Photoelasticity is an experimental method for analyzing stress or strain fields in mechanics . Non-crystalline transparent materials, such as polymeric plastics, are optically isotropic under normal conditions but become doubly refractive when stressed. This basic physical characteristic of photoelasticity was first observed by Brewster in 1816 . The method of photoelasticity allows one to obtain the principal stress difference and the principal stress direction in a model. The principal stress difference and the principal direction are presented as isochromatic and isoclinic, respectively . In 1990, Brown and Sullivan  introduced use of polarization stepping for whole field isoclinic determination in a plane polariscope with a monochromatic light source. Petrucci  utilized the optical arrangement of Brown and Sullivan and replaced the monochromatic light source with a white light source. Lei
The isoclinic and isochromatic parameters are obtained only in a wrapped form . In order to unwrap the isoclinic phase map, researchers [12-16] reported several methods to make the continuous isoclinic phase map in the true phase interval. Siegmann
This paper concentrates on unwrapping isoclinic phase maps using a plane polariscope with a white light source. By comparing two arctangent functions, a new isoclinic phase map unwrapping method guided by morphological techniques is introduced. The motivation of this work is to produce an algorithm to resolve the ambiguity in isoclinic phase map that use a simple approach but retains the correctly demodulated regions of the isoclinic phase map.
II. ISOCLINIC PARAMETER ESTIMATION
Figure 1 shows a generic plane polariscope. In dark field arrangement with white light as a source, and a color camera, the intensity of light transmitted in R, G and B sensors of the camera are given by
Equation (1) can be written as
In the automatic polarization stepping, using a 4-step approach for isoclinic determination, a set of images with
Due to the fact that in white light there is no full extinction of isochromatic intensity apart from points where
In general, the isoclinic value
Correctly evaluating the isoclinic values is very important in photoelasticity. By using Mohr’s circle, the individual stress equations are expressed by
Some researchers use an approximated method to unwrap the isoclinic phase map in the range of
III. DESCRIPTION OF THE ALGORITHM
To show the procedure of isoclinic phase unwrapping, the benchmark problem of a disc under diametral compression, 35 mm in diameter and 4 mm thick is used. Experimental discs are made of polycarbonate, material fringe value F
Isoclinic phase maps over the domain are calculated based on Eq. (5), Fig. 2(a) shows the wrapped isoclinic evaluated by
[FIG. 2.] Steps involved in unwrapping isoclinic phase map for the problem of a disc under diametrical compression: (a) wrapped isoclinic phase map evaluated by atan2() function; (b) wrapped isoclinic phase map evaluated by atan() function; (c) difference between (a) and (b); (d) modified difference error after threshold; (e) after erosion and labeling operation; (f) automatically unwrapped isoclinic.
The A, B, C, D and E 5 zones are connected to each other, in order to separate 5 zones the morphological erosion  is performed using MATLAB V7. Erosion is a fundamental operation in morphological image processing in which the spatial form or structure of objects within an image are modified. With erosion an object in binary image shrinks uniformly. Figure 2(e) shows the eroded logical ‘0’ zones, 5 zones are completely separated. Using morphological techniques, the implementation procedure of unwrapping isoclinic is shown in the flow diagram (Fig. 3). By the labeling operation, the logical ‘0’ zones are automatically labeled as shown in Fig. 2(e). Zone E is labeled to 1 and has the greatest area and can be determined as the correctly evaluated isoclinic zones. Exclude the data in the correctly evaluated zone the rectifying process is performed within the specimen domain. The coordinates in zone 1 are used to rectify the data in Fig. 2(a). To start rectifying, a start point can be selected anywhere on the boundary of the correctly evaluated isoclinic zone. Four neighboring pixels adjacent to the selected point are rectified based on the rules  mentioned in Table 1. The whole field unwrapped isoclinic phase map is shown in Fig. 2(f).
[TABLE 1.] Table showing rectifying rules for different pixel position in isoclinic phase map
Table showing rectifying rules for different pixel position in isoclinic phase map
Next, the other benchmark problem of a multiply connected ring is taken up. The ring is made of polycarbonate under diametrical compression, heavily loaded of 206 N. Inner and outer diameters are 20 mm and 40 mm respectively, thickness 4 mm. Initially, isoclinic phase maps over the domain are calculated using Eq. (5). Figure 4(a) shows the wrapped isoclinic evaluated by
[FIG. 4.] (a) wrapped isoclinic phase map evaluated by atan2() function; (b) wrapped isoclinic phase map evaluated by atan() function; (c) modified difference error after threshold; (d) after erosion and labeling operation; (e) automatically unwrapped isoclinic; (f) comparison of unwrapped isoclinic value with theoretical isoclinic value along ling A-A indicated in (e).
As known, the determination of the isoclinic parameter is not a simple task. In this paper, a new method for automatic evaluation of the isoclinic parameter is presented. The influences of principal stress direction and the range of isoclinic phase upon stress separation are discussed. It has been demonstrated that it is possible to determine the isoclinic parameter in its true phase interval of −