Abstract:
A system and method for determining instantaneously the three-dimensional coordinates of large sets of points in space is disclosed. This system uses two or more CCD cameras (or any other type of camera), each with its own lens and pinhole. The CCD&#39;s are all arranged so that the pixel arrays are within the same plane. The CCD&#39;s are also arranged in a predefined pattern. The combination of the multiple images acquired from the CCD&#39;s onto one single image forms a pattern, which is dictated by the predefined arrangement of the CCD&#39;s. The size and centroid on the combined image are a direct measure of the depth location Z and in-plane position (X,Y), respectively. The use of a predefined pattern enables high speed computation through simple algorithmic procedures. Moreover, the use of CCD cameras allows for the recording of such datasets at the corresponding image frame rate, thus opening the use of the invention to the mapping of dynamical systems.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS  
       [0001]    This application is a continuation-in-part of U.S. application Ser. No. 09/258,160 filed Feb. 25, 1999, which claims the benefit of U.S. provisional application Ser. No. 60/078,750, filed on Feb. 25, 1998. 
     
    
     STATEMENT AS TO FEDERALLY SPONSORED RESEARCH  
       [0002] The U.S. Government may have certain rights in this invention pursuant to Grant No. N00014-97-1-0303 awarded by the U.S. Navy. 
     
    
     
       BACKGROUND  
         [0003]    Different techniques are known for three dimensional i maging.  
           [0004]    It is known to carry out three dimensional particle imaging with a single camera. This is also called quantative volume imaging. One technique, described by Willert and Gharib uses a special defocusing mask relative to the camera lens. This mask is used to generate multiple images from each scattering site on the item to be imaged. This site can include particles, bubbles or any other optically-identifiable image feature. The images are then focused onto an image sensor e.g. a charge coupled device, CCD. This system allows accurately, three dimensionally determining the position and size of the scattering centers.  
           [0005]    Another technique is called aperture coded imaging. This technique uses off-axis apertures to measure the depth and location of a scattering site. The shifts in the images caused by these off- axis apertures are monitored, to determine the three-dimensional position of the site or sites.  
           [0006]    There are often tradeoffs in aperture coding systems.  
           [0007]    [0007]FIG. 1A shows a large aperture or small f stop is used. This obtains more light from the scene, but leads to a small depth of field. The small depth of field can lead to blurring of the image. A smaller F stop increases the depth of field as shown in FIG. 1B. Less image blurring would therefore be expected. However, less light is obtained.  
           [0008]    [0008]FIG. 1C shows shifting the apertures off the axis. This results in proportional shifts on the image plane for defocused objects.  
           [0009]    The FIG. 1C system recovers, the three dimensional spatial data by measuring the separation between images related to off-axis apertures b, to recover the “z” component of the images. The location of the similar image set is used find the in-plane components x and y.  
           [0010]    Systems have been developed and patented to measure two-component velocities within a plane. Examples of such systems include U.S. Pat. Nos. 5,581,383, 5,850,485, 6,108,458, 4,988,191, 5,110,204, 5,333,044, 4,729,109, 4,919,536, 5,491,642. However, there is a need for accurately measuring three-component velocities within a three-dimensional volume. Prior art has produced velocimetry inventions, which produce three-component velocities within a two-dimensional plane. These methods are typically referred to as stereo imaging velocimetry, or stereoscopic velocimetry. Many such techniques and methods have been published, i.e. Eklins et al. “Evaluation of Stereoscopic Trace Particle Records of Turbulent flow Fields” Review of Scientific Instruments, vol. 48, No. 7, 738-746 (1977); Adamczyk &amp; Ramai “Reconstruction of a 3-Dimensional Flow Field” Experiments in Fluids, 6, 380-386 (1988); Guezennec, et al. “Algorithms for Fully Automated Three Dimensional Tracking Velocimetry” , Experiments in Fluids, 4 (1993).  
