Research

Fourier Ptychography Microscopy

Fourier ptychography microscopy (FPM) is a recently developed super-resolution imaging technique that offers an alternative way to bypass the resolution limit imposed by the numerical aperture (NA) of the objective lens, by creating a synthetic NA. Typically an FPM system uses an array of light-emitting diodes (LEDs) to provide angularly varying illumination and acquire a sequence of images. By iteratively stitching together many of these low-resolution intensity images in the Fourier space, FPM recovers a high-resolution complex image of the sample. FPM addresses the challenge of the low space bandwidth product (SBP) in optical microscopy, which determines the trade-off between the FOV and the resolution of an imaging system in a conventional optical microscope. This is achieved through the creation of a higher synthetic NA. 

In the ongoing work, we have proposed an advanced FPM system by creating a sequence of programmable beams to illuminate the sample with varying angles using re-configurable binary grating patterns. Unlike the conventional LED-based FPM system, the proposed system facilitates uniformization of intensity, realization of different imaging modalities, and compensation of aberrations, of the illumination beams directly. The proposed programmable FPM system provides a number of flexibilities and controllability without altering the optical design or increasing system complexities. It transforms physical challenges, into computational problems that can be resolved with minimal effort, offering a streamlined and adaptable imaging solution.

Figure: The schematic diagram of a programmable FPM system developed at the Indian Institute of Space Science and Technology is shown which consists of the set-up and the reconstruction process. The below figure shows the FPM reconstruction simulation (without aberration correction and with aberration correction) and experimental results using a Siemens star and human blood sample, respectively.

Tunable Wavelength Laser Surface Profilometry through Tilted Interference  

Frequency-tunable lasers allow the removal of phase ambiguities in interferometric profilometry through the synthetic wavelength longer than height variations in the sample. The subsequent measurements lowering synthetic wavelengths and updating  phase difference values improves the measurement. The surface profilometry on samples with tilted interference can lead to an initial synthetic phase map, though locally unambiguous, getting globally wrapped whose unwrapping can be difficult in the presence of noise.  Starting with the synthetic phase map that is locally unambiguous but globally wrapped can still update the phase values through a recursive algorithm. The artefact of 2π jumps in the initial wrapped synthetic phase just gets carried forward which can be easily removed from the final phase map obtained with the shortest possible synthetic wavelength. Choosing a point on the sample surface as the point of comparison, the proposed interferometry scheme can be made immune to surrounding vibrations while tuning wavelengths. 

Analysis of biospeckle pattern using grey-level and color-channel assessment methods

Biospeckle offers a practical tool for contact-free testing and monitoring of biological samples, providing unique insights into dynamics of biological processes. In the present work, we design an experimental arrangement to perform quality assessment on biological samples using biospeckle patterns. We analyse the speckle patterns and evaluate its important parameters by constructing a grey-level co-occurrence matrix (GLCM). Furthermore, we propose an alternative and reliable method to study the biospeckle patterns by constructing a color-channel assessment matrix. The proposed approach provides both qualitative and quantitative information of the sample under study, with minimum speckle images and no stringent requirement of correct parameter selection, unlike in the case of GLCM method. Proof-of-concept experimental results are provided that demonstrate.

Estimating unwrapped phase through phase gradients

An algorithm to extract phase in its unwrapped form from an interferogram is proposed and studied. Phase gradients are extracted from an interferogram using the Hilbert transform, and phase-shifting method. The phase is then estimated from their gradients using the method of least squares. The gradients are defined through the finite difference coefficients acting on the phase values. The gradients defined for the lowest order of accuracy correspond to the Hudgin geometry. The implementation of the numerical derivative is extended to all even higher orders. The matrix inversion required for implementing the method of least squares is carried out analytically by exploiting the symmetries made available in the numerical derivative matrix. The algorithm is checked through numerically generated interferograms by evaluating intensity gradients for both high and low-frequency fringes. It is seen that the accuracy of the phase inversion increases with increasing order of accuracy of the numerical derivatives The algorithm is demonstrated on experimentally obtained interferograms in a Mach–Zehnder interferometer setup for both high and low-frequency fringes.

