A comparison of temporal and spatial unwrapping on a photoelastic isochromatic phase map is discussed. The analytical results show that the two-dimensional Macy’s spatial unwrapping can yield a quite good retrieval if an inconsistency-free isochromatic map is to be treated as is true in most of the photoelastic problem cases. While only temporal wrapped data are provided for the phase retrieving work, the success strongly depends on providing the correct changing ratio between the two (or more) temporal states, (e.g., percentage variation of load or wavelength step). The simulation of an incorrect ratio of the temporal isochromatic work on the accuracy of the retrieving work is performed. Experimental results show that temporal unwrapping error is more easily occurs near a highly stressed zone.
π Photoelasticity plays an important role in the field of stress analysis. Not only because it is a non-contact whole field
optical method, but it provides isoclinic (principal stress direction) and isochomatic (principal stress difference) data as
well, which serve as the two most important parameters in the field. But, unfortunately, the coupling between these two
parameters induces phase ambiguity problem in the isochromatic data unless the isoclinic data have been correctly
procured first. In this paper, a novel spatial phase unwrapping is first applied for retrieving the correct isoclinic data,
which is then substituted into the isochromatic calculation to solve the 2 ambiguity problem conducted by wrapped
isoclinic data. The result is checked with that from the theoretical analysis and shown to be with limited error. The same
problem is solved in a different way - by the temporal approaches, load stepping or multiple wavelengths sourcing in
advance. The intercomparison depicts that the spatial approach is more noise-immune than the temporal approach is. It is
because that by the spatial approach the algorithm can check data not only of themselves but consult data also from their
neighbors. As a result, any small localized error can be eliminated accordingly.
A local histogram-data-orientated filtering algorithm is proposed to remove noise from the deformation phase map obtained by a phase stepping electronic speckle pattern interferometry (ESPI). The proposed filter can successfully eliminate any speckle-generated residues of a real dislocation free map. Since the filtered result is totally free from any phase inconsistency, a simple unwrapping rule, like Macy's method, can be applied for the correct phase retrieval. The motivation and theory of the proposed method is described. A simulated noisy wrapped map is employed to detail its implementation. An intercomparison of the present study and two well-known methods is performed to present the performance of the proposed method. In addition, several ESPI experiments are conducted to provide successful filtering of practical phase maps and to prove the effectiveness of the proposed method.
The e-beam lithography commonly used in the semiconductor industry is used to create large format grating image holograms. Delicate and bright images with extremely fine features can be generated using this newly developed method. In this paper, a quantitative and qualitative analysis related to the grating image hologram is discussed in detail. Using the optimized condition derived based on the quantitative analysis, the e-beam lithography technique commonly used to generate semiconductor masks has been implemented to create images with extremely fine features. The optimized condition together with the simplistic nature of the grating written to the image, the grating image holograms generated will be bright and colorful under white light illumination. The above mentioned generic characteristics plus the optimized condition obtained from our analysis make the e-beam lithography technique a versatile and powerful method in creating image holograms. High end products such as kinegrams can be easily implemented by using this technique. Furthermore, kinegrams with extremely fine features to generate a continuous and smooth imaging effect can be effectively created by this newly developed technique. The orientation and the pitch of the grating written to the grating image hologram determines two important characteristics of the grating image. More specifically, the grating orientation determines the viewing angle while the grating pitch determines the color projected to the viewer. As the grating image hologram is typically being illuminated by an inclined incident white light, the incident light beams will be diffracted into a colorful curved surface extending from the illuminated grating pixel. Taking a realistic extended illuminating light source into consideration, a single grating pixel actually will diffract the illuminating light cone into a colorful surface ensemble. With this understanding, it is possible for us to design the grating image hologram using the colorful surface ensemble as one of the design parameters available to us. In other words, we can use the colorful surface ensemble to shape the final image created by illuminating the grating image hologram with prespecific extended white light conditions. Two grating image holograms, one of which is a 5 by 5 centimeters square grating and the other a 3.5 centimeters by 2 centimeters elliptical kinegram, were successfully created by utilizing the analysis mentioned above. It was discovered that the limitation of the field size available to today's e-beam machine poses an important design consideration. That is, when field stitching is required to create a large area grating image hologram, the images being written should be carefully chosen so as to minimize the mismatch effect among the junction of each field. The two newly completed holograms showed that with the design methodology presented in this article, high quality large area grating image holograms can be created.