TITLE

"HIDDEN CHANGE DISTRIBUTION GRATING AND USE IN

3D MOIRE MEASUREMENT SENSORS AND CMM APPLICATIONS" BACKGROUND OF THE INVENTION

The present invention is directed to miniaturized X-Y-Z data collection devices and systems. The present invention is directly applicable to many important surface inspection and measurement tasks that have not been successfully or practically accomplished in the prior art because of overly-large 3D measurement sensor sizes and/or costs.

In the prior art, the fundamental X-Y-Z data collection sensors were based on small single-point contact touch probe technologies. A major off-line measurement industry was created using these sensors incorporating equipment known as Coordinate Measuring Machines (CMM's) . These CMM's generally consist of mechanical slides or linear motions to provide a three degree-of-freedom (3-D.O.F.) translation of the small sensor relative to the part being inspected. In many CMM configurations a two-axis rotational unit known as a pan/tilt head is attached between the quill or mast of the CMM and the sensor to provide an additional two degree-of-freedom (2-D.O.F.) rotation to the sensor for part measurement flexibility. Some CMM versions will also include translations and rotations to help manipulate the part.

Due to its importance to the off-line measurement industry (the measurement of parts off the assembly line) , the CMM has a long and successful development history. More than 40 years have permitted the perfection of the CMM to maximize reliability and

SUBSTITUTE SHEET

measurement accuracies while minimizing costs. Standardization of a number of CMM versions has been achieved. Their proliferation has been so great that virtually every manufacturing facility that is required to meet some quality control standard has at least one CMM version in operation.

The success of the CMM has also created a major paradox in the measurement industry in meeting current and future goals. One side of the paradox is that the CMM was designed and developed to hold small light weight measurement sensors weighing only a few ounces. However these sensors were generally of a single point type (i.e. only one X-Y-Z data measurement point is available for each motion of the CMM) . The resulting data collection times are so slow that the accelerating requirements of higher speed inspection and measurement needed to meet new manufacturing quality control goals cannot be met with these single-point sensors. The small advancement of the single-point sensor from a contact type to a single-point non-contact type has not addressed the new data collection speed requirements which are forecasted to be 100% inspection at on-line production rates.

The other side of the paradox is that current stand-alone sensors designed to generate large X,Y,Z data arrays in one view are much too large and heavy to be mounted on existing CMM's. The investment cost and risk of replacing the traditional well-proven CMM in order to use these sensors are so great aε to have severely handicapped the measurement industry in attempting to achieve its quality control goals.

SUMMARY OF THE INVENTION A moire sensor technique (U.S. Serial No. 775,432 now allowed and hereby incorporated by reference) has

provided a general approach to collecting large X-Y-Z data bases at data rates sufficient to meet the measurement industry goals. This disclosed moire sensor technique has the ability to collect data much more rapidly than either single point or single line (laser line scanning) techniques and has the ability to collect extremely dense X-Y-Z data (e.g. approximately 250,000 X-Y-Z data points in a 480 x 512 grid for a typical solid state CCD video camera) in snapshot views of the part. Higher density data is achievable with cameras with higher density detector arrays. This disclosed moire technique does not require the moire sensor to be held stationary with respect to the part for data collection, thereby permitting the achievement of high speed data collection for the measurement industry.

A miniature moire (Mini-Moire) sensor in its smallest configuration and with the highest speed response would contain the following minimal size-impacting elements listed in Table 1:

TABLE 1 - MINIMAL SIZE-IMPACTING ELEMENTS

FOR THE MINI-MOIRE SENSOR

1) One 2D CCD Detector Element Array

2) One Lens for CCD

3) One Fringe Pattern Element 4) One White Light Source for Projector 5) One Lens for Projector Additional elements could result in a potentially larger and more expensive moire sensor. The ultimate performance features desired of a miniature moire sensor

are the same as those achieved by the reference U.S. Serial No. 775,432 and are listed in Table 2.

TABLE 2 - DESIRED FEATURES FOR THE MINI-MOIRE SENSOR

ITEM I - Use highest resolution Fringe Pattern Element possible with a Nyguest Limit fringe period p ₀ for highest resolution x,y,z measurements and coverage of smallest part areas.

ITEM II - Solve 27t Problem in same snapshot instant of CCD image collection in order to support high speed part scanning including continuous scans.

The "2π Problem" is the shift of a fringe pattern a full period to create a new identical looking pattern indistinguishable using standard interfero etric fringe processing techniques.

Items I and II are in direct conflict with each other and moire sensor implementations have compromised either I or II (and often both) except for the embodiment depicted in U.S. Serial No. 775,432 which has compromised size (Item III) . The moire sensor techniques that are currently used are itemized in Table 3 according to which Item I, II, or III is compromised.

TABLE 3 CURRENT MOIRE TECHNIQUE GROUPED ACCORDING TO DEFICIENCIES

TECHNIQUES THAT TECHNIQUES THAT TECHNIQUES THAT COMPROMISE ITEM I COMPROMISE ITEM II SOLVE ITEMS I & II AND NOT ITEM II AND NOT ITEM I BUT COMPROMISE SIZE (ITEM III)

A. Fringe Patterns with D. Sequential X. Use of two or Optical Tags and Switching of more CCD camera Fiducials Patterns at arrays to (US Patent Pattern Element simultaneously 4,867,570) (US Patent view high 4,874,941 , resolution US Serial No. fringe pattern 775,432) with no tags (US Serial No. 775,432)

B. Large Period E. Sequential Patterns Switching of (US Patents multiple 4,842,41 1 , projectors 4,895,448) (EOIS MK VII Moire Sensor)

. Gauge only large F. Moving Fringe smooth surfaces (Phase Shift and count or track Interferometric) each fringe through Method "fringe reconstruction" (US Patents on smooth unbroken 4,212,073, surface 4,742,237) (US Patent 4,273,448)

G. Sequential Changing or movement of lens elements. (US Patents

4,874,955,

4,818,108)

The key to eliminating the extra CCD elements is to use an improved fringe pattern element. Current fringe pattern designs use clearly visible and distinct optical marks, tags and fiducials which are implanted into a basic Ronchi grating or sinusoidal pattern of constant period. At each optical mark, the grating pattern is destroyed and x, y, z data in the immediate vicinity to the mark cannot be generated. In order to gauge small parts or areas, the optical marks are required to be more closely spaced, creating a greater loss of data. The less dense the mark spacing, the larger the part surface area needs to be to support fringe counting and reconstruction techniques. The multiple camera approach described in U.S. Serial No. 775,432 eliminated the requirement of the distinct optical marks and tags in patterns.