           [0011]    Several stereoscopic systems have also been patented. Raffel et al., under two patents, U.S. Pat. No. 5,440,144 and 5,610,703 have described PIV (Particle Image Velocimetry) systems for measuring three-component velocities within a two-dimensional plane. U.S. Pat. No. 5,440,144 describes an apparatus using 2 cameras, while U.S. Pat. No. 5,610,703 describes an apparatus and method using only one camera to obtain the three-component velocity data. U.S. Pat. No. 5,905,568 describes a stereo imaging velocimetry apparatus and method, using off-the-shelf hardware, that provides three-dimensional flow analysis for optically transparent fluid seeded with tracer particles.  
           [0012]    Most recently, a velocimetry system that measures three-component velocities within a three-dimensional volume has been patented under U.S. Pat. No. 5,548,419. This system is based upon recording the flow on a single recording plate by using double exposure, double-reference-beam, and off-axis holography. This system captures one velocity field in time, thereby preventing acquisition through time, and analysis of time evolving flows.  
           [0013]    There therefore still exists a need for a system and method by which accurate three-component velocities can be obtain within a three-dimensional volume using state-of-the-art analysis for any optically transparent fluids seeded with tracer particles.  
           [0014]    Three-Dimensional Profilometry is another technique, often used for measuring the three-dimensional coordinate information of objects: for applications in speeding up product development, manufacturing quality control, reverse engineering, dynamical analysis of stresses and strains, vibration measurements, automatic on-line inspection, etc.. Furthermore, new fields of application, such as computer animation for the movies and game markets, virtual reality, crowd or traffic monitoring, biodynamics, etc, demand accurate three-dimensional measurements. Various techniques exist and some are now at the point of being commercialized. The following patents describe various types of three-dimensional imaging systems:  
           [0015]    U.S. Pat. No. 3,589,815 to Hosterman, Jun. 29, 1971;  
           [0016]    U.S. Pat. No. 3,625,618 to Bickel, Dec. 7, 1971;  
           [0017]    U.S. Pat. No. 4,247,177 to Marks et al, Jan. 27, 1981;  
           [0018]    U.S. Pat. No. 4,299,491 to Thornton et al, Nov. 10, 1981;  
           [0019]    U.S. Pat. No. 4,375,921 to Morander, Mar. 8, 1983;  
           [0020]    U.S. Pat. No. 4,473,750 to Isoda et al, Sep. 25, 1984;  
           [0021]    U.S. Pat. No. 4,494,874 to DiMatteo et al, Jan. 22, 1985;  
           [0022]    U.S. Pat. No. 4,532,723 to Kellie et al, Aug. 6, 1985;  
           [0023]    U.S. Pat. No. 4,594,001 to DiMatteo et al, Jun. 10, 1986;  
           [0024]    U.S. Pat. No. 4,764,016 to Johansson, Aug. 16, 1988;  
           [0025]    U.S. Pat. No. 4,935,635 to O&#39;Harra, Jun. 19, 1990;  
           [0026]    U.S. Pat. No. 4,979,815 to Tsikos, Dec. 25, 1990;  
           [0027]    U.S. Pat. No. 4,983,043 to Harding, Jan. 8, 1991;  
           [0028]    U.S. Pat. No. 5,189,493 to Harding, Feb. 23, 1993;  
           [0029]    U.S. Pat. No. 5,367,378 to Boehnlein et al, Nov. 22, 1994;  
           [0030]    U.S. Pat. No. 5,500,737 to Donaldson et al, Mar. 19, 1996;  
           [0031]    U.S. Pat. No. 5,568,263 to Hanna, Oct. 22, 1996;  
           [0032]    U.S. Pat. No. 5,646,733 to Bieman, Jul. 8, 1997;  
           [0033]    U.S. Pat. No. 5,661,667 to Bordignon et al, Aug. 26, 1997; and  
           [0034]    U.S. Pat. No. 5,675,407 to Geng, Oct. 7, 1997.  
           [0035]    U.S. Pat. No. 6,252,623 to Lu, Jun. 26, 2001.  
