CHAPTER ONE INTRODUCTION CHAPTER ONE INTRODUCTION 1.1 Optical techniques In the last several decades, the drive for higher performance and reliability of devices, structures and processes in various engineering fields has pushed the rapid development of advanced testing methods. Among these methods, optical technique is one of the most important methods in many practical applications, such as optical metrology, microscopy, biology and encryption. Obvious advantages of optical techniques over other techniques (such as a mechanical sensor) are non-contact and full-field measurements. Optical techniques can be mainly divided into two types, i.e., incoherent method and coherent method. Incoherent method makes use of the geometrical features of light beams, and typical incoherent methods are moiré, digital image correlation and fringe projection. Moiré technique is a versatile set of techniques for in-plane and out-of-plane deformation measurement, topographic contouring, and slope and curvature measurement (Asundi, 2002). Moiré technique was proposed by Meadows et al. (1970) and Takasaki (1970). The basis for moiré technique is the grating, and moiré technique can be mainly divided into shadow moiré and projection moiré according to the optical arrangement system. Digital image correlation (Chu et al., 1986) is another typical incoherent method, which is a relatively simple technique for optical metrology. This technique uses a measurement system which contains one or two digital cameras to capture an CHAPTER ONE INTRODUCTION object surface image before and after the deformation. Digital image correlation can directly provide the full-field displacement of object surface to sub-pixel accuracy, and strain distribution can be calculated directly or calculated by further processing of the displacement distribution. Digital image correlation technique has been widely applied to experimental mechanics due to its advantageous features of simple experimental setup, high measurement resolution and low requirement on the measurement environment (Hild and Roux, 2006; Pan et al., 2009a, 2009b). Fringe projection technique (Rowe and Welford, 1967) is another incoherent technique which was proposed to achieve a rapid, non-contact and full-field assessment of an object surface profile. Before the advent of digital fringe projector, gratings usually served as the source of fringe patterns. Takeda and Mutoh (1983) proposed Fourier transform algorithm for a fringe pattern with a spatial carrier to extract phase data from a square wave fringe pattern. With the advent of digital fringe projector, the intensity and grating pitch can be numerically modified without changing the physical setup. Digital fringe projection technique has been applied for the object surface profilometry in many previous studies (Fang and Zheng, 1997; Chen et al., 2005). The second type of optical technique is the coherent method, which is based on the physical properties of light wave such as interference and diffraction. Typical coherent methods are electronic speckle pattern interferometry (ESPI), shearography and holography. The ESPI (Lokberg, 1980; Rastogi, 2001; Federico and Kaufmann, 2002a; Fu et al., 2004) is a coherent method to measure optical path changes caused by the deformation of an opaque object or refractive index variations within transparent media. The ESPI is a non-destructive and whole-field technique for high-resolution CHAPTER ONE INTRODUCTION static and dynamic measurements. In ESPI, Fourier transform approach and phaseshifting technique are usually applied to retrieve the phase maps from the recorded speckle patterns. Shearography (Hung and Liang, 1979; Hung, 1997) is a laser optical method originally developed for the strain distribution measurement. Conventional shearographic technique employs photographic emulsion as a recording medium. Recently, digital shearography has been developed by using video recording, and is proven to be a practical non-destructive testing technique (Hung, 1997). Holography was observed by Gabor (1948), who invented holography in an attempt to solve the problem of the aberration of lens used in electron microscopy. In his experiment, an object was exposed to a radiation beam of strong coherence. The waves weakly scattered by the object interferes with the background wave on a photographic film to form an interference pattern. Gabor demonstrated how his experiment was possible to reconstruct the original test object by illuminating the recorded film with the original reference wave. However, the existence of twin-image and zero-order term has made the resolution of a reconstructed image quite low. Subsequently, the twin-image problem was solved by Leith and Upatnieks (1962, 1963), who developed an off-axis experimental setup. With this type of experimental setup, real image, twin-image and zero-order term can be sufficiently separated. With the advent of laser (Maiman, 1960) and couple-charged device (CCD), holographic technique (Schnars and Jüptner, 1994a; Schnars, 1994) has attracted much more attention from many research areas, such as biology (Marquet et al., 2005; Massatsch et al., 2005; Charrière et al., 2006). Some methods have been proposed to enhance the measurement capabilities of holographic technique, such as numerical reconstruction algorithms. In this thesis, holographic technique (i.e., digital holography) is CHAPTER ONE INTRODUCTION investigated, and more descriptions and reviews about this technique can be found in Section 1.2 and Chapter 2. 