It is an object of the present invention to eliminate the use of multiple cameras in order to obtain miniaturization and will eliminate the use of data-destroying marks and tags. The resultant is that the ideal miniature moire sensor will contain both the minimal elements discussed in Table 1 and the desired features in Table 2.

The present invention is a new fringe pattern element identified as the Hidden Change Distribution

Grating (HCDG) , the resultant miniature moire (Mini-Moire) sensor configurations, CMM applications and extensions to other grating applications. An important special case of the HCDG is the Hidden Change Ronchi Grating (HCRG) and matrix versions.

The HCDG has all the properties of a high resolution linear fringe grating of small period p ₀ without any distinguishable optical marks, tags or fiducials. Consequently x, y, z data can be generated using standard interferometric processing techniques throughout the full pattern without interference from optical marks traditionally used to solve the 2π Problem. The 2π Problem is solved because the HCDG design is based on hidden signal stochastic principles. The HCDG is a pseudo-random grating pattern in which the nominal fringe pattern is of a small uniform period p ₀ (i.e. the ideal high resolution grating) to permit the high resolution generation of x, y, z data. "Hidden" variations in the HCDG pattern (as small as p _o /100) are distributed statistically across the grating. Known hidden signal statistical processing techniques are used to extract the grating fringe positions to solve the 2π Problem.

The key new property of the HCDG is that these fringe changes are made to be so small that at any one

point on the grating its "noise-like" effect is on the order of the moire sensor Noise Equivalent Phase, NEQ _ψ . NEQ^ is a measure of the effect of sensor image noise in terms of interferometric fringe pattern noisy phase shifts (e.g. 2π/100 radians) . Thus the accuracy of the x, y, z data generated by the HCDG remains essentially the same as that of the ideal uniform pattern of period (assuming that the 2π Problem was somehow solved for this ideal) . The "energy" of the hidden modulation pattern is statistically distributed over the full HCDG. A matched filter operation over a processor-determined Integration Length permits the pattern location to be extracted from the fringe pattern image. The hidden pattern uniqueness over the HCDG will provide the necessary location uniqueness to solve the 2π Problem. The HCDG also permitε this 2π Problem solution to occur at any point in the image where suitable fringes exist. Solutions are not relegated to predetermined tag locations of conventional marking techniques. The HCDG used in fixed moire proceεsing will accommodate all surfaces except "knife" edges that are parallel to the pattern linear bands. Therefore, the HCDG is extended to a Hidden Change Distribution Matrix (HCDM) pattern to accommodate this anomaly. The HCDM pattern generally consistε of two HCDG patternε oriented

at right angles to each other. An extension to a Polarization Sensitive HCDM (PS-HCDM) is also presented to permit simpler processing than that for the HCDM.

The invention of the HCDG and HCDM now permit the minimal configuration possible for the Mini-Moire Sensor. Miniaturizations are available for each of the following components which make up the sensor. 1) Miniature CCD Array

- Detached Electronics 2) CCD Lens and Holder

3) Projector Lens and Holder

4) Glass Slide: HCDG or HCDM or Variations

- Mounts in Projector Holder

5) Miniature Light Bulb and Heat Sink Holder - Strobe or Continuous

- Detached Power Supply

- Miniature Size Eliminates Condenser Lens

Requirement

- Fiber Optic Options to remote bulbs are also possible

6) Window: Glass, Plastic, Safety Glass, etc.

7) Two Piece Case: Metal, Ceramics, Composites, etc.

- 1 Piece Bottom Half to Serve as Optically rigid Structure for Mini-Moire Sensor

Components

- 1 Piece Top Half to Provide Access Ports to Components and to Provide Strain Relief Support at Cable Exit Position between Matching Halves Several embodiments and variations of the Mini-Moire Sensor include an added white light source, polarization control light source, extra projector, extra CCD lens grating, etc.

The Mini-Moire Sensor is capable of providing high-density 3D moire images of a part at image frame rates compatible to typical CMM motions. The CMM, however, is only required to provide mechanical moves between image footprints rather than at every single X-Y-Z data point. The Mini-Moire Sensor will also permit continuous CMM motions to cover the part without stopping. In order to take advantage of the Mini-Moire Sensor and to avoid overly costly computers or computer technologies that are not reliable or readily available, the invention includes an architecture for the Mini-Moire Computer. This architecture separates the functions of high speed image storage, raw x-y-z data processing and application software. The architecture permits the maximum part scan speeds posεible with the fastest throughput of data to the end user. The invention includes a new CMM application unachievable with other technologies. Conventional CMM's perform measurementε only after script files are generated through manual "Teach" modes or CAD-Aided Teach modes. The measurements are then taken by the CMM. If at a later time another measure is required, then the labor intensive and time consuming cycle of Teach and Gauge is repeated. The Mini-Moire Sensor can now be mounted on the CMM for extremely fast data gathering and

continuouε scan capability. The new CMM application is for the part to be fully scanned by the CMM and Mini-Moire Sensor in an automatic mode avoiding labor-intensive and time-consuming Teach Modes. The availability of a full x, y, z data base permits the measurements of the part to be made, potentially in a CAD analysis software environment, after data collection. No measurement decisions are required before part measurement. Thus changes in measurement strategies, and requirements can be made on an existing data base and does not require repeating the cycle of Teach and Gauge resulting in unnecessary usage of the CMM.