           [0036]    If contact methods are still a standard for a range of industrial applications, they are condemned to disappear: as the present challenge is on non-contact techniques. Also, contact-based systems are not suitable for use with moving and/or deformable objects, which is the major achievement of the present method. In the non-contact category, optical measurement techniques are the most widely used and they are constantly updated, in terms of both of concept and of processing. This progress is, for obvious reasons, parallel to the evolution observed in computer technologies, coupled with the development of high performance digital imaging devices, electro-optical components, lasers and other light sources.  
           [0037]    The following briefly describe techniques:  
           [0038]    The time-of-flight method is based on the direct measurement of the time of flight of a laser or other light source pulse, e.g. the time between its emission and the reception time of the back reflected light. A typical resolution is about one millimeter. Light-in-flight holography is another variant where the propagating optical wavefront is regenerated for high spatial resolution interrogation: sub-millimeter resolution has been reported at distances of 1 meter. For a surface, such technique would require the scanning of the surface, which of course is incompatible with the measurement of moving objects.  
           [0039]    Laser scanning techniques are among the most widely used. They are based on point laser triangulation, achieving accuracy of about 1 part in 10000. Scanning speed and the quality of the surface are the main factors against the measurement accuracy and system performance.  
           [0040]    The Moire method is based on the use of two gratings, one is a reference (i.e. undistorted) grating, and the other one is a master grating. The typical measurement resolution is {fraction (1/10)} to {fraction (1/100)} of a fringe in a distance range of 1 to 500 mm.  
           [0041]    Interferometric shape measurement is a high accuracy technique capable of 0.1 mm resolution with 100 m range, using double heterodyne interferometry by frequency shift. Accuracies {fraction (1/100)} to {fraction (1/1000)} of fringe are common. Variants are under development: shearography, diffraction grating, wavefront reconstruction, wavelength scanning, conoscopic holography.  
           [0042]    Moire and interferometer based systems provide a high measurement accuracy. Both, however, may suffer from an inherent conceptual drawback, which limits depth accuracy and resolution for surfaces presenting strong irregularities. In order to increase the spatial resolution, one must either use shift gratings or use light sources with different wavelengths. Three to four such shifts are necessary to resolve this limitation and obtain the required depth accuracy. This makes these techniques unsuitable for time-dependent object motion. Attempts have been made with three-color gratings to perform the Moire operation without the need for grating shift. However, such attempts have been unsuccessful in resolving another problem typical to fringe measurement systems: the cross-talk between the color bands. Even though some systems deliberately separate the bands by opaque areas to solve this problem, this is done at the expense of a much lower spatial resolution.  
           [0043]    Laser radar 3D imaging, also known as laser speckle pattern sampling, is achieved by utilizing the principle that the optical field in the detection plane corresponds to a 2D slice of the object&#39;s 3D Fourier transform. Different slices can be obtained by shifting the laser wavelength. When a reference plane is used, this method is similar to two-wavelegnth or multi-wavelength speckle interferometry. The measurement range goes from a micrometer to a few meters. Micrometer resolutions are attained in the range of 10 millimeters.  
           [0044]    Photogrammetry uses the stereo principle to measure 3D shape and requires the use of bright markers, either in the form of dots on the surface to be measured of by projection of a dot pattern. Multiple cameras are necessary to achieve high accuracy and a calibration procedure needs to be performed to determine the imaging parameters of each of them. Extensive research has been done on this area and accuracies in the order of one part in 100000 are being achieved. Precise and robust calibration procedures are available, making the technique relatively easy to implement.  
           [0045]    Laser trackers use an interferometer to measure distances, and two high accuracy angle encoders to determine vertical and horizontal encoders. There exist commercial systems providing accuracies of +/−100 micrometers within a 35-meter radius volume.  
           [0046]    Structured light method is a variant of the triangulation techniques. Dots or lines or projected onto the surface and their deformed pattern is recorded and directly decoded. One part over 20000 has been reported.  
           [0047]    Focusing techniques that have received a lot of attention because of their use in modern photographic cameras for rapid autofocusing. Names like depth-from-focus and shape-from-focus have been reported. These techniques may have unacceptably low accuracy and the time needed to scan any given volume with sufficient resolution have confined their use to very low requirement applications.  
