Image Reconstruction of a Charge Coupled Device Based Optical Tomographic Instrumentation System for Particle Sizing

Abstract

This research investigates the use of charge coupled device (abbreviated as CCD) linear image sensors in an optical tomographic instrumentation system used for sizing particles. The measurement system, consisting of four CCD linear image sensors are configured around an octagonal shaped flow pipe for a four projections system is explained. The four linear image sensors provide 2,048 pixel imaging with a pixel size of 14 micron × 14 micron, hence constituting a high-resolution system. Image reconstruction for a four-projection optical tomography system is also discussed, where a simple optical model is used to relate attenuation due to variations in optical density, [R], within the measurement section. Expressed in matrix form this represents the forward problem in tomography [S] [R] = [M]. In practice, measurements [M] are used to estimate the optical density distribution by solving the inverse problem [R] = [S]−1[M]. Direct inversion of the sensitivity matrix, [S], is not possible and two approximations are considered and compared—the transpose and the pseudo inverse sensitivity matrices.

Tomographic image reconstruction of monitoring flaws on gas pipeline based on reverse ultrasonic tomography

“…Then, the calculated output will be used to determine the image of the object tested by using back projection process. The attenuation coefficient of air and solid (assume as flaw) is estimated to be 0.00142 mm -1 and 10 mm -1 , respectively [22].…”

“…In this case, it is nearly impossible to obtain the number of projections equal to the number of cells involved (square matrix) [22]. Therefore, a pseudo inverse of the matrix is used as it is equivalent to the inversion of the matrix as shown in (5).…”

“…It involved with the mathematical relationship between the measurement made by the instrumentation system and the distribution of physical properties in an object. It is widely used to visualize the image of the process flow and equipment designs [22]. The mathematical process involves forward and inverse problem in order to generate an image based on the data measurement acquired.…”

“…In order to calculate the expected output (measurement values), the theoretical values of attenuation coefficient of each materials or boundary from sensor to the pipe and the sensitivity matrix are required [22].…”

Imaging particles in solid/air flows using an optical tomography system based on complementary metal oxide semiconductor area image sensors

“…The use of image sensors in tomography results in high-resolution images of samples that are over ten times larger than the samples imaged using other optical tomographic techniques [10][11][12][13]. For example, Idroas uses a charge coupled device (CCD) linear image sensor in her optical tomography system, which has a spatial resolution of less than 0.01%.…”