| Digital holography uses charge coupled devices (CCD) and other photoelectric recorder instead of traditional holographic recording material to record holograms in the digital way. The original object light wave can then be reconstructed through data processing with corresponding algorithms. It is easy to achieve the digitization of the process of hologram recording, storage, management and reconstruction, and has wide application prospect on optical imaging and display, optical measurement and testing as well as information security. And the digital holography now is one of the research hotspot in information optics and related aera. Similar with optical holography, the digital holography can be divided into in-line and off-axis digital holography based on the whether the object wave and reference wave are coaxial. Only if the resolution of the recording device is high enough and the angle between object wave and reference wave meets certain condition, off-axis digital holography can achieve the spatial sparation of the zero term, conjugate image and object image, and eliminates the zero term and conjugate image with the Fourier transform frequency spectrum filtering method to reconstructed object wave, thus reconstructing the object wave. The advantage of off-axis digital holography lies in that only one interferogram is needed to achieve the reconstruction. However, limited by the poor resolution of current photoelectric recording device, the angle between object wave and reference wave can not be too large, leading to the field of view and resolution limitation of off-axis digital holography. Compared with off-axis digital holography, in-line digital holography reduces the requirement on the resolution of area array photoelectric device. It can make full use of the space bandwidth of area array photoelectric device, and has a relative large field of view and spatial resolution. However, as the same with in-line optical holography, the digital holography needs to solve the problem of the reconstructed object wave, the zero term and conjugate image. How to eliminate or decrease the effect of zero term and conjugate image on reconstructed object wave becomes one of the research hotspot in digital holography field. Then phase-shifting interferometry (PSI) becomes the most typical one which combines the phase-shifting technique with digital holography.PSI is a technique measuring wavefront phase which could obtain the phase distribution of the tested object wave from the related interferograms. The tested object wave phase contains lots of useful information, when it is obtained, several kinds of measurement can be achieved. PSI has high measurement accuracy, and is an important technique in optical interference precision measurement; therefore, it has extensive use in optical measurement and testing field. However, traditional PSI requires special phase shifts or equal value which needs to demarcate the phase shifter accurately. To overcome these disadvantages, researchers proposed various PSI algorithms and error amending algorithms. In addition, to enlarge its range of application, generalized phase-shifting interferometry (GPSI) is proposed. It does not need to preset phase shifts but extract them from interferograms, and then reconstruct the object wave with corresponding formula. These phase shifts can be arbitrary unknown, and can be unequal. So, GPSI decreased the demand on the phase shifter calibration and decreased the environmental effect, increase its error immunity and convenience, thus enlarging the application range of GPSI and reducing the cost.To eliminate zero term and conjugate wave and increase the imaging and measuring accuracy, researchers introduced the PSI and GPSI to digital holography. Generalized phase-shifting digital holography is the combination of GPSI and digital holography which has the advantages of both of them, and has a bright future.Although GPSI does not need to preset and accurately control the phase shifts, it needs to extract phase shifts from interferograms with corresponding algorithms, and then reconstruct the object wave with the extracted phase shifts with corresponding reconstructing algorithms. Firstly, the phase-shift accuracy will affects the reconstructed object wave accuracy, and finally affects the result accuracy. So, proposing new phase-shift extraction algorithm and improving its accuracy is the key of PSI, and is also one of the research hotspots and key points. Secondly, different phase-shift extraction algorithms have different principle and sensitivity to different errors, therefore, to evaluate whether certain algorithm can extract accurate phase shift, to consider its applied condition and to evaluate different algorithms have very important theory meanings and application values. In addition, researching on the application of PSI is becoming more and more attracting. So the above three points are the main task for this paper that is researching on proposing new algorithms, comparison and evaluation and application in PSI. The main content and innovation points are listed below:1. Phase-shift extraction and object wave reconstruction(1) We proposed an improved phase-shift extraction iterative algorithm in PSI, which use polarization phase shifter producing phase shift of π/2. Then π/2being the initial value, accurate phase shift can be obtained by iterative method (as close as the actual phase shift), at last, object wave is reconstructed with obtained phase shift. In spite of errors which make the actual phase shift deviates from π/2, the actual one must be around π/2, so using π/2as the initial value can reduce the iterative time. Computer simulation and optical experiment verified its feasibility and validity; compared with other method, it increases the computing accuracy, reduced iterative time and increase the computing speed.(2) We proposed a new phase-shift extraction and object wave reconstruction non-iterative algorithm in GPSI. In this algorithm, object with known phase distribution is used as reference, at the same time recording two groups of interferograms formed by standard object wave and reference wave as well as the tested object wave and reference wave. The two groups have the same phase shifts. Then least-square method is used to extract phase shifts from the interferogram corresponding to standard object, after that, the tested object wave can be reconstructed. This algorithm is suitable for equal to or more than two-step PSI, and is valid for phase-type and amplitude-type objects. Computer simulation demonstrates that the relative phase-shift errors are less than0.6%, and in this algorithm, phase shifts between0and π can be used. Computer simulation verified its feasibility and validity.2. Evaluation and comparison on phase-shift extraction algorithms in PSIWe proposed a quantitative evaluation and comparison method for GPSI algorithms based on detectable amount which could be implemented in both computer simulation and optical experiment. This method makes use of the recording and reconstruction principle of off-axis digital holography. Introducing PSI to off-axis digital holography and defining reconstruction signal-to-noise, we take it as the rule to evaluate and compare phase-shift extraction algorithms in PSI. The rationality of this method is demonstrated from the principle and the feasibility and validity is verified by experiment. Various error sources exist in phase-shifting digital holography and PSI measurement, choosing proper algorithm can obtain the most accurate result. Some of the proposed comparison methods can make the comparison only in computer simulation and some take the result obtained from certain algorithm as the rule, these methods can not confirm which GPSI algorithm can get the best result in current condition in practical application. The method proposed in this paper can not only make the comparison in computer simulation, but also can make it based on detectable amount in experiment which is very meaningful for choosing the best algorithm to avoid errors.3. Study on application generalized phase-shifting digital holographyOptical inhomogeneity and thickness variation are two important parameters for optical window, thin film, chip and crystal. In this paper a method to measure thickness variation and optical inhomogeneity based on dual-wavelength generalized phase-shifting photorefractive digital holography is proposed. In this method, we first discussed the relationship between optical inhomogeneity and wavelength based on Lorentz dispersion model and Lorentz-Lorenz equation, and get the conclusion that in certain wavelength range, the change of optical inhomogeneity corresponding to the wavelength change can be neglected. Then the simultaneous measurement of optical inhomogeneity and thickness variation is achieved with dual-wavelength and GPSI based on photorefractive holography structure. Compared with other methods, this method has no special requirement on the sample surfaces, doesn’t need additional operation as coating refractive index match liquid and doesn’t to adjust the sample during measurement process. Besides, thanks to the photorefractive holography interferometry, wavefront distortion caused by optical system can be compensated automatically. Computer simulation and optical experiment verified its feasibility and validity. |
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