Vibration measurement by temporal Fourier analyses of a digital hologram sequence

A method for whole-field noncontact measurement of displacement, velocity, and acceleration of a vibrating object based on image-plane digital holography is presented. A series of digital holograms of a vibrating object are captured by use of a high-speed CCD camera. The result of the reconstruction is a three-dimensional complex-valued matrix with noise. We apply Fourier analysis and windowed Fourier analysis in both the spatial and the temporal domains to extract the displacement, the velocity, and the acceleration. The instantaneous displacement is obtained by temporal unwrapping of the filtered phase map, whereas the velocity and acceleration are evaluated by Fourier analysis and by windowed Fourier analysis along the time axis. The combination of digital holography and temporal Fourier analyses allows for evaluation of the vibration, without a phase ambiguity problem, and smooth spatial distribution of instantaneous displacement, velocity, and acceleration of each instant are obtained. The comparison of Fourier analysis and windowed Fourier analysis in velocity and acceleration measurements is also presented.     

Identification of Specimen Position and Orientation Using Standard Deviation of Intensity in Phase‐Shifting Digital Holography1

Abstract: Phase‐shifting digital holography is a useful method to measure the displacement distribution and the strain distribution of an object surface. The complex amplitude distribution of an object surface is obtained as the complex amplitude distribution at a reconstruction distance. It is, however, difficult to measure the reconstruction distance by actual measurement. We discovered that the standard deviation of the intensity on the reconstructed image becomes the maximum value when the reconstruction distance is the same as the actual optical path length. The displacement distributions are obtained for the x‐, y‐ and z‐directions. When the normal direction of an object surface inclines from the z‐direction, the displacements defined on the xyz‐coordinate system should be transformed into the object coordinate system. It is, therefore, required to develop a measurement method of the orientation of the object to obtain the parameters for transforming from the xyz‐coordinate system into the object coordinate system. In this paper, the method to identify the position and the orientation of a specimen using the standard deviation of the intensity distribution is proposed.     

Speckle interferometry: three-dimensional deformation field measurement with a single interferogram

An electronic speckle interferometer, arranged for out-of-plane sensitivity and with an off-axis reference beam to produce spatial phase bias, is used for three-dimensional deformation field measurements. The complex amplitude of the object wave is calculated by application of a Fourier-transform method to a single interferogram. The change in phase after object deformation yields the out-of-plane component of the displacement field. The two in-plane components are obtained by cross correlation of subimages of the reconstructed object wave's intensity, a method that is also referred to as digital speckle photography. The Fourier-transform algorithm is extended and modified, leading to random measurement errors that are below widely accepted theoretical limits and also to an extended measuring range. These properties and the mutually combined information improve the accuracy of both methods compared with their usual single implementation. The performance is evaluated in experiments with pure out-of-plane, pure in-plane, and combined deformations and compared with theoretical values. An example of a practical application is given.     

Fast acquisition system for digital holograms and image processing for three-dimensional display with data manipulation

A three-dimensional (3D) digital holographic display system with image processing is presented. By use of phase-shifting digital holography, we obtain the complex amplitude of a 3D object at a recording plane. Image processing techniques are introduced to improve the quality of the reconstructed 3D object or manipulate 3D objects for elimination and addition of information by modifying the complex amplitude. The results show that the information processing is effective in such manipulations of 3D objects. We also show a fast recording system of 3D objects based on phase-shifting digital holography for display with image processing. The acquisition of 3D object information at 500 Hz is demonstrated experimentally.     

Effects of Window Size on Accuracy and Spatial Resolution in Windowed Phase‐Shifting Digital Holographic Interferometry1

Abstract: Phase‐shifting digital holographic interferometry is a new method to measure displacement distribution on the surface of an object. Usually holography has speckle noise, which leads to a large error in the analysis of displacement and strain distributions. We previously proposed windowed phase‐shifting digital holographic interferometry (windowed PSDHI). The use of this method leads to accurate displacement analysis, decreasing the effect of speckle patterns. However, noise reduction involves a defect, which renders the spatial resolution low. In this paper, by comparing the conventional noise reduction method using spatial averaging with the windowed PSDHI on spatial resolution, the effectiveness of noise reduction is discussed.     

Iterative algorithm of phase determination in digital holography for real-time recording of real objects

We propose a numerical method to obtain complex amplitude distribution of a three-dimensional (3D) object from a digital hologram. The method consists of two processes. The first process is to measure simultaneously a hologram of the 3D object and an object intensity distribution by two image sensors. These intensity distributions give us the amplitude and absolute value of phase of the 3D object at the image sensor plane. The second process is the determination of phase distribution by a proposed iterative process based on the criterion that the reconstructed 3D object is in focus and its conjugate reconstruction is out of focus. Numerical and experimental results show the effectiveness of the proposed method.     

