Patent Publication Number: US-8976367-B2

Title: Structured light 3-D measurement module and system for illuminating a subject-under-test in relative linear motion with a fixed-pattern optic

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims benefit under 35 U.S.C. 119(e) of U.S. Provisional Application No. 61/413,969 filed 15 Nov. 2010 by the applicants on behalf of the assignee, the complete disclosure of which—including attached materials—is incorporated herein by reference, to the extent the disclosure provides support and further edification hereof. 
    
    
     FIELD OF THE INVENTION 
     In general, the invention relates to the field of three-dimensional (3-D) measurement of surfaces using structured light illumination (SLI) techniques. Herein, “SLI” is used to represent the terms Structured Light Illumination, or often referred to, simply, as Structured Light. More-particularly, the invention is directed to the use of a new optical technique and system to measure and record the 3-D dimensional characteristics of 3-D surfaces of an object-under-test in relative linear motion with the measurement apparatus by projecting a selected superimposed SLI pattern composed of a plurality of SLI patterns, through a fixed-pattern optic, to illuminate a surface of interest of the area/object-under-test in motion. Furthermore, the invention is directed to a novel SLI inspection system of objects or items moving in a predictable linear fashion with respect to the inspection device, for example: for use along the interior of a pipeline (the measurement module moves linearly with respect to the interior surface of the pipeline-under-test); over semiconductor wafers undergoing fabrication along an assembly line, printed circuit board (PCB) or printed wiring board (PWB) defect inspection while the boards are moving on a conveyor belt, and other such surface inspection of a good or product-of-manufacture (parts, assemblies, foodstuff, packaging) traveling along a conveyor belt or assembly. 
     BACKGROUND OF THE INVENTION 
     Historical Perspective 
     The object measurement technique referred to as Structured Light (or, SLI) has been in use for measuring the 3-D characteristics of objects for many years. However, current implementations are computationally heavy and available systems have large footprints. Because conventional SLI surface measuring systems employ sophisticated electronically-driven SLI signal processing projection units to project SLI patterns—with each SLI pattern projected requiring a dedicated projector unit—it has been impractical to employ conventional SLI surface measuring systems to perform real-time measurements to monitor surfaces located in relatively small spaces (volumes), such as, surfaces located: inside the mouth or ear of a mammal (intra-oral and intra-aural surfaces), inside machinery (for example, machinery found in manufacturing plants); within a pipeline, and so on. Furthermore, the nature of projecting multiple sophisticated SLI patterns requisite for making 3-D surface measurements—where each conventional SLI pattern projected requires a dedicated projector unit—has further led way from the application of conventional SLI surface measuring systems to make real-time measurements of 3-D surfaces. 
     Structured Light (i.e., Structured Light Illumination), confocal imaging, time-of-flight, and parallel confocal microscopy are each considered 3-D measurement techniques. SLI is currently used to observe a surface-of-interest by projecting multiple SLI patterns (grid, stripes, ellipical patterns, and so on) with a projector onto a surface-of-interest while measuring, with a camera (lens and processing unit) the image reflected off the surface-of-interest to deduce resultant distortions of the patterns produced on the surface-of-interest. Knowing camera and projector geometry (many conventional techniques exists for such mapping), point-by-point depth information about the surface distortions is calculated by way of triangulation. World coordinates to camera are calculated using conventional well known mapping techniques such as that found at vision.caltech.edu/bouguetj/calib_doc/: “This toolbox works on Matlab 5.x, Matlab 6.x and Matlab 7.x on Windows, Unix and Linux systems and does not require any specific Matlab toolbox (for example, the optimization toolbox is not required).” Using the conventional camera calibration toolbox for Matlab, one computes the necessary coefficients to map world coordinates onto the coordinate system of the camera and the projector. In this manner, a mathematical relationship is defined between the camera (i.e., each individual pixel in the camera), the projector, (i.e., the origin of projected rows of information), and an object-under-test located in an external frame of reference, often referred to as the ‘real world’ coordinate system. 
     U.S. Pat. No. 6,788,210 entitled “METHOD AND APPARATUS FOR THREE DIMENSIONAL SURFACE CONTOURING AND RANGING USING A DIGITAL VIDEO PROJECTION SYSTEM,” uses a complex series of interconnected dedicated projector units engaged to generate a desired projected multi-pattern image on a surface of interest; FIG. 5 from U.S. Pat. No. 6,788,210 illustrates one conventional optical configuration for a projection system. U.S. Pat. No. 5,633,755 provides additional detail regarding the configuration of an optical system and its electronic control system. U.S. Pat. No. 6,874,894 B2 entitled “DMD EQUIPPED PROJECTOR” details a system known as “Texas Instruments DMD” projector, i.e., the ‘DLP device’ of a projection apparatus. 
     As one can appreciate, the system depicted in FIG. 5 from U.S. Pat. No. 6,788,210 and the system depicted in FIG. 5 of U.S. Pat. No. 6,874,894 are structurally and functionally the same. As explained in U.S. Pat. No. 6,788,210, to generate an image, component  46  is used. This component has been labeled  113  in FIG. 6 of U.S. Pat. No. 6,874,894 B2 as PRIOR ART. The Texas Instruments DMD, also known as the DMD or the DLP device, is an complicated semiconductor device, specifically referred to as an optical MEMS device. The DMD is further detailed in Hornbeck, Larry J., “ Digital Light Processing for High - Brightness, High - Resolution Applications ,” SPIE Vol. 3013 pps. 27-40; by way of background only, the content found on the Internet at the domain dlp.com. 
     U.S. Pat. No. 6,977,732 describes an application of the DMD to measure the three dimensional shape of small objects. As explained therein, additional complex electronic systems are needed to operate the DMD-based projection system: It has an electronic micro-display for three dimensional measurements. Seiko-Epson manufactures liquid crystal devices for projection applications. Sony, Omnivision, and JVC each manufacture liquid crystal on silicon devices for projection applications. Like the DMD, conventional devices are electronically-controlled so that projection of light patterns requires complicated optical control electronics and optics structures. 
     Computerized Devices, Memory and Storage Devices/Media 
     I. Digital computers. A processor is the set of logic devices/circuitry that responds to and processes instructions to drive a computerized device. The central processing unit (CPU) is considered the computing part of a digital or other type of computerized system. Often referred to simply as a processor, a CPU is made up of the control unit, program sequencer, and an arithmetic logic unit (ALU)—a high-speed circuit that does calculating and comparing. Numbers are transferred from memory into the ALU for calculation, and the results are sent back into memory. Alphanumeric data is sent from memory into the ALU for comparing. The CPUs of a computer may be contained on a single ‘chip’, often referred to as microprocessors because of their tiny physical size. As is well known, the basic elements of a simple computer include a CPU, clock and main memory; whereas a complete computer system requires the addition of control units, input, output and storage devices, as well as an operating system. The tiny devices referred to as ‘microprocessors’ typically contain the processing components of a CPU as integrated circuitry, along with associated bus interface. A microcontroller typically incorporates one or more microprocessor, memory, and I/O circuits as an integrated circuit (IC). Computer instruction(s) are used to trigger computations carried out by the CPU. 
     II. Computer Memory and Computer Readable Storage. While the word ‘memory’ has historically referred to that which is stored temporarily, with storage traditionally used to refer to a semi-permanent or permanent holding place for digital data—such as that entered by a user for holding long term—however, the definitions of these terms have blurred. A non-exhaustive listing of well known computer readable storage device technologies compatible with a variety of computer processing structures are categorized here for reference: (1) magnetic tape technologies; (2) magnetic disk technologies include floppy disk/diskettes, fixed hard disks (often in desktops, laptops, workstations, host computers and mainframes interconnected to create a ‘cloud’ environment, etc.), (3) solid-state disk (SSD) technology including DRAM and ‘flash memory’; and (4) optical disk technology, including magneto-optical disks, PD, CD-ROM, CD-R, CD-RW, DVD-ROM, DVD-R, DVD-RAM, WORM, OROM, holographic, solid state optical disk technology, etc. 
     BACKGROUND OF THE INVENTION 
     Use of Multi-Frequency Patterns 
     The instant new technique and system disclosed herein, leverage the unique technique disclosed in U.S. Provisional Patent Application 61/371,626, Liu et al., filed 6 Aug. 2010 entitled “Dual-frequency Phase Multiplexing (DFPM) and Period Coded Phase Measuring (PCPM) pattern strategies in 3-D structured light systems, and Lookup Table (LUT) based real-time data processing for phase measuring pattern strategies,” fully incorporated herein by reference for its technical background discussion. U.S. utility application Ser. No. 13/205,607, Liu et al., filed 8 Aug. 2011 (“Util App &#39;607”) was granted priority to U.S. Provisional Patent Application 61/371,626, Liu et al. (“Provisional Application &#39;626”): the technical disclosures of both Provisional Application &#39;626 and Util App &#39;607 are hereby fully incorporated herein by reference to the extent consistent with the instant technical specification. While Provisional Application &#39;626 and Util App &#39;607 were commonly owned upon filing of the latter, neither Provisional Application &#39;626 or Util App &#39;607 is commonly owned by the assignee of the instant patent application. The unique SLI patterning technique disclosed in Provisional Application &#39;626 and Util App &#39;607 comprises:
         (1) a unique pattern strategy component (further detailed in technical discussions found in Provisional Application &#39;626 as labeled Section A. “Dual-frequency pattern scheme for high-speed 3-D shape measurement” and as labeled Section B. “Period Coded Phase Measuring Strategy for 3-D Realtime Acquisition and Data Processing”—each of these Sections A. and B. covers an example of a new multi-frequency pattern introduced by way of analogy to the following two traditional electrical circuitry signal/current propagation types: AC, alternating current, and DC, direct current, as further explained below); and   (2) a unique de-codification image processing component (further detailed in the technical discussion of Provisional Application &#39;626 and labeled Section C. “LUT-based processing for structured light illumination real-time phase and 3-D surface reconstruction”).       