BRIEF DESCRIPTION OF THE DRAWINGS The features of the present invention which are believed to be novel, are set forth with particularity in the appended claims. The invention, together with further objects and advantages, may best be understood by reference to the following description taken in conjunction with the accompanying drawings, in the several Figures in which like reference numerals identify like elements, and in which:

Figure 1 is a schematic diagram of the basic Mini-Moire Sensor configuration utilizing the Hidden Change Ronchi Grating (HCRG) to achieve high speed, high resolution, large depth of range for 3D surface mapping and gauging;

Figure 2 is a front view of the Figure l Mini-Moire Sensor;

Figure 3 is a schematic diagram of an extended- capability Mini-Moire Sensor with a Polarization Sensitive - Hidden Change Ronchi Matrix (PS-HCRM) element to accommodate parts with "knife edges" through polarization light control;

Figure 4 is a schematic diagram depicting a Mini-Moire Sensor with a Hidden Change Ronchi Matrix (HCRM) in which no light switching is required to accommodate objects with knife edges; Figures 5A-5E illustrate the Mini-Moire Sensor

Subsystem embodiment for converting conventional Coordinate Measuring Machines (CMM's) to high speed 3D measurement and mapping systems;

Figure 6 is a block diagram of the Mini-Moire Computer Architecture embodiment to best support the high speed data collection capabilities of the Mini-Moire Sensor configurations; and

Figureε 7A-7H illustrate the principles of operation of the fundamental embodiment of the Hidden Change Ronchi Grating (HCRG) .

DESCRIPTION OF THE PREFERRED EMBODIMENT

The theory of the Hidden Contrast Distribution

Grating (HCDG) has general applicability, but there are three versions of the HCDG that exist that have the most advantage in high speed, 3D Miniature Moire "Mini-Moire"

Measurement Syεtemε as depicted in Figures 1 through 4.

The basic Mini-Moire Sensor of the present invention is illustrated in Figures 1 and 2. A key element of thiε system is the Hidden Change Ronchi Grating (HCRG) which permits the minimal components of the Mini-Moire Sensor. It also permits the highest resolution x-y-z data, the largest measurement range

(i.e. variation of measurement depth), and the ability for virtually instant data collection without delays due to multiple imaging and multiple projector requirements.

The HCRG is illuminated by a white light bulb/reflector unit which projects the HCRG pattern through the projector imaging lens through the Mini-Moire window to

the part. In this preferred embodiment of the Mini-Moire design, a condenser lens between the white light bulb 2 and the HCRG 1 is eliminated due to the construction of the bulb internal reflector optics. The light source can be either a CW light bulb for continuous operation, or a strobe bulb for flash illumination in a high speed moving environment. This Mini-Moire design will also accommodate bulbs with both a continuous and strobe capability. The image of the HCRG pattern is diffusely reflected from the surface of the object 5, for collection by the CCD camera imaging lens for reimaging on the CCD array. The on-line CCD camera electronics relays the electronic signal of the 2D image to the remote CCD electronics. For typical CCD arrays and camera electronics 9 and 10, and video transfer link the transfer rates occur at approximately 33 frames/second or approximately 0.33 milliseconds per CCD image. In remote CCD electronics 10 the video electronics are further amplified and transferred to the remote Mini-Moire Computer. The basic embodiment of the Mini-Moire Sensor utilizeε the propertieε of the HCRG to collect all neceεεary data in one "snapshot" view of patch 6 so that full x-y-z surface information can be generated by the Mini-Moire Computer. In the preferred embodiment, the camera electronics 9 and 10, will contain electronic shutters in which imagery can be frozen into the CCD array, Item 8, in .001 seconds or less. This permits high speed relative motion between the Mini-Moire Sensor 30 and the object 5. Strobe illumination has the advantage of providing intense illumination in 10 microsecondε or leεε. The white light illuminator control and power supply 13, are alεo remote from the bulb 2.

The primary elements of the Mini-Moire Sensor are mounted in a molded case consiεting of two halveε: an optical-bench half 14 and a cover half 15. The optical-bench half 14 iε an optically and thermally ridged structure for the direct mounting of the projector opticε bracket 16 and the camera opticε bracket 17. Also directly connected to the external portion of the optical-bench half 14 is the Mini-Moire connection bracket 18 for the Coordinate Measuring Machine (CMM) interface or other external mechanical interface. The cover half 15 iε primarily intended aε a dust cover and protection aid and is reduced in weight to insure a light weight Mini-Moire Sensor Package.

In the preferred embodiment of the Mini-Moire Sensor in Figure 1, an additional white light illumination bulb 19 is included. This bulb 19, with its internal reflection optics, will project white light onto the object 5, in the patch area 6. No imaging optics are required for this white light illumination, thereby minimizing the weight and size impact of the bulb 19 which can be either continuous or strobe. The white light illumination in the absence of the HCRG fringe pattern can provide 2D information to the CCD array 8 for other image procesεing functionε. In certain cases, the white light illuminator will provide information useful for moire procesεing including sharp intensity changes in the part reflectance pattern. The illuminator control and power supply 20 for the bulb 19 are located remote from the Moire Sensor. In the preferred embodiment of the Mini-Moire

Sensor in Figure 1, maintenance ease and replacement of bulbs 2 and 19 is accomplished. Each bulb is easily inserted into receptacles in a bulb mount/heat sink 21.

The wire connections for the bulbs, 2 and 19, are interfaced from the heat sink 21 to the caεe of the Mini-Moire Sensor 30 through sliding contact connections 22. This permits the heat sink 21, with bulbs 2 and 19, to be easily extracted through the rear of the Mini-Moire Sensor 30 to an external location 23.

