Rishikesh Kulkarni

Simultaneous measurement of in-plane and out-of-plane displacements using pseudo-Wigner-Hough transform.

A new method based on pseudo-Wigner-Hough transform is proposed for the simultaneous measurement of the in-plane and out-of-plane displacements using digital holographic moiré. Multiple interference phases corresponding to the in-plane and out-of-plane displacement components are retrieved from a single moiré fringe pattern. The segmentation of the interference field allows us to approximate it with a multicomponent linear frequency modulated signal. The proposed method accurately and simultaneously estimates all the phase parameters of the signal components without the use of any signal separation techniques. Simulation and experimental results demonstrate the efficacy of the proposed method and its robustness against the variations in object beam intensity.

Estimation of phase derivatives using discrete energy separation algorithm in digital holographic interferometry

This Letter proposes a new method for the estimation of the first- and second-order phase derivatives corresponding to strain and curvature from a single fringe pattern in digital holographic interferometry. The method is based on a discrete energy separation algorithm, which provides a biased phase derivative estimate in a noisy environment. Subsequently, the least-squares spline approximation with optimal number of knots selection technique is used to obtain the accurate estimation of phase derivatives. The accuracy and computational efficiency of the proposed method is validated with simulation and experimental results.

Measurement of in-plane and out-of-plane displacements and strains using digital holographic moiré

The paper proposes a non-destructive method for simultaneous measurement of in-plane and out-of-plane displacements and strains undergone by a deformed specimen from a single moiré fringe pattern obtained on the specimen in a dual beam digital holographic interferometry setup. The moiré fringe pattern encodes multiple interference phases which carry the information on multidimensional deformation. The interference field is segmented in each column and is modeled as multicomponent quadratic/cubic frequency-modulated signal in each segment. Subsequently, the product form of modified cubic phase function is used for accurate estimation of phase parameters. The estimated phase parameters are further utilized for direct estimation of the unwrapped interference phases and phase derivatives. The simulation and experimental results are provided to validate the effectiveness of the proposed method.

Simultaneous estimation of phase and phase derivative using a difference equation representation of the interference field

A computationally efficient technique for fringe analysis in digital holographic interferometry using a difference equation representation of the interference field is presented. The spatially varying coefficient of the difference equation is estimated accurately by constraining it in the subspace spanned by the linearly independent basis functions. The coefficient estimated provides an accurate estimation of the interference phase derivative and enables the linear estimation of the interference field. Thereupon, the interference phase is estimated using a simple unwrapping algorithm. The performance of the proposed method is validated with the help of simulation and experimental results.

Phase derivative estimation from a single interferogram using a Kalman smoothing algorithm

We report a technique for direct phase derivative estimation from a single recording of a complex interferogram. In this technique, the interference field is represented as an autoregressive model with spatially varying coefficients. Estimates of these coefficients are obtained using the Kalman filter implementation. The Rauch-Tung-Striebel smoothing algorithm further improves the accuracy of the coefficient estimation. These estimated coefficients are utilized to compute the spatially varying phase derivative. Stochastic evolution of the coefficients is considered, which allows estimating the phase derivative with any type of spatial variation. The simulation and experimental results are provided to substantiate the noise robustness and applicability of the proposed method in phase derivative estimation.

Iterative signal separation based multiple phase estimation in digital holographic interferometry

We propose a new method for signal separation from a multicomponent interference field recorded in a digital holographic interferometry setup. The setup consisting of multiple object illuminating beams results in an interference field containing multiple signal components. The proposed method utilizes an amplitude discrimination criteria established by setting different intensities to the object illuminating beams in order to separate the signal components iteratively. The signal separation is performed in a small block of the interference field at a time. The augmentation of the block matrix with its own rows and columns is performed which has an effect of noise subspace inflation. This operation offers an improved noise robustness to the signal separation capability of the proposed method. The simulation and experimental results are provided to substantiate the applicability of the proposed method in multidimensional deformation measurement.

Digital holographic moiré for the direct and simultaneous estimation of strain and slope fields

A novel method is proposed for the direct and simultaneous estimation of multiple phase derivatives corresponding to strain and slope fields from a single moiré fringe pattern in digital holographic moiré. The interference field in a given row/column is a multicomponent complex exponential signal and is represented as a spatially-varying autoregressive (SVAR) process. The spatially-varying coefficients of the SVAR model are computed by approximating them as the linear combination of linearly independent basis functions. Further, the spatially varying poles of the transfer function corresponding to the SVAR model are computed which provide the accurate estimation of the multiple phase derivatives. The simulation and experimental results are provided to substantiate the effectiveness of the proposed method.

Simultaneous estimation of phase derivative and phase using parallel Kalman filter implementation

This paper proposes a technique for the simultaneous estimation of interference phase derivative and phase from a complex interferogram recorded in an optical interferometric setup. The complex interferogram is represented as a spatially varying autoregressive process in a given row or column at a time. The phase derivative is estimated from the poles of the transfer function representation of the autoregressive process. The poles are computed using the spatially varying autoregressive coefficients which are estimated by a computationally efficient Rauch-Tung-Striebel smoothing algorithm. The estimated phase derivative is used as a control input to a state space model designed for the phase estimation at each pixel. The unscented Kalman filter is utilized to deal with the nonlinear measurement process for the accurate estimation of the unwrapped phase. Numerical and experimental results substantiate the ability of the proposed method in handling noisy phase fringe patterns.

Multiple phase estimation via signal separation using a windowed Fourier transform in digital holographic interferometry

This paper proposes a novel method for the simultaneous estimation of multiple interference phases from a single recording of the interference field in a multi-wave digital holographic interferometry set-up. The method involves the separation of signal components from the recorded interference field based on windowed Fourier transform based filtering and amplitude discrimination criteria. The proposed method possesses the advantages offered by windowed Fourier transform based filtering such as noise robustness and a high quality reconstruction of the signal components. The performance of the method is validated with numerical and experimental examples.

Fringe filtering technique based on local signal reconstruction using noise subspace inflation

A noise filtering technique is proposed to filter the fringe pattern recorded in the optical measurement set-up. A single fringe pattern carrying the information on the measurand is treated as a data matrix which can either be complex or real valued. In the first approach, the noise filtering is performed pixel-wise in a windowed data segment generated around each pixel. The singular value decomposition of an enhanced form of this data segment is performed to extract the signal component from a noisy background. This enhancement of matrix has an effect of noise subspace inflation which accommodates maximum amount of noise. In another computationally efficient approach, the data matrix is divided into number of small-sized blocks and filtering is performed block-wise based on the similar noise subspace inflation method. The proposed method has an important ability to identify the spatially varying fringe density and regions of phase discontinuities. The performance of the proposed method is validated with numerical and experimental results.