  27 ,  29  have been added facilitating detection, in combination with detector element  28 , of speckle movement in a direction substantially perpendicular to the direction of movement detected by the combination of optical detector elements  26 ,  28 ,  30 .  
         [0128]      FIG. 35  is a front view of a displacement sensor system  130  for determination of displacement in two dimensions and in-plane rotation, simultaneously. The system  130  comprises a VCSEL  132  positioned behind a collimating lens  134  whereby the object is illuminated by a collimated light beam. Three lenticular cylindrical lens arrays  136 ,  138 ,  140  are positioned in a common plane with a mutual angular separation of approximately 120° for determination of velocity components indicated by the respective arrows  142 ,  144 ,  146 . Detectors  148 ,  150 ,  152  are positioned behind the respective lenticular arrays for conversion of received light to an electrical signal.  
         [0129]     Velocity components V x  and V y  are defined by the co-ordinate system  154 . V x  and V y  and rotational velocity V φ , are calculated according to the equations  156 .  
         [0130]      FIG. 36  is a front view of a displacement sensor system  160  for determination of displacement in two dimensions and in-plane rotation, simultaneously. The system  160  comprises a VCSEL  162  in the drawing positioned behind a collimating lens  164  whereby the object is illuminated by a collimated light beam. Four lenticular cylindrical lens arrays  166 ,  168 ,  170 ,  172  are positioned in a common plane with a mutual angular separation of approximately 90° for determination of velocity components indicated by the respective arrows  174 ,  176 ,  178 ,  180 . Detectors  182 ,  184 ,  186 ,  188  are positioned behind the respective lenticular arrays for conversion of received light to an electrical signal. Velocity components V x  and V y  and rotational velocity V φ  are calculated according to the equations  190 .  
         [0131]      FIG. 37  shows a fundamental detector element configuration  80  of an embodiment of the invention.  FIG. 38  is a plot of the detector signal  82  and  FIG. 39  is a plot of the power spectrum  84  of the detector signal. It should be noted that the low frequency part  86  and the second harmonic  88  of the spectrum  84  are quite significant. The low frequency noise leads to a variation of the running mean value which will introduce significant errors in velocity determinations based on zero-crossing detection. The width of the detector has been selected for optimum suppression of the third harmonic of the fundamental frequency. The detector element is assumed to have a rectangular shape and thus, the power spectrum of the detector function is a sinc-function. In order to eliminate every third harmonic of the detector output signal, the width of each detector element is selected to be substantially equal to one third of the full width of the detector array that is selected to be equal to the width repetitively swept by a speckle traversing the input plane. In  FIG. 34 , a configuration of two matched detector elements  92 ,  94  is shown. The distance between the elements corresponds to a phase shift of 180°. The output signals from the detector elements are subtracted for suppression of the low frequency part of the signals and the even harmonic frequencies of the fundamental frequency. The difference signal  96  is plotted in  FIG. 41 , and the power spectrum  98  is plotted in  FIG. 42 . The suppression of the low frequency part  86  and the second harmonic  88  is clearly demonstrated by comparison with  FIG. 39 .  
         [0132]     An almost-phase-quadrature detector configuration  100  is shown in  FIG. 43 , wherein six detectors of equal size form two subtracted signals  102 ,  104 . The two subtracted signals  102 ,  104  are 60 degrees out of phase, and therefore suitable for determination of e.g. direction of the speckle translation or sub-radian phase resolution. In this configuration  100 , an exact phase quadrature can not be achieved without changing the detector width  106  thereby reducing the suppression of the third harmonic. The subtracted almost-phase-quadrature signals  108 ,  110  are plotted in  FIG. 44 , and  FIG. 45  is a phase plot  112  of the signals  108 ,  110 . The phase plot  112  has an elliptical shape which facilitates determination of the direction of the speckle translation and eventually sub-radian measurement accuracy. However, due to the elliptically shape of the phase plot this configuration will be noise sensitive.  