An important extension of the invention is the embodiment of the Mini-Moire Sensor with the element: The Polarization Sensitive - Hidden Change Ronchi Matrix (PS-HCRM) as depicted in Figure 3. The PS-HCRM is divided into two polarization senεitive - Hidden Change Ronchi Gratings: PS-HCRG _A 32 and PS-HCRG _B 33. PS-HCRG _A and PS-HCRG _B are similar to standard Ronchi grating construction with clear and opaque bands except that the PS-HCRG _A opaque bands are made of linearly polarized material so that the opaque bands only occur for polarization in the direction L^. Similarly, the PS-HCRG _B opaque bands are made of polarization material so that they become opaque only for polarization in the direction L _B . The PS-HCRG _A and PS-HCRG _B patterns are located back-to-back at an interface 34, to insure focus under white light illumination. Polarization control is accomplished by the linear polarizer 50%/50% window 35, situated between the PS-HCRM 31, and the Pattern A illuminator bulb 36 and the Pattern B illuminator bulb 37. The remote white light control units 38 and 39, will provide the appropriate switching between the light sources to provide illumination of either Pattern A or Pattern B. As in the Mini-Moire Sensor configuration embodiment, Figure 1, Pattern A is the primary pattern of illumination for general objects 40. Pattern B is only used for special objects 41, which contain knife

edgeε 42, oriented along the Pattern A fringe dimensional L^. For this condition, the fixed Pattern A does not provide enough fringes acrosε the knife edge surface area 42, to generate sufficient imagery data for moire processing. However by being able to switch to Pattern B through the use of the PS-HCRM 41, fringes now will occur acrosε the knife edge 42, in the form of a fringe pattern, 43, that can be processed if sufficient triangulation exiεts between the Pattern B line-of-sight and the camera line-of-sight. In order to insure triangulation, the PS-HCRM 41, is rotated at an angle θ between 0° and 45°. Generally to insure maximum triangulation between the more common Pattern A and the camera line-of-sight, the angle θ is generally less than 30°. The fringe pattern imagery is collected by the CCD array 45, for moire interferometric data procesεing. The PS-HCRM 41 has permitted this function to occur without the addition of a second projector imaging optics and fringe pattern element. The PS-HCRM 41 has also permitted the same basic number of elements, except for the addition of a small illuminator bulb 37, to be used aε in the baεic Mini-Moire package of Figure 1. Therefore all the featureε of the Mini-Moire package including weight, small size and maintainability are the same between the embodiments of Figure 1 and Figure 3.

A third extension of the Mini-Moire Sensor utilizes the Hidden Change Ronchi Matrix (HCRM) without polarization control as depicted in Figure 4. The HCRM

51 is projected directly to object surfaces 52 and 53. Two crossing patterns are simultaneouεly provided by the HCRM 51 for all object εurfaceε including knife edgeε 54. Aε for the PS-HCRM embodiment of Figure 3, an angle θ iε

used to insure triangulation of fringe Patterns A and B for moire procesεing. The processing requirements are more complex for the HCRM then for the HCRG. There is a significant advantage if Pattern A and B decoupling occur by rotating the CCD array 56, the same angle θ. The advantage of this Mini-Moire embodiment utilizing the HCRM over that of the PS-HCRM in Figure 3, is that no switching of light sourceε iε required between objects. Therefore there is no decision procesε required in an automatic scan operation where the pattern (Pattern A or Pattern B) is dependent on the part surface characteristics. The use of the HCRM in this Mini-Moire embodiment results in exactly the same number of elements as for the basic Mini-Moire Sensor depicted in Figure 1. Therefore all features of the Figure 1 embodiment hold for the Figure 4 embodiment.

The preferred embodiment of the invention of converting a conventional Coordinate Meaεuring Machine (CMM) to a high speed X-Y-Z data gathering device iε shown in Figure 4. CMM's such as CMM 61 are in vast proliferation in the U.S. industry and are a catalogue item stock from a number of CMM manufacturing companies. The CMM's generally have the property of being highly accurate, but extremely slow in the gauging because of the single point touch probe technology that is utilized. However these CMM's do have the ability to rapidly move the X-axis element 62, Y-axis element 63 and Z-axiε element 64 rapidly between toucheε. The key interface point to the CMM iε the quill 65, or maεt of the CMM. Attached to thiε maεt 65, iε a pan/tilt head 66, that iε also readily available in a number of configurations from different manufacturerε. The invention of the Mini-Moire Senεor 30 in the embodimentε of Figureε 1-4 permits the

Senεor 30 to be directly mounted to the pan/tilt head 66. The invention of the Mini-Moire Senεor 30 also permits the collection of sufficient imagery footprints 68, in time intervals as short as 0.001 secondε to permit rapid data collection. The Mini-Moire Senεor 30 permits the continuous scan of this footprint 68, by the CMM 61, so that the interruptive stopping of the CMM to make measurementε iε eliminated. Orientationε of the pan/tilt unit 66, permit the full part 69 to be gauged from all angular aspects. This resultε in the change of a CMM from an occaεional product Validation Mode to a potential 100% on-line high speed Gauge Mode. The speed enhancement is further increased through the addition of a removable rotary table 70. This rotary table iε able to εupport partε and eliminate the extensive X-axis and Y-axis motions of the CMM 61. The Mini-Moire Subsystem that would be used for a CMM upgrade or for a CMM-based εyεtem are the Mini-Moire Senεor 30 the Mini-Moire Computer 12, the Quick Look Diεplay/Operator Interface 71 and the Optional Removable Rotary Table 70.

The invention of converting a conventional CMM to a high εpeed X-Y-Z gauging device alεo greatly simplifies the traditional CMM Train Mode. The Train Mode iε the requirement to program the CMM prior to part gauging. In conventional CMM applicationε, thiε iε a labor intenεive operation in which the part measurements need to be known in advance of the programming of the Train Mode. Some extensions have been made so that training can occur automatically from a Computer Aided Design (CAD) file of known parts. The problems still exist for unknown parts in Reverse Engineering applications. However with either approach, if after the Gauge Mode, additional measurementε are determined to be made, the

requirement is to regenerate the train mode and regauge the part. The current invention now permits a completely new strategy in training partε. The unknown part (or known part) will be automatically scanned to generate a full X-Y-Z data surface map of the part without necessarily any regard to the measurements to be made. Referring to Figures 5A-5E, this rapid scan is a result of the Mini-Moire Sensor 30, being able to collect sufficiently high density moire imagery in single snapshot views during a continuouε scan (or intermittent scan) . This imagery iε collected and proceεεed in the Mini-Computer Architecture to generate a vaεt X-Y-Z data file for the part. However εufficient memory iε currently available, or will be soon, to store this data conveniently. The operator after gauging can then generate the specific measurements that are needed. If at a later time additional measurementε are required, the moire εurface map X-Y-Z data file exists so that the measurements can be taken directly from the Mini-Computer data base and not require the time-consuming Train Mode and repeat of the part Gauging Mode. This will free the CMM to meet the requirements of a 100% inεpection at on-line product manufacturing rateε without unneceεεary "down" time or uεage. In order to accommodate the high εpeed Mini-Moire data generation feature and the CMM uεage of the data for the high speed Train Mode and High Speed Gauge mode, a preferred embodiment of the invention for the Mini-Moire Computer Architecture is shown in Figure 6. The Mini-Moire Computer Architecture will consiεt of three distinct controller/proceεεor unitε and two diεtinct data tranεfer/network unitε. The Moire Video Controller (MVC) 81 iε the primary interface to the Mini-Moire Sensor and

