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.     

Quantization noise and its reduction in lensless Fourier digital holography

Digital holography is an imaging technique that enables recovery of topographic 3D information about an object under investigation. In digital holography, an interference pattern is recorded on a digital camera. Therefore, quantization of the recorded hologram is an integral part of the imaging process. We study the influence of quantization error in the recorded holograms on the fidelity of both the intensity and phase of the reconstructed image. We limit our analysis to the case of lensless Fourier off-axis digital holograms. We derive a theoretical model to predict the effect of quantization noise and we validate this model using experimental results. Based on this, we also show how the resultant noise in the reconstructed image, as well as the speckle that is inherent in digital holography, can be conveniently suppressed by standard speckle reduction techniques. We show that high-quality images can be obtained from binary holograms when speckle reduction is performed.     

Simultaneous measurement of out-of-plane displacement and slope using a multiaperture DSPI system and fast Fourier transform

The simultaneous quantitative measurement of out-of-plane displacement and slope using the fast Fourier transform method with a single three-aperture digital speckle pattern interferometry (DSPI) arrangement is demonstrated. The method coherently combines two sheared object waves with a smooth reference wave at the CCD placed at the image plane of an imaging lens with a three-aperture mask placed in front of it. The apertures also introduce multiple spatial carrier fringes within the speckle. A fast Fourier transform of the image generates seven distinct diffraction halos in the spectrum. By selecting the appropriate halos, one can directly obtain two independent out-of-plane displacement phase maps and a slope phase map from the two speckle images, one before and the second after loading the object. It is also demonstrated that by subtracting the out-of-plane displacement phase maps one can generate the same slope phase map. Experimental results are presented for a circular diaphragm clamped along the edges and loaded at the center.     

Pulsed digital holography for deformation measurements on biological tissues

Digital holograms are recorded of biological tissues by use of a Q-switched double-pulsed ruby laser. An image-plane digital holography setup is used with a CCD camera for capturing two holograms with a short time separation (20-800 mus). Subtraction of the phase distribution in two digital holograms yield a fringe phase map that shows the change in deformation of the tissue surface between the recordings. Experiments are performed on tissue from a pig that was excited by a short-shock pulse and on a human hand that was excited by sinusoidal stimulation. Results when the object is imaged through an endoscope are also presented. The technique could be an approach for measuring parameters like elasticity on biological tissues.     

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.     

Parallel two-step phase-shifting digital holograph microscopy based on a grating pair

An optical configuration for parallel two-step phase-shifting digital holographic microscopy (DHM) based on a grating pair is proposed for the purpose of real-time phase microscopy. Orthogonally circularly polarized object and reference waves are diffracted twice by a pair of gratings, and two parallel copies for each beams come into being. Combined with polarization elements, parallel two-step phase-shifting holograms are obtained. Based on the proposed configuration, two schemes of DHM, i.e., slightly off-axis and on-axis DHM, have been implemented. The slightly off-axis DHM suppresses the dc term by subtracting the two phase-shifting holograms from each other, thus the requirement on the off-axis angle and sampling power of the CCD camera is reduced greatly. The on-axis DHM has the least requirement on the resolving power of the CCD camera, while it requires that the reference wave is premeasured and its intensity is no less than 2 times the maximal intensity of the object wave.     

Fourier-domain digital holographic optical coherence imaging of living tissue

Digital holographic optical coherence imaging is a full-frame coherence-gated imaging approach that uses a CCD camera to record and reconstruct digital holograms from living tissue. Recording digital holograms at the optical Fourier plane has advantages for diffuse targets compared with Fresnel off-axis digital holography. A digital hologram captured at the Fourier plane requires only a 2D fast Fourier transform for numerical reconstruction. We have applied this technique for the depth-resolved imaging of rat osteogenic tumor multicellular spheroids and acquired cross-section images of the anterior segment and the retinal region of a mouse eye. A penetration depth of 1.4 mm for the tumor spheroids was achieved.     

Phase evaluation and speckle averaging in pulsed television holography

Double-pulsed (image-plane) TV holograms of transient bending waves in plates are recorded on separate frames in a CCD camera. A small angular offset between the reference and object beams, giving a spatial-frequency bias to the recorded pattern, permits quantitative evaluation of the phase of the interference. The Fourier spectrum of the image exhibits distinct parts that can be filtered out and inverse transformed to yield the phase information. Three different apertures of the imaging system are tested: a single slit, a double slit, and a three-hole aperture. Spatial speckle averaging is possible in the cases of the double-slit and three-hole apertures.     