     As noted above and detailed further in Provisional Application &#39;626 and Util App &#39;607, the two examples set forth in Sections A. and B. of the new multi-frequency patterns disclosed in Provisional Application &#39;626 were introduced in terms of analogies to traditional electrical circuitry signal/current propagation types: An AC flavor and DC flavor. These same Sections A. and B. were integrated into applicants&#39; Provisional Application No. 61/413,969 filed 15 Nov. 2010, incorporated herein by reference as noted above. The multi-frequency pattern detailed in Section A. fashioned after principals governing AC electrical systems was coined “Dual-frequency Phase Multiplexing” (DFPM). As noted in applicants&#39; Provisional Application No. 61/413,969, the material in Section A. was earlier published as 1 Mar. 2010/Vol. 18, No. 5/Optics Express 5233 and is noted in the section of Util App &#39;607 labeled EXAMPLE 01. The multi-frequency pattern detailed in Section B. fashioned after principals governing DC electrical systems was coined “Period Coded Phase Measuring” (PCPM). Dual-frequency Phase Multiplexing (DFPM) patterns comprise two superimposed sinusoids, one a unit-frequency phase sine wave and the other a high-frequency phase sine wave, whereby after receiving/acquiring the pattern data by an image sensor, the phase of the two patterns is separated. The unit-frequency phase is used to unwrap the high-frequency phase. The unwrapped high-frequency phase is then employed for 3-D reconstruction. Period Coded Phase Measuring (PCPM) patterns—fashioned after DC current propagation—are generated with the period information embedded directly into high-frequency base patterns, such that the high-frequency phase can be unwrapped temporally from the PCPM patterns. 
     As explained in Util App &#39;607—the specification of which is quoted extensively below—using unique multi-frequency patterns, the &#39;607 technique accomplishes:
         3-D triangulation-based image acquisition of a contoured surface-of-interest (or simply, “contour” or “contour-of-interest”) under observation by at least one camera, by projecting onto the surface-of-interest a multi-frequency pattern comprising a plurality of pixels representing at least a first and second superimposed sinusoid projected simultaneously, each of the sinusoids represented by the pixels having a unique temporal frequency and each of the pixels projected to satisfy       

     
       
         
           
             
               
                 
                   
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              where I n   p  is the intensity of a pixel in the projector for the n th  projected image in a particular instant/moment in time (p, to represent projector); K is an integer representing the number of component sinusoids (e.g., K=2 for a dual-frequency sinusoid pattern, K=3 for a triple-frequency sinusoid, and so on), each component sinusoid having a distinct temporal frequency, where K≦(N+1)/2. The parameter B k   p  represents constants that determine the amplitude or signal strength of the component sinusoids; A p  is a scalar constant used to ensure that all values of I n   p  are greater than zero, 0 (that is to say, that the projector unit will not project less than 0 magnitude of light); f k  is the spatial frequency of the k th  sinusoid corresponding to temporal frequency k; and y p  represents a spatial coordinate in the projected image. For example, y p  may represent a vertical row coordinate or a horizontal column coordinate of the projected image; n represents phase-shift index or sequence order (e.g., the n=0 pattern is first projected, and then the n=1 pattern, and so on, effectively representing a specific moment in discrete time). N is the total number of phase shifts—i.e., the total number of patterns—that are projected, and for each pattern projected, a corresponding image will be captured by the camera (or rather, the camera&#39;s image sensor). When used throughout, the superscript “c” references parameters relating to an image or series of images (video) as captured by the camera, whereas superscript “p” references the projector. 
           
         
       
    
     Where pixels are projected to satisfy Eq. 1.1, the pixels of the images then captured by the camera are defined according to the unique technique governed by the expression: 
                     I   n   c     =       A   c     +       ∑     k   =   1     K     ⁢       B   k   c     ⁢     cos   ⁡     (       2   ⁢           ⁢   π   ⁢           ⁢     f   k     ⁢     y   p       +       2   ⁢           ⁢   π   ⁢           ⁢   kn     N       )           +   η             Eq   .           ⁢     (   1.2   )                 
The term η (“eta”) represents a noise due to a certain amount of error introduced into the image by the light sensor of the camera. Recall, a camera image is made up of a multitude of pixels, each pixel defined by Eq. 1.2, with values for A c , B k   c , and η c  different for each pixel. The “c” superscript indicating a value is dependent on the position of the pixel as referenced in the camera sensor (‘camera space’). To obtain phase terms from the pixels projected in accordance with Eq. 1.2, the unique expression, below, is carried-out for each k:
 
                     2   ⁢           ⁢   π   ⁢           ⁢     f   k     ⁢     y   p       =     arc   ⁢           ⁢     tan   (         ∑     n   =   0       N   -   1       ⁢       I   n   c     ×     cos   ⁡     (       2   ⁢           ⁢   π   ⁢           ⁢   kn     N     )               ∑     n   =   0       N   -   1       ⁢       I   n   c     ×     sin   ⁡     (       2   ⁢           ⁢   π   ⁢           ⁢   kn     N     )             )               Eq   .           ⁢     (   1.3   )                 
where, as before, y p  represents a spatial coordinate in the projected image. In EXAMPLE 01, herein below, where K is set equal to 2, the phase terms for the cases where k=1 and k=2 (i.e., for the two superimposed sinusoids) must be determined.  FIGS. 8A ,  8 B are reproductions of computer-generated/implemented images;  FIG. 8C  is  FIG. 8B , enlarged to view representative stripes numbered from the top 1 through 10, by way of example.  FIG. 8A  is an image representing phase for the k=1 term where f=1 (unit-frequency).  FIGS. 8B ,  8 C are reproductions of an image representing the phase term for k=2 where f=20 (i.e., the high-frequency sinusoid). Note that the stripped pattern in FIGS.  5 B/C has 20 stripes.
 
     When applying the use of temporal unwrapping techniques, for the case where k=2 using Eq. 1.1, one can determine that the projected pixels will satisfy 
                       I   n   p     =       A   p     +       B   2   p     ⁢     cos   ⁡     (       2   ⁢           ⁢   π   ⁢           ⁢     f   2     ⁢     y   p       +       2   ⁢           ⁢   π   ⁢           ⁢   2   ⁢   n     N       )             ,     k   =   2             Eq   .           ⁢     (   1.1   )                 
Where this leads to 20 stripes (as shown, for example, in  FIG. 8B  as a pattern projected on a human hand, the enlargement of which is labeled  FIG. 8C  to better view stripes), one must determine which of the 20 stripes each particular pixel falls in the projected image (e.g.,  FIG. 8C ). Using a traditional phase unwrapping approach to determine where each pixel fell in the projected image would require a mathematical form of ‘stripe counting’—which is computationally quite burdensome.
 
     Rather, according to the instant invention, a second set of patterns (k=1) all unit-frequency sinusoids (i.e., f=1) is superimposed with a high-frequency sinusoid, such as one of 20 stripes, k=2 pattern. The unit-frequency signal is defined by an adaptation of Eq. 1.1 
                       I   n   p     =       A   p     +       B   1   p     ⁢     cos   ⁡     (       2   ⁢           ⁢   π   ⁢           ⁢     f   2     ⁢     y   p       +       2   ⁢           ⁢   π   ⁢           ⁢   n     N       )             ,     k   =   1             Eq   .           ⁢     (   1.1   )                 
Therefore, rather than projecting a total of N patterns onto the contoured surface-of-interest, there are now 2*N patterns projected (such that K=2 and each pixel projected from the projector is comprised of a dual-frequency pattern, one is a unit-frequency sinusoid and the second is a high-frequency sinusoid). However, very unique to the applicants&#39; technique according to the invention, the plurality of pixels projected using Eq. 1.1 are ‘instantly decodable’ such that the computerized processing unit (CPU) of the computerized device in communication with the projector and camera units, at this point already, has the data and the means to determine (closely enough) which stripe each projected pixel I n   p  is in, while determining 2πf 2 y p  (i.e., phase) of the camera image (of pixel intensity, I n   c ), according to Eq. 1.3—reproduced again, below, for handy reference:
 
                     2   ⁢           ⁢   π   ⁢           ⁢     f   k     ⁢     y   p       =     arc   ⁢           ⁢     tan   (         ∑     n   =   0       N   -   1       ⁢       I   n   c     ×     cos   ⁡     (       2   ⁢           ⁢   π   ⁢           ⁢   kn     N     )               ∑     n   =   0       N   -   1       ⁢       I   n   c     ×     sin   ⁡     (       2   ⁢           ⁢   π   ⁢           ⁢   kn     N     )             )               Eq   .           ⁢     (   1.3   )                 
To carry-out phase unwrapping of the high-frequency sinusoid the following steps can be taken:
 
             unitPhase   =     arc   ⁢           ⁢     tan   ⁡     (       cos   ⁢           ⁢   Σ   ⁢           ⁢     K   1         sin   ⁢           ⁢   Σ   ⁢           ⁢     K   1         )                     highPhase   =     arc   ⁢           ⁢       tan   ⁡     (       cos   ⁢           ⁢   Σ   ⁢           ⁢     K   2         sin   ⁢           ⁢   Σ   ⁢           ⁢     K   2         )       /     f   2                     tempPhase   =     round   ⁡     (       (     unitPhase   -   highPhase     )         (     2   ⁢           ⁢   π     )     ⁢     f   2         )                   finalPhase   =     tempPhase   +     highPhase   *       (     2   ⁢           ⁢     π   /     f   2         )     .               
Or, summarized in pseudo code short-hand notation as done in  FIG. 19 , the above computational steps may be rewritten as:
         unitPhase=arctan(cosSumK1/sinSumK1);   highPhase=arctan(cosSumK2/sinSumK2)/F2;   tempPhase=round((unitPhase-highPhase)/(2*PI)*F2);   finalPhase=tempPhase+highPhase*2*PI/F2       

