Phase-shifting Digital Holographic Interferometry Research Articles

Deformation studies of cylindrical nanostructured silica aerogels by using phase shifting digital holographic interferometry

In this paper, we have studied the deformation of cylindrical nanostructured silica aerogels prepared with methyltrimithoxysilane (MTMS) precursor. Two beam phase-shifting digital holographic interferometry (PSDHI) is applied along with a two-beam illumination technique to study in-plane displacements. To obtain the aerogels with different densities, the MeOH/MTMS molar ratio was systematically increased from the value 20 to 26. The cylindrical aerogels are loaded with various loads from the top surface. Phase shifted holograms of silica aerogels with varying densities, with and without deformation, are recorded with two beam illumination by CCD camera. Fresnel Diffraction integral is used to reconstruct the complex amplitude of aerogel samples. For in-plane displacements, phase distribution in deformed aerogels is determined by measuring the change in the two-phase distributions. The patterns corresponding to the phase distribution of aerogels for different loads and densities are recorded. It has been observed that the deformation of silica aerogels reduces by the value 0.02058 cm to 0.0017 cm, with an increase in bulk density 0.01742 gm/cc to 0.1952 gm/cc. The elastic behavior of aerogels has been explained under various loads by considering the phase distribution patterns and condensation reaction.

Characterization of graded index optical fibers by digital holographic interferometry

For the first time to our knowledge, digital holography is used to determine the distribution of parabolic or nonparabolic refractive index fields in graded index optical fibers. The fiber is embedded in an index matching fluid whose refractive index can be varied to a matching and mismatching index with respect to that of the cladding. In experiments for both cases high precision phase-shifting digital holographic interferometry is applied with numerical evaluation employing the multilayer model for recognition of the refraction. Due to the higher redundancy in the multiple phase-shifted holograms better accuracy can be obtained compared to classical two-beam interferometry. Therefore the holographic method is recommended as a nondestructive and noncontacting method for characterizing graded index optical fibers.

EDITORIAL

This is a special issue on ‘Digital Holography and Speckle Interferometry’. The papers of this issue were presented at the symposium on ‘Digital Holography – Exploring Possibility of Using Digital Holography for Experimental Mechanics’, organised by the authors at the ‘13th International Conference on Experimental Mechanics’ (ICEM13), Alexandroupolis, Greece, 1–6 July, 2007, chaired by Emmanuel E. Gdoutos, School of Engineering, Democritus University of Thrace, Xanthi, Greece. The call for papers of the symposium is explained in the following: “Recent progress of digital holography makes it possible to measure various mechanical and geometrical parameters accurately and quickly without film development. This technique has the potential to replace other current techniques in the near future. This session focuses on new developments and techniques of digital holography as well as their applications to various engineering problems, industrial fields and real structures. The contributions on similar techniques such as moiré, conventional holography, speckle interferometry and related techniques will also be presented in this symposium. Please join this symposium if you have interests in digital holography and related techniques.” The history of digital holographic interferometry is not so long. Schnars and Jüptner developed direct recording of Fresnel holograms with a CCD sensor in 1993. Yamaguchi and Zhang developed phase-shifting digital holography in 1997. The system is very simple, capable of whole-field analysis and high process speed. The system is similar to the system of speckle interferometry, which is widely used in the market. It is valuable to compare these techniques. This gave impetus for the publication of this special issue on ‘Digital Holography and Speckle Interferometry’. This issue contains five papers on digital holography and three papers on speckle interferometry. The first paper on the digital holography by I. Yamaguchi et al. deals with the measurement of both position and shape of an object using dual wavelengths. Yamaguchi developed the phase-shifting digital holography. In this paper they also proposed a new method to measure object shapes using both the amplitude and phase of the averaged conjugated product of complex amplitudes recorded before and after wavelength shift of a laser diode. The position determination is related to the fourth paper by M. Fujigaki et al. The second paper by G. Sheoran et al. proposes shape measurement using dual index immersion. It also proposes speckle noise reduction using 5 by 5 median filtering which is compared with the third paper. The third paper by Y. Morimoto et al. presents the effect of window size on accuracy and spatial resolution in windowed phase-shifting digital holographic interferometry. The accuracy is of the sub-nanometre level by decreasing the effect of speckle noise, though the spatial resolution becomes worse according to the number of windows. The fourth paper by M. Fujigaki et al. proposes a method to determine the reconstruction distance using the standard deviation of the intensity on the reconstructed image. It also proposes a method to obtain the orientation of the specimen. The fifth paper by Y. Zhang et al. concerns with the terahertz digital holography for the future. It provides useful applications to biology and medical sciences. The first paper on speckle interferometry by A. Moreau et al. deals with vibration measurement by time average speckle interferometry and by Doppler vibrating. The second paper by G. Kalogiannakis et al. investigates the feasibility of shearographic imaging of acoustic cross-modulation. It was motivated by the latest advances in nonlinear laser Doppler vibrometry and nonlinear ultrasonic, The third paper by F. Chiang et al. presents a new approach to 3D surface countering and surface strain measurement using speckle gap effect. Although it is not an ordinary speckle interferometry, the digital speckle photography technique applied to a flat surface is extended to 3D surface countering and strain measurement of a human heart. In addition to the above eight papers, a plenary paper of ICEM13 on ‘Three-Dimensional Displacement Analysis by Windowed Phase-Shifting Digital Holographic Interferometry’ by Y. Morimoto et al. should be mentioned. This paper extends the method of a windowed phase-shifting digital holographic interferometry mentioned in the third paper of digital holography to analyse three-dimensional displacement components in a microscope. This paper was published in the January 2008 issue of Strain. Digital holography and speckle interferometry are useful methods for measurement of whole-field displacement and strain distributions in ordinary rough surface of structures. They are superior of strain gauges, which measure point strains. Use of whole-field methods requires standardization. The symposium on ‘Digital Holography and Speckle Interferometry’ was initially organized with Dr. Satoru Yoneyama of Aoyama Gakuin University. The authors would like to acknowledge his support. Unfortunately, he could not attend the symposium because of his movement to a new position.