the external controllers included the Mini-Moire white light source, the CMM controller, and the optional removable rotary table controller. The εecond proceεsor is the Moire Data Procesεor (MDP) 82 which provides extensive procesεing of the X-Y-Z data and εtorage of that data. A Data Analysis Procesεor (DAP) 83 iε the primary uεer interface for analyεiε, reverεe engineering of the data.

The Moire Video Network (MVN) 84 is the primary connection between MVC and MDP. The Data Transfer Network (DTN) 85, is the primary transfer between the MDP and DAP. These elements are εummarized aε followε: o Moire Video Controller (MVC) 81

- Digitizeε and εtoreε imageε in real time (30 frames/sec) 86

- Provides "Quick-Look" Calculations for Automatic Scan Operation 87

- Provides correction controls to CMM controller and Other External Controllers 88

o Moire Data Procesεor (MDP) 82

- Processes Moire Image Patterns 89

- Generates raw X-Y-Z data "clouds" 90

- Reduces X-Y-Z cloud data to surface model and measurement entities 90 - Stores X-Y-Z cloud data base, surface model and entities 91

o Data Analysiε Proceεsor (DAP) 83

- CAD 92

- Reverse Engineering 93 - Tolerance Analysiε 94

- Others

o Moire Video Network (MVN) 84

- High-Speed backplane transfer of moire images from MVC to MDP

- Tranεfer rates do not effect MVC speeds

o Data Transfer Network (DTN) 85

- High-Speed X-Y-Z data and entity transfer from MDP to DAP

- Transfer rates do not effect MDP speeds

The major expense and potential performance limitation to the Mini-Moire Computer are contained in the elements of the MDP 82. However this architecture permits the high-speed characteristicε of the MVC 81, and CMM mechanical moves to continue as if ideal components for the MDP were available. The MDP 82, is designed to process εtored digital imagery and to "catch up" during natural lullε in the manufacturing/ measurement procesε such as part loading/unloading, etc. Aε the component capabilitieε of the MDP Item 2 improve, the proceεεing algorithmε can alεo improve to achieve greater performance goalε for the HCRG and HCRM fringe patternε in order to achieve higher resolution X-Y-Z measurementε. The Mini-Moire Computer Architecture permitε the reεultant "slow down" of the MDP 82, relative to the MVC 81, and provides an implementation path for additional higher performance components for the MDP 82. Similarly the architecture permits independent developments in work stationε and image digitizerε to be incorporated into the DAP 83, and MVC 81 aε upgradeε without effecting the critical MDP functionε. The invention of the Hidden Change Ronchi Grating (HCRG) and the Hidden Change Ronchi Matrix (HCRM) iε a

subset of a broader class of gratings, including sinusoidal, trapezoidal, etc., known as Hidden Change Distribution Gratings (HCDG's) and Hidden Change Distribution Matrices (HCDM's) . The general processing and design of these gratings are set forth below. Figures 7A-7H illuεtrate the concept of one of the preferred embodimentε uεed in the Mini-Moire Senεor HCRG. The HCRG object pattern 101, iε a Ronchi grating with two componentε: the ideal nominal Ronchi pattern 102, and the small statiεtical variationε in the pattern frequency 103. These are known as Hidden Changes (HC) and are designed so that the phase calculations asεociated with the pattern changes are not only unique, but hidden in the noise of the moire procesε 104. Thiε moire proceεsing noise is dependent on CCD noise, optical quality, projector illumination power, and part surface characteristics. The phase 105 for the ideal nominal Ronchi pattern is zero. The HCRG is designed so that it iε to obtain phase information of the highest resolution and highest accuracy poεsible asεociated with any grating pattern. In such patterns, moire interferometric processing techniques lose count of the pattern lines k=l,2,3,.... The theory of the HCRG permits the introduction of hidden statiεtical changes in the pattern 103, such that the changes are not readily observable at any single pixel i in the measurement procesε. When the HCRG object pattern 101, iε projected onto a εurface it iε diεtorted into an HCRG image 106. The intenεity of a εingle cross-section 107 which appears sinusoidal in the Mini-Moire Optics, contains distortionε according to an ideal surface phase 108. This ideal surface phase (i _/ j.øi) is directly relatable to the 3D surface information (X _; , Y _; , Z;) through a one-to-one map that is

predetermined. The ideal surface phase φ _t 108, contains a 2π modulus N. Consequently the interferometric processing only generates the residual phase δφ _{i t} ranging between ±π . The HCRG grating also introduces the Hidden Change Phase (HC Phase) G _; 104, εuperimpoεed on this residual phaεe Sφ _t 110. Thiε HC Phase Gj occurs at each pixel i, but it is so small that it cannot be directly measurable and relatable to a Ronchi pattern line number k. Therefore this invention includes the method of recovering the pattern location in utilizing the fundamental theories of hidden signal recovery techniques such as discussed in the classical reference: Helstrom, Carl W. , Statiεtical Theory of Signal Detection, Pergamon Preεε, NY 1960. Thiε invention includeε a noise-optimal proceεεing technique for the HCRG. The image intensity 107, is passed through a First Pass Filter 111, to generate the residual phase plus hidden pattern phase 110. This signal or its functions are in turn processed by the matched filter 112. The matched filter useε as itε reference the known HC Phaεe 113. The output of the matched filter 112, is the unique autocorrelation function h_- 113, of the HC Phase G _j . Its peak at the location of the 2π modulus N for the particular i pixel being procesεed. A N moduluε map 114, iε thus available for every pixel of interest in the moire sensor field-of-view. From this information, the phase is reconstructed 115, to generate the full surface phase φ_ . For a well designed HCRG pattern, the effect of the HC Phaεe G; should be negligible at this point. However, the HCRG design theory permits larger hidden change phases to occur which would require the use of a Second Pass Filter 116, to remove itε effect on the final

surface phase estimate 117. The one-to-one map from i,j,øi to Xi,Y _j ,Zi is then used to generate the part cloud data. An important feature of the HCRG invention is that the 2π modulus N can potentially be calculated for every pixel i,j in the camera field-of-view and not be limited to conventional optical tags or fiducial mark locations which require surface continuity between marks. Theεe conventional tagging techniqueε also destroy the high resolution moire data in the vicinity of the marks; a condition avoided by the HCRG. The deεign parameterε for both the grating and the procesεing algorithm are a function of the noiεe levelε in the Mini-Moire sensor and will now be explained in more detail.