Turbulence Impacted Wavefront Corrections Using Beam Modulation Technique

New experimental technique have been proposed to discuss the turbulence impact reduction using beam shaping technique. In first phase of experiments, turbulence Impacted Vortex beam shaping technique has been introduced for a propagating beam which is effected by Kolmogorov type lab based turbulence simulator using Pseudo Random Phase Plate (PRPP). The new technique is executed with a spatially filtered collimated Gaussian beam that is propagated through computer controlled rotating PRPP to introduce the lab based turbulence on the beam profile. The turbulence impacted beam is then propagated through Vortex Phase Plate (VPP) to shape that beam into different topological charged Laguerre Gaussian modes and further collimated using two lens based configuration. We have measured the scintillation index of the spatial intensity profile collected from CCD. Comparative studies have been done by placing the image plane in five different positions on the propagation path of the beam so that we can detect Collimated, diverging and converging outputs. Four topological charges of LG beams and Gaussian beam have been used to envisage results.

Accurate phase reconstruction in digital holography microscopy using Fresnel biprism

Digital holography microscopy (DHM) has emerged as a powerful digital holographic imaging technique for dynamic three-dimensional phase reconstruction of microscopic samples. Recently, a Fresnel biprism has been introduced into the conventional DHM arrangement, making the configuration common path, off-axis and eliminating the requirement for different optical components, such as, beam-splitter, mirrors, etc. The recorded hologram in a DHM is mostly contaminated with speckle noise, which makes it difficult to interpret the phase information correctly. In the present work, we investigate the phase reconstruction accuracy in a Fresnel biprism based DHM, utilizing different Fourier terms, in the presence of low and high coherent sources. Different Fourier terms has been realised by modifying the recorded hologram in order to minimize the contribution of speckle noise in the reconstructed phase. Proof-of-concept simulation and experimental results are included for blood sample to demonstrate the accuracy in phase reconstruction in a Fresnel biprism based DHM.

Nonlinear phase accumulation for a linear path delay in low coherence fourier transform spectral interferometry

A scheme to measure path delay in spectral interferometry by observing the phase accumulated by the superposed field is presented. Through the interference with an additional reference beam maintained at an out-of-phase condition near zero optical path delay with respect to the sample probe beam, a nonlinearity in measured phase is observed. A detailed simulation is presented, and its experimental proof-of concept demonstration is attempted using the classic low coherence spectral interferometry. The spectral phase is measured from the modulations in the recorded spectral interference using Fourier transform method of fringe analysis. A systematic calibration for setting up the experiment even with unknown parameters like amplitude ratio among the interfering fields, and location of the zero optical path delay is also provided.

Insensitivity of partially coherent Gaussian -Schell model beams to the impact of dynamic Kolmogorov type turbulence

The effect of dynamic Kolmogorov kind of turbulence on Gaussian- Schell model beams in different coherence regimes have been explored in detail. The propagation characteristics of such turbulence impacted beams are quantitatively verified at the laboratory level by calculating beam wandering, scintillation index, and Zernike polynomials. It has been experimentally verified that Gaussian Schell model beams are more resilient to the impact of turbulence compared to their fully coherent counterparts under different turbulence strengths. These results find applications in free-space optical communications.

Robustness of partially coherent vortex beams to the impact of dynamic Kolmogorov kind of turbulence

The wave propagation characteristics of Gaussian-Schell model vortex beams passing through a dynamic Kolmogorov type of turbulence are analyzed at the laboratory level. The effect of a rotating pseudo-random phase plate, which simulates Kolmogorov-type atmospheric turbulence, on the Gaussian-Schell model beams carrying twist phase is characterized by calculating the scintillation index and intensity line profiles. Our analysis proves the resilience of Gaussian-Schell model vortex beams to the impact of dynamic turbulence. Simulation studies are further used to validate the experimental results. Because of the resemblance between our investigation conditions and real-world atmospheric turbulence, these findings have potential applications in free-space communication systems.