     The first and second superimposed sinusoid may comprise, for example as noted in EXAMPLE 01, below, a unit-frequency sinusoid (in this context, ‘unit’ refers to having a magnitude value of 1) superimposed on a high-frequency sinusoid, the unit-frequency sinusoid and high-frequency sinusoid being projected simultaneously (i.e., effectively ‘on top of one another’ over a selected epoch/duration of frames, n) from a projection unit, or projector, as a plurality of pixels such that each of the pixels projected satisfy the expression 
               I   n   p     =       A   p     +       B   1   p     ⁢     cos   ⁡     (       2   ⁢   π   ⁢           ⁢     f   h     ⁢     y   p       -       2   ⁢   π   ⁢           ⁢   n     N       )         +       B   2   p     ⁢     cos   ⁡     (       2   ⁢   π   ⁢           ⁢     f     u   ⁢               ⁢     y   p       -       4   ⁢   π   ⁢           ⁢   n     N       )                 
where I n   p  is the intensity of a pixel in the projector, A p , B 1   p , and B 2   p  are constants set such that the value of I n   p  falls between a target intensity range, (e.g., between 0 and 255 for an 8-bit color depth projector), f h  is the high frequency of the sine wave, f u  is the ‘unit’ frequency of the sine wave. The unit-frequency signal/sinusoid is used during a demodulation step to produce a decodable, unwrapped-phase term temporally.
 
     Additionally, the process includes a decoding of the projected patterns by carrying-out a lookup table (LUT)-based processing of video image data acquired by at least one image-capture device. The decoding step is performed to extract, real-time, coordinate information about the surface shape-of-interest. The LUT-based processing includes the step of implementing (or, querying) a pre-computed modulation lookup table (MLUT) to obtain a texture map for the contoured surface-of-interest and implementing (or, querying) a pre-computed phase lookup table (PLUT) to obtain corresponding phase for the video image data acquired of the contoured surface-of-interest. Furthermore, use of conventional digital image point clouds can be made to display, real-time, the data acquired. 
     In one aspect, the unique computer-implemented process, system, and computer-readable storage medium with executable program code and instructions, can be characterized as having two stages. The first being a dual-frequency pattern generation and projection stage, the dual-frequency pattern characterized by the expression 
               I   n   p     =       A   p     +       B   1   p     ⁢     cos   ⁡     (       2   ⁢   π   ⁢           ⁢     f   h     ⁢     y   p       -       2   ⁢   π   ⁢           ⁢   n     N       )         +       B   2   p     ⁢     cos   ⁡     (       2   ⁢   π   ⁢           ⁢     f     u   ⁢               ⁢     y   p       -       4   ⁢   π   ⁢           ⁢   n     N       )                 
where I n   p  is the intensity of a pixel in the projector, A p , B 1   p , and B 2   p  are constants that are preferably set, by way of example, to make the value of I n   p  fall between 0 and 255 for an 8-bit color depth projector, f h  is the high frequency of the sine wave, f u  is the unit frequency of the sine wave and equals 1, n represents phase-shift index, and N is the total number of phase shifts and is preferably greater than or equal to 5. The second stage comprises a de-codification stage employing a lookup table (LUT) method for phase, intensity/texture, and depth data.
 
     By way of using lookup tables (LUT) to obtain modulation (M) and phase (P) according to 
     
       
         
           
             
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     Next, a conversion of phase to X, Y, Z point clouds is implemented using the following: 
                 Z   w     =         M   z     ⁡     (       x   c     ,     y   c       )       +         N   z     ⁡     (       x   c     ,     y   c       )       ⁢   T         ,     
     ⁢       X   w     =           E   x     ⁡     (       x   c     ,     y   c       )       ⁢     Z   w       +       F   x     ⁡     (       x   c     ,     y   c       )                         Y   w     =           E   y     ⁡     (       x   c     ,     y   c       )       ⁢     Z   w       +       F   y     ⁡     (       x   c     ,     y   c       )                   where                   E   x     ⁡     (       x   c     ,     y   c       )       =                 (         m   22   c     ⁢     m     33   ⁢             c       -       m   23   c     ⁢     m   32   c         )     ⁢     x   c       +       (         m   13   c     ⁢     m   32   c       -       m   12   c     ⁢     m   33   c         )     ⁢     y   c       +               (         m   12   c     ⁢     m   23   c       -       m   13   c     ⁢     m   22   c         )                       (         m   21   c     ⁢     m   32   c       -       m   22   c     ⁢     m   31   c         )     ⁢     x   c       +       (         m   12   c     ⁢     m   31   c       -       m   11   c     ⁢     m   32   c         )     ⁢     y   c       +               (         m   11   c     ⁢     m   22   c       -       m   12   c     ⁢     m   21   c         )               ,     
     ⁢         F   x     ⁡     (       x   c     ,     y   c       )       =                 (         m   22   c     ⁢     m   34   c       -       m   24   c     ⁢     m   32   c         )     ⁢     x   c       +       (         m   14   c     ⁢     m   32   c       -       m   12   c     ⁢     m   34   c         )     ⁢     y   c       +               (         m   12   c     ⁢     m   24   c       -       m   14   c     ⁢     m   22   c         )                       (         m   21   c     ⁢     m   32   c       -       m   22   c     ⁢     m   31   c         )     ⁢     x   c       +       (         m   12   c     ⁢     m   31   c       -       m   11             ⁢   c       ⁢     m   32   c         )     ⁢     y   c       +               (         m   11   c     ⁢     m   22   c       -       m   12   c     ⁢     m   21   c         )               ,     
     ⁢         E   y     ⁡     (       x   c     ,     y   c       )       =                 (         m   23   c     ⁢     m   31   c       -       m   21   c     ⁢     m   33   c         )     ⁢     x   c       +       (         m   11   c     ⁢     m   33   c       -       m   13   c     ⁢     m   31   c         )     ⁢     y   c       +               (         m   13   c     ⁢     m   21   c       -       m   11   c     ⁢     m   23   c         )                       (         m   21   c     ⁢     m   32   c       -       m   22   c     ⁢     m   31   c         )     ⁢     x   c       +       (         m   12   c     ⁢     m   31   c       -       m   11   c     ⁢     m   32   c         )     ⁢     y   c       +               (         m   11   c     ⁢     m   22   c       -       m   12   c     ⁢     m   21   c         )               ,   and                   F   y     ⁡     (       x   c     ,     y   c       )       =                   (         m   21   c     ⁢     m   32   c       -       m   22   c     ⁢     m   31   c         )     ⁢     x   c       +       (         m   12   c     ⁢     m   31   c       -       m   11   c     ⁢     m   32   c         )     ⁢     y   c       +               (         m   11   c     ⁢     m   22   c       -       m   12   c     ⁢     m   21   c         )                       (         m   21   c     ⁢     m   32   c       -       m   22   c     ⁢     m   31   c         )     ⁢     x   c       +       (         m   12   c     ⁢     m   31   c       -       m   11   c     ⁢     m   32   c         )     ⁢     y   c       +               (         m   11   c     ⁢     m   22   c       -       m   22   c     ⁢     m   21   c         )             .           
Implementing the 7 parameters M z , Z z , C, E x , E y , F x , and F y  by means of table look-up for indices (x c , y c ) (camera column and row indices), reduces the total computational complexity associated with deriving the 3-D point cloud from the phase term to 7 look-ups. 4 additions. 3 . . . end quoted text from Util App &#39;607 . . . .
 
     The flow diagram FIG. 19 from Util App &#39;607 summarizes Liu et al&#39;s technique  200  as quoted extensively immediately above. By way of example, the diagram  FIG. 19  is incorporated herein and added and made part of the instant disclosure as  FIG. 10 ; the technique of Liu et al. referenced at  1100  as PRIOR ART. 
     The compact module and system of the invention employs a light source  410 , a plurality of lens elements  420  as well as  440 , and a unique fixed-pattern optic  430  from which a superimposed/overlaid SLI pattern composed of a plurality of SLI patterns (for example, as shown in  FIG. 6 ,  600  and  FIG. 7 ,  710 ) is output  435  to illuminate a surface of a 3-D object/subject-under-test or a 3-D area-under-inspection, as the case may be. The pixel intensity profile pattern ( FIG. 6 ,  600  or  FIG. 7 ,  710 ) fixed into the fixed-patterned optic  430  ( FIG. 4 ) can be comprised of two sinusoids at least one of which is a unit-frequency sinusoid (i.e., having a magnitude value of 1) superimposed onto a high-frequency sinusoid, such that the unit-frequency sinusoid and high-frequency sinusoid are projected simultaneously over a selected epoch/duration of frames, n, such that each of the pixels projected satisfy the expression  650 ,  FIG. 6  which is the same as expression  750 ,  FIG. 7 , and reproduced below. The expression, below, is likewise the same as that referred to as prior art eqn. (8) in Section A. of applicants&#39; Provisional Application No. 61/413,969 and in Section A. of Provisional Application &#39;626, as well as further explained in EXAMPLE 01 of Util App &#39;607: 
     
       
         
           
             
