Full-field automated photoelasticity by use of a three-wavelength approach to phase stepping

Abstract

An overdeterministic least-squares phase-stepping method for automated photoelasticity is described. Problems associated with isochromatic-isoclinic interaction are solved by use of a three-wavelength method to calculate the value of the isochromatic parameter and the isoclinic angle. The ramped isoclinic phase map can now be unwrapped to give the orientation of the principal stresses with respect to a reference axis of the polariscope unambiguously. A three-wavelength approach to determination of the absolute value of the isochromatic parameter is shown to give reliable results also.

Computer aided photoelasticity by an optimum phase stepping method

“…(10) Equations (4)- (7) allow the isoclinic parameter 0, that is, the angle between the reference axis and the direction of the closest principal stress, to be obtained as Due to the periodicity of the arctangent function, eq (11) produces isoclinic values in the range -45 ~ < 0 < 45 ~ The angle of one of the principal stresses can be directly obtained in the range -90 ~ < 0 < 90 ~ applying an unwrapping procedure to the 0 values. It consists of performing a pixel by pixel scan of the field of view, starting from an arbitrary point, and adding or subtracting =/2 to the pixel data when the difference with the adjacent point data exceeds an established value (slightly lower than 180~ The values obtained will be the ct parameter or c~ + =/2 depending on the value assumed by 0 at the starting point of the procedure.…”

Birefringence measurement by four-step phase-shifting method on triple-polarizer plane polariscope

“…Phase-shifting methods 1 are well-known to be the most effective ways in whole-field or point-scanning measurements for birefringence. They generally fall into three categories: the methods based on plane polariscope, [2][3][4][5][6] Senarmont polariscope, 7 and circular polariscope. [8][9][10][11] The latter two categories should take use of quarter-wave plates, which will introduce major errors and additional dependence on both temperature and wavelength, while the first class has the simplest optical setup and also no errors from quarter-wave plates.…”

“…[8][9][10][11] The latter two categories should take use of quarter-wave plates, which will introduce major errors and additional dependence on both temperature and wavelength, while the first class has the simplest optical setup and also no errors from quarter-wave plates. However, the previously proposed plane-polariscopic methods-such as the three-step 2 and six-step 5 methods, multiwavelength methods, 3,4 and spectropolarimetric method 6 , did not take into account the fluctuations of incident light. When laser is used as the light source, the fluctuations of both output intensity and polarization state of the laser will produce significant adverse effects on the measurement, and should be rigidly considered.…”

Separation of isoclinics and isochromatics from photoelastic data with a regularized phase-tracking technique

“…For that goal phase-measuring techniques have been applied. [1][2][3][4][5][6][7][8][9][10] For a complete isoclinic-isochromatic phase recovery many images are required ͑three or four for isoclinics and six-eight for isochromatics͒ for performing the complete analysis and separating the fringe patterns. This is a drawback in some situations: For instance, in the method of threedimensional stress analysis of Plouzenec et al, 11 it is difficult to obtain the necessary number of images to apply phase-shifting techniques; however, it is well known that, in the phase-shifting technique, the fewer the images used, the more sensitive the corresponding method is to errors such as nonsinusoidal patterns, nonlinearity in the detector, errors in the phase shifts, and background correction.…”