2.1 Surface and Solid Model Reconstruction
2.1.2 Principles of Imaging
with an accuracy of about 35 μm. The Leica T-Scanner can digitize all types of surfaces by projecting a laser beam onto them.
Compared to the contact probe, the noncontact laser scanner is more sophisticated and expensive. It captures millions of data points to better define larger parts with free-form shapes and contours. It is usually used for large parts with complex or curved lines. A large number of data points are needed to accurately capture the intricacies of the design to create digi- tal representations of these objects. The automatic process and feature-rich software requires less training and supervision, and provides faster feed- back. The metrology technology and devices are becoming more environ- mentally friendly: less and less hardware has to be prepared with coating or paint for proper measurements, and thus eliminating the adverse envi- ronmental effects of coating and paint due to their chemical contents. The quality of these tools has also improved with every new generation, allow- ing for higher precision and the measurement of smaller dimensions. The latest scanning technology is more intelligent and can integrate data collec- tion and feature identification together. For instance, the reverse engineer- ing software Rapidform XOR does not just capture the geometric shape of the scanned object; it also captures the original design intent. It automati- cally detects features, such as revolves, extrusions, sweeps, and fillets, on the scanned object.
Both the contact probe and laser scanner work by digitizing an object into a discrete set of points. In contrast to analog signals that are continuous, digi- tal signals are discrete. Therefore, a digital image can only be an approxima- tion of the object it represents. The image resolution depends on the area and rate of scanning. To obtain the required information within a reasonable amount of time, the engineer usually tracks the sharp edges of the object with a direct-contact probe for better-defined details and combines this information with the results of a laser scan.
Small and economically affordable contact probes, as well as sophisticated laser scanners, are available for reverse engineering applications. This afford- ability has eased many engineers’ reliance on outside services, allowing them to purchase their own devices and keep their digitizing design work in-house. Work in-house means shorter turnaround times, better control of the design process, and better security of proprietary information. New digi- tizers are also packaged with feature-rich software that makes it easier to turn static raw physical data into dynamic computer images.
on the accuracy of the alignment of these scans. The operator will then pho- tograph this subject setting with a digital camera. Based on these pictures, the coordinates of the reference markers are determined using photogram- metric technology. The 3D spatial coordinates (x, y, z) of a surface point are calculated and formatted in a point cloud file, and a 3D “constellation”
reflecting the shape of the subject will then be created. Point clouds collected with laser-based measurement devices may also include characteristics such as intensity and color. These scanned images will be automatically aligned to the 3D constellation created earlier to establish the final configuration for the reverse engineering process.
Photogrammetry is a three-dimensional coordinate measuring technology that uses photographs as the principal medium. In reverse engineering it is used to determine the geometric characteristics of an object and reconstruct it. The fundamental principle of photogrammetry is triangulation; however, many other disciplines, including optics and projective geometry, are also used. By taking photographs from two different locations, common points are identified on each image. A line of sight (also referred to as a ray) can be constructed from the camera location to the point on the object to produce the three-dimensional coordinates of the point of interest using the principle of triangulation. It is a stereoscopic technique and uses the law of sines to find the coordinates and distance of an unknown point by forming a triangle with it and two known reference points. In Figure 2.5, A and B are the two reference locations given by the camera locations, and C is the location of the object point of interest. The distance from A to B can be measured as c, and the angles α and β can also be measured. The angle θ = 180° – (α + β) because the sum of three angles in any triangle equals 180°. Following the law of sines, as described in Equation 2.1, the distances a and b can be calculated.
If the coordinates of A and B are known, then the coordinate of C can also be calculated. Triangulation is also the way our human eyes work together to gauge distance. In addition to reverse engineering, photogrammetry is used in many other fields, including topographic mapping, architecture, and manufacturing.
a b c
sinα =sinβ= sinθ (2.1)
Photogrammetry was used in a National Aeronautics and Space Administration (NASA) program: Airborne Research Integrated Experiments System. Over time, a Boeing 757-200 aircraft, as shown in Figure 2.6, has gone through numerous customizations and modifications in this program.
NASA needed to further modify the fairings of this aircraft, and therefore required much higher quality CAD data in certain sections than the CAD data on file. The fairing is an airframe structure whose primary function is to produce a smooth outline and reduce drag. The 757-200 aircraft has canoe-
shaped flap track fairings connecting the wing to the flaps. They protect and streamline the flap-deploying mechanisms. 3DScanCo/GKS Global Services was contracted to perform on-site 3D scanning on this aircraft at Langley Air Force Base in Virginia. Using bolt hole locations and existing features of the plane to align the data, 3DScanCo/GKS Global Services scanned five sec- tions of the 757 for fairing attachment placement. Each section was aligned with the existing scan data based on known distances in rivet placement on the plane, and the rivet placements in the scan area. Photogrammetry was used to ensure that the scan data, and the rivet distances in particu- lar, were accurate for the critical alignment. 3DScanCo/GKS Global Services used this scan data to reverse engineer the aircraft surfaces that were then incorporated into the existing CAD data. Figure 2.7a illustrates photogram- metry, and Figure 2.7b shows the scan compilation (3DScanCo/GKS Global Services, 2009a).
Several portable 3D measurement systems have been developed that can measure very large objects, such as cars or jet engines. They use laser light
a b
β α
θ C
c B A
FIgurE 2.5
Schematic of law of sines.
FIgurE 2.6
A Boeing 757-200 aircraft showing fairings under the wing. (Reprinted from 3DScanCo/GKS Global Services. With permission.)
to illuminate the targets with a 3D grid of interferometric waves for high- accuracy surface measurement, and are capable of acquiring up to 4 million data points in 1 minute, with better than 50 μm of accuracy. Interferometry is the technique of superimposing two or more waves together to detect differences between them. It is based on the physical principle that two waves with the same frequency and the same phase will add to each other (constructive interference), while two waves with the same frequency but opposite phases will subtract from each other (destructive inference). It is applied in a wide variety of fields, from astronomy to metrology. Typically in an interferometer, a wave is split into two or more coherent component waves that travel along different paths. These component waves are later combined to create interference. When the paths differ by an even number
(a)
(b)
FIgurE 2.7 (See color insert following p. 142.)
(a) Photogrammetry. (b) Scan compilation. (Both reprinted from 3DScanCo/GKS Global Services. With permission.)
of half-wavelengths, the superposed waves are in phase and interfere con- structively, increasing the amplitude of the output wave. When they differ by an odd number of half-wavelengths, the combined waves are 180° out of phase and interfere destructively, decreasing the amplitude of the output.
This makes interferometers sensitive measuring instruments for anything that changes the phase of a wave, such as path length. Optical interferom- etry is a technique of interferometry combining light from multiple sources in an optical instrument in order to make various precision measurements.
Optical interferometry might use white light, monochromatic light such as a sodium lamp, or coherent monochromatic light such as a laser light. The main difference between these types of light is their coherence lengths: for the white light, the coherence length is only a few microns, but for the laser light it can be decimeters or more. Therefore, they show different formability of interference fringes.