Real-time three-dimensional object reconstruction by use of a phase-encoded digital hologram

A three-dimensional (3D) object reconstruction technique that uses only phase information of a phase-shifting digital hologram and a phase-only spatial-light modulator is proposed. It is well known that a digital hologram can store both amplitude and phase information of an optical electric field and can reconstruct the original 3D object in a computer. We demonstrate that it is possible to reconstruct optically 3D objects using only phase information of the optical field calculated from phase-shifting digital holograms. The use of phase-only information enables us to reduce the amount of data in the digital hologram and reconstruct optically the 3D objects using a liquid-crystal spatial light modulator without optical power loss. Numerical evaluation of the reconstructed 3D object is presented.     

Compression of digital holograms for three-dimensional object reconstruction and recognition

We present the results of applying lossless and lossy data compression to a three-dimensional object reconstruction and recognition technique based on phase-shift digital holography. We find that the best lossless (Lempel-Ziv, Lempel-Ziv-Welch, Huffman, Burrows-Wheeler) compression rates can be expected when the digital hologram is stored in an intermediate coding of separate data streams for real and imaginary components. The lossy techniques are based on subsampling, quantization, and discrete Fourier transformation. For various degrees of speckle reduction, we quantify the number of Fourier coefficients that can be removed from the hologram domain, and the lowest level of quantization achievable, without incurring significant loss in correlation performance or significant error in the reconstructed object domain.     

Distortion-tolerant three-dimensional object recognition with digital holography

We present a technique to implement three-dimensional (3-D) object recognition based on phase-shift digital holography. We use a nonlinear composite correlation filter to achieve distortion tolerance. We take advantage of the properties of holograms to make the composite filter by using one single hologram. Experiments are presented to illustrate the recognition of a 3-D object in the presence of out-of-plane rotation and longitudinal shift along the z axis.     

Recognition and classification of three-dimensional phase objects by digital Fresnel holography

We demonstrate the validity of wavelet-based processing for recognition and classification of three-dimensional phase objects. One Fresnel digital hologram of each of the three-dimensional (3-D) phase objects to be classified is recorded. The electronic holograms are processed digitally to permit 3-D object information to be retrieved as two-dimensional digital complex images. We use a Mexican-hat wavelet- matched filter (WMF) to enhance the correlation peak and discriminate between the objects. The WMF performs a wavelet transform (WT) to enhance the significant features of the images and the correlation of the WT coefficients thus obtained. We compare the feasibility of a WMF-based object classifier with the matched-filter-based classifier to classify our four 3-D phase objects in a 3-D scene into true or false classes with minimal error.     

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.     

Secure three-dimensional data transmission and display

An optical three-dimensional (3D) display system interfaced with digital data transmission is proposed. In this system, an original 3D object is encrypted by use of a random phase mask and then the encrypted pattern is recorded as a digital hologram. The digital hologram key is also recorded for optical decryption. Both the encrypted digital hologram and the digital hologram key are transmitted to a receiver through a conventional communication data channel. At the receiver, the 3D scene is reconstructed and displayed optically in a retrieval system based on a joint-transform correlation. Experimental results are presented. We investigate the influence of quantization of the joint power spectrum in the optical correlator on the quality of the reconstructed image.     

Three-dimensional angle measurement based on propagation vector analysis of digital holography

We propose what we believe to be a novel method for highly accurate three-dimensional (3D) angle measurement based on propagation vector analysis of digital holography. Three-dimensional rotations in space can be achieved by use of a CCD camera and a multifacet object, which reflects an incident wave into different directions. The propagation vectors of the reflected waves from the object can be extracted by analyzing the object spectrum of the recorded hologram. Any small rotation of the object will induce a change in the propagation vectors in space, which can then be used for 3D angle measurement. Experimental results are presented to verify the idea.     

Comparison of passive ranging integral imaging and active imaging digital holography for three-dimensional object recognition

We present an overview of three-dimensional (3D) object recognition techniques that use active sensing by interferometric imaging (digital holography) and passive sensing by integral imaging. We describe how each technique can be used to retrieve the depth information of a 3D scene and how this information can then be used for 3D object recognition. We explore various algorithms for 3D recognition such as nonlinear correlation and target distortion tolerance. We also provide a comparison of the advantages and disadvantages of the two techniques.     

Three-dimensional identification of stem cells by computational holographic imaging.

We present an optical imaging system and mathematical algorithms for three-dimensional sensing and identification of stem cells. Data acquisition of stem cells is based on holographic microscopy in the Fresnel domain by illuminating the cells with a laser. In this technique, the holograms of stem cells are optically recorded with an image sensor array interfaced with a computer and three-dimensional images of the stem cells are reconstructed from the Gabor-filtered digital holograms. The Gabor wavelet transformation for feature extraction of the digital hologram is performed to improve the process of identification. The inverse Fresnel transformation of the Gabor-filtered digital hologram is performed to reconstruct the multi-scale three-dimensional images of the stem cells at different depths along the longitudinal direction. For recognition and classification of stem cells, a statistical approach using an empirical cumulative density function is introduced. The experiments indicate that the proposed system can be potentially useful for recognizing and classifying stem cells. To the best of our knowledge, this is the first report on using three-dimensional holographic microscopy for automated identification of stem cells.     

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.     

Object recognition using three-dimensional optical quasi-correlation

A novel method of three-dimensional (3-D) object recognition is proposed. Several projections of a 3-D target are recorded under white-light illumination and fused into a single complex two-dimensional function. After proper filtering, the resulting function is coded into a computer-generated hologram. When this hologram is coherently illuminated, a correlation space is reconstructed such that light peaks indicate the existence and locations of true targets in the observed 3-D scene. Experimental results and comparisons with results of another 3-D object recognition technique are presented.     