1.2 Digital holography Since conventional optical holography requires the use of photosensitive recording materials to record holograms, the reconstruction procedure contains tedious wetchemical processing which is costly and time-consuming. In addition, the reconstructed results are of low resolution. Goodman and Lawrence (1967) were the first to propose the idea of numerical reconstruction of a recorded hologram, and subsequently Kronrod et al. (1972) also conducted a numerical reconstruction. Onural and Scott (1987) and Onural and Ozgen (1992) improved the reconstruction algorithm and applied it to a particle measurement. With the advent of CCD and the development of computer techniques, digital holography has been rapidly developed. Digital holography records the whole field information of an object using an electronic device, and object reconstruction can be numerically carried out (Kreis, 2005; Schnars and Jueptner, 2005). Processing of holograms can be digitally realized without any intermediate photographic recordings, and some algorithms (Wagner et al., 1999; Cuche et al., 1999b; Grilli et al., 2001; Kreis, 2005) have been proposed for numerically reconstructing an object wave. Several types of holographic techniques, such as off-axis digital holography (Schnars and Jüptner, 1994a, 1994b, 2002) and phase-shifting digital holography (Creath, 1985; Yamaguchi and Zhang, 1997; Yamaguchi et al., 2003), have been developed. Off-axis digital holography is realized by a separated propagation direction between the reference wave and the object wave. However, this holographic CHAPTER ONE INTRODUCTION technique is limited by the low resolution of the existing CCD, so the size of a test object is limited. Phase-shifting digital holography can partially overcome the above problem by using several frames with a phase shift, and can also enhance the quality of reconstructed images (Yamaguchi and Zhang, 1997; Zhang and Yamaguchi, 1998; Yamaguchi et al., 2001). However, more experimental effort should be made, and the technique with a phase shift seems not to be promising in the investigation of a dynamic situation. Compared to other optical techniques mentioned in Section 1.1, digital holography possesses some distinctive features which are summarized as follows: (1) The reconstruction step can be numerically completed, and there is no need for any time-consuming wet-chemical processing; (2) numerical reconstruction can provide high flexibility for numerical focusing and phase aberration correction; (3) optical recording, numerical reconstruction, and phase evaluation can be integrated into one system; (4) both intensity and phase distributions can be extracted from the reconstructed complex amplitude; (5) high spatial and temporal resolution can be realized; (6) interference phase distributions are easily obtained by a digital phase subtraction method, which can avoid to process the intensity fringe pattern that is usually disturbed by noise. 1.3 Phase evaluation techniques In the optical field, it is important to extract a phase map from the recorded fringe pattern since the extracted phase map is directly related to the practical physical quantities. In the last several decades, many phase evaluation algorithms have been proposed. Among these algorithms, three prominent algorithms are Fourier transform CHAPTER ONE INTRODUCTION method with and without a carrier (Takeda et al., 1982; Takeda, 1990; Kreis, 1986), phase-shifting method (Creath, 1985; Yamaguchi and Zhang, 1997) and advanced fringe-pattern analysis methods (Mallat, 1999). Fourier transform method with a carrier was proposed by Takeda et al. (1982). The Fourier transform of a fringe pattern usually has two side lobes centered on the mean fringe frequency and one central lobe called zero-order term. After the processing in the frequency domain, the corresponding phase distribution is extracted by an arc-tangent operation, and the extracted phase distribution is modulo 2π . However, the resolution of this method is low due to the limited spectral area for the test object, and the accurate selection of the correct spectral area is difficult in practice. Kreis (1986) proposed a Fourier transform method without a spatial carrier. However, another intensity distribution was required to overcome the inherent sign-ambiguity problem. Moore and Santoyo (1995) proposed a spatial synchronous detection method for phase demodulation. This method has advantages of computational efficiency and low cost in real-time situations, but it is usually less accurate than the conventional Fourier transform method. Phase-shifting technique (Creath, 1985; Yamaguchi and Zhang, 1997; Micó et al., 2009) is another effective algorithm for phase extraction. In the phase-shifting method, a phase map is calculated by an evaluation of several phase-shifted intensities pixel by pixel. A commonly-used temporal phase retrieval approach is the N-frame phase shifting method, in which N is usually larger than 2. Many kinds of phaseshifting techniques have been proposed, such as three-frame phase shifting with a known phase shift, or with an unknown phase shift (Tay et al., 2005). Compared with Fourier transform method, phase-shifting technique can effectively enhance the spatial resolution but need more experimental effort. CHAPTER ONE INTRODUCTION Recently, some advanced analysis methods, such as continuous wavelet transform (CWT) and short-time Fourier transform (STFT) (Mallat, 1999; Watkins et al., 1999; Zhong and Weng, 2005; Qian, 2007; Fu et al., 2007a) have been proposed to process fringe patterns, and can be considered alternative approaches to conventional phase evaluation methods. In CWT and STFT, there are two main phase evaluation approaches, i.e., instantaneous frequency extraction and direct phase extraction. Instantaneous frequency extracted can be integrated to determine a continuous phase map without any phase unwrapping algorithm. However, compared with direct phase extraction method, instantaneous frequency extraction method will produce higher phase errors. In digital holography, there are three defined planes, i.e., object plane, hologram (or CCD) plane and image plane. The phase evaluation techniques mentioned above can be employed and carried out in the hologram plane (or image plane), and then a numerical reconstruction method, such as Fresnel Approximation method (Goodman, 1996) is further applied in order to extract the original complex amplitude in the object plane. Finally, a phase distribution is determined by an arctangent operation from the resultant complex amplitude. The extracted phase map can be further used to measure the practical physical quantities. More detailed descriptions and reviews about basic principles, numerical reconstruction and phase evaluation techniques in digital holography are presented in Chapter 2. 