The thesis introduces novel techniques in the field of fringe analysis for direct estimation of phase gradients or derivatives. A pseudo Wigner-Ville distribution based method is proposed to reliably estimate the phase derivatives from a single fringe pattern. The method's ability for estimating rapidly varying phase derivatives is enhanced by developing an adaptive windowing technique. Further, the two-dimensional extension of the method is presented to handle fringe patterns with severe noise. In addition, a generalized approach is described to enable direct estimation of arbitrary order phase derivatives. Subsequently, methods based on digital holographic moiré and multi-component polynomial phase formulation are introduced to measure the in-plane and out-of-plane displacements and their derivatives for a deformed object in digital holographic interferometry. These methods permit the simultaneous estimation of multiple phases and their derivatives without the need of multiple fringe patterns and complex experimental configurations, which is hitherto not possible with the current state-of-the-art fringe analysis methods. The major advantages of the developed techniques are the ability to directly estimate phase derivatives without relying on complex unwrapping, filtering and numerical differentiation operations, high computational efficiency and strong robustness against noise. In addition, the requirement of a single fringe pattern makes these techniques less error-prone in the presence of vibrations and external disturbances and enhances their applicability for dynamic measurements. Further, the developed techniques offer a potential solution to the challenging problem of simultaneous multi-dimensional deformation analysis in digital holographic interferometry. The reliable performance of these techniques is validated by numerical simulation and their practical applicability is demonstrated in digital holographic interferometry and fringe projection for slope and curvature measurement, defect detection, surface slope evolution studies and measurement of in-plane and out-of-plane displacements and their derivatives. These techniques offer substantial advancements in fringe analysis and exhibit significant application potential in areas such as non-destructive testing, biomechanics, reliability analysis, material characterization and experimental mechanics.