Simultaneous measurement of in-plane and out-of-plane displacement derivatives using dual-wavelength digital holographic interferometry

The paper introduces a method for simultaneously measuring the in-plane and out-of-plane displacement derivatives of a deformed object in digital holographic interferometry. In the proposed method, lasers of different wavelengths are used to simultaneously illuminate the object along various directions such that a unique wavelength is used for a given direction. The holograms formed by multiple reference-object beam pairs of different wavelengths are recorded by a 3-color CCD camera with red, green, and blue channels. Each channel stores the hologram related to the corresponding wavelength and hence for the specific direction. The complex reconstructed interference field is obtained for each wavelength by numerical reconstruction and digital processing of the recorded holograms before and after deformation. Subsequently, the phase derivative is estimated for a given wavelength using two-dimensional pseudo Wigner-Ville distribution and the in-plane and out-of-plane components are obtained from the estimated phase derivatives using the sensitivity vectors of the optical configuration.     

Accuracy verification of a simple local three-dimensional displacement measurement method of DIC with two images coordinates

There are two methods applied for three-dimensional digital image correlation method to measure three-dimensional displacement. One is to measure the spatial coordinates of measuring points by analyzing the images. Then, the displacement vectors of these points can be calculated using the spatial coordinates of these points obtained at different stages. The other is to calibrate the parameters for individual measuring points locally. Then, the local displacements of these points can be measured directly. This study proposes a simple local three-dimensional displacement measurement method. Without any complicated distortion correction processes, this method can be used to measure small displacement in the three-dimensional space through a simple calibration process. A laboratory experiment and field experiment are carried out to prove the accuracy of this proposed method. Laboratory test errors of one-dimensional experiment are similar to the accuracy of the XYZ table; the error in Z-direction is only 0.0025% of the object distance. The measurement error of laboratory test is about 0.0033% of the object distance for local three-dimensional displacement measurement test. Test and analysis results of field test display that in-plane displacement error is only 0.12 mm, and the out-of-plane error is 1.1 mm for 20 m × 30 m measuring range. The out-of-plane error is only about 10 PPM of the object distance. These test and analysis results show that this proposed method can achieve very high accuracy under small displacement for both of laboratory and field tests.     

Submicrometer optical tomography by multiple-wavelength digital holographic microscopy

We present a method for submicrometer tomographic imaging using multiple wavelengths in digital holographic microscopy. This method is based on the recording, at different wavelengths equally separated in the k domain, in off-axis geometry, of the interference between a reference wave and an object wave reflected by a microscopic specimen and magnified by a microscope objective. A CCD camera records the holograms consecutively, which are then numerically reconstructed following the convolution formulation to obtain each corresponding complex object wavefront. Their relative phases are adjusted to be equal in a given plane of interest and the resulting complex wavefronts are summed. The result of this operation is a constructive addition of complex waves in the selected plane and destructive addition in the others. Tomography is thus obtained by the attenuation of the amplitude out of the plane of interest. Numerical variation of the plane of interest enables one to scan the object in depth. For the presented simulations and experiments, 20 wavelengths are used in the 480-700 nm range. The result is a sectioning of the object in slices 725 nm thick.     

Computer-generated holograms of three-dimensional realistic objects recorded without wave interference

We propose a method of synthesizing computer-generated holograms of real-life three-dimensional (3-D) objects. An ordinary digital camera illuminated by incoherent white light records several projections of the 3-D object from different points of view. The recorded data are numerically processed to yield a two-dimensional complex function, which is then encoded as a computer-generated hologram. When this hologram is illuminated by a plane wave, a 3-D real image of the object is reconstructed.     

Short-coherence digital microscopy by use of a lensless holographic imaging system

An optical system based on short-coherence digital holography suitable for three-dimensional (3D) microscopic investigations is described. The light source is a short-coherence laser, and the holograms are recorded on a CCD sensor. The interference (hologram) occurs only when the path lengths of the reference and the object beam are matched within the coherence length of the laser. The image of the part of the sample that matches the reference beam is reconstructed by numerical evaluation of the hologram. The advantages of the method are high numerical aperture (this means high spatial resolution), detection of the 3D shape, and a lensless imaging system. Experimental results are presented.     

Direct Three-Dimensional Shape Measurement by Digital Light-in-Flight Holography

A method for direct shape measurement with short laser light pulses and digital holography with a CCD array is proposed. An in-line holographic setup is used in which the reference beam is reflected from a blazed reflection grating, i.e., a Littrow setup. By this method a relatively large optical delay is created between the reference and the object beams even with a small object-reference angle, which is necessary because of the limited resolution of the CCD. The delay varies continuously across one axis of the CCD array. In this way different object sections are reconstructed from different parts of the CCD, which in turn correspond to a certain path length from the object. By putting the sections together, one can evaluate the three-dimensional shape. Theoretical as well as experimental results are presented.     

