Absolute interferometric testing of a flat surface based on the Laplacian method.

In the present study, a method is introduced for absolute interferometric testing. An interferometer is used to measure the phase difference distributions at five positions of the reference surface with respect to the test surface. The Laplacian of the phase distribution is calculated from the measured phase difference distributions. Then, the reference phase distribution is reconstructed by solving the Laplacian equation by the Fourier method. The accuracy of the method with respect to the amount of the displacement and noise is investigated by simulation and compared with the conjugate differential method. It is shown that the spatial frequencies of the phase distributions reconstructed by the Laplacian method are less filtered out with respect to the conjugate differential methods. Finally, the experimental result is presented.

Accurate testing of aspheric surfaces using the transport of intensity equation by properly selecting the defocusing distance.

In the last decade, the transport of intensity has been increasingly used in microscopy, wavefront sensing, and metrology. In this study, we verify by simulation and experiment the use of the transport of intensity equation (TIE) in the accurate testing of optical aspheric surfaces. Guided by simulation results and assuming that the experimental setup parameters and the conic constants are known, one can estimate an appropriate defocusing distance Δz that leads to an accurate solution of the TIE. In this paper, this method is verified through the construction of a non-nulled experiment for testing the 2D profile of an aspheric surface. The theoretical method and experimental results are compared to validate the results. Finally, to validate the TIE methodology, the phase distribution obtained by TIE is compared with the phase distribution obtained by a Shack-Hartmann sensor.

Fully automated, high speed, tomographic phase object reconstruction using the transport of intensity equation in transmission and reflection configurations.

While traditional transport of intensity equation (TIE) based phase retrieval of a phase object is performed through axial translation of the CCD, in this work a tunable lens TIE is employed in both transmission and reflection configurations. These configurations are extended to a 360° tomographic 3D reconstruction through multiple illuminations from different angles by a custom fabricated rotating assembly of the phase object. Synchronization circuitry is developed to control the CCD camera and the Arduino board, which in its turn controls the tunable lens and the stepper motor to automate the tomographic reconstruction process. Finally, a MATLAB based user friendly graphical user interface is developed to control the whole system and perform tomographic reconstruction using both multiplicative and inverse radon based techniques.

Application of transport-of-intensity equation in fringe analysis.

The transport-of-intensity equation (TIE) is applied in the reconstruction of two interfering wavefronts by analyzing the interference patterns and their derivatives along their common propagation directions. The TIE is extended from one wave to two waves and is then applied to calculate the phase of the interference field. Finally, the phase shift concept is applied to reconstruct the phase distribution of two waves. The consistency of the method is verified by simulation.

Detection of intralayer alignment in multicomponent lipids by dynamic speckle pattern analysis.

Multicomponent mixtures of bilayer lipids, thanks to the coexistence of liquid-crystalline phases in their structures, may be used in the development of functional membranes. In such membranes interlayer ordering distributes across membrane lamellae, resulting in long-range alignment of phase-separated domains. In this paper, we explore the dynamics of this phenomenon by laser speckle pattern analysis. We show that cholesterol content decreases the activity, and the rate of the domains size development is related to the change of physical roughness of the multicomponent lipid mixture. Our results are in agreement with the previous experimental reports. However, our experimental procedure is an easy-to-implement and effective methodology.

Reconstructing the phase distribution of two interfering wavefronts by analysis of their nonlocalized fringes with an iterative method.

This paper presents a technique for reconstructing two interfering wavefronts by analyzing their 3D interference field pattern. The method is based on the numerical inverse problem and will present a robust algorithm for reconstructing of wavefronts. Several simulations are done to validate the proposed method.

Superimposing the waves diffracted from two similar hot and cold wires provides the temperature profile around the hot one.

When two similar small objects that are installed in the arms of a Mach-Zehnder interferometer are illuminated in such a way that the image of one object in the second beam splitter is located on the other object, the diffracted waves from the objects are exactly superimposed in the interference field. The superimposed diffraction patterns disappear for a phase difference equal to an odd multiple of pi. The phase change induced by imposing changes on the medium surrounding one of the objects can be determined very accurately only by measuring the intensity distribution that appears on the superimposed diffraction patterns. Using this technique we have determined the temperature profile around a wire of diameter 0.26 mm carrying different electric currents by evaluating the phase changes at 700 points on the superimposed diffraction patterns to the accuracy of pi/200. This technique allows us to eliminate the effect of light diffraction from the geometry of an object, to measure the amplitudes of the interfering diffracted waves accurately, and to evaluate the phase difference of the diffracting waves reliably.

Non-invasive in situ monitoring of bone scaffold activity by speckle pattern analysis.

Scaffold-based bone tissue engineering aims to develop 3D scaffolds that mimic the extracellular matrix to regenerate bone defects and damages. In this paper, we provide a laser speckle analysis to characterize the highly porous scaffold. The experimental procedure includes in situ acquisition of speckle patterns of the bone scaffold at different times under preserved environmental conditions, and follow-up statistical post-processing toward examining its internal activity. The activity and overall viscoelastic properties of scaffolds are expressed via several statistical parameters, and the variations in the computed parameters are attributed to time-varying activity of the samples during their internal substructure migration.

Digital holographic microscopy of phase separation in multicomponent lipid membranes.

Lateral in-homogeneities in lipid compositions cause microdomains formation and change in the physical properties of biological membranes. With the presence of cholesterol and mixed species of lipids, phospholipid membranes segregate into lateral domains of liquid-ordered and liquid-disordered phases. Coupling of two-dimensional intralayer phase separations and interlayer liquid-crystalline ordering in multicomponent membranes has been previously demonstrated. By the use of digital holographic microscopy (DHMicroscopy), we quantitatively analyzed the volumetric dynamical behavior of such membranes. The specimens are lipid mixtures composed of sphingomyelin, cholesterol, and unsaturated phospholipid, 1,2-dioleoyl-sn-glycero-3-phosphocholine. DHMicroscopy in a transmission mode is an effective tool for quantitative visualization of phase objects. By deriving the associated phase changes, three-dimensional information on the morphology variation of lipid stacks at arbitrary time scales is obtained. Moreover, the thickness distribution of the object at demanded axial planes can be obtained by numerical focusing. Our results show that the volume evolution of lipid domains follows approximately the same universal growth law of previously reported area evolution. However, the thickness of the domains does not alter significantly by time; therefore, the volume evolution is mostly attributed to the changes in area dynamics. These results might be useful in the field of membrane-based functional materials.

Optical diffractometry.

Interference of light has numerous metrological applications because the optical path difference (OPD) can be varied at will between the interfering waves in the interferometers. We show how one can desirably change the optical path difference in diffraction. This leads to many novel and interesting metrological applications including high-precision measurements of displacement, phase change, refractive index profile, temperature gradient, diffusion coefficient, and coherence parameters, to name only a few. The subject fundamentally differs from interferometry in the sense that in the latter the measurement criterion is the change in intensity or fringe location, while in the former the criterion is the change in the visibility of fringes with an already known intensity profile. The visibility can vary from zero to one as the OPD changes by a half-wave. Therefore, measurements with the accuracy of a few nanometers are quite feasible. Also, the possibility of changing the OPD in diffraction allows us to use Fresnel diffraction in Fourier spectrometry, to enhance or suppress diffracted fields, and to build phase singularities that have many novel and useful applications.