               I 
               n 
               p 
             
             = 
             
               
                 A 
                 p 
               
               + 
               
                 
                   B 
                   1 
                   p 
                 
                 ⁢ 
                 
                   cos 
                   ⁡ 
                   
                     ( 
                     
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           f 
                           h 
                         
                         ⁢ 
                         
                           y 
                           p 
                         
                       
                       - 
                       
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           π 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           n 
                         
                         N 
                       
                     
                     ) 
                   
                 
               
               + 
               
                 
                   B 
                   2 
                   p 
                 
                 ⁢ 
                 
                   cos 
                   ⁡ 
                   
                     ( 
                     
                       
                         2 
                         ⁢ 
                         π 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           f 
                           u 
                         
                         ⁢ 
                         
                           y 
                           p 
                         
                       
                       - 
                       
                         
                           4 
                           ⁢ 
                           π 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           n 
                         
                         N 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     where I n   p  is the intensity of a pixel in the projector, A p , B 1   p , and B 2   p  are constants set such that the value of I n   p  falls between a target intensity range, (e.g., between 0 and 255 for an 8-bit color depth projector), f h  is the high frequency of the sine wave, f u  is the ‘unit’ frequency of the sine wave. The unit-frequency signal/sinusoid is used during a demodulation step to produce a decodable, unwrapped-phase term temporally. Preferably, pixel intensity profile pattern  600  or  710  is ‘fixed’ into a transparent lens member, by way of etching into, depositing onto, or otherwise ‘fixing’ into the lens member, causing light entering the patterned optic  430 , to exit as pattern light output  435 ,  FIG. 4  having the pixel intensity profile pattern  600  or  710 . 
     The unique compact measurement apparatus and system adapted to make high-resolution measurements in real-time, leverage off the SLI patterning technique detailed further in Provisional Application &#39;626 and Util App &#39;607 resulting in a unique. 
     SUMMARY OF THE INVENTION 
     One will appreciate the distinguishable features of the system and associated technique described herein from those of known 3-D shape recognition techniques, including any prior designs invented by one or more of the applicants hereof. Certain of the unique features, and further unique combinations of features—as supported and contemplated herein—may provide one or more of a variety of advantages, among which include: (a) ready integration and flexibility/versatility (i.e., use in a wide variety of environments to gather 3-D surface data about a multitude of different areas/subjects/objects-under-test); (b) single ‘snap-shot’ investigation of an area/subject/object-under-test and/or provide ongoing monitoring/investigation/test of an area/subject/object without disruption of the surface environment around the area/object/subject; and/or (c) speed of measurements and real-time results, particularly useful to minimize artifacts that may result from motion of an object or subject (e.g., mammal) that is in motion when surface data is measured. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       For purposes of illustrating the innovative nature plus the flexibility of design and versatility of the new system and associated technique, as customary, figures are included. One can readily appreciate the advantages as well as novel features that distinguish the instant invention from conventional computer-implemented tools/techniques. The figures as well as any incorporated technical materials have been included to communicate the features of applicants&#39; innovation by way of example, only, and are in no way intended to limit the disclosure hereof. 
         FIG. 1  A high-level block diagram schematically illustrating a Measurement module  100  having Measurement module thermal isolation chamber/case  150  enclosing a Projection system  110  and single camera system  120 . 
         FIG. 2  A high-level schematic illustrating a second Measurement module  200  in communication with a System controller and data storage case/housing  255  enclosing a System controller  260  and the Data storage  270 . 
         FIG. 3  A high-level block diagram schematically illustrating a Camera system  300  for capturing an image of the illuminated Object/subject-under-test  570 , as shown in  FIGS. 5A and 5B . 
         FIG. 4  A high-level block diagram schematically illustrating Projection system architecture  400  having a Light source  410 , optical system  420 , Fixed-pattern optic  430  in communication with an Optic shifting element  431  and Projection optical system  440 . 
       FIGS.  5 . 1 A- 5 . 4 A High-level block diagrams schematically illustrating a Measurement module  550  (general case) in operation measuring, respectively, Area(s)-under-inspection  511 - 514 ,  521 - 524 ,  531 - 534 ,  541 - 544 . 
       FIGS.  5 . 1 B- 5 . 4 B Alternative embodiment of the Measurement module  550  wherein the Object-under-test  570 ,  571  comprises the inside wall of a pipeline or tubing ( 570 ,  571  representing cross-sections thereof), within which a fluid (non-compressible fluids, such as oil or water, or compressible fluids, such as natural gas) can flow. 
         FIG. 6  A graphical representation of Profile pixel intensity pattern  600  composed of four strips  610 ,  620 ,  630 ,  640  of a SLI pattern, wherein each strip is offset by phase and labeled as detailed elsewhere. 
         FIG. 7  Graphical representations of a Profile pixel intensity pattern  710  and base pattern intensity shown as a function of position profile  705 , along with an Equation/expression  750 . 
         FIG. 8  A high-level block diagram similar to  FIG. 5.3B , representing an implementation of an alternative embodiment of the invention wherein a defect  880  is shown on the object-under-test  870 . 
         FIG. 9  Depicting certain features akin to those illustrated by the block diagrams of  FIGS. 1 and 2 ,  FIG. 9  schematically illustrates an alternative Measurement module  900 . 
         FIG. 10  A high level flow diagram (labeled PRIOR ART) depicting the unique technique  1100 —disclosed in Provisional Application &#39;626 and Util App &#39;607—leveraged by the compact measurement apparatus and system of the invention. 
     
    
    
     DESCRIPTION DETAILING FEATURES OF THE INVENTION 
     By viewing the figures, the technical reference materials incorporated by reference herein, one can further appreciate the unique nature of core as well as additional and alternative features of the new apparatus/module and associated system disclosed herein. Back-and-forth reference and association has been made to various features and components represented by, or identified in, the figures. While “FIG.  1 ” may be interchangeably referred to as “FIG.  1 ”, as used throughout, either is intended to reference the same figure, i.e., the figure labeled  FIG. 1  in the set of figures. Structural and functional details have been incorporated herein—by way of example only—to showcase the use of the compact module and system of the invention employing a light source  410 , a plurality of lens elements  420  as well as  440 , and a unique fixed-pattern optic  430  from which a superimposed/overlaid SLI pattern composed of a plurality of SLI patterns (for example, as shown in  FIG. 6 ,  600  and  FIG. 7 ,  710 ) is output  435  to illuminate a surface of a 3-D object/subject-under-test or a 3-D area-under-inspection, as the case may be. 
     Uniquely and according to the invention: Inspecting an Object-under-test using a ‘fixed’ SLI pattern optic  430  with relative linear motion between the measurement module and the Object-under-test, eliminates the conventional requirement of projecting multiple SLI patterns in time-sequential fashion at a surface of an object of interest. The projection system of the invention employs a fixed-pattern optic fabricated to project requisite superimposed SLI patterns, simultaneously, using a unique technique. In one preferred implementation ( FIG. 6 ,  600 ), a four phase pattern comprised of strips ( 610 ,  620 ,  630 ,  640 ) of a core SLI pattern, is projected, in effect projecting four adjacent patterns ‘simultaneously’ at a surface of interest. The patterns are offset from each other spatially,  FIG. 6 ,  600 . A camera system  120 ,  220 ,  221  ‘simultaneously’ inspects the entire projected area (intersection of areas defined by  145  and  146 ,  FIG. 1 , intersection of areas defined by  245  and  246 , intersection of areas defined by  945  and  946 ). As the object under test moves, the portion of the object under test is time-sequentially illuminated by each of the projected patterns. In this manner, the camera can acquire the necessary pixel data which, when combined with the calibration data, enable calculation of the 3-D characteristics of the Object-under-test. 
     In addition, the velocity of the Object-under-test can be acquired, or retrieved, from the pixel data collected/measured with the camera. If the velocity changes during data acquisition, this can be detected and the change in the velocity incorporated—i.e., fed back—into the 3-D calculations to further improve the accuracy of the measurement. 
     Below is a list of components/features/assemblies shown and labeled throughout the Figures matching reference numeral with terms selected for the components/features/assemblies depicted: 
     
       
         
           
               
               
             
               
                   
               
               
                 Refer- 
                   
               
               
                 ence 
                   
               
               
                 numeral 
                 component/feature description 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 100 
                 Measurement module 
               
               
                 110 
                 Projection system 
               
               
                 120 
                 Single camera system 
               
               
                 130 
                 Measurement module mechanical mount 
               
               
                 140 
                 Calibration fixture 
               
               
                 145 
                 Projector illumination area 
               
               
                 146 
                 Camera field of view 
               
               
                 150 
                 Measurement module case 
               
               
                 155 
                 System controller and data storage case 
               
               
                 160 
                 System controller 
               
               
                 170 
                 Data storage 
               
               
                 180 
                 System controller and data storage mechanical mount 
               
               
                 185 
                 Control and data bus 
               
               
                 190 
                 Projector aperture 
               
               
                 195 
                 Camera aperture 
               
               
                 200 
                 Alternative measurement module 
               
               
                 210 
                 Projection system 
               
               
                 220 
                 First camera system 
               
               
                 221 
                 Second camera system 
               
               
                 230 
                 Measurement module mechanical mount 
               
               
                 240 
                 Calibration fixture 
               
               
                 245 
                 Projector illumination area 
               
               
                 246 
                 First camera field of view 
               
               
                 247 
                 Second camera field of view 
               
               
                 250 
                 Measurement module case 
               
               
                 255 
                 System controller and data storage case 
               
               
                 260 
                 System controller 
               
               
                 270 
                 Data storage 
               
               
                 280 
                 System controller and data storage mechanical mount 
               
               
                 285 
                 Control and data bus 
               
               
                 290 
                 Projector aperture 
               
               
                 295 
                 First camera aperture 
               
               
                 296 
                 Second camera aperture 
               
               
                 300 
                 Camera system architecture 
               
               
                 310 
                 Image sensor 
               
               
                 320 
                 Camera lens 
               
               
                 321 
                 Camera lens elements 
               
               
                 330 
                 Camera pixel data output format 
               
               
                 350 
                 Camera power unit 
               
               
                 360 
                 Camera mechanical frame 
               
               
                 365 
                 Camera pixel data output bus 
               
               
                 370 
                 Camera pixel data processing device 
               
               
                 400 
                 Projection system architecture 
               
               
                 410 
                 Light source (source of illumination) 
               
               
                 415 
                 Light output from light source 
               
               
                 420 
                 Illumination optical system 
               
               
                 421 
                 Illumination system lens element 
               
               
                 422 
                 a second illumination system lens element 
               
               
                 425 
                 Light output from light source shaped by upstream  
               
               
                   
                 illumination system at 420 
               
               
                 430 
                 Fixed-pattern optic structure (transparent support and  
               
               
                   
                 etched-pattern layer) 
               