The following theory of HCDG Processing and Deεign is presented as an example of how a single CCD snapshot of an HCDG fringe pattern image can be procesεed εimultaneously to extract the high resolution part surface data and to solve the 2π Problem. Since the HCDG is a linear fringe pattern with fringe length along the direction j, the following analysis is along the crosε-εection in the direction i (expreεεible in termε of the intenεitieε of a εingle row of detectorε in the CCD array) . For an ideal high resolution grating of period p„, which can be treated as the nominal or statistical mean pattern for the HCDG, the intensity expression is given by:

Ii ^* = a + b cos(27;i + φ ^* ) (1) where I _; ^* = "Ideal" Nominal Pattern intenεity at pixel i in the CCD array. In a typical CCD array, i = 1, ... ,512. The j variable (typically j = 1,...,480) haε been εuppresεed for convenience.

a,b = Surface diffuse reflectance parameters. Generally unknown but slowly variable p„ = Ideal grating period φ ^* = Phase shift representing surface change for each pixel (Note: a unique predetermined transform existε between i, j, φ' and part surface x, y, z.

The challenge of moire processing iε to extract the phaεe φ ^* from the image pattern of Equation 1. Note however that the intenεity in Equation 1 iε indiεtinguiεhable from the following:

Ii ^* = a + b coε ( 27ti + δφ ^* ) (2) where

-7T < δφ ^* < 7T 2 2

φ ^* = δφ ' + N ^• 2π (3)

Moire proceεεing techniqueε for ideal untagged patternε will extract the "reεidual" phase δφ ^* , but not the 2π modulus N. This is referred to as the "2π Problem".

For the HCDG, it is convenient to number the grating cycles, k=l,2,3,..., and to treat each cycle aε having period p _k . This can be expresεed in termε of the nominal period, p ₀ , aε: p _k = p ₀ + M _k ^• p ₀ (4)

where M _k iε the HCDG modulation coefficient for cycle k. For the caεe when there iε no εurface contribution (e.g. at a reference calibration surface) , the intensity pattern for the HCDG is given as: I = a + b cos ( 2ιti - Gj) (5)

Po where G ₍ is the HCDG Phase Sequence {G ₍ } at every camera pixel i. Its values are conεtant in thiε example over the grating cycle k (extenεionε to varying Gj within a cycle are alεo possible) . At each cycle k, it is convenient to define G(k) aε the value of the HCDG Cycle Phaεe Sequence {G(k)}. G,, G(k) and M _k are related aε followε: for kp ₀ < i < (k+1) _Po (7) where

G(k) = 2π«M(k) (8) 1+M(k) where

M(k) = M _k - M(k-l) (9)

For small M _k values, the HCDG Phase Sequence values

G; can be made to be on the same order as the phase variations due to noise. That is, its standard deviation σ _G is close to the Noise Equivalent Phase NEQ _ψ . Typical values for well designed moire senεor opticε and low

noise CCD's are

« 0.06 radianε

Although the known random-like HCDG Phaεe Sequence valueε G _; appear at the εame noiεe level aε NEQ _Ψ , the sequence itself {G.} has energy distributed (generally in a statistical uniform manner) over the full HCDG. Since the Gj values are known a. priori, the HCDG Phase Sequence position can be extracted by a Matched Filter Procesεor and uεed to solve the 2π Problem. The noise-optimality and methodology of extracting known hidden signals is well known (Reference: Helstrom, Carl W. , Statistical Theory of Signal Detection. Pergamon Preεs, NY 1960) . The method of deεign and parametric trade-offε for this example will be discussed shortly.

When surface variations are present, Equation (5) is modified to accommodate the correεponding surface phase variations φ _t ^~

I; = a + b cos (27ji + φ, - G _^ ) (11) _Po

Due to the 2π Problem, I _; is indiεtinguiεhable from the contribution of the reεidual εurface phaεe δφ _{

I;= a + b coε ( 27ti + δφ; - G,_ _υ ) (12)

where

Note however, that the HCDG Phase Sequence {Gj} has also shifted by an amount u. When its value is found by the Matched Filter Processor, it can be related to N as follows:

N = NEAREST INTEGER (u/p (14) where p ₀ is the period in pixels (theoretically as low as 3, typically 5 < p ₀ < 10).

Several procesεorε will be uεed in the example to extract { δφ.} and {G _i1 }. Important propertieε that will be used are that each of the sequenceε are uncorrelated with reεpect to each other with εpatial frequencieε that are either at or less than the Nyguest limit frequency l/p ₀ . The First Pasε Processor will operate on the intensity sequence {I _; } in Equation (12) to obtain the values of sin(<5ø _j - G _iI ) and coε(<Søj - Gj. _u ) . The Sj operation iε defined aε followε:

= -εin 277 ( i+i ' ) ^• I _¥ ( 16) The overbar is a convenient notation for summing. From Equation (12) and the uncorrelated sequence

properties, it follows that S _j = b sin(5ø _j - Gi-u) (17)

The C _j operation is defined as follows:

C _; = cos2π (i+i') ^• I _j . (18)

Po

It followε that

C _; = b cos(<Sø _j -G _j . _u ) (19)

The Matched Filter Processor will operate on the sequences {S _j } and {C over an Integration Length L with the objective of locating the HCDG Phase Sequence {G _j }. Important propertieε of the HCDG Phaεe Sequence are: |G _j | « 1 (20)

