Improved-resolution digital holography using the generalized sampling theorem for locally band-limited fields

We describe the recording conditions that, together with the appropriate numerical reconstruction process, permit high-lateral-resolution reconstruction of in-line digital holograms. By high resolution, we mean a resolution that is beyond the Nyquist frequency, which is achieved by common methods. The proposed method is based on a previously reported generalized sampling theory that presents the conditions to precisely reconstruct fields that in certain cases may be sampled with a sampling rate lower than the Nyquist rate. We examine the hologram-recording process in the Wigner space. On the basis of this analysis, we demonstrate a simple high-resolution numerical reconstruction method.     

Remote metrology by comparative digital holography

A method for the remote comparison of objects with regard to their shape or response to a load is presented. The method allows interferometric sensitivity for comparing objects with different microstructure. In contrast to the well-known incoherent techniques based on inverse fringe projection this new approach uses the coherent optical wave field of the master object as a mask for the illumination of the sample object. The coherent mask is created by digital holography to allow instant access to the complete optical information of the master object at any place desired. The mask is reconstructed by a spatial light modulator (SLM). The optical reconstruction of digital holograms with SLM technology allows modification of reconstructed wavefronts with respect to improvement of image quality, the skilled introduction of additional information about the object (augmented reality), and the alignment of the master and test 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.     

Simple method for direct determination of bending strains by use of digital holography

A computer-based technique is described for direct determination of bending strains in beam and plate structures. First a displacement-related phase-change map is constructed by digital holography and computer-vision techniques. Subsequently the computer generates an exact replica of the phase-change map, then overlays the two identical maps and, finally, rotates one of the maps through 180 degrees relative to the other in their planes about a point of interest. The local curvatures and the local twist of the bent surface at the point of interest are determined from the conic sections that are reconstructed from the algebraic sum of the phase changes at the vicinity of this point, thus permitting further calculation for determination of the local bending strains. When the need arises, bending moments and stresses may be determined concurrently. As the optical setup is simple, with computer-based data acquisition and processing, the entire system is user friendly, and rapid measurement is achieved.     

Light-in-flight digital holography display

We present a digital speckle-pattern interferometric setup that can be operated at TV frame rates (30 ms) to display the locus of the points at which the optical-path difference between the reference and object beams is within the coherence length. Experimental results are shown.     

Detection of surface strain by three-dimensional digital holography

Three-dimensional digital holography with three object-illuminating beams has been successfully used for the detection of surface strain in metallic objects. The optical setup that uses illuminating beams to irradiate the object from three directions means that all three object surface displacement components, x, y, and z, can be independently calculated and used to find the strain gradients on the surface. The results show the conversion of the complete surface displacement field into a surface strain field. The method is capable of measuring microstrains for out-of-plane surface displacements of less than 10 microm.     

Pulsed digital holography for high-speed contouring that uses a two-wavelength method

A two-wavelength method for a fast shape measurement by use of a pulsed ruby laser is presented. The wavelength change is produced by alteration of the distance between the plates of the laser's output etalon. One plate of the etalon is mounted on a vibrating piezoelectric element; this allows a fast wavelength change. Two holograms at different wavelengths are recorded in a few microseconds by use of a CCD. The holograms are reconstructed digitally, and the wave-front phase is calculated. The shape is obtained by subtraction of the phases of the wave fronts recorded at different wavelengths. Environmental disturbances at low frequencies, such as air turbulence, vibrations, and object drift, have no influence on the measurement. Experimental results are presented.     

Parallel three-step phase-shifting digital holography

We propose parallel three-step phase-shifting digital holography as a technique capable of noiseless instantaneous measurement of three-dimensional objects based on phase-shifting interferometry. The proposed digital holography carries out three-step phase shifting at the same time by using a phase-shifting array device located in the reference beam. The array device has a periodic three-step phase distribution, and its configuration is simplified compared with that required for conventional parallel phase-shifting digital holography. Therefore the optical system of the proposed parallel phase-shifting digital holography is more suitable for the realization of the proposed holography. We conduct both a numerical simulation and a preliminary experiment. The results of the simulation and experiment agree well with those of the conventional phase-shifting method and are superior to the results obtained by conventional digital holography by using the Fresnel transform alone. Thus the effectiveness of the proposed technique is verified.     

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.     

Parallel two-step phase-shifting digital holography

We propose a parallel two-step phase-shifting digital holography technique capable of instantaneous measurement of three-dimensional objects, with a view toward measurement of dynamically moving objects. The technique is based on phase-shifting interferometry. The proposed technique carries out the two-step phase-shifting method at one time and can be optically implemented by using a phase-shifting array device located in the reference beam. The array device has a periodic two-step phase distribution, and its configuration is simplified compared with that required for three-step and four-step parallel phase-shifting digital holographies. Therefore the optical system of the proposed technique is more suitable for the realization of a parallel phase-shifting digital holography system. We conduct both a numerical simulation and a preliminary experiment in the proposed technique. The results of the simulation and the experiment agree well with those of sequential phase-shifting digital holography, and results are superior to those obtained by conventional digital holography using the Fresnel transform alone. Thus the effectiveness of the proposed technique is verified.     