Fried’s coherence length measurement of dynamic Kolmogorov type turbulence using the autocorrelation function

A new method to find the Fried’s coherence length of a dynamic Kolmogorov type turbulence in a laboratory environment is reported in this paper. This method utilises the autocorrelation function obtained from the quantitative characteristics of a rotating pseudo random phase plate in one of the arms of a Mach–Zehnder interferometer. Theoretical formalism and experimental verification are presented.

Amplified sensing of optical phase difference through the phase of the resultant field

A generalized scheme to enhance the sensitivity in the measurement of phase difference in an optical interference by measuring the phase of the resultant field is presented. In the proposed scheme, the weak measurement in scalar optical interferometry is achieved by directly accessing the phase of the output state, rather than looking at the centroid shift in the intensity. The spatial confinement or beam-like characteristics for the optical field, an essential criterion for centroid calculation, is not a requirement for the scheme. The ability to uniquely sense and distinguish contributions to the phase difference from individual optical fields; an aspect with potential to improve the measurement accuracy in optical gyroscopes and gravitational wave sensing, is also presented.

Spectral switch anomalies in a Sagnac interferometer with respect to a Galilean frame

We report the spectral switch shift around spectral anomalies in a gyroscopic Sagnac interferometer, which is normally used to calibrate the angular momentum of a gyroscope. The spectral shift in the rotating gyroscope is explained with respect to the longitudinal Doppler shift of the counterpropagating beams in the Sagnac interferometer.

Estimation of dislocated phases and tunable orbital angular momentum using two cylindrical lenses

A first-order optical system consisting of two cylindrical lenses separated by a distance is considered. It is found to be non-conserving of orbital angular momentum of the incoming paraxial light field. The first-order optical system is effectively demonstrated to estimate phases with dislocations using a Gerchberg–Saxton-type phase retrieval algorithm by making use of measured intensities. Tunable orbital angular momentum in the outgoing light field is experimentally demonstrated using the considered first-order optical system by varying the distance of separation between the two cylindrical lenses.

Polarization-spatial Gaussian entanglement in partially coherent light fields

The problem of bipartite entanglement in partially coherent paraxial vector light fields is addressed. A generalized uncertainty principle suited for the polarization-spatial degrees of freedom is introduced. Partial transpose is implemented through the obtained generalized uncertainty principle. Partial transpose is shown to be necessary and sufficient in detecting entanglement for a class of partially coherent vector light fields which have a spatial part to be Gaussian. An experimental realization of the studied entangled states using classical optical interferometry is outlined.

Detection of polarization-spatial classical optical entanglement in partially coherent light fields using intensity measurements

Detection of polarization-spatial classical optical entanglement through implementation of partial transpose on measured intensities is explored. A sufficient criterion for polarization-spatial entanglement in partially coherent light fields based on intensities measured at various orientations of the polarizer, as implied through partial transpose, is outlined. Detection of polarization-spatial entanglement using the outlined method is demonstrated experimentally through a Mach–Zehnder interferometer setup.

Implementation of reference-less wavefront sensing in a grating array-based wavefront sensor

In the present work, we propose a novel reference-less wavefront sensing method in a grating array-based wavefront sensor (GAWS). The proposed sensing method utilizes both +1 and -1 diffraction orders. The key idea is that when there is a local tilt in the wavefront, the array of +1 and -1 diffracted spots move in opposite directions due to their optical phase conjugate relationship but share a common reference position. By determining the displacement of these spots, the reference position can be precisely determined, and the local slope can be extracted from which the incident wavefront can be estimated. The proposed sensing method facilitates wavefront estimation using a single camera frame and is compatible with standard wavefront estimation algorithms. This proposed method proves particularly advantageous in scenarios where a highquality wavefront is unavailable as a reference. We have validated the effectiveness of our proposed method through simulation results.