           [0048]    Laser trackers, laser scanning, structured light and time-of-flight methods require a sweeping of the surface by the interrogation light beam. Such a scanning significantly increases the measuring period. It also requires expensive scanning instruments. The Moire technique requires very high resolution imaging devices to attain acceptable measurement accuracy. Laser speckle pattern sampling and interferometric techniques are difficult and expensive to implement. For large-scale measurements, they require also more time to acquire the image if one wants to take advantage of the wavelength shifting method. Photogrammetry needs a field calibration for every configuration. Furthermore, the highest accuracy is obtained for large angular separations between the cameras, thus increasing the shading problem.  
           [0049]    There is thus a widely recognized need for a method and system to rapidly, accurately and easily extract the surface coordinate information of as large as possible number of designated features of the scene under observation, whether these features are stationary, in motion, and deforming. The technique should be versatile enough to cover any range of measurement, and with accuracy comparable to or surpassing that of systems available today. The technique should allow for fast processing speeds. Finally, the technique should be easy to implement for the purpose of low cost manufacturing. As we will describe, the present invention provides a unique alternative since it successfully addresses these shortcomings, inherent partially or totally to the presently know techniques.  
         SUMMARY  
         [0050]    The present system caries out aperture-induced three dimensional measuring by obtaining each image through each aperture. A complete image detector is used to obtain the entire image. The complete image detector can be a separate camera associated with each aperture, or a single camera that is used to acquire the different images from the different apertures one at a time.  
           [0051]    The optical train is preferably arranged such that the aperture coded mask causes the volume to be imaged through the defocusing region of the camera lens. Hence, the plane of focus can be, and is intentionally outside of, the volume of interest. An aperture coded mask which has multiple openings of predefined shape, not all of which are necessarily the same geometry, and is off the lens axis, is used to generate multiple images. The variation and spacing of the multiple images provides depth information. Planar motion provides information in directions that are perpendicular to the depth. In addition, the capability to expose each of the multiple images onto a separate camera portion allows imaging of high density images but also allows proper processing of those images. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0052]    These and other aspects will now be described in detail with the accompanying drawings, wherein:  
         [0053]    FIGS.  1 A- 1 C show views of different systems for 3 dimensional imaging;  
         [0054]    [0054]FIG. 2 shows a geometric analysis of a specified lens aperture system;  
         [0055]    [0055]FIG. 3 shows a camera diagram with camera components;  
         [0056]    [0056]FIG. 4 shows a drawing of the preferred camera; and  
         [0057]    [0057]FIG. 5 and 6 shows more detailed drawings of the optical relays of the camera shown in FIG. 4.  
         [0058]    [0058]FIG. 7 is a schematic perspective view of the previously disclosed three-dimensional system, where one single lens is used with a three-aperture mask and a set of three separated cameras, each of which is associated with one aperture.  
         [0059]    [0059]FIG. 8 is a schematic perspective view of the present invention where 3 lens-aperture sets are used in combination with a set of three separated cameras, each of which is associated to one lens-aperture set. The drawing shows how the pattern defined by the geometry of the lens-aperture system (an equilateral triangle in this case) changes with the position in space of the corresponding source point.  
         [0060]    [0060]FIG. 9 is geometrical model of the present invention, using the 2-aperture arrangement for sake of clarity, and displaying all the parameters defining the optical principle of defocusing and upon which the present invention will be described in the following sections. The same parameters apply to a system with more than 2 lens-aperture systems.  
         [0061]    [0061]FIG. 10 is a flow diagram showing the sequence of program routines forming DE2PIV and used in the preprocessing of the combined images provided by a system with 3 lens-aperture sets.  
         [0062]    [0062]FIG. 11 is a flow diagram showing the sequence of program routines forming FINDPART and used in the image processing of the preprocessed images provided by DE2PIV. The program determines the three-dimensional coordinates of the scattering sources randomly distributed within a volume or on a surface.  
         [0063]    [0063]FIG. 12 is a flow diagram showing the sequence of program routines forming FILTERPART and used in the processing of the results provided by FINDPART. Operations such as volume-of-interest, source characterization, 3D geometrical operations, are possible.  