_L i+L/2 G _j = Σ G _j K 0 (21) i'=i-L/2

G. = A„ (23)

i+L/2

G _j *G _j Σ (G _j .) (G _j . _+i ) (24) i'=i-L/2

= A: (25)

A _; is the autocorrelation function of {G _; } over the Integration Length L with its peak at i = 0. A ₀ is a measure of the energy in the Gj} sequence. The

objective of the Matched Filter Processor is to calculate {A _; } and to locate its peak. The following four operations are used in this example:

l/i = S. (26)

F _2/i = (27)

F _Λ , = G.-C; (29)

It follows from the HCDG Phase Sequence properties of Equations (21) - (24) that

F _2/i « b cos <Sø _j (31)

F _3/i K -b-A _j . _u cos <S0 _j (32)

F _4/i K b-A _j . _u sin fiø _j (33)

It followε that

~ ^F 3/i ^{+ F} /i

A _j . _u = (34) F,,; + ¥ .

Other relationεhipε for A _j . _u are alεo poεεible utilizing equationε (30)-(32) .

The peak of the correlation sequence { j. _u } occurs at i=u. From this and Equation (14) , N can be found and the 27t Problem is solved. Note that the HCDG principle permits a value for N to be found for each pixel i and to be asεigned to δφ_. That situation is not achievable with conventionally spaced feature-marking techniques.

The Second Pasε Processor is an optional procesεor which will operate on {I _; } to find the reεidual phaεe sequence {6 ^" ø _j }. Two example operations are defined

S _Vl = -sin(2πi - Gj. _u ) ^• Ij (35)

It followε that C _j/j = b cos δφ, (38 )

The residual phase can be calculated aε follows:

The reconstructed phaεe iε This can be related to the "ideal" phase in Equation

(1) for the nominal grating of period p _c .

for kp ₀ < i < (k+l)p ₀ (42)

It should be pointed out that the Second Pass Processor may not be needed since the HCDG Phase

Sequence values G _f may be so small as not to have any appreciable effect on the δφ-. measurement, thus

«Søj = ARCTAN(Sj/Cj) (43)

If a conservative approach is taken with larger G _j values taken, then the Second Pass Filter would remove its effect.

An important feature of a well designed HCDG is that the value of N is available for each pixel i in the CCD pixel row j for which the phaεe £øj can be calculated. This permits small part areas to be gauged as long as they subtend the Integration Length L of the HCDG Phase Sequence. Due to the noise optimality of the HCDG design, L is much smaller than the spacing of optical marks in conventional grating tagging approaches. For these conventional cases, the optical tag is initially located and then fringeε are counted from that point to the meaεurement location of interest. A lost fringe due to noise, part flaw or

other cause would create failure. The HCDG, due to itε HCDG Phase Sequence distribution and autocorrelation properties, iε virtually immune to these problems if enough pattern energy exists in the Integration Length L.

The deεign of the HCDG iε baεed on the theory of white noiεe sequence generation. Many scientific software applications packages, such aε FORTRAN, will have a subroutine to provide the following white noise sequence: w w ₂ , w ₃ ,...,w _m ... (44) with properties:

E{w _m } = 0 (45)

E{w _m ² } = 1 (46) E{w _m w _n } = 0 for m≠n (47) w _m Probability Distribution = UNIFORM or GAUSSIAN where

E{ ^• } denotes statistical mean. The HCDG Phase Sequence {GJ is generated in the following example: The ideal high resolution grating of uniform period p ₀ (the nominal of the HCDG) is asεigned a count for each cycle (k=l,2,3,...). The HCDG Cycle Phase Sequence {G(k)} will be conεtrained have conεtant valueε for each of theεe cycleε. The

relation between G _; and G(k) iε

G _j = G(k) for k _Po <i<(k+l)p ₀ (48) where typical values for p ₀ in camera pixel space is

3<p ₀ <10. G(k) can be permitted to change for each cycle k, although a more general case would be for change at a cycle multiple m ₀ where the phase is denoted aε the Phaεe Change Sequence {S _m }. The relationεhipε are:

S _m = m ₀ ^• G(k) (49) for m=l,2,3,... m ₀ m+(l-m ₀ ) < k < (m ₀ +l)m-m ₀ where m _c = cycle multiple. (50) Typical valueε for m ₀ are 1 or 2. For the deεired variance σ _G ² of G _j , the variance of S _m iε σ _s ² = m ₀ ² -p ₀ ^{2 •} σ _G ²

The Phase Change Sequence {S _m } is generated from the available white noise sequence {w _m } in Equation (44) aε followε:

S _m = σ _B ^• w _ro (51) m = 1, 2, 3,...

The HCDG Cycle Phase values are:

G(k) = G(k+1) =...G(k+m ₀ -l) = S _m /m ₀ (52)

This construction provides all the desired propertieε of {G;} in Equationε (21) - (24) . The autocorrelation function of {G _f } over the integration Length L iε of the form:

A- = l>' -_P ₀ σ _a ^l {1- (53)

A is the output signal of the Matched Filter Processor and is imbedded in filtered noise with its peak value occurring at i = u. u is related to N by Equation (14) . The peak signal to filtered noise (SNR) at the procesεor output iε given by

where σ _G ² = Variance of HCDG Phase Sequence value G _;

NEQ _ψ = Noise Equivalent Phase of Moire Senεor

L = Integration Length in pixelε in Matched Filter Proceεεor Sum ationε p ₀ = Nominal grating period in pixelε uεed in Firεt Paεε Proceεεor

Equation (54) can now be uεed to εelect HCDG deεign parameterε. For a "truly hidden" HCDG Phase Sequence, (σ _G /NEQ _φ )«l. Parametric values of

L = 20 pixels

p ₀ = 5 pixels will provide a matched filter output of SNR=2. This is sufficient to detect the correlation peak position u. Note that its accuracy need not be at the pixel level because of the integer round-off in Equation

(14) . The Second Phase Procesεor option would not be required for thiε caεe due to the ε all G _; valueε. Note that a smaller Integration Length L is still poεεible to permit the gauging of even εmaller part areas. Select a larger σ _G to achieve the following operating characteristics: σ _G /NEQ _ψ = 7s 2 = 2.83

P _o = 5

SNR = 2 Thiε reεultε in

L = 10. The Second Paεε Processor option would eliminate the "noisy" effect of the larger G _; values.

