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Computed Tomography (CT) for Reverse Engineering
December 31, 1969 |Estimated reading time: 9 minutes
By Jon Dupree, YXLON International
Reverse engineering is a powerful tool for generating a computer-aided design (CAD) model from the data of a physical part that lacks documentation or has changed from the original design. Reverse engineering also is used by businesses to bring existing products into digital environments, to make a digital 3D record of their own products, or to assess competitors' products. The range of uses includes analyzing a sample to determine how it works, determining what components it comprises, identifying potential patent infringement, etc.
Reverse engineering often involves taking something apart to analyze its workings in detail, measure the spatial dimensions, and try to make a new device that does the same thing without using anything from the original. If the sample cannot be examined in a destructive fashion, there are nondestructive evaluations (NDEs) that can be performed. The nondestructive reverse engineering process involves measuring an object without taking it apart and then reconstructing it as a 3D model. The process of digitizing a part and creating a CAD model from 3D scan data is less time-consuming and can provide greater accuracy than manually measuring the part and designing the components from scratch in CAD. The physical object can be measured using 3D scanning technologies like coordinate measurement machines (CMMs), laser scanners, or structured light digitizers.
The 3D model can be exported to many different formats including point cloud or STL, compatible with most CAD software. Modern CAD packages frequently allow rotations in three dimensions, allowing views of a designed object from any desired angle, even from the inside looking out. Since standard 3D scanning techniques rely upon touch or line-of-sight to model a sample, the interior structure is not defined. The measured data from a CMM, usually represented as a point cloud, lacks internal information. Often it is thought that only a destructive cross-sectioning could provide the internal information for reverse engineering.
Computed TomographyUsing computed tomography (CT), it is possible to virtually cross-section a 3D object using X-rays. A CT image is called a slice, similar to an X-ray image of a slice from a loaf of bread. This analogy is apt, because just as a slice of bread has a thickness, a CT slice corresponds to a certain thickness of the object being scanned. Therefore, whereas a typical digital image is composed of pixels, a CT slice image is composed of voxels (volume pixels). These voxels can be combined to form a 3D model to be exported as STL or point data. CT has only recently been considered for reverse engineering now that some current industrial CT systems can provide internal dimensional measurements at a precision competitive with destructive measurement. Additionally, since it is based on X-ray, CT is indifferent to surface finish, composition, and material, and it can measure part coordinates as fast as a laser scanner orders of magnitude faster than CMMs.
In conventional radiography, the three-dimensional object situated between the X-ray source and detector is reproduced in the X-ray image on a 2D surface. The 2D image provides limited information, as the position of features only can be differentiated if they are not behind one another in the X-ray image. This, in turn, means that only a limited amount of information about the spatial arrangement of features can be gained from one single X-ray image.
A three-dimensional understanding of the sample materializes when radiographic images are captured from different angles. In other words, to obtain a precise representation of the inner and outer geometry of an object to be inspected, it is necessary to take X-ray images from as many angles as possible. In a CT system, the X-ray tube, the detector, and the manipulator are arranged such that X-ray images are possible to capture from all angles, 360° at best. To generate a CT dataset, an X-ray beam penetrates the object, and the object's X-ray "shadow" is projected onto a line of pixels where the beam intensity at each pixel is measured. Each such "projection" is obtained at a slightly different angle as the object rotates. The 2D dataset is a set of X-ray views projected at different angles around the test article.
The next step to create the CT image is to back-project the views. Back-projection consists of projecting each view "back" along a line corresponding to the angle in which the projection data were collected. The back-projections, when enough views are used, form a faithful reconstruction of the object. On the basis of the back-projections of the X-rays taken at various angles, a cross-sectional image the so-called tomogram is calculated via a mathematical algorithm. If a tomogram of one layer has been created by the CT unit, now additional layers can be scanned. To create a volume set that can be converted to point cloud data, a tomogram of one layer is joined with additional layers.
System ConsiderationsOne concern regarding reverse engineering is that, as the width of the detector line increases, the impact of the penumbra (the geometric unsharpness caused by the magnified divergence of the X-rays from the center beam) can affect the final resolution of the CT image. The smaller the spacing of the individual layers, the better the ability to reproduce the item to be inspected in greater detail. At some point, pixel size will start to limit their ability to absorb the X-ray energy. Therefore, careful consideration must be given on selecting the right width detector for a given CT system's energy range.
