学号********** 昆明理工大学专业英语专业光学姓名辜苏导师李重光教授分数导师签字日期2015年5月6日研究生部专业英语考核In digital holography, the recording CCD is placed on the ξ-ηplane in order to register the hologramx ',y 'when the object lies inthe x-y plane. Forthe reconstruction ofthe information ofthe object wave,phase-shifting digital holography includes two steps:(1) getting objectwave on hologram plane, and (2) reconstructing original object wave.2.1 Getting information of object wave on hologram plateDoing phase shifting N-1 times and capturing N holograms. Supposing the interferogram after k- 1 times phase-shifting is]),(cos[),(),(),,(k k b a I δηξφηξηξδηξ-⋅+= （1） Phase detection can apply two kinds of algorithms:synchronous phase detection algorithms [9]and the least squares iterative algorithm [10]. The four-step algorithm in synchronous phase detection algorithm is in common use. The calculation equation is)2/3,,(),,()]2/,,()0,,([2/1),(πηξπηξπηξηξηξiI I iI I E --+=2.2 Reconstructing original object wave by reverse-transform algorithmObject wave from the original object spreads front.The processing has exact and clear description and expression in physics and mathematics. By phase-shifting technique, we have obtained information of the object wave spreading to a certain distance from the original object. Therefore, in order to get the information of the object wave at its initial spreading position, what we need to do is a reverse work.Fig.1 Geometric coordinate of digital holographyexact registering distance.The focusing functions normally applied can be divided into four types: gray and gradient function, frequency-domain function, informatics function and statistics function. Gray evaluation function is easy to calculate and also robust. It can satisfy the demand of common focusing precision. We apply the intensity sum of reconstruction image as the evaluation function:min ),(11==∑∑==M k Nl l k SThe calculation is described in Fig.2. The position occurring the turning point correspondes to the best registration distanced, also equals to the reconstructing distance d '.It should be indicated that if we only need to reconstruct the phase map of the object wave, the registration distance substituted into the calculation equation is permitted having a departure from its true value.4 Spatial resolution of digital holography4.1 Affecting factors of the spatial resolution of digital holographyIt should be considered in three respects: (1) sizes of the object and the registering material, and the direction of the reference beam, (2) resolution of the registering material, and (3) diffraction limitation.For pointx2on the object shown in Fig.3, the limits of spatial frequency are λξθλθθ⎥⎦⎤⎢⎣⎡⎪⎪⎭⎫ ⎝⎛-'-=-=-0211maxmax tan sin sin sin sin z x f R R Fig.2 Determining reconstructing distanceλξθλθθ⎥⎦⎤⎢⎣⎡⎪⎪⎭⎫ ⎝⎛-'-=-=-0211minmin tan sin sin sin sin z x f R R Frequency range isλξξ⎥⎦⎤⎢⎣⎡⎪⎪⎭⎫ ⎝⎛-'-⎥⎦⎤⎢⎣⎡⎪⎪⎭⎫ ⎝⎛-=∆--02110211tan sin tan sin z x z x f so the range is unrelated to the reference beam.Considering the resolution of registering material in order to satisfy the sampling theory, phase difference between adjacent points on the recording plate should be less than π, namely resolution of the registration material.c f f f =∆η21)(min max 4.2 Expanding the spatial resolution of reconstruction imageExpanding the spatial resolution can be realized at least in three ways: (1) Reducing the registration distance z 0 can improve the reconstruction resolution, but it goes with reduction of the reconstruction area at the same ratio.Therefore, this method has its limitation. (2) Increasing the resolution and the imaging size of CCD with expensive price. (3) Applying image-synthesizing technique [11]CCD captures a few of images between which there is small displacement (usually a fraction of the pixel size) vertical to the CCD plane, shown in Fig.4(Schematic of vertical moving is the same).This method has two disadvantages. First, it is unsuitable for dynamic testing and can only be applied in the static image reconstruction. Second, because the pixel size is small (usually 5μm to 10μm) and the displacement should a fraction of this size (for example 2μm), it needs a moving table with high resolution and precision. Also it needs high stability in whole testing.In general, improvement of the spatial resolution of digital reconstruction isFig.3 Relationship between object and CCDstill a big problem for the application of digital holography.Fig.4 Image capturing by moving CCD along horizontal direction5 Testing resultsFig.5 is the photo of the testing system. The paper does testing on two coins. The pixel size of the CCD is 4.65μm and there are 1 392×1 040 pixels. The firstis one Yuan coin of RMB (525 mm) used for image reconstruction by phase-shifting digital holography. The second is one Jiao coin of RMB (520 mm) for the testing of deformation measurement also by phase-shifting digital holography.Fig.5 Photo of the testing system5.1 Result of image reconstructionThe dimension of the one Yuancoin is 25 mm. The registrationdistance measured by ruler isabout 385mm. We capture ourphase-shifting holograms andreconstruct the image byphase-shifting digital holography.Fig.6 is the reconstructed image.Fig.7 is the curve of the auto-focusfunction, from which we determine the real registration distance 370 mm. We can also change the controlling precision, for example 5mm, 0.1 mm,etc., to get more course or precision reconstruction position.Fig.6 Reconstructed image Fig.7 Auto-focus function5.2 Deformation measurementIn digital holography, the method of measuring deformation measurement differs from the traditional holography. It gets object wave before and after deformation and then subtract their phases to obtain the deformation. The study tested effect of heating deformation on the coin of one Jiao. The results are shown in Fig.8, Where (a) is the interferential signal of the object waves before and after deformation, and (b) is the wrapped phase difference.Fig.8 Heating deformation results5.3 Improving the spatial resolutionFor the tested coin, we applied four sub-low-resolution holograms to reconstruct the high-resolution by the image-synthesizing technique. Fig.9 (a) is the reconstructed image by one low-resolution hologram, and (b) is the high-resolution image reconstructed from four low-resolution holograms.Fig.9 Comparing between the low and high resolution reconstructed image6 SummaryDigital holography can obtain phase and amplitude of the object wave at the same time. Compared to other techniques is a big advantage. Phase-shifting digital holography can realize image reconstruction and deformation with less noise. But it is unsuitable for dynamic testing. Applying the intensity sum of the reconstruction image as the auto-focusing function to evaluate the registering distance is easy, and computation is fast. Its precision is also sufficient. The image-synthesizing technique can improve spatial resolution of digital holography, but its static characteristic reduces its practicability. The limited dimension and too big pixel size are still the main obstacles for widely application of digital holography.外文文献译文：标题：图像重建中的相移数字全息摘要：相移数字全息术被用来研究研究艺术品的内部缺陷。