         [0064]    [0064]FIG. 13 is a flow diagram showing the sequence of program routines forming FINDFLOW and used in the processing of the results provided by FILTERPART. The program calculates the 3D displacement of the scattering sources as a function of time, i.e. the 3D velocity.  
         [0065]    [0065]FIG. 14 is a flow diagram showing the sequence of program routines forming FILTERFLOW and used in the processing of the results provided by FINDFLOW. The program validates the results and outputs the data to various standard formats. Every dataset of scattering sources is characterized by a 3D vector field comprising the 3D coordinates of every source, the 3D velocity. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT  
       [0066]    [0066]FIG. 2 shows a geometric analysis in which a camera lens of focal length F is located at z=0. Two small apertures are placed within the lens, separated a distance d/2 away from the optical centerline 200 which also corresponds to the z axis. The apertures are shown as pinholes in this diagram to simplify the model. The theory for larger and more complex apertures would be similar.  
         [0067]    The following equations can be determined by using lens laws and self similar triangle analysis: 
           Z= 1/((1/ L )+ Kb )   (1) 
         [0068]    where 
           K= ( L −ƒ)/( ƒdL )   (2) 
         [0069]    The remaining two coordinates x, y are found from the geometrical center (X 0 ,Y 0 ) of the image pair B′ using: 
           X= (− x   0   Z ( L−ƒ))/(   ƒL )   (3) 
           Y= (− y   0   Z ( L −ƒ))/(ƒ L )   (4) 
         [0070]    Solving (1) for the image separation b reveals several interesting performance characteristics of the lens/aperture system:  
           b= 1 /K ((1 /Z )−(1 /L ))   (5) 
         [0071]    The inventors recognized that if all this information was obtained by a single camera, an image crowding problem could exist. This would limit the system to a lower density of number of images.  
         [0072]    The defocusing masses requires multiple spatially-shaped holes. If there are n holes, then each scattering site has been imaged n times onto a single CCD. Hence, n times as many pixels are exposed. This means, however, that the capacity of the technique, i.e. the number of scattering sites that can be imaged, is correspondingly reduced by a factor of n.  
         [0073]    The present system addresses this and other issues.  
         [0074]    A first aspect addresses the image crowding problem by exposing each of the multiple exposures using a separate camera portion. The camera system can be electronic or photographic based. The separate camera portion requires that a whole camera imaging portion is used to obtain the images from each aperture at each time. This can use multiple separate cameras, a single camera with multiple parts, or a single camera used to obtain multiple exposures at different times.  
         [0075]    Another aspect obtains image information about the objects at a defocused image plane, i.e. one which is not in focus by the lens. Since the image plane is intentionally out of focus, there is less tradeoff regarding depth of field.  
         [0076]    The first embodiment, as described above, uses image separation to expose each of the multiple exposures to its own electronic or photographic camera portion. The image separation can be effected by color filters, by time coding, by spacial filters, or by using multiple independent cameras.  
         [0077]    The color filter embodiment is shown in FIG. 3. A color camera and mask combination is shown with three separate CCD cameras  300 ,  302 ,  304 .  
         [0078]    Light is input through mask  342 , which includes an opaque aperture plate with three apertures formed therein. In this embodiment, the apertures are generally in the shape of a triangle. The light passes to a lens assembly  346 , which directs the light into the chamber that houses the camera.  
         [0079]    The color camera uses three monochrome CCD cameras, situated around a three way prism  310  which separates the incoming light according to its colors. A micro positioner assembly  312  is provided to precisely adjust the cameras  300 ,  302 ,  304  such that each will view exactly the same area. Once those adjustments are made, the three cameras are locked into place so that any vibration affects each of them the same. Each camera includes an associated band filter. The filter  330  is associated with CCD camera  300 , filter  332  is associated with camera  302 , and filter  334  is associated with camera  304 . Each of these narrow band filters passes only one of the colors that is passed by the coded apertures. The filters are placed adjacent the prism output to correspond respectively to each of the primary colors, e.g. red, green and blue. Hence, the filters enable separating the different colors.  
