Variable Shearing Holography

From the perspective of manufacturing, it is not always ideal to use conventional methods of surface and optical metrology. Most optical metrology systems require a stable and pressure-temperature controlled environment in a laboratory setting as they are sensitive to such disturbances. The main contributing factor to these levels of sensitivity is the presence of a reference mirror. In most interferometric systems, interference patterns are generated by overlapping the wavefield generated from the object being measured with that generated from a reference mirror. Different algorithms can be used further by modulating the interference patterns to generate three-dimensional surface maps. Similar setups and algorithms could be used to not only generate the surface maps but also the object complex wavefield which extends its applications in digital holography. The goal of this research is to develop interferometric holography systems that are robust to environmental effects and suitable for in-situ metrology in manufacturing processes. Part 1 of this dissertation focuses on developing a lateral shear interferometric holography system using a pair of geometric-phase (GP) gratings. Two designs are proposed which allowed for different shear selection strategies. The proposed designs are robust to environmental effects by virtue of their design as a self-referenced and common-path configuration. A polarized camera sensor is used to record the interferograms with different phase shifts. Using an alternating projection algorithm, the recorded intensity maps are used to estimate the object wavefield. The errors generated by the algorithm are studied as a function of the shears selected to record the interferograms using synthetic intensity maps for both designs. The correlation is investigated using spatial and frequency information density functions and the errors generated by both designs are compared. Part 2 investigates the limitations of selected shears from the perspective of the spatial information density function. The major outcome from Parts 1 and 2 is proof that the shear selection strategies, the shear amounts, and the shear orientations affect the wavefield reconstruction. This leads to Part 3 of the dissertation which focuses on the optimal selection of shears for this system. Due to the complexity of the equations that govern the effect of shears on the reconstruction of different surface frequencies, a statistical approach was used to optimize the shears based on simulations that reconstructed a defocused point source wavefield. A point source wavefield is used for these simulations because it is the ideal wavefield demonstrating the reconstruction of all possible frequencies within the field of view. The results were compared to frequency information density maps to correlate the results. Parts 1,2 and 3 show a complete work starting from exploring designs to identifying optimal shear settings for a coherent digital holography system to measure transmissive and reflective samples. Part 4 shows a secondary application for this system that uses the GP grating pairs to make a fringe projection system that is suitable for diffused surfaces. The proposed system provides flexibility to adjust the characteristics of the projected fringes easily by changing the space between the gratings and the grating pair orientation. Example measurements are presented, and the capabilities of the setup are demonstrated. The proposed design can produce adjustable fringe patterns with fringe spacing varying from large values to as small as sub-millimeter distances. The fringe orientation can also be changed, and the patterns can be projected on objects of a wide range of sizes without losing the fringe contrast.