Three-dimensional matching by use of phase-only holographic information and the Wigner distribution

Matching of three-dimensional (3-D) objects is achieved by Wigner analysis of the correlation pattern between the phase-only holographic information of a reference object and that of a target object. First, holographic information on the reference object and on the target object is extracted by use of optical scanning holography as a form of electrical signal. This electrical information is then stored in a computer for digital processing. In the digital computer, the correlation between the phase-only information of the hologram of the reference object and that of the target object is calculated and analyzed by use of a Wigner distribution. The Wigner distribution yields a space-frequency map of the correlation pattern that indicates whether the 3-D image of the target object matches that of the reference object. When the 3-D image of the target object matches that of the reference object, the Wigner distribution gives a well-defined line that directly indicates the 3-D location of the matched target object. Optical experiments with digital processing are described to demonstrate the proposed matching technique.     

Quantitative space-bandwidth product analysis in digital holography

The space-bandwidth product (SBP) is a measure for the information capacity an optical system possesses. The two information processing steps in digital holography, recording, and reconstruction are analyzed with respect to the SBP. The recording setups for a Fresnel hologram, Fourier hologram, and image-plane hologram, which represent the most commonly used setup configurations in digital holography, are investigated. For the recording process, the required SBP to ensure the recording of the entire object information is calculated. This is accomplished by analyzing the recorded interference pattern in the hologram-plane. The paraxial diffraction model is used in order to simulate the light propagation from the object to hologram-plane. The SBP in the reconstruction process is represented by the product of the reconstructed field-of-view and spatial frequency bandwidth. The outcome of this analysis results in the best SBP adapted digital holographic setup.     

Three-dimensional Displacement Analysis by Windowed Phase-shifting Digital Holographic Interferometry

Abstract:  Phase-shifting digital holography is a new method for measuring the displacement distribution on the surface of an object. The authors previously proposed a windowed phase-shifting digital holographic interferometry (windowed PSDHI). This method provides accurate displacement distributions by decreasing the effect of speckle patterns. In this study, the method is extended to analyse three-dimensional displacement components in a microscope. Three object laser beams in the optical system are used. Four phase-shifted holograms are recorded for each object laser beam. The complex amplitude of each reconstructed light at the object is calculated by the Fresnel diffraction integral of the complex amplitude of the hologram. The reconstructed distance is obtained at the point with the maximum of the standard deviation of the intensities of the object reconstructed with changing the reconstruction distance. The three phase-difference values between before and after deformation provide the three-dimensional displacement components. Theoretical treatment and experimental results of three-dimensional displacement measurement using this method are shown.     

Shift-invariant three-dimensional object recognition by means of digital holography

We present an optoelectronic method to analyze three-dimensional (3D) scenes that is able to detect the presence, and also the position and orientation, of a reference 3D object. The data-acquisition procedure is based on digital holography. A phase-shifting interferometer records a single digital Fresnel hologram of the 3D scene with an intensity-recording device. Holographic information of the 3D reference object is also obtained with the same method. Correlation techniques are then applied to recognize the presence and position of the 3D reference object in the 3D scene. The technique also allows us to detect the 3D reference with a small out-of-plane rotation. Preliminary experimental results are presented that demonstrate the theory.     

Optical image recognition of three-dimensional objects

A three-dimensional (3-D) optical image-recognition technique is proposed and studied. The proposed technique is based on two-pupil optical heterodyne scanning and is capable of performing 3-D image recognition. A hologram of the 3-D reference object is first created and then is used to modulate spatially one of the pupils of the optical system; the other pupil is a point source. A 3-D target object to be recognized is then scanned in two dimensions by optical beams modulated by the two pupils. The result of the two-dimensional scan pattern effectively displays the correlation of the holographic information of the 3-D reference object and that of the 3-D target object. A strong correlation peak results if the two pieces of the holographic information are matched. We analyze the proposed technique and thereby lay a theoretical foundation for optical implementations of the idea. Finally, computer simulations are performed to verify the proposed idea.     

Three-dimensional object feature extraction and classification with computational holographic imaging

We address three-dimensional (3D) object classification with computational holographic imaging. A 3D object can be reconstructed at different planes by use of a single hologram. We apply principal component and Fisher linear discriminant analyses based on Gabor-wavelet feature vectors to classify 3D objects measured by digital interferometry. Experimental and simulation results are presented for regional filtering concentrated at specific positions and for overall grid filtering. The proposed technique substantially reduces the dimensionality of the 3D classification problem. To the best of our knowledge, this is the first report on the use of the proposed technique for 3D object classification.     

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 depth determination of multiple objects by focus analysis in digital holography

Focus analysis techniques from computer vision are applied to digital holography to determine the depth (range) of multiple objects and their surfaces from a single hologram capture. With this method the depths of objects can be determined from a single hologram capture without the need for manual focusing and without prior information on object location. Variance and the Laplacian of Gaussian are analyzed as focus measures, and techniques are proposed for focus plane determination from the focus measure curves. The algorithm is described in detail and demonstrated through simulation and optical experiment.     

Iterative algorithm with a constraint condition for numerical reconstruction of a three-dimensional object from its hologram

A novel method to obtain the three-dimensional mathematical model of a transparent object from its hologram is presented. The proposed method can numerically extract the object information from the fringe pattern of the hologram. Then an iterative algorithm is used to imitate an imaging system by focusing on different layers of the object; and by operating in both the spatial domain and the frequency domain, the algorithm produces a series of two-dimensional layer images. The object is finally reconstructed layer by layer. A constraint condition should be satisfied, and the noise distribution can be rearranged in different reconstruction cycles so as to get better reconstruction quality. Numerical simulations have proved the effectiveness of the proposed method.