         [0080]    This color camera assembly is used in conjunction with an image lens assembly  340  and a aperture coded mask  342 . The system in FIG. 3 shows the aperture coded mask having three mask portions in the form of an equilateral triangle. Each aperture is color coded according to the colors of the camera filters. This color coding can be done by, for example, using color filters on the apertures.  
         [0081]    The image from each aperture goes to a separate one of the cameras  302 ,  304 ,  300 . The output from the camera is processed by the CCD electronics  350  and coupled to output cables shown as  352 . These three values are processed using a conventional processing software. The three values can be compensated separately.  
         [0082]    While the system describes using three colors and three apertures, it should be understood that any number of colors or apertures could be provided.  
         [0083]    A second embodiment separates the images from the different apertures using rapid sequential imaging. An embodiment is shown in FIG. 4. A scene is imaged through a mask  400  that includes multiple apertures. Each aperture has an associated selective blocking means  402 . The blocking means is a device that either allows light to pass through the aperture or blocks light from passing through the aperture under control of an applied control signal  404  from a control element  400 . The aperture blocking means  402  can be a mechanical blocker e.g. a mechanical shutter, solid state optics, such as a liquid crystal which is selectively allowed to pass light, or a digital mirror which selectively reflects the light to the aperture or the like. Light from the scattering sites  410  is allowed to pass through each aperture at a separate time, under control of the controller  406 . The passed light is sent to a single camera  430  that produces an image indicative of the passed light. Three different images are obtained at three different times. Each image is based on passage of the light through a different aperture.  
         [0084]    Alternate ways of obtaining the three images could be used. A purely mechanical means can be provided to pass light through only a single aperture by rotating the blocking element such that the blocking element is associated with different apertures at different times and hence provides different illuminations at different times.  
         [0085]    In either case, each of the corresponding cameras is exposed only when the corresponding aperture is allowed to receive light. The system shown in FIG. 4A shows a CCD camera assembly  430  receiving the light from the various apertures.  
         [0086]    Another embodiment uses spacial filters to separate the different light values. FIG. 5 shows a preferred configuration of a spatially coded camera. The system includes a focusing lens assembly  500 ,  504 , with an aperture system  506  between the two portions of the focusing lens  500 ,  504 . An exploded view of the components is shown in FIG. 6. Each of the prisms  510 ,  512 ,  514  is directly located behind each aperture orifice. A three CCD camera  520  views the three images through the three aperture orifices, thereby providing three simultaneous views of the image.  
         [0087]    The lenses within the focusing lens assembly  500 ,  504  direct the scattered light from the scene through each of the three orifices at 1200 angles with each other. The light is then collected through the aperture orifices and directed to the separate CCD cameras. Each of the images on each of the three cameras is recorded simultaneously and then processed to provide three dimensional spacial locations of the points on the scene.  
         [0088]    An alternative, but less preferred embodiment, uses three separate cameras, in place of the one camera described above.  
         [0089]    The system as described and shown herein includes several advantages. The system allows superior camera alignment as compared with other competing images such as stereoscopic techniques. This system is also based on a defocusing technique as compared with stereoscopic techniques that require that the camera be focused on the area of interest. This system has significant advantages since it need not be focused on the area of interest, and therefore has fewer problems with trade offs between aperture size and other characteristics. (here) FIG. 7 shows a composite and changed version of this 3D camera using one single large lens  700  with a mask  710  with 3 apertures. This solution, depending on the application, may also require a lens assembly  720 , where F# &lt;1 (where F# is defined as f/d, where f is the lens′ focal length, and d is the diameter of the lens). This latter lens may increase the cost of the assembly. In some embodiments, the lenses might need to be custom made.  
         [0090]    In the FIG. 7 implementation, three prisms  730 ,  730  to,  734  are used to redirect the light away from the optical axis of the camera. This may simplify the design.  