               
                 431 
                 Optic shifting element (shifts, or reorients, fixed-pattern  
               
               
                   
                 optic structure at 430) 
               
               
                 435 
                 Patterned light output 
               
               
                 440 
                 Projection optical system 
               
               
                 441 
                 Projection system lens element 
               
               
                 442 
                 a second projection system lens element 
               
               
                 450 
                 Projector power unit 
               
               
                 500 
                 Object/subject-under-test measurement system 
               
               
                   
                 (FIGS. 5A and 5B) 
               
               
                 511 
                 Area-under-inspection 
               
               
                 550 
                 Measurement module 
               
               
                 560 
                 Carrier/housing for measurement module 
               
               
                 570 
                 Object-under-test (FIG. 5A, general case, FIG. 5B,  
               
               
                   
                 mammalian tooth, et al.) 
               
               
                 580 
                 Defect on object-under-test 
               
               
                 700 
                 Patterned optic implementation 
               
               
                 705 
                 Base pattern intensity versus position profile 
               
               
                 710 
                 Profile intensity pattern 
               
               
                 750 
                 Equation for base intensity pattern versus position (Eqn (8)) 
               
               
                 500.1 
                 Architecture for taking Object-under-test measurement at 
               
               
                   
                 time t1 
               
               
                 500.2 
                 Architecture for taking Object-under-test measurement at 
               
               
                   
                 time t2 
               
               
                 500.3 
                 Architecture for taking Object-under-test measurement at 
               
               
                   
                 time t3 
               
               
                 500.4 
                 Architecture for taking Object-under-test measurement at 
               
               
                   
                 time t4 
               
               
                 511 
                 Area under inspection by first portion of camera at time t1 
               
               
                 512 
                 Area under inspection by second portion of camera at time t1 
               
               
                 513 
                 Area under inspection by third portion of camera at time t1 
               
               
                 514 
                 Area under inspection by fourth portion of camera at time t1 
               
               
                 521 
                 Area under inspection by first portion of camera at time t2 
               
               
                 522 
                 Area under inspection by second portion of camera at time t2 
               
               
                 523 
                 Area under inspection by third portion of camera at time t2 
               
               
                 524 
                 Area under inspection by fourth portion of camera at time t2 
               
               
                 531 
                 Area under inspection by first portion of camera at time t3 
               
               
                 532 
                 Area under inspection by second portion of camera at time t3 
               
               
                 533 
                 Area under inspection by third portion of camera at time t3 
               
               
                 534 
                 Area under inspection by fourth portion of camera at time t3 
               
               
                 541 
                 Area under inspection by first portion of camera at time t4 
               
               
                 542 
                 Area under inspection by second portion of camera at time t4 
               
               
                 543 
                 Area under inspection by third portion of camera at time t4 
               
               
                 544 
                 Area under inspection by fourth portion of camera at time t4 
               
               
                 550 
                 Measurement module (either 400, 900) 
               
               
                 560 
                 Carrier/housing for measurement module 
               
               
                 570 
                 Object-under-test (FIGS. 5.1A-5.4A general case,  
               
               
                   
                 FIGS. 5.1B-5.4B pipeline) 
               
               
                 580 
                 Defect on object-under-test (FIGS. 5.1A-5.4A general,  
               
               
                   
                 FIGS. 5.1B-5.4B pipeline) 
               
               
                 590 
                 Particle flowing within fluid-under-test (FIGS. 5.1B-5.4B  
               
               
                   
                 pipeline embodiment) 
               
               
                 595 
                 Direction of motion (FIGS. 5.1A-5.4A general case, 
               
               
                   
                 FIGS. 5.1B-5.4B pipeline) 
               
               
                 600 
                 Patterned optic implementation 
               
               
                 605 
                 Base pattern intensity versus position profile 
               
               
                 610 
                 Phase One intensity pattern 
               
               
                 620 
                 Phase Two intensity pattern 
               
               
                 630 
                 Phase Three intensity pattern 
               
               
                 640 
                 Phase Four intensity pattern 
               
               
                 650 
                 Base pattern intensity versus position equation] 
               
               
                 700 
                 Alternate patterned optic implementation 
               
               
                 705 
                 An alternate base pattern intensity versus position profile 
               
               
                 710 
                 An alternate intensity pattern 
               
               
                 750 
                 An alternate equation for base intensity pattern versus position 
               
               
                 800 
                 Oil (or other fluid) pipeline measurement at time t4 
               
               
                 811 
                 Area under inspection by first portion of camera at time t1 
               
               
                 812 
                 Area under inspection by second portion of camera at time t1 
               
               
                 813 
                 Area under inspection by third portion of camera at time t1 
               
               
                 814 
                 Area under inspection by fourth portion of camera at time t1 
               
               
                 850 
                 Ring measurement module configuration 
               
               
                 860 
                 Carrier for measurement module 
               
               
                 861 
                 Rear annulus for stabilizing rear of measurement module  
               
               
                   
                 carrier and establishing thrust from flow 
               
               
                 862 
                 Front annulus for stabilizing rear of measurement module  
               
               
                   
                 carrier and establishing thrust from flow 
               
               
                 863 
                 Another front annulus for stabilizing rear of measurement  
               
               
                   
                 module carrier and establishing thrust from flow 
               
               
                 870 
                 Bottom of pipeline wall (6 O&#39;Clock position) 
               
               
                 871 
                 Top of pipeline wall (12 O&#39;Clock position) 
               
               
                 880 
                 Defect on oil pipeline wall 
               
               
                 885 
                 Oil 
               
               
                 890 
                 Particle floating in the oil 
               
               
                 895 
                 Direction of motion 
               
               
                 900 
                 Ring measurement module 
               
               
                 910 
                 Projection system 
               
               
                 920 
                 Single camera system 
               
               
                 930 
                 Measurement module mechanical mount and cooling system 
               
               
                 945 
                 Projector illumination area 
               
               
                 946 
                 Camera field of view 
               
               
                 950 
                 Measurement module thermal isolation chamber 
               
               
                 955 
                 System controller and data storage thermal isolation chamber 
               
               
                 960 
                 System controller 
               
               
                 970 
                 Data storage 
               
               
                 970 
                 Bottom of pipeline wall (6 O&#39;Clock position) 
               
               
                 971 
                 Top of pipeline wall (12 O&#39;Clock position) 
               
               
                 980 
                 System controller and data storage mechanical mount and  
               
               
                   
                 cooling system 
               
               
                 985 
                 Control and data bus 
               
               
                 990 
                 Projector aperture 
               
               
                 995 
                 Camera aperture 
               
               
                   
               
            
           
         
       
     