数字同轴和数字离轴全息系统分析

利用最高空间频率分析法,通过逐点分析记录在 CCD 上的空间频率信息,研究了物体可允许记录的最大横向尺寸、最小记录距离、全息图的信息量、空间分辨力、再现像的横向分辨力、轴向分辨力及散斑大小,并得到了数学表达式。理论分析和实验结果表明,数字同轴全息系统放宽了对 CCD 分辨力的要求,有较高的分辨力,较低的散斑噪声、灵活、简单的系统结构及较高的 CCD 空间带宽利用率,在增强系统性能方面要优于数字离轴全息系统。这一研究为数字全息系统的设计和操作提供了一定的理论和实验指导。     

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.     

Encrypting three-dimensional information with digital holography

A method for optical encryption of three-dimensional (3D) information by use of digital holography is presented. A phase-shifting interferometer records the phase and amplitude information generated by a 3D object at a plane located in the Fresnel diffraction region with an intensity-recording device. Encryption is performed optically by use of the Fresnel diffraction pattern of a random phase code. Images of the 3D object with different perspectives and focused at different planes can be generated digital or optically after decryption with the proper key. Experimental results are presented.     

Full-field vibrometry with digital Fresnel holography

A setup that permits full-field vibration amplitude and phase retrieval with digital Fresnel holography is presented. Full reconstruction of the vibration is achieved with a three-step stroboscopic holographic recording, and an extraction algorithm is proposed. The finite temporal width of the illuminating light is considered in an investigation of the distortion of the measured amplitude and phase. In particular, a theoretical analysis is proposed and compared with numerical simulations that show good agreement. Experimental results are presented for a loudspeaker under sinusoidal excitation; the mean quadratic velocity extracted from amplitude evaluation under two different measuring conditions is presented. Comparison with time averaging validates the full-field vibrometer.     

Simultaneous two-wavelength Doppler phase-shifting digital holography

This paper presents a method based on the use of an image sensor for obtaining the complex amplitudes of beams diffracted from an object at two different wavelengths. The complex amplitude for each wavelength is extracted by the Doppler phase-shifting method. The principle underlying the proposed method is experimentally verified by using the method with two lasers having different wavelengths to measure the surface shape of a concave mirror.     

Digital holography using a digital photo-camera

The possibilities of running digital holography using commonly available digital zoom photo-cameras are studied. A new modified method of the holographic set-up exploiting the properties of a photo-camera is suggested. This method offers a straightforward and simple way of both digital hologram recording and reconstructing. In order to verify the feasibility of the method, the holograms acquired are digitally reconstructed using a computer code based on the fast Fourier transform algorithm. Experimental results obtained are presented and discussed.     

Penalized-likelihood image reconstruction for digital holography

Conventional numerical reconstruction for digital holography using a filter applied in the spatial-frequency domain to extract the primary image may yield suboptimal image quality because of the loss in high-frequency components and interference from other undesirable terms of a hologram. We propose a new numerical reconstruction approach using a statistical technique. This approach reconstructs the complex field of the object from the real-valued hologram intensity data. Because holographic image reconstruction is an ill-posed problem, our statistical technique is based on penalized-likelihood estimation. We develop a Poisson statistical model for this problem and derive an optimization transfer algorithm that monotonically decreases the cost function at each iteration. Simulation results show that our statistical technique has the potential to improve image quality in digital holography relative to conventional reconstruction techniques.     

Exact complex-wave reconstruction in digital holography

We address the problem of exact complex-wave reconstruction in digital holography. We show that, by confining the object-wave modulation to one quadrant of the frequency domain, and by maintaining a reference-wave intensity higher than that of the object, one can achieve exact complex-wave reconstruction in the absence of noise. A feature of the proposed technique is that the zero-order artifact, which is commonly encountered in hologram reconstruction, can be completely suppressed in the absence of noise. The technique is noniterative and nonlinear. We also establish a connection between the reconstruction technique and homomorphic signal processing, which enables an interpretation of the technique from the perspective of deconvolution. Another key contribution of this paper is a direct link between the reconstruction technique and the two-dimensional Hilbert transform formalism proposed by Hahn. We show that this connection leads to explicit Hilbert transform relations between the magnitude and phase of the complex wave encoded in the hologram. We also provide results on simulated as well as experimental data to validate the accuracy of the reconstruction technique.     

Coal powder measurement by digital holography with expanded measurement area

The field of view of digital in-line holography for flow field diagnostics is restricted to a small volume due to the finite size and the low spatial resolution of the available CCD. Expansion of the measurement cross section of digital holographic particle image velocimetry was investigated with a lens-based holography configuration. By sampling the chirp signal in the center lobe completely and undersampling the chirp signal in the second- and higher-order lobes by a magnified virtual recording plane produced by an imaging camera lens, the field of view is expanded. Simulation results show that the three-dimensional (3D) location and size of the relatively large particle can be reconstructed with good accuracy. A digital holographic particle image velocimetry system was established for coal particle flow field diagnostics. Compared with the lensless configuration, the field of view of the digital holography system was enlarged 1.9 times, up to 2.78 cm × 2.78 cm × 3 cm. The 3D location, size distribution, and the 3D vector field of coal powder were obtained. The results show that the application of digital in-line holography to measure large particle flow field is feasible.