Accelerated algorithm for three-dimensional computer generated hologram based on the ray-tracing method

An accelerated algorithm for three-dimensional computer generated holograms (CGHs) based on the ray-tracing method is proposed. The complex amplitude distribution from the center point of an object is calculated in advance and the field distributions of rest points on the hologram plane can be given by doing a small translation and an aberration to the pre-calculated field. A static two-dimensional car, a three-dimensional teapot, and a dynamic three-dimensional rotating teapot are reconstructed from CGHs calculated with the accelerated algorithm to prove its validity. The simulation results demonstrate that the accelerated algorithm is eight times faster than the conventional ray-tracing algorithm.     

Determination of three-dimensional displacement using two-dimensional digital image correlation

A novel method that uses a two-dimensional (2D) digital image correlation (DIC) based on a single CCD camera to measure three-dimensional (3D) displacement and deformation is proposed. Rigid-body displacement in 3D space consists of both in-plane and out-of-plane components. The presence of an in-plane displacement component results in a shift of the center of the image displacement vector, while the slope of the image displacement vector is related to the out-of-plane displacement component. Global DIC is employed to determine the displaced position of each point on an object based on a linear distribution characteristic of the displacement vector. Speckle images with deformation introduced by 3D displacement are generated to demonstrate the feasibility of the proposed method. In the 3D rigid-body displacement, both in-plane and out-of-plane displacement components are separated by determining the intercept and slope of the image displacement vector. In the 3D deformation, a zero order displacement (pure rigid-body displacement) mode is assumed in a small subset of pixels. Simulated and experimental results demonstrate that both in-plane and out-of-plane displacements can be accurately retrieved using the proposed method.     

Phase retrieval from experimental far-field intensities by use of a Gaussian beam

The noniterative phase-retrieval method by use of Gaussian filtering is applied to the reconstruction of phase objects from experimental far-field intensities. In this method, the complex amplitude of transmitted light through an object is reconstructed from three far-field intensities, which are measured with the modulation of the object by laterally shifted and unshifted Gaussian filters. In the experiment, the amplitude of a Gaussian beam illuminating objects is utilized as a Gaussian filter, and, as the phase objects, a converging lens with a small exit pupil and a plastic fiber immersed in optical adhesive are used. The experimental results show that the Gaussian beam of a laser is capable of retrieving the phases of those objects with the accuracy of the range from approximately 1/10 to 1/4 of the laser's wavelength.     

Shape connection by pattern recognition and laser metrology

Shape connection based on the pattern recognition of three-dimensional shapes is presented. In this technique, the object shape is reconstructed by laser scanning and image processing. The object is reconstructed from multiple views when an object occlusion appears. From this process, multiple parts of the object are reconstructed. Then, these parts are assembled to obtain the complete object shape. To perform the assembling, a matching procedure is applied to a transverse section of the multiple views by Hu moments. The depth of the transverse section is computed by an approximation network based on the behavior of the laser line and the camera position. Also, vision parameters are deduced by the network and image processing. In this manner, the shape connection is achieved automatically by computational algorithms. Therefore, errors of physical measurement are not passed to the reconstruction system. Thus, the performance and the accuracy of the reconstruction system are improved. This is elucidated by the comparison between the obtained results by the proposed technique and the obtained results by a contact method. Thus, a contribution in laser metrology for shape connection is achieved.     

Aberration compensation of holographic particle images using digital holographic microscopy

Characterisation of small and large-scale vortices in turbulent flows demands a system with high spatial resolution. The measurement of high spatial resolution, three-dimensional vector displacements in fluid mechanics using holography, is usually hampered by aberration. Aberration poses some problems in particle image identification due to low fidelity of real image reconstruction. Phase mismatch between the recording and the reconstruction waves was identified as the main source of aberration in this study. This paper demonstrates how aberration compensation can be achieved by cross-correlating the complex amplitude of an aberrated reconstructed object with the phase conjugate of a known reference object in the plane of the hologram (frequency space). Results favourably show significant increase in Strehl ratio and suppression of background noise that are more pronounced for particle images of 10 and 5 microns. It is clear from the work conducted that wavefront aberration measurement and compensation of holographic microscopic objects are now possible with the use of a variant digital holographic microscope.     

Binary representation of interference patterns for phase-shifting digital hologram

Phase-shifting digital holograms can completely record the complex (amplitude and phase) wavefront information, containing three-dimensional object shape and relative position. In this study, we examine a binary representation for a phase-shifting digital hologram and apply it to three-dimensional object recognition and reconstruction. For this purpose, we derive an optimal threshold and quantized value for the binary representation of the interference patterns. The recognition results indicate that even with only one bit to represent the digital hologram, there is still enough information for us to recognize the three-dimensional objects. By using the proposed algorithms, one can easily implement the overall recognition process in real-time applications.     

Digital Double-pulsed Holographic Interferometry for Vibration Analysis

Abstract

In this paper we describe a digital double-pulsed holographic system. Two separate holograms of an object under test are recorded within a few microseconds using a charge-coupled device camera and stored in a frame grabber. The holograms are digitally reconstructed using a computer, by simulation of the Fresnel diffraction of the hologram illuminated by the reference wave. The phases of the two reconstructed wave fields are calculated from the complex amplitude and the deformation is obtained from the phase difference. Experimental results are presented.