     One aspect of the invention includes a compact system  400  employing: a light source  410 ; an Illumination optical system  420  (comprising a plurality of lens elements) in front of a unique fixed-pattern optic  430  from which a superimposed/overlaid SLI pattern such as  600 ,  710  (composed of a plurality of SLI patterns) is output  435  to illuminate a surface of a 3-D object/subject-under-test (e.g.,  570 ,  870 ) or area-under-inspection (e.g.,  511 - 514 ,  811 - 814 ), as the case may be; and a Projection optical system  440  (comprising a plurality of lens elements downstream of fixed-pattern optic  430 ). A second related aspect of the invention includes a method that eliminates the need for complex traditional phase unwrapping algorithms for 3-D measurements based on SLI; the method incorporates operation of the unique fixed-pattern optic  430  from which a superimposed/overlaid SLI pattern (composed of a plurality of SLI patterns) is output  435  to illuminate a surface of a 3-D object/subject-under-test (e.g.,  570 ,  870 ) or area-under-inspection (e.g.,  511 - 514 ,  811 - 814 ), as the case may be. SLI ‘phase unwrapping algorithms’ are traditionally required and used to enable positioning of precise measurements within a larger field of view. 
     As noted above and detailed further in Provisional Application &#39;626 and Util App &#39;607, the two examples set forth in Sections A. and B. of the new multi-frequency patterns disclosed in Provisional Application &#39;626 were introduced in terms of analogies to traditional electrical circuitry signal/current propagation types: An AC flavor and DC flavor. These same Sections A. and B. were integrated into applicants&#39; Provisional Application No. 61/413,969 filed 15 Nov. 2010, incorporated herein by reference as noted above. The multi-frequency pattern detailed in Section A. fashioned after principals governing AC electrical systems was coined “Dual-frequency Phase Multiplexing” (DFPM). As noted in applicants&#39; Provisional Application No. 61/413,969, the material in Section A. was earlier published as 1 Mar. 2010/Vol. 18, No. 5/Optics Express 5233 and is noted in the section of Util App &#39;607 labeled EXAMPLE 01. The multi-frequency pattern detailed in Section B. fashioned after principals governing DC electrical systems was coined “Period Coded Phase Measuring” (PCPM). Dual-frequency Phase Multiplexing (DFPM) patterns comprise two superimposed sinusoids, one a unit-frequency phase sine wave and the other a high-frequency phase sine wave, whereby after receiving/acquiring the pattern data by an image sensor, the phase of the two patterns is separated. The unit-frequency phase is used to unwrap the high-frequency phase. The unwrapped high-frequency phase is then employed for 3-D reconstruction. Period Coded Phase Measuring (PCPM) patterns—fashioned after DC current propagation—are generated with the period information embedded directly into high-frequency base patterns, such that the high-frequency phase can be unwrapped temporally from the PCPM patterns. 
     The module and system of the invention employs a fixed-pattern optic  430  that has multiple sine wave patterns overlaid, i.e., superimposed, into a resultant SLI pattern such as is described in Section A and Section B, of applicants&#39; Provisional Application No. 61/413,969. And more-particularly, the fixed-pattern optic is preferably adapted to project—as detailed above and in Util App &#39;607 and represented at  1100  in FIG.  10 —a multi-frequency pattern comprising a plurality of pixels representing at least a first and second superimposed sinusoid projected simultaneously, each of the sinusoids represented by the pixels having a unique temporal frequency and each of the pixels projected to satisfy 
                     I   n   p     =       A   p     +       ∑     k   =   1     K     ⁢       B   k   p     ⁢     cos   ⁡     (       2   ⁢           ⁢   π   ⁢           ⁢     f   k     ⁢     y   p       +       2   ⁢           ⁢   π   ⁢           ⁢   kn     N       )                     Eq   .           ⁢     (   1.1   )                 
where I n   p  is the intensity of a pixel in the projector for the n th  projected image in a particular instant/moment in time (p, to represent projector); K is an integer representing the number of component sinusoids (e.g., K=2 for a dual-frequency sinusoid pattern, K=3 for a triple-frequency sinusoid, and so on), each component sinusoid having a distinct temporal frequency, where K≦(N+1)/2.
 
     Where pixels are projected to satisfy Eq. 1.1, the pixels of the images then captured by the camera are defined according to the unique technique governed by the expression: 
                     I   n   c     =       A   c     +       ∑     k   =   1     K     ⁢       B   k   c     ⁢     cos   ⁡     (       2   ⁢           ⁢   π   ⁢           ⁢     f   k     ⁢     y   p       +       2   ⁢           ⁢   π   ⁢           ⁢   kn     N       )           +   η             Eq   .           ⁢     (   1.2   )                 
The term η (“eta”) represents a noise due to a certain amount of error introduced into the image by the light sensor of the camera. To obtain phase terms from the pixels projected in accordance with Eq. 1.2, the unique expression, below, is carried-out for each k:
 
                     2   ⁢           ⁢   π   ⁢           ⁢     f   k     ⁢     y   p       =     arc   ⁢           ⁢     tan   (         ∑     n   =   0       N   -   1       ⁢       I   n   c     ×     cos   ⁡     (       2   ⁢           ⁢   π   ⁢           ⁢   kn     N     )               ∑     n   =   0       N   -   1       ⁢       I   n   c     ×     sin   ⁡     (       2   ⁢           ⁢   π   ⁢           ⁢   kn     N     )             )               Eq   .           ⁢     (   1.3   )                 
where, as before, y p  represents a spatial coordinate in the projected image.
 
     When applying the use of temporal unwrapping techniques, for the case where k=2 using Eq. 1.1, one can determine that the projected pixels will satisfy 
     
       
         
           
             
               
                 
                   
                     
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     A second set of patterns (k=1) all unit-frequency sinusoids (i.e., f=1) is superimposed with a high-frequency sinusoid, such as one of 20 stripes, k=2 pattern. The unit-frequency signal is defined by an adaptation of Eq. 1.1 
                       I   n   p     =       A   p     +       B   1   p     ⁢     cos   ⁡     (       2   ⁢           ⁢   π   ⁢           ⁢     f   2     ⁢     y   p       +       2   ⁢           ⁢   π   ⁢           ⁢   n     N       )             ,     k   =   1             Eq   .           ⁢     (   1.1   )                 
Therefore, rather than projecting a total of N patterns onto the contoured surface-of-interest, there are now 2*N patterns projected (such that K=2 and each pixel projected from the projector is comprised of a dual-frequency pattern, one is a unit-frequency sinusoid and the second is a high-frequency sinusoid).
 
     To carry-out phase unwrapping of the high-frequency sinusoid the following steps can be taken: 
             unitPhase   =     arctan   ⁡     (       cos   ⁢           ⁢   Σ   ⁢           ⁢     K   1         sin   ⁢           ⁢   Σ   ⁢           ⁢     K   1         )                   highPhase   =       arctan   ⁡     (       cos   ⁢           ⁢   Σ   ⁢           ⁢     K   2         sin   ⁢           ⁢   Σ   ⁢           ⁢     K   2         )       /     f   2                   tempPhase   =     round   ⁡     (       (     unitPhase   -   highPhase     )         (     2   ⁢   π     )     ⁢     f   2         )                   finalPhase   =     tempPhase   +     highPhase   *     (     2   ⁢     π   /     f   2         )               
Or, summarized in pseudo code short-hand notation as done in  FIG. 19 , the above computational steps may be rewritten as:
         unitPhase=arctan(cosSumK1/sinSumK1);   highPhase=arctan(cosSumK2/sinSumK2)/F2;   tempPhase=round((unitPhase-highPhase)/(2*PI)*F2);   finalPhase=tempPhase+highPhase*2*PI/F2       

     The first and second superimposed sinusoid may comprise, for example, a unit-frequency sinusoid (having a magnitude value of 1) superimposed on a high-frequency sinusoid, the unit-frequency sinusoid and high-frequency sinusoid being projected simultaneously over a selected epoch/duration of frames, n, as a plurality of pixels such that each of the pixels projected satisfy the expression  750 ,  FIG. 6 , below 
               I   n   p     =       A   p     +       B   1   p     ⁢     cos   ⁡     (       2   ⁢   π   ⁢           ⁢     f   h     ⁢     y   p       -       2   ⁢   π   ⁢           ⁢   n     N       )         +       B   2   p     ⁢     cos   ⁡     (       2   ⁢   π   ⁢           ⁢     f     u   ⁢               ⁢     y   p       -       4   ⁢   π   ⁢           ⁢   n     N       )                 
where I n   p  is the intensity of a pixel in the projector, A p , B 1   p , and B 2   p  are constants set such that the value of I n   p  falls between a target intensity range, (e.g., between 0 and 255 for an 8-bit color depth projector), f h  is the high frequency of the sine wave, f u  is the ‘unit’ frequency of the sine wave. The unit-frequency signal/sinusoid is used during a demodulation step to produce a decodable, unwrapped-phase term temporally.
 
     Additionally, the process includes a decoding of the projected patterns by carrying-out a lookup table (LUT)-based processing of video image data acquired by at least one image-capture device. The decoding step is performed to extract, real-time, coordinate information about the surface shape-of-interest. The LUT-based processing includes the step of implementing (or, querying) a pre-computed modulation lookup table (MLUT) to obtain a texture map for the contoured surface-of-interest and implementing (or, querying) a pre-computed phase lookup table (PLUT) to obtain corresponding phase for the video image data acquired of the contoured surface-of-interest. Furthermore, use of conventional digital image point clouds can be made to display, real-time, the data acquired. 
     Therefore, the fixed-pattern optic may be adapted to project—as detailed and represented in  FIGS. 6 and 7  respectively at  650 ,  750 , and further shown at  1100  in FIG.  10 —a multi-frequency pattern characterized as having two stages. The first being a dual-frequency pattern generation and projection stage, the dual-frequency pattern characterized by the expression, below 
               I   n   p     =       A   p     +       B   1   p     ⁢     cos   ⁡     (       2   ⁢   π   ⁢           ⁢     f   h     ⁢     y   p       -       2   ⁢   π   ⁢           ⁢   n     N       )         +       B   2   p     ⁢     cos   ⁡     (       2   ⁢   π   ⁢           ⁢     f     u   ⁢               ⁢     y   p       -       4   ⁢   π   ⁢           ⁢   n     N       )                 
where I n   p  is the intensity of a pixel in the projector, A p , B 1   p , and B 2   p  are constants that are preferably set, by way of example, to make the value of I n   p  fall between 0 and 255 for an 8-bit color depth projector, f h  is the high frequency of the sine wave, f u  is the unit frequency of the sine wave and equals 1, n represents phase-shift index, and N is the total number of phase shifts and is preferably greater than or equal to 5. The second stage comprises a de-codification stage employing a lookup table (LUT) method for phase, intensity/texture, and depth data. By way of using lookup tables (LUT) to obtain modulation (M) and phase (P) according to
 
               MLUT   ⁡     [     U   ,   V     ]       =           1   3     ⁡     [       3   ⁢     V   2       +     U   2       ]       0.5     ⁢           ⁢   and                   PLUT   ⁡     [     U   ,   V     ]       =         tan     -   1       ⁡     [         3   0.5     ⁢   V     U     ]       .           
Thereafter, a conversion of phase to X, Y, Z point clouds is implemented using the expressions:
 
 Z   w   =M   z ( x   c   ,y   c )+ N   z ( x   c   ,y   c ) T,  
 
 X   w   =E   x ( x   c   ,y   c ) Z   w   +F   x ( x   c   ,y   c )
 
 Y   w   =E   y ( x   c   ,y   c ) Z   w   +F   y ( x   c   ,y   c )
 
Further details concerning solutions and use of the three expressions above can be found elsewhere herein and in Util App &#39;607.
 
