Using heat to scan transparent surfaces

Today, with quality control gaining importance, reconstruction solutions that lead to a full-quality 2D and 3D inspection are being developed. However, when objects are highly transparent or highly specular, 3D reconstruction becomes very difficult. Classical scanning approaches using light patterns projected on the surface and triangulation are neither efficient nor reliable for transparent materials. For instance, a glass bottle scanned by a Minolta VI-910 Non Contact 3D Digitizer cannot be properly reconstructed because of reflections and refractions of the projected laser line.

Researchers have proposed different approaches for handling transparent objects, including the shape-from-distortion technique to recover the surface shape of a glass object,¹ and the structure-from-motion^2,3 technique. Others⁴ investigated several applications of direct ray measurement and proposed a practical algorithm to reconstruct two interface refractive light interactions using a three-viewpoint setup and measuring the exitant ray directions. Lastly, several studies have proposed using shape-form polarization.^5,6

The approach presented here, called 'scanning from heating'⁷ (SFH), benefits from two interesting properties of glass material: its opacity in the IR domain and its emissivity. Figure 1 illustrates the percentage of light transmission in the IR domain of the most commonly used glasses. For each type, there is a wavelength such that transmission is close to 0%. This wavelength is called the IR cut-off, and it depends on the glass composition.⁸ At a wavelength higher than 10μm, the glasses presented in Figure 2 can be considered as opaque. Figure 1(b) shows an image of a silicon dioxide glass bottle placed in front of an IR illumination and observed with a long-wave IR camera sensitive to 8–13μm. The object does not transmit the light coming from the source and appears to be opaque.

Figure 1. a) Percentage of light transmission in the IR domain of commonly used glasses b) Image taken with a long wave IR camera sensitive to 8–13μm.

The second property of glass material is its emissivity. All substances continuously emit electromagnetic radiation because of the molecular and atomic agitation associated with their internal energy, which is proportional to the material temperature. Emissivity specifies how well a real object radiates energy compared to an ideal body, called a blackbody. (A blackbody is considered a perfect absorber and emitter in each direction at every wavelength.) For glass, which has the angular emissivity of a dielectric sphere, the radiation approaches a Lambertian source.

The choice of a wavelength range up to 10μm makes it possible to overcome the problem of transparency. However, the key step is to locally heat the surface and then observe the radiation emitted by it.

The idea is shown in Figure 2. P₁ is the heated point at the surface of the object at Position 1, and (X₁,Y₁,Z₁) are its world coordinates. The projection of P₁ on the camera plane is called P_c1, and its coordinates (X_c1,Y_c1) are in the camera coordinate system (O_c,X_c,Y_c). P₂ is the heated point at Position 2, and (X₂,Y₂,Z₂) are its world coordinates. The projection of P₂ on the camera plane is called P_c2, and its coordinates are (X_c2,Y_c2). The variation of height between P₁ and P₂, called Z, can be obtained by triangulation using a pinhole camera model.

Figure 2. A schematic of the method. P₁ and P₂are the heated points at the surface of the object at Positions 1 and 2, respectively, and Z is the height variation between the two points. P_c1 and P_c2are the projection of P₁ and P₂on the camera plane, respectively.

Figure 3. Transparent objects a), c) and their 3D reconstructions b), d) using the SFH method.

Figure 3 shows the results from scanning a complex transparent glass object 7×7×15cm in size from 2100 points and results obtained from another complex transparent glass object 9×9×14cm in size from 1300 points. This demonstrates that the system can be applied to a wide range of objects—from surfaces used in the automotive industry to more complex objects in the packaging industry.

Figure 4. (a) A transparent plastic bottle was (b) reconstructed using the SFH method. (c) A powdered plastic bottle was (d) reconstructed with a Minolta VI-910 Non Contact 3D Digitizer. (e) Histogram and (f) 3D representation of the difference between the two reconstructions.

In this experimental setup, we used a CO₂ laser, but the same principle can be applied with other heating systems so that the material absorbs the incident radiation and emits radiations in the IR domain. Figure 4 compares a 3D reconstruction of a plastic bottle by the SFH method to one obtained by a Minolta VI-910 Non Contact 3D Digitizer of the same bottle, powdered on the surface. The results fit reasonably well, and the average deviation is 200μm.

In summary, we developed a new method to determine the surface shape of transparent objects using laser surface heating and thermal imaging. The results for glass objects are promising. Future work will include the design of an experimental system that can project a specific pattern (line, grid, matrix of points, etc.) to improve the 3D point acquisition speed. While we have only studied the method for transparent glass, we will also study its application to different materials (and the effects on the reconstruction, laser type, and power). Finally, we envisage an industrial prototype.