Application of Three-Dimensional Displacement and Strain Distribution Measurement by Windowed Phase-Shifting Digital Holographic Interferometry

In order to measure 3D displacement components and surface strain distributions of objects, three systems for digital holographic interferometry were developed. In this study, these three systems are introduced and the applications to measurement of 3D displacement components and surface strain distributions of cantilevers are shown.

Editorial

Editorial

Subnanometer displacement measurement by averaging of phase difference in windowed digital holographic interferometry

In phase-shifting digital holographic interferometry for measuring the displacement distribution of an object, holograms and reconstructed images have speckle noise, and they cause large errors in the calculation of the displacement analysis. In order to reduce the effect of speckle noise and hence to increase the sensitivity of the measurement of the displacement, we previously proposed a method using windowed holograms. In this paper, we propose a new method for averaging the obtained phase-difference values. Many phase-difference values at a point of the reconstructed image obtained with different windows for a hologram are averaged with weights. In order to check the effect on accuracy, the number n of windows used for averaging is varied. The weight, which is the m'th power of the absolute value of the complex amplitude of the reconstructed object, is also varied. As a result, when n becomes larger, the standard deviation of the errors becomes smaller. When the power m is 2, the error becomes a minimum. The standard deviation of the errors in the case of a flat plate with 316-nm out-of-plane displacement is 88 pm when n=1024 and m=2.

Simultaneous Measurement of Out-of-Plane and In-Plane Displacements by Phase-Shifting Digital Holographic Interferometry

In this paper, we apply phase-shifting digital holographic interferometry to simultaneous measurement for out-of-plane and in-plane displacements by employing two beam illuminations for an object. Phase-shifted holograms before and after displacements of the object using each of two beams are recorded by a CCD camera, separately. The complex amplitude at each pixel of the CCD plane is analyzed from the holograms taken with phase-shifting. The complex amplitude of he object is reconstructed from the complex amplitude distribution on the CCD plane using the Fresnel diffraction integral. Each directional phase difference distribution is obtained by calculating the phases before and after deformation for each directional beam. The phase distribution for out-of-plane displacements is obtained by calculating the sum of the two phase difference distributions. The phase distribution for in-plane displacements is obtained by calculating the difference of the two phase difference distributions. The phase values provide accurate displacement distribution information. Actually, when the object deforms in both out-of-plane and in-plane directions, it is possible to analyze the displacement distribution in each direction. The theory and an experiment are shown.

Phase-Shifting Method with Unknown Intervals in Phase-Shifting Digital Holography

Displacement measurement can be performed with high accuracy using phase-shifting method. In phase-shifting method, it is often used four steps of phase-shifting for one cycle. In conventional method, to measure the displacement of an object by an interferometer, the phase of a reference beam should be shifted by every π/2 in the four-step phase-shifting. In this paper, a phase-shifting method with unknown intervals is proposed. This method does not need to shift a phase by every π/2. It can detect an intensity distribution and a phase distribution from five fringe images with equal intervals even if the phase-shift amount is unknown. Using this method, we propose a displacement measurement of phase-shifting digital holographic interferometry using spherical wave as reference wave.

223 移動窓関数を用いた位相シフトデジタルホログラフィ干渉法によるひずみ分布計測(OS4-2 相関,ホログラフィ,スペックル,OS4 実験力学手法の新展開3)

223 移動窓関数を用いた位相シフトデジタルホログラフィ干渉法によるひずみ分布計測(OS4-2 相関,ホログラフィ,スペックル,OS4 実験力学手法の新展開3)