The accuracy of the slice data is related to many aspects of the CT system. The algorithm that is used to back-project the tomogram includes calculations of the focal-spot-to-object distance, the focal-spot-to-detector distance, the perpendicular angle of the detector to the X-ray center beam, as well as the coplanarity of the sample's center of rotation to the detector. A CT system with only two axes of motion (the sample rotate, and the sample height adjust to move each subsequent layer into the X-ray beam) will have the most accurate CT slice data. With each additional axis of motion, the opportunity for error increases, and additional calibration is required before each CT scan. While a multiple use system can generate accurate CT data, in practice a dedicated system is easier and more consistent for reverse engineering applications.
In addition to the system mechanics, other aspects can also affect the quality of the CT data. Because both X-ray generation and the scattering events that produce attenuation (reduction in signal intensity) within the object are chaotic processes, the X-ray signal is inherently noisy: affected by background X-ray scatter and variations. As the variations in sample density are conveyed to the computer by the pixel's grey-value measurement, noise limits the scanner's ability to differentiate nearby volume details from similar noise attenuation. Thus, it may be difficult to determine if variations in the X-ray signals come from noise effects or from the variations arising from the sample itself. The CT mathematical algorithm creates a model based on the gray-value changes to a pixel with each angle of rotation, so any variation that is not due to the sample geometries, such as X-ray tube fluctuation, X-ray noise, or detector irregularities, can cause artifacts in the CT image. As used here, an artifact is anything in the image that does not accurately reflect true structure in the part being inspected. Because they are not real, artifacts limit the ability to quantitatively extract density, dimensional, or other data from an image. For failure analysis (FA) the user must learn to recognize and be able to discount common artifacts subjectively, but for reverse engineering, these artifacts can be disastrous. Therefore, not all CT systems should be considered for this use.
System TypesThe two main types of CT systems used for industrial purposes can be defined as a fan-beam and a cone-beam style. The fan-beam system is based on a 1D X-ray detector and an electronic X-ray source, creating 2-dimensional cross-sections of the object. A fan beam creates cross-section images by projecting a thin-beam X-ray through one plane of an object from many different angles. Reconstruction essentially builds the CT image from the data collected and represents a cross-section of the object. LDAs are used in fan beam systems to minimize the effect of scatter and, at least in the vertical axis, the penumbra. The most accurate X-ray information is that which is generated by the X-ray center beam. Since a fan-beam CT scanner only collects a thin line of X-ray information, it provides a set of images that are minimally affected by the X-ray penumbra in the vertical direction. Since the sample is rotating, the effect on the horizontal direction naturally is minimized as well.
In the case of cone-beam CT, an entire volume is generated using one single scan on an array detector. Instead of using a single row of detectors, as fan-beam methods do, a cone-beam system uses an array detector to perform a volume CT. Subsequently, reconstruction software is applied on the cone-beam CT volumetric data to produce a stack of 2D slice images of the sample. This allows for faster data acquisition, as the data required for multiple slices can be acquired in one rotation. However, it is also computationally more intensive, prone to distortion, and in many cases provides lower-resolution images. Mostly, this is due to an array detector requiring calibration as there is the chance for a pincushion distortion of the image. Pincushion distortion is a geometric, nonlinear magnification across the image. The magnification difference at the periphery of the image results from a combination of the penumbra of the X-ray beam and, in the case of an image intensifier detector, the projection of the X-ray beam onto a curved input surface.
Whereas volume CT has been largely perfected for some of the most advanced medical systems, for industrial scanners it does not yet provide the same quality of imagery as single-slice arrangements. As magnification increases, the differences between a fan-beam and a cone-beam system also increase.
CT LimitationsAs with any modality, CT has its limitations. The most fundamental is that potential objects for examination must be small enough to be accommodated by the handling system of the CT equipment. The objects also must be translucent at the X-ray energies employed by that particular system.
ConclusionComputed tomography is a radiographic method that provides an ideal examination technique whenever the primary goal is to locate and size planar and volumetric detail in three dimensions. Because of the relatively good penetrability of X-rays, CT permits the nondestructive physical examination and documentation of the internal structure of materials. The ability of a CT system to image thin cross-sectional areas of interest through an object makes it a powerful NDT method. A dedicated CT system using a fan-beam technology with a linear array detector has the accuracy and precision to compete with other NDE measurement systems, and can minimize destructive analysis in many cases.
Jon Dupree, product marketing manager, YXLON International Inc., 3400 Gilchrist Road, Akron, Ohio 44260, may be contacted at jon.dupree@yxlon.com.