High-speed digital holographic interferometry for vibration measurement

A system based on digital holographic interferometry for the measurement of vibrations is presented. A high-power continuous laser (10 W) and a high-speed CCD camera are used. Hundreds of holograms of an object that has been subjected to dynamic deformation are recorded. The acquisition speed and the time of exposure of the detector are determined by the vibration frequency. Two methods are presented for triggering the camera in order to acquire at a given phase of the vibration. The phase of the wavefront is calculated from the recorded holograms by use of a two-dimensional digital Fourier-transform method. The deformation of the object is obtained from the phase. By combination of the deformations recorded at different times it is possible to reconstruct the vibration of the object.     

Polarization imaging by use of digital holography

We present what we believe to be a new digital holographic imaging method that is able to determine simultaneously the distributions of intensity, phase, and polarization state at the surface of a specimen on the basis of a single image acquisition. Two reference waves with orthogonal polarization states interfere with the object wave to create a hologram that is recorded on a CCD camera. Two wave fronts, one for each perpendicular polarization state, are numerically reconstructed in intensity and phase. Combining the intensity and the phase distributions of these two wave fronts permits the determination of all the components of the Jones vector of the object-wave front. We show that this method can be used to image and measure the distribution of the polarization state at the surface of a specimen, and the obtained results indicate that precise quantitative measurements of the polarization state can be achieved. An application of the method to image the birefringence of a stressed polymethyl methacrylate sample is presented.     

Digital-holographic interferometry with an image-intensifier system

A method for recording digital holograms on an image intensifier coupled with a CCD sensor is presented. The advantage of the image intensifier is that it can be gated (electronic shutter action produced by controlling of the image intensifier's photocathode voltage). This allows us to record holograms with a short exposure time. Two holograms of an object submitted to dynamical displacements (e.g., vibrations) are recorded by two short exposures. The phase of the wave front recorded at different times is calculated from the recorded intensity by use of a digital Fourier-transform method. By comparison of the phases recorded it is possible to get the displacement of the object during a short interval. Experimental results are presented, and the problems related to the noise and to the spatial resolution are discussed.     

Phase-error correction in digital holography

The quality of images computed from digital holograms or heterodyne array imaging is degraded by phase errors in the object and/or reference beams at the time of measurement. This paper describes computer simulations used to compare the performance of digital shearing laser interferometry and various sharpness metrics for the correction of such phase errors when imaging a diffuse object. These algorithms are intended for scenarios in which multiple holograms can be recorded with independent object speckle realizations and a static phase error. Algorithm performance is explored as a function of the number of available speckle realizations and signal-to-noise ratio (SNR). The performance of various sharpness metrics is examined in detail and is shown to vary widely. Under ideal conditions with >15 speckle realizations and high SNR, phase corrections better than lambda/50 root-mean-square (RMS) were obtained. Corrections better than lambda/10 RMS were obtained in the high SNR regime with as few as two speckle realizations and at object beam signal levels as low as 2.5 photons/speckle with six speckle realizations.     

Pulsed digital holographic interferometry for dynamic measurement of rotating objects with an optical derotator

A method for measuring dynamic deformations of rotating objects with pulsed digital holography is described. An optical derotator is used to compensate for the rotation. A CCD camera is used to record two holograms with a short time separation (20 mus). Results of deformations between the recordings are obtained after subtraction of the phase distribution between the two digital holograms. Fringe phase maps of the phase subtraction of two holograms compensated by the derotator and recorded with a Q-switched double-pulsed ruby laser are presented. A flat disk and the blades of a fan were investigated. We used an optical arrangement that allowed us to improve laser illumination and energy efficiency. Experimental results on quantitative evaluation of dynamical out-of-plane deformations are presented.     

Miniaturized digital holography sensor for distal three-dimensional endoscopy

A miniaturized sensor head for endoscopic measurements based on digital holography is described. The system was developed to measure the shape and the three-dimensional deformation of objects located at places to which there is no access by common measurement systems. A miniaturized optical sensor, including a complete digital holographic interferometer with a CCD camera, is placed at the end of a flexible endoscope. The diameter of the head is smaller than 10 mm. The system enables interferometric measurements to be made at speeds of as many as five reconstructions per second, and it can be used outside the laboratory under normal environmental conditions. Shape measurements are performed with two wavelengths for contouring, and the deformation is measured by digital holographic interferometry. To obtain full three-dimensional data in displacement measurements we illuminate the object sequentially from three different illumination directions. To increase the lateral resolution we use temporal phase shifting.     