     Effectively identical expressions  650 ,  750  ( FIGS. 6 and 7 ) define a profile pattern of pixel intensity ( 600 ,  710 ) for use with the fixed-patterned optic  430  ( FIG. 4 ). Preferably, pixel intensity profile pattern  600 ,  710  is ‘fixed’ into a transparent lens member, by way of etching into, depositing onto, or otherwise ‘fixing’ into a transparent lens member, causing light entering the patterned optic  430  to exit as pattern light output  435  having the intended pixel intensity profile pattern  600 ,  710 . As a result, the projected pattern (physically etched or deposited onto a transparent lens member) is comprised of, for example, a high frequency sine wave pattern and a low frequency sinewave pattern (this combination of sine waves is graphically represented at  605 ,  FIGS. 6 and 705 ,  FIG. 7 ). The high frequency pattern enables precise measurement of the 3-D shape of objects. The low frequency pattern enables course measurement of the distance between the object under test and the measurement system. As mentioned elsewhere, this eliminates the conventional employment of additional, sophisticated computer processing required when applying phase unwrapping algorithms. The low frequency measurement provides a rough (course) estimate of the 3-D coordinates of a measured point. The high frequency measurement precisely locates the point (fine measurement). 
     Once again, the high-level block diagram in  FIG. 1  schematically illustrates a Measurement module  100  having Measurement module thermal isolation chamber/case  150  enclosing a Projection system  110  and single camera system  120 , in communication with a System controller and data storage case/housing  155  enclosing a System controller  160  and Data storage  170 . The high-level schematic in  FIG. 2  illustrates a second Measurement module  200  in communication with a System controller and data storage case/housing  255  enclosing a System controller  260  and the Data storage  270 . The high-level block diagram in  FIG. 3  schematically illustrates a Camera system  300  for capturing an image of the illuminated Object/subject-under-test  570 ,  FIGS. 5A and 5B . Camera system  300  has an Image sensor  310 , Camera lens  320  comprising Camera lens elements (generally labeled  321 ), Camera pixel data processing device  370 , Camera pixel data output bus  365 , and means for connection to Camera power  350 . 
     The high-level block diagram in  FIG. 4  schematically illustrates Projection system architecture  400  having a Light source  410 , optical system  420 , Fixed-pattern optic  430  in communication with an Optic shifting element  431  (for shifting, or reorienting, the fixed-pattern optic structure  430 ), and Projection optical system  440 . 
     The high-level block diagrams in FIGS.  5 . 1 A- 5 . 4 A schematically illustrate a Measurement module  550  (general case) in operation measuring, respectively, Area(s)-under-inspection  511 - 514 ,  521 - 524 ,  531 - 534 ,  541 - 544  within which an Object-under-test  570  (having a defect  580 ) is being investigated by the Measurement module  550 . Direction arrow  595  represents the relative linear motion between module  550  and Object-under-test  570  such that defect  580  under Measurement module  550  moves into a new Area-under-inspection  511 ,  512 ,  513 ,  514  with-respect-to the four fixed-pattern phases:  610 ,  620 ,  630 ,  640  (see  FIG. 6 ). As labeled, the pattern projected on first Area-under-inspection  511  at time “t 1 ” ( FIG. 5.1A ) results from light that passes through the Phase One intensity pattern  610  portion of the fixed-pattern optic  430 . The pattern projected on second Area-under-inspection  512  at time “t 2 ” ( FIG. 5.2A ) results from light that passes through the Phase Two intensity pattern  620  portion of the fixed-pattern optic  430 , and so on. 
     An alternative embodiment of the Measurement module  550  is depicted in FIGS.  5 . 1 B- 5 . 4 B highlighting the case where an Object-under-test  570 ,  571  comprises the inside wall of a pipeline or tubing ( 570 ,  571  representing cross-sections thereof), within which a fluid (non-compressible fluids, such as oil or water, or compressible fluids, such as natural gas) can flow; wall-under-test  570  is shown, by way of example, with defect  580  (representing as a small area of decay such as a fracture, fission, crack(s), etc.) in Wall-under-test  570 . Also shown is a Particle  590  flowing within the fluid-under-test between walls  570 ,  571 . In a manner similar to FIGS.  5 . 1 A- 5 . 4 A, shown is a Measurement module  550  adapted/retrofitted for moving along walls  570 ,  571 . In operation, as shown in FIGS.  5 . 1 B- 5 . 4 B module  550  moves along walls  570 ,  571  measuring Area(s)-under-inspection, respectively,  511 - 514 ,  521 - 524 ,  531 - 534 ,  541 - 544 . Direction arrow  595  represents the relative linear motion between module  550  and Wall-under-test  570  such that defect  580  moves into a new Area-under-inspection  511 ,  512 ,  513 ,  514  with-respect-to module  550 . As labeled, the pattern projected on first Area-under-inspection  511  at time “t 1 ” ( FIG. 5.1B ) results from light that passes through the Phase One intensity pattern  610  portion of the fixed-pattern optic  430 . The pattern projected on second Area-under-inspection  512  at time “t 2 ” ( FIG. 5.2B ) results from light that passes through the Phase Two intensity pattern  620  portion of the fixed-pattern optic  430 , and so on, for  FIGS. 5.3B ,  5 . 4 B. 
       FIG. 6  includes a graphical representation of Profile pixel intensity pattern  600  composed of four strips  610 ,  620 ,  630 ,  640  of a SLI pattern, wherein each strip is offset by phase and labeled as follows: Phase One intensity pattern  610 , Phase Two intensity pattern  620 , Phase Three intensity pattern  630 , and Phase Four intensity pattern  640 ; and, a graphical representation of base pattern intensity shown as a function of position profile  605 , along with an Equation/expression  650  for base intensity pattern as a function of position.  FIG. 7  includes graphical representations of a Profile pixel intensity pattern  710  and base pattern intensity shown as a function of position profile  705 , along with an Equation/expression  750  for base intensity pattern as a function of position. 
     The high-level block diagram of  FIG. 8 , similar to  FIG. 5.3B , represents an implementation of an alternative embodiment of the invention wherein a defect  880  is shown on the object-under-test  870  (here, the object-under-test are walls  870 ,  871  of a pipeline/piping) and a particle  890  is shown floating within the fluid flowing along pipeline  870 ,  871 . 
     Depicting certain features akin to those illustrated by the block diagrams of  FIGS. 1 and 2 ,  FIG. 9  schematically illustrates an alternative Measurement module  900  having Measurement module thermal isolation chamber/case  950  enclosing a Projection system  910  and single camera system  920 , in communication with a System controller and data storage case/housing  955  enclosing a System controller  960  and Data storage  970 . 
     Returning, now, to  FIG. 1 : This diagram illustrates one embodiment of the Measurement module,  100 , comprising a Projection system  110 , a Single camera system  120 , a Measurement module mechanical mount and cooling system  130 , a Measurement module thermal isolation chamber/case  150 , a System controller and data storage case  155 , a System controller  160 , Data storage  170 , a System controller and data storage mechanical mount and cooling system  180 , a Control and data bus  185 , a Projector aperture  190 , and a Camera aperture  195 . 
     The Projection system  110  projects a pattern through the Projector aperture  190  that is focused onto the object-under-test  570 ,  870  (FIGS.  5 . 1 A- 5 . 4 A,  5 . 1 B- 5 . 4 B, and  8 ) and creates a Projector illumination area  145 . The pattern is distorted by the shape of the object according to the object&#39;s 3-D characteristics. Provided the distorted pattern is within the Camera field of view  146 , the distortions are recorded by the Single camera system  120  which observes the object under test through the Camera aperture  195 . Only portions of the object under test within the Projector illumination area  145  and within the Camera field of view  146  can be measured. The Projection system  110  and the Single camera system  120  are held in place with an assembly labeled  130  which uniquely incorporates within Measurement module  100  the functionalities of Measurement module mechanical mount and cooling system. In order to ensure suitably accurate 3-D measurements, a Calibration fixture  140  is used to precisely establish the relative physical positions of the Projection system  110  and the Single camera system  120 . Since the physical shape of the Measurement module mechanical mount and cooling system,  130 , will change a result of environmental conditions (i.e., physical dimensions of  130  will expand and contract slightly with temperature changes), a pre-calibration of the Measurement module  100  using the Calibration fixture  140  is done over a wide range of environmental conditions. Pre-calibration is preferably done under controlled environment, prior to monitoring of an object-under-test  570 . 
     For example, a temperature range from  31  40 C to 120 C might be used during pre-calibration of the Measurement module  100 . Calibration data, along with measurement results, are stored in Data storage  170  by the System controller  160 . Data and control information are passed between the Projection system  110 , the Single camera  120  and the System controller  160  via the Control and data bus  185 . The System controller and data storage case  155  maintains the System controller  160  and the Data storage  170  within their respective operating temperatures ranges. The Measurement module thermal isolation chamber/case  150 , along with the Measurement module mechanical mount and cooling system  130 , aids in maintaining the Projection system  110  and the Single camera system  120  within respective target operating temperature ranges. 