         [0091]    Another design is shown in FIG. 8. The camera in FIG. 8 is redesigned so that each photo sensor  804  has its own lens-aperture system  801 ,  802 . Still, however, the global optical axis  805  of the camera is preserved and is unique. The system behaves as if we had replaced the original lens by a lens with infinite focal length. The use of small lenses  802  in front or behind the apertures  801  may also improve the collection of light as to produce small images on the imaging sensors  805 , which allows the use of variable apertures and therefore allows to work in a wide range of lighting conditions. The flexibility of this lens assembly allows for more accurate 3D imaging, as no complex optics are used, thus minimizing the optical imperfections, making the manufacturing easier and the system ruggedized for field applications where environmental concerns are an important factor. Moreover, the geometrical parameters can be freely modified to match the specific requirements of the application, such as size of volume, depth resolution, etc The present embodiment preserves the same geometrical information as in the original design. In this arrangement, the 3 imaging sensors are arranged so that they form an equilateral triangle. FIG. 8B shows how a point A placed on the reference plane  803  is imaged as one unique image  807  on the combined imaged  806 . Points B and C placed in between the lens-aperture plane and the reference plane will image as equilateral triangles  808  and  809 , respectively. This is due to the fact that the 3 imaging sensors were arranged to form an equilateral triangle, thereby resulting in the equilateral triangles shown by  808  and  809 . The size and the centroid of such triangles are directly related to the depth and plane location of the corresponding source point, respectively. It is understood that there would be such triangle patterns for any source point, each of them uniquely identifiable, making the invention suitable for the instantaneous mapping of large number of points, and consecutively suitable for real-time imaging of such sets at a frame rate defined either by the recording capabilities or by the dynamical system under observation. It is important to note that the arrangement of the 3 imaging sensors in the form of an equilateral triangle is not unique, and that any identifiable pattern could have been chosen.  
         [0092]    This present invention allows for the  3  separate sensor/lens assemblies to be movable while maintaining the same geometric shape. For example, if the 3 sensor/lens sets are arranged so that they outline an equilateral triangle of a certain size, the 3 sensor/lens assemblies can be moved, thus allowing for visualizing smaller or larger volumes, in a manner that will preserve the equilateral triangle in their outline. Furthermore, the lens/pinhole assembly will be interchangeable to allow for imaging of various volume sizes. Such features will also allow the user to vary the working distance at their convenience.  
         [0093]    Such improvements make the proposed system a new invention as it offers an improvement over the previous embodiments.  
         [0094]    It is emphasized again that the choice of an equilateral triangle as the matching pattern, or equivalently of the number of apertures/imaging sensors (with a minimum of two), is arbitrary and is determined based on the needs of the user. It is also emphasized that the shape of the apertures is arbitrary and should only be defined by the efficiency in the collection of light and image processing. Furthermore, these apertures can be equipped with any type of light filters that would enhance any given features of the scene, such as the color. It is furthermore understood that the size of such apertures can be varied according to the light conditions, by means of any type of mechanical or electro-optical shuttering system. Finally, it is emphasized that the photo sensors can be of any sort of technology (CCD, CMOS, photographic plates, holographic plates . . . ) and/or part of an off-the-shelf system (movie cameras, analog or digital, high speed or standard frame rate, color or monochrome). This variety of implementations can be combined to map features like the color of the measured points (for example in the case of measuring a live face), their size, density, etc.  