         [0133]     The detector configuration  114  shown in  FIG. 46  provides a substantially exact phase-quadrature detector arrangement. Seven detectors of three different sizes form two subtracted signals  116 ,  118 . The two signals  116 ,  118  are 90 degrees out of phase and therefore facilitate determination of direction of object velocity and sub-radian phase resolution.  FIG. 47  is a plot of the subtracted phase-quadrature signals  120 ,  122 , and  FIG. 48  is the corresponding phase plot  124 . The phase plot  124  is circular facilitating determination of the direction of the object velocity and sub-radian measurement accuracy. The circular shape of the traces in the phase plot makes this configuration less sensitive to noise.  
         [0134]      FIGS. 49 and 50  show preferred miniaturized embodiments of the present invention. The working distance between the input plane and the target surface is 40 mm. The pitch of the cylindrical lens array is 30 μm and the focal length is 38.7 μm. The distance between detector elements  26 ,  28  is 1.6 mm, and the distance between the lens  22  and the detector elements  26 ,  28  is 3.2 mm.  
         [0135]     In the following and with reference to  FIGS. 51-54 , an embodiment  200  of the invention is disclosed, wherein the optical member  12  is a cylinder lens array  12  and is utilized both for transmission of coherent light towards the object  204  and for reception of light emanating from the object  204 . In the embodiment, the light beam emitted from the VCSEL  202  is collimated by the lens  22  and divided into a plurality of beams by the cylinder lens array  12  for illumination of the object  204 . This leads to two significant advantages: 1) The signal caused by the speckles are modulated by the plurality of beams whereby the speckle spectrum is concentrated in a frequency range that is optimized for the system. 2) Safety classification of the system will be based on the power in each of the individual beams.  
         [0136]     In many applications direct access to the emitted radiation may pose a problem since the wavelength is in the near infrared region (app. 850 nm), where the safety regulations are most severe. This is due to the fact that the eye is able to focus the radiation on the retina, yet the sensitivity of the eye is extremely low in this wavelength region. This means that a damaging radiation could occur without proper warning from the sensory system, i.e. the visual impact. Therefore this issue is of vital importance for the user of laser-based systems, especially in consumer products.  
         [0137]     The laser safety standard: “Safety of laser products, Part 1, IEC 60825-1, Ed. 1.1, 1998-01 describes the main safety hazard for the visible and near infrared region to retinal damage. A maximum permissible emission level (AEL) is assigned for a particular class of laser products. The lowest class for laser products is Class 1. It is desired that laser-based products for the consumer market fall within class 1.  
         [0138]     For a 850 nm collimated light beam having a diameter of 1 mm, the AEL is 0.24 mW below which no retinal damage is foreseen. However for most applications this is insufficient for generation of acceptable signals.  
         [0139]     However, with the illustrated embodiment, a VCSEL  202  emits a 850 nm light beam with a diameter of 0.4 mm. The diffraction-limited spot at the retina is app. 0.12 mm provided that the diameter of the eye is app. 50 mm. When collimated light beams are emitted, as schematically illustrated in  FIG. 54 , with an angular separation of app. 3°, separate spots are formed on the retina with a mutual distance of app. 2.5 mm. There is substantially no spot overlap, and therefore the AEL maximum requirement should be fulfilled for each of the individual spots. However, the total power emitted by the VCSEL may be several times the AEL value.  
         [0140]     By illumination of the object with a plurality of beams, the speckles are modulated with a periodic structure that matches the periodic structure of the lens array. This causes a Moiré-like effect with an expected stronger signal as a result. The embodiment is schematically illustrated in  FIG. 51 . The intensity distribution at the illuminated object  204  is illustrated in  FIG. 53  with the following parameters: 
    A s  is the aperture diameter at the lens array position     w d  is the distance to the object     λ is the wavelength of the emitted light     Λ 0  is the width of the individual lenses in the array, i.e. the pitch of the array.     f c  is the focal length of the lens array.    
 
         [0146]     For an embodiment with A s =1 mm, w d =3 mm, λ=1 μm, Λ 0 =15 μm, and f c =30 μm, the horizontal spot separation is 200 μm and the spot height is 1.5 mm. The speckle spectrum at the lens array will exhibit a peak at a spectral position given by the product of the wavelength and the distance from the object to the lens array divided by the spot separation as given by the expression in  FIG. 53 .  
         [0147]     For determination of two-dimensional movement two perpendicularly overlapping lens arrays may be provided in the light path.