1.4 Scope and outline of thesis Although digital holographic technique has gained rapid development, there are still considerable concerns and challenges on the development of phase evaluation CHAPTER ONE INTRODUCTION techniques in digital holography to meet higher requirements for practical applications. The concerns and challenges are summarized as follows: (1) In the spatial domain, the quality of an extracted phase map is highly affected by speckle noise, so it is difficult to further measure high-quality higher-order displacement derivatives. In addition, a practical method has not been proposed to estimate a fringe density map which can guide the phase unwrapping procedure. (2) In the temporal domain, few studies have been carried out to evaluate the phase distributions from a series of holograms and analyze a dynamic procedure, especially for a detailed derivation of the extraction of instantaneous frequency and profiling of a discontinuous object. Another issue also in the temporal domain is that it is difficult to evaluate the influence of phase-shifting error and make a corresponding compensation in phase-shifting digital holography. (3) In some applications with digital holographic technique, many problems still exist, such as a small depth of focus. The objectives of this research work are to develop new spatial and temporal phase evaluation techniques in digital holography, and to overcome the existing problems in some applications with digital holographic technique. These objectives are summarized as follows: (1) In the spatial domain, a new method using the concept of complex phasor is proposed to determine the phase difference map. Not only the deformation distribution of a test object is obtained, but higher-order displacement derivatives, such as first-order and second-order displacement derivatives, are also determined. In addition, a new algorithm using an advanced analysis approach is proposed to effectively estimate a fringe density map which can greatly facilitate the subsequent phase unwrapping step. (2) In the temporal domain, an adaptive-window short-time Fourier transform is proposed to process a series of reconstructed phase images pixel by pixel. This method is used to study the continuous deformation of a CHAPTER ONE INTRODUCTION cantilever beam and profiling of an object with height steps. Furthermore, in the temporal domain, detection and compensation of phase-shifting errors in phaseshifting digital holography are also investigated. Several novel methods, such as spectral analysis, are proposed to detect the phase-shifting error and enhance the quality of reconstructed images. (3) In the applications with digital holographic technique, extended depth of focus for a particle field, complex-valued object reconstruction and optical image encryption are investigated. Several new methods are proposed to overcome the problems in these applications. A list of publications arising from this research work during the candidate’s Ph.D. period is included in Appendix B. The results presented in this thesis are mainly from these publications, but broader areas are discussed and general information in digital holography is also included. The research work in this thesis may contribute to a better understanding of digital holographic principles, and may also shed some light on the further development of digital holographic technique in the practical applications. The thesis consists of the following six chapters. In Chapter 1, a brief introduction of optical techniques (especially digital holography) and phase evaluation techniques is given. In addition, some challenges existing in digital holography are described, and the objectives and significance of this research work are also presented. In Chapter 2, a literature review is conducted with three parts. In the first part, basic principles in digital holography, i.e., wave theory of light, spatial and temporal coherence, interference, diffraction and speckle, are introduced. In the second part, optical holography and optical holographic interferometry are first described, and then digital holography and digital holographic interferometry are presented. Several commonly-used numerical reconstruction methods are also reviewed. In the last part, CHAPTER ONE INTRODUCTION different spatial and temporal phase evaluation techniques are reviewed, and a postprocessing with spatial and temporal phase unwrapping is described. In Chapter 3, the theories of the proposed spatial and temporal phase evaluation techniques are presented, and the proposed theories to address the existing challenges in some applications with digital holographic technique are also described. In Chapter 4, simulation and experimental work based on digital holography are presented, and the descriptions about equipment and specimens are also included. In Chapter 5, the results of the proposed spatial and temporal phase evaluation techniques are presented, and the results in the applications with digital holographic technique are also demonstrated. This chapter also contains three parts. In the first part, the results of the proposed spatial phase evaluation techniques are presented. In the second part, the results of the proposed temporal phase evaluation techniques are illustrated. In the last part, extended depth of focus for a particle field, complexvalued object reconstruction and optical image encryption are classified as the applications with digital holographic technique, and the corresponding results are demonstrated. In addition, the advantages, disadvantages and the accuracy of the proposed techniques are analyzed in detail within these three parts. In Chapter 6, this research work is concluded, and the research directions for the further study are recommended. 10 . types of holographic techniques, such as off-axis digital holography (Schnars and Jüptner, 19 94a, 19 94b, 2002) and phase- shifting digital holography (Creath, 19 85; Yamaguchi and Zhang, 19 97;. reviewed. In the last part, CHAPTER ONE INTRODUCTION 10 different spatial and temporal phase evaluation techniques are reviewed, and a post- processing with spatial and temporal phase unwrapping. also in the temporal domain is that it is difficult to evaluate the influence of phase- shifting error and make a corresponding compensation in phase- shifting digital holography. (3) In some