Analysis of fringe patterns for the accurate estimation of phase and phase derivatives is of crucial importance in optical interferometry as these quantities provide important information on the physical parameters under study. A wide range of applications including the measurement of object surface displacement, strain, changes in the refractive index and object shape are made possible by accurate fringe analysis. The essential characteristics of any fringe analysis technique include noise robustness, high accuracy, computational efficiency and single frame demodulation capability. The thesis proposes a wide range of fringe analysis techniques to address the problem of accurate estimation of phase and phase derivatives. It also offers solution to the problem of simultaneous estimation of multiple phase and phase derivatives from a single frame of the interference field. For the purpose of our study, we have considered single/multicomponent real/complex sinusoidal fringe patterns recorded in single/multi-wave digital holographic/speckle interferometry setups. A piecewise polynomial phase approximation allows for the simultaneous estimation of multiple phases. Signal processing techniques are exploited for the accurate estimation of the polynomial coefficients. The autoregressive model of the fringe pattern provides a generalized and powerful approach for the direct estimation of phase derivatives from single/multi-component real/complex sinusoidal fringe patterns. The technique based on matrix enhancement and matrix pencil is proposed for the simultaneous estimation of multiple phase derivatives. The matrix enhancement approach provides a unique way for the reliable filtering of highly noisy fringe patterns. In a different approach more adopted to the multicomponent signal analysis, techniques based on windowed Fourier transform and noise subspace inflation are proposed for the robust and reliable separation of the multiple signal components. Independent analysis of these signal components further provides the multiple phase or/and phase derivatives estimates. In the case of complex sinusoidal fringe pattern, we have also proposed for the first time a method for the simultaneous estimation of unwrapped phase and phase derivatives of arbitrary order. The thesis ends by providing a solution to the difficult yet important problem of closed fringe pattern demodulation. The proposed methods are evaluated with number of simulation examples under different variable parameters such as signal to noise ratio, amplitude ratio of signal components, window size, basis dimension, etc. The error analyses performed with respect to these variables demonstrate the noise robustness offered by the proposed methods. The proposed methods are also found capable of handling complex fringe patterns in a computationally efficient manner. Experimental validations of the proposed methods are performed with fringe patterns recorded in single/multi wave digital holographic interferometry and digital speckle pattern interferometry setups. The single frame fringe analysis capability of the proposed methods makes them highly suitable for dynamic measurement applications.