         [0095]    The invention will be presented in terms of the simplest implementation, which makes use of 2 lens-aperture sets. For this purpose, a simplified geometric model of a two-aperture defocusing optical arrangement is represented in FIG. 3. The interrogation domain is defined by a cube of side a. The back face of this cube is on the reference plane, which is placed at a distance L from the lens plane. The image plane is materialized by a photo sensor (e.g. CCD) of height h. Let d be the distance between apertures, f the focal length of the converging lens and 1 the distance from the lens to the image plane. The physical space is attached to a coordinate system originating in the lens plane, with the Z-axis on the optical axis of the system. Coordinates in the physical space are designated (X,Y,Z). The image coordinate system is simply the Z-translation of the physical system onto the sensor plane, i.e. at Z=-l. The coordinates of a pixel on the imaging sensor are given by the pair (x, y). Point P(X,Y,Z) represents a light scattering source. For Z&lt;L, P is projected onto points P1(x′ 1,y′ 1) and P2(x′ 2,y′ 2), such that  
         P   1     =     {             x   1   ′     =       M                  2      Z              [       d        (     L   -   Z     )       -     2      LX       ]                     y   1   ′     =       -   l          Y                Z                 }               P   1     =     {             x   2   ′     =       M                  2      Z              [       -     d        (     L   -   Z     )         -     2      LX       ]                     y   2   ′     =       -   l          Y                Z                 }                           
 
         [0096]    where M is the magnification. The separation b of these images on the combined image (as in part  6  of FIG. 2 for a 3 lens-aperture system) is then defined by  
         b        (           b   x               b   y           )       =     (             x   1   ′     -     x   2   ′                   y   1   ′     -     y   2   ′             )             b   =       Md   Z          (     L   -   Z     )                             
 
         [0097]    Such definitions are identical to the previous formulation for the previous embodiments.  
         [0098]    [0098]FIG. 9 shows a geometric diagram of the aperture mask.  
         [0099]    The image and information that is obtained from this system may be processed as shown in the flowcharts of FIGS.  10 - 14 . In FIG. 10, step  1000  defines reading in three images from the three CCD cameras of any of the previous embodiments. At 1010, preprocessing parameters may be set up which may be used for noise processing, and background image removal. Particle peaks are identified at 1020. These particle peaks may be identified by locally identifying peaks, building a particle around each peak, and then accounting for particle overlap. In this way, preprocessed peaks are obtained at 103, with the particle peaks being highlighted.  
         [0100]    These results are input to the second flowchart part, shown in FIG. 11. At 1100, a particle is built around the peaks, using the minimum and maximum particle size. A slope threshold is used to determine the particle boundaries, and to build support sets around the pixels. These support sets are used to optimize the particle parameters such as maximum, intensity, size and center coordinates. At 1110, the particle coordinates are “dewarped”. This is done by using a calibration image of a known pattern. Distortions are determined by what is acquired as compared with what is known. The warped file is then output. The warping may thus accommodate for nonlinear imaging.  
         [0101]    At 1120, particle triplets per point are identified. This may be done using the conditions that triplets must form an inverted equilateral triangle. Each of the particle exposures on the CCD&#39;s may be used to identify particles to accommodate for particle exposure overlap. At 1130, the three-dimensional coordinates are obtained from the size of the triangle pattern, and the 3-D particle spacing is output at 1140 based on location.  
         [0102]    In FIG. 12, the thsu obtained results are further processed at 1202 identify the volume of interest, to translate the data set, and to rotate the data set. A radius is determined at 1210 based on intensity as input from the calibration data set and the scattering formulation. The size related terms determined at 1220 such as size histograms and void fraction. At 1230, an output particle data field is obtained within the constraints given in the input parameter file.  
         [0103]    Three-dimensional particle data pairs are thus obtained and are fed to the flowchart of FIG. 13. In FIG. 13, at 1300, flow window lattice information is set up to specify Voxel size and Voxel spacing. For each window, the velocity is calculated in 3-D space at 1310. This may be done once or twice. In the second calculation, the second voxel may be locally shifted. This may be used to detect outliers and reinterpret those values. In general, this uses three-dimensional correlation of particles with in the Voxel. The correlation is not done by pixels, but rather by particle location and size. The results are output at 1320 as components of velocity within the spatial P2.  
         [0104]    Filtering is carried out in FIG. 14. Again, the input parameters at 1400 may include a region of interest, velocities of interest, and outlier correction. The velocity data may be output into various formats at 1410.  
         [0105]    Although only a few embodiments have been described in detail above, other embodiments are contemplated by the inventor and are intended to be encompassed within the following claims. In addition, other modifications are contemplated and are also intended to be covered. For example, different kinds of cameras can be used. The system can use any kind of processor or microcomputer to process the information received by the cameras. The cameras can be other types that those specifically described herein. Moreover, the apertures can be of any desired shape.