Separation of isochromatics and isoclinics using Fourier transform

In photoelasticity, the image obtained in the field of a plane polariscope scope consists of isochromatics and isoclinics.1 In analysis of stress, the basic method is to obtain the difference of the principal stress and the principal stress direction using the iso-chromatic fringes and the isoclinics fringes.2–5 However, the isochromatic fringes obtained in a circular polariscope have the error due to the ellipticity of the circular polarized incident light and so on.5 The positions of the isoclinics obtained in a plane polariscope are not so accurate because of the wide width of the isoclinic lines and the accuracy of quarter wave plates. Moreover, photoelastic stress analysis of the whole field of a specimen is tedious and time consuming. Recently, image processing is widely used to analyze the images obtained in photoelasticity.2–9 Umezaki et al.8 proposed a method to separate the isoclinic lines from many images obtained by rotating the crossed polaroids in a plane polariscope. Image processing allows high speed and more accurate analysis. The ability of computers has been remarkably progressed in memory space and processing speed. By using this ability, the authors9 developed a software of 3-D image processing, and applied it to the analysis of the 3-D (x, y, θ) image data consisted with the spatial coordinates (x, y) and the angle θ of the crossed polaroids. In the method of Ref. (9), the isochromatics is obtained by adding up all the brightness values on each (x, y) of the (x, y, θ) 3-D image. The distribution of principal stress direction is obtained by detecting the angle θ when the brightness value is the maximum on each (x, y). The detected angle θ of the polaroids is the same as the principal stress direction on each (x, y). By using the 3-D image processing, various analysis became easier and faster than using 2-D one.