The construction of the HCDG pattern now follows in a straightforward manner. Identify each cycle as k = 1,2,3,.... The "zeroth" cycle is asεigned the physical period p ₀ . In the treatment, the p _k values are physical pattern dimensionε with p ₀ aε the nominal ideal period of HCDG. Each εubsequent cycle k iε

attached to the end of the preceding cycle k-1. The general relationship is p _k = _Po (1+M _k ) (55) where M _k = M(k)+M(k-1) (56) and

M(k) = G(k 2π (57) l-G(k)/2π

An important special caεe of the HCDG iε the Hidden Change Ronchi Grating (HCRG) made up of clear and opaque bandε. These gratings are simple to conεtruct from white and black pattern bandε. In thiε case the period p _k in Equation (56) is divided between the white and black band that make up the kth cycle. That iε : kth White Band Width = p _k /2 (58) kth Black Band Width = p _k /2

In the deεign of the HCRG (and HCDG) , it may be deεirable from a grating pattern mask construction stated point to have only finite values or states for the phase modulation coefficient. example if N stateε were permitted in the conεtruction around the nominal period p _c , the reεultant pattern would repeat itεelf in (N-1) ^M cycleε when M = m ₀ -L/p ₀ . For example if N=3,

m ₀ =2, p ₀ =5, L=10, then the HCRG pattern would repeat itself in 16 cycles and may not be useful. If N is increased to 5, then the pattern would repeat every 256 cycle which would be more than εufficient for conventional camera CCD arrays ranging in size to 1024 x 1024.

Other important special cases of the HCDG and HCRG are the Minimal Change Distributed Grating (MCDG) and the Minimal Change Ronchi Grating (MCRG) . In this case the "energy" of the Phase Change Sequence Gj is unevenly distributed throughout the grating pattern. In the extreme, optical tag-like features would occur. Separations occur with periods G _; = 0 for no changeε and optical fiducialε occur when G, iε larger than normal. However the HCDG theory and itε noise-optimal, matched filter, procesεing methodε permit the "tagε" to be deεigned to have "minimal" effect on data generation. The construction of the MCDG and MCRG is the same as for the HCDG and HCRG utilizing Equations (55) through (57) .

The above example for the HCDG theory was for a fixed fringe method where sampling of the grating occurred across the pattern the HCDG principles also apply to the phase measurement moire technique (moving

fringe methods) when sampling occurs in time as the pattern changeε poεition.

An important class of surfaces exist that cannot be measured with the linear fixed pattern whether of the ideal Ronchi-type or HCDG-type for fixed pattern moire processing techniques. These are the sharp (knife) edges or corners that lie along the band direction vector Lrj. This condition prevents the Ronchi grating period p ₀ to effectively sample the edge to generate on i,j,ø map. If the edges do not fall along L _Q and crosε a full grating period, then the i,j,ø map for the edge can be generated. Methodε that reεolve L ₀ -direction edge phaεe meaεurementε include moving fringe patternε (phase shift moire method) , adding extra projectors at an orthogonal orientation, or rotating the full camera/projector moire package. All of these methods are either time consuming, add extra size and weight, or add cost.

This invention therefore includes the extension of the linear HCDG to a Hidden Change Distribution Matrix (HCDM) form. The HCDM consists of two HCDG patterns denoted as "Pattern 0" and "Pattern 1" (generally orthogonal to each other) with fundamental Ronchi periods p ₀ and P _] and band directions L _o and L,. An important special case is the Hidden Change Ronchi Matrix (HCRM) .

The design and analysis for the HCRM is the same as for the HCRG except that two band and panel patterns are generated. Ronchi matrix forms have been impractical in the prior art for high resolution x,y,z measurements for moire procesεing techniqueε becauεe of the serious spatial resolution degradation of Pattern 0 by Pattern 1. This is particularly true if both patterns are of 50% duty cycle (equal width opaque and transparent bands) . However for the Mini-Moire Sensor, Pattern 0 is to be the dominant pattern and Pattern 1 is only uεed for I-o-direction edge meaεurementε. In general, Pattern 0 will have 50% duty cycle Ronchi periodε of p ₀ , while Pattern 1 will have larger Ronchi periodε p, and εmaller duty cycleε (e.g. 10% opaque and 90% tranεparent) with the HCRM conεtruction rule:

Tranεparent ₀ ^• Tranεparent- = Tranεparent (59)

Opaque ₀ • Transparent- = Opaque

Transparent ₀ ^• Opaque, = Opaque

Opaque ₀ ^• Opaque, = Opaque Aε for the HCDG, the conεtruction of the HCDM applieε to sinusoidal patternε, trapezoidal patternε, etc.

The HCDM will εignificantly reduce the physical size of a moire εenεor and εimplify the sensor procesεor if properly installed. The HCDM is installed in the same

optical position as the HCDG at angle μ ₀ between projector and camera line-of-sightε. However the HCDM is then rotated an angle θ to insure that the following triangulation requirements hold: L _o ^T (LOS, X LOS _p ) = C ₀ ≠ 0 (60) , ^T (LOS. X LOS,,) = C, ≠ 0 Where LOS, and LOS _p are the line-of-sight vectors for the moire camera and projector. Generally C ₀ > C,, since Pattern 0 iε the dominant pattern for the Mini-Moire Senεor. If the CCD array iε also rotated an angle θ so that its i,j grid lines up with the HCDM V _Q , V, pattern directions, then the computer processing for the i,j,ø map is simplified due to near decoupling in the i,j directions, thereby permitting lower costs and higher speeds.

The invention is not limited to the particular details of the apparatus and method depicted and other modifications and applications are contemplated. Certain other changes may be made in the above described apparatus and method without departing from the true spirit and scope of the invention herein involved. It is intended, therefore, that the subject matter in the above depiction shall be interpreted aε illustrative and not in a limiting sense.