     An alternative preferred embodiment of the invention is shown in  FIG. 2 . In this embodiment, the Projection system  210  projects a pattern through the Projector aperture  190  that is focused onto the object-under-test (e.g., at  570 , FIGS.  5 . 1 A- 5 . 4 A,  5 . 1 B- 5 . 4 B, or at  870 ,  FIG. 8 ) producing a Projector illumination area defined at  245 . The resultant pattern illuminating an object-under-test ( 570 ,  870 ) becomes distorted by the shape of the object according to the object&#39;s 3-D surface characteristics. Provided the distorted pattern is within a composite Camera field of view  246  of the First and Second Camera Systems  220  and  221 , the distortions are recorded by the Camera systems  220 ,  221 . Only portions of the object-under-test within the Projector illumination area defined at  245  and, at the same time, within the composite Camera field of view  246  will be measured. The Projection system  210  and Single camera system  220  are held in place using the Measurement module mechanical mount and cooling system  230 . In order to ensure accurate 3-D measurements, a Calibration fixture  240  is used to precisely establish relative physical positions of (or, relative distances between) the Projection system  210  and First Camera System  220  and the projection system  210  and Second Camera System  221 . Because the Measurement module mechanical mount and cooling system  230  will change shape (even if only a slight difference in original dimensions) as a result of environmental conditions, a calibration of the Measurement module  200  using the Calibration fixture  240  is done over a wide range of environmental conditions prior to placing the Measurement module in operation. 
     For example, a temperature range from −40 C to 120 C might be used during calibration of the Measurement module  200 . Calibration data, along with measurement results, are stored in Data storage  270  by the System controller  260 . Data and control information are passed between the Projection system  210 , the First Camera System  220 , the Second Camera System  221  and the System controller  260  via the Control and data bus  285 . The System controller and data storage case  255  maintains the System controller  260  and the Data storage  270  within their respective operating temperatures ranges. The Measurement module thermal isolation chamber/case  250  combined with the Measurement module mechanical mount and cooling system  230  maintain the Projection system  210  and the Single camera system  220  within a respective target operating temperature range. 
     Embodiments of the Projection system  110  (as well as alternative Projection system labeled  210 ,  FIGS. 2 and 910 ,  FIG. 9 ) are discussed, next, in connection with Projection system architecture  400 ,  FIG. 4  (further discussion of embodiments depicted in FIGS.  5 . 1 B- 5 . 4 B,  8  and  9  are found under “EXAMPLES|alternative useful structures”). Projection system architecture  400  includes a Light source  410  for producing a light emission  415  incident upon an Illumination optical system  420  having first and second Illumination system lens elements  421 ,  422  whose output is focused on the Patterned optic  430  which, in turn, produces the Patterned light output  435 . Patterned light output  435  is then focused by the Projection optical system  440  onto the object-under-test (e.g., at  570 , FIGS.  5 . 1 A- 5 . 4 A,  5 . 1 B- 5 . 4 B, or at  870 ,  FIG. 8 ). As depicted in the schematics of  FIG. 4 , Projector power  450  supplies power to elements of  400  of projection system  110 ,  FIG. 1  or  910 ,  FIG. 9 . 
     Embodiments of the Fixed-pattern optic  430  are illustrated in  FIGS. 6 and 7  (respectively at  600 ,  710 ). The graphic representations in  FIG. 6  and those in  FIG. 7 , each collectively represent alternative Patterned optic implementations for fixed-pattern optic  430 . Preferably, as mentioned elsewhere, fixed-pattern optic  430  is comprised of a glass substrate on which a reflective material is etched, deposited, or otherwise ‘fixed’ to the glass substrate (transparent lens member), such that the transmittance of light through the patterned optic results in the Profile intensity pattern labeled  600 ,  710 . The Base pattern intensity vs. position profile at  605 ,  705  are each graphical representations of the Equation for base intensity pattern vs. position  650 ,  750 , identified and further explained elsewhere herein. 
     FIGS.  5 . 1 A- 5 . 4 A, as well as the embodiment represented in FIGS.  5 . 1 B- 5 . 4 B, illustrate respective implementations  500 . 1 ,  500 . 2 ,  500 . 3 ,  500 . 4  of a Measurement Module  100 ,  200 ,  900  in operation while taking a measurement of an Object-under-test  570  (labeled in the embodiments shown in FIGS.  5 . 1 A- 5 . 4 A and in FIGS.  5 . 1 B- 5 . 1 B). The Object-under-test  570  is shown with a Defect on the object under test  580  and with a Direction of motion  595  relative to the measurement system. Measurements of the object-under-test  570  will occur within that area where the projected image and the camera field of view overlap. 
     In  FIGS. 5.1A  and  5 . 1 B at  500 . 1 , the Measurement Module  550  is shown located inside a Carrier/housing for the measurement module  560 . As shown in the embodiment  500 . 1  of  FIG. 5.1B , attached to the Carrier/housing  560  is a Rear annulus for stabilizing rear of measurement module carrier and establishing thrust from flow  561 , a Front annulus for stabilizing rear of measurement module carrier and establishing thrust from flow  562 , and a Second front annulus for stabilizing rear of measurement module carrier and establishing thrust from flow  563 . The combination of  561 ,  562 , and  563  stabilize the motion of the  560  and ensure that  560  moves with the flow rate of the Material  585 , gas or liquid, that is inside the pipeline. Measurement of the pipeline wall will occur on all surfaces.  571  is the Top of the pipeline wall, herein referred to as the 12 O&#39;Clock position.  570  is the Bottom of the pipeline wall, herein referred to as the 6 O&#39;Clock position. The Measurement module  550  will differentiate between a Particle  590  floating in the fluid (a compressible fluid such as natural gas, or a non-compressible, such as oil or water) within pipeline walls  570 ,  571  and a Defect  580 . Differentiation is done by means of the distance of the particle of defect from the measurement module. This distance relates directly to the measured phase. To streamline the measurement process, a phase threshold can be established. The phase threshold can be defined to be the zero phase position. Particles and defects with positive phase are then captured; those with negative phase are ignored (or vice versa). 
     In the embodiment of  500 . 1  using pattern  600  ( FIG. 6 ), the pattern projected on Area-under-inspection by first portion of camera at time t 1  (this Area-under-inspection is  511 ) results from light that passes through the Phase One intensity pattern  610  portion of the Patterned optic  430 . Thus, the Defect  580  is illuminated with a Phase One intensity pattern  610  and inspected by the camera system. Because the Object-under-test  570  moves in the Direction of motion  595 , after a certain time, which is based on the velocity of the Object-under-test  570 , the Carrier/housing  560  will have moved such that the Defect  580  is illuminated by the Phase Two intensity pattern  620 . The embodiment labeled  500 . 2  illustrates this case (i.e., illuminating Area-under-test  512  with  620 ). Through successive motion, likewise illustrated at  500 . 3  and  500 . 4  ( FIGS. 5.3A  and  5 . 4 A as well as  FIGS. 5.3B  and  5 . 3 B), the Object-under-test  570  moves such that the Defect  580  is illuminated and observed, respectively, through Phase Three intensity pattern  630  and Phase Four intensity pattern  640 . As a result, measurement of the Defect  580  with a four phase PMP pattern is achieved. 
     The Measurement module  550  measures an Area-under-inspection  511 , as shown in  FIGS. 5A and 5B . An Object-under-test  570  is within the Area-under-inspection  511 . The Object-under-test  570  is first illuminated with the Profile intensity pattern  710 . Once the camera system (for example, that shown as  300  in  FIG. 3 ), has captured an image of an Object-under-test  570  undergoing illumination with Profile intensity pattern  710 , the Patterned optic shifting element  431  acts on the fixed-pattern optic  430  to shift the pattern spatially by, for example, 90 degrees of the fine pitch pattern. In this manner, the fixed-pattern optic  430  is shifted according to the high frequency cosine function in Equation/expression  750 . Expression  750  represents the relationship between base intensity pattern vs. position. 
     As also explained elsewhere: The module and system of the invention employs a fixed-pattern optic  430  that has multiple sine wave patterns overlaid, i.e., superimposed, into a resultant SLI pattern such as is described in Section A, of applicants&#39; Prov App No. 61/413,969; a special case of which—when one sinusoid of the multi-frequency pattern is set to unit magnitude—is reflected in expression  750  (identical to  650 ). Other shifts are contemplated hereby: Shifting the fixed-pattern optic  430  in increments of 90 degrees is one of a multitude of contemplated embodiments. Shifting the fixed-pattern optic 90 degrees in separate increments—through one full 365 degree rotation—will provide 3-D measurements about targeted surfaces of an Object-under-test  570  in a manner consistent with a four PMP approach. 
     Examples|Alternative Useful Structures 
     Embodiments depicted in  FIGS. 8-9 . The technique and system of the invention are useful in operation to make real-time calculations of 3-D data measured with a camera from a surface of an object-under-test  870  or area-under-inspection  811 - 814 , such as a surface within the interior of a pipeline/tubing. It is contemplated that a multitude of objects and surfaces may be inspected according to the invention. As explained elsewhere,  FIG. 9  shows an alternative embodiment of the Measurement Module  900  that enables simultaneous inspection of the interior circumference of the pipeline with a single measurement module. In this embodiment, the field of view of the camera system and the projection system encompass the interior circumference of the pipeline. 
     While certain representative embodiments and details have been shown for the purpose of illustrating features of the invention, those skilled in the art will readily appreciate that various modifications, whether specifically or expressly identified herein, may be made to these representative embodiments without departing from the novel core teachings or scope of this technical disclosure. Accordingly, all such modifications are intended to be included within the scope of the claims. Although the commonly employed preamble phrase “comprising the steps of” may be used herein, or hereafter, in a method claim, the applicants do not intend to invoke 35 U.S.C. §112 ¶6 in a manner that unduly limits rights to its claimed invention. Furthermore, in any claim that is filed herewith or hereafter, any means-plus-function clauses used, or later found to be present, are intended to cover at least all structure(s) described herein as performing the recited function and not only structural equivalents but also equivalent structures.