Pulsed digital holographic interferometry with 694- and 347-nm wavelengths

A method for deformation analysis and shape measurement based on digital holography is presented. Two wavelengths, 694 and 347 nm, are used. The object is illuminated with the two wavelengths at the same time, and digital holograms are recorded on a CCD chip. The information corresponding to the two wavelengths is separated in the Fourier domain, and the phase corresponding to the wave fronts is calculated. By recording holograms with two different wavelengths at the same time, we can get measurements of deformations or shape with different sensitivities. Experimental results are presented.     

Quantitative phase microscopy using dual-plane in-line digital holography

We present detailed theoretical evaluation and thorough experimental investigation of quantitative phase imaging using our previously demonstrated dual-plane in-line digital holographic microscopy technique [Opt. Lett. 35, 3426 (2010)]. This evaluation is based on the recording of two interferograms at slightly different planes and numerically reconstructing the object information. The zero-order diffracted wave is eliminated by using the method of subtraction of average intensity of the entire hologram, and the twin-image diffracted wave is removed by Fourier domain processing of the two recorded holograms. Experiments are performed using controlled amplitude and phase objects and human muscle cells to demonstrate the potential of this technique.     

Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement

Abstract

Measurement of in-plane displacements of a diffuse object by observing the temporal fluctuation of the speckle pattern in a dual-beam illumination speckle interferometer is illustrated. To conceive the temporal changes the object is displaced in its plane continuously. A high-speed camera is used to acquire a number of frames of the image of the object motion sequentially. Through Fourier transformation and inverse Fourier transformation of the frames stacked together, the total phase is determined. Finally, the magnitude of the in-plane displacement of the object motion is extracted. The range of displacement that can be measured using this novel method lies between few microns and over 100 μm on the upper end. Theory together with experimental results are presented in this paper.     

Phase-shifting digital holography with a phase difference between orthogonal polarizations

Phase-shifting digital holography with a phase difference between orthogonal polarizations is proposed. The use of orthogonal polarizations can make it possible to record two phase-shifted holograms simultaneously. By combining the holograms with the distributions of a reference wave and an object wave, the complex field of the object's wavefront can be obtained. Preliminary experimental results are shown to confirm the proposed method.     

Comparative study of various endoscopes for pulsed digital holographic interferometry

A comparison of several endoscopes as object image carriers in pulsed digital holography is presented. Three multicore flexible fiber endoscopes of different spatial resolution and one rigid endoscope are investigated. The four endoscopes are integrated in a setup for the recording of digital holograms on a CCD camera. A double-pulsed ruby laser is used as the light source. A spatial carrier is introduced by an off-axis reference beam, which permits quantitative evaluation of the phase difference between two holograms recorded with a short time separation (5-600 micros). From reported studies it may be inferred that the quality of the phase maps so derived from digital holographic interferometry has a strong correlation to the spatial resolution of the multicore fiber used in these endoscopes. With the endoscopic technique combined with pulsed digital holography a number of useful applications (in areas such as medical endoscopy, micromechanics, and microelectronics) are envisaged for which access to the objects of interest is otherwise difficult.     

Time Resolved Digital Holographic Interferometry for Investigations of Dynamical Events in Mechanical Components and Biological Tissues

Abstract:  In the first part (section 2) of the paper, a system based on digital holographic interferometry for the measurement of vibrations is presented. A high-power continuous laser (10 W) and a high-speed charge coupled device camera are used. Hundreds of holograms of an object that was subjected to dynamic deformation are recorded. The phase of the wave front is calculated from the recorded holograms by use of a two-dimensional digital Fourier-transform method. The deformation of the object is obtained from the phase. By combination of the deformations recorded at different time it is possible to reconstruct the vibration of the object. In the second part (section 3) of our paper, the holographic method is used for the measurements of the elastic properties of the bone. Samples of bone were loaded and deformed and a large number of interferograms (digital holograms) were recorded over a short period of time. In the third part (section 4) of the paper, we show how the holographic systems are adapted for performing measurements in hidden cavities.