LUO Yong, LI Tuo, LI Gui-lin, SHI Yi-shi*

(1.School of Optoelectronics,University of Chinese Academy of Sciences,Beijing 100049,China； 2.Academy of Opto-Electronics,Chinese Academy of Sciences,Beijing 100094,China； 3.School of Science,Xijing University,Xi′an 710123,China)

Abstract: In a traditional single beam multiple-intensity reconstruction(SBMIR) system, error is accumulated by multiple translational image sensors, which reduces the imaging effect and the effective resolution of the photoelectric imaging system. In this paper, a three-step coherent diffraction imaging system based on parallel plates is proposed. Three different diffraction planes are obtained by inserting or extracting two parallel plates and imaging and restoration reconstruction of complex amplitude objects are achieved. The numerical simulation and experiments show that the system overcomes the error accumulation problem of several translations in the SBMIR system, and one only needs to record three diffraction surfaces to avoid oversampling. The proposed optical system is easy to implement and has high repeatability.

Key words: the single-beam multiple-intensity;coherent diffraction imaging;parallel plates;complex amplitude

1 Introduction

引 言

Coherent Diffraction Imaging(CDI) is a lensless diffraction imaging technique[1-3]that has been rapidly developing with applications in adaptive X-ray imaging and related fields[4-8]. The CDI methods implemented in nowadays involve holography[9-10], wavefront detection reconstruction[11]and Gerchberg-Saxton′s(GS) algorithm for multiple diffraction information surfaces[12-13]. In general, single-step diffraction imaging is not suitable for complex amplitude recovery reconstruction because only one diffraction pattern is recorded. Therefore, an improved GS algorithm was produced[14-15], along with random binary pure phase modulation[16], rotational phase modulation[17], single-beam multi-intensity wavefront reconstruction(SBMIR) and other technical solutions[18-21]. However, among the many schemes, most of them are limited to the use of computers for numerical simulation. Also, specific optical imaging experiments for the schemes have not been implemented and they have no proposed specific experimental procedure. For this reason, further verification is needed to give plausibility to the methods and reproducibility of their experiments. Traditional SBMIR technology has been studied using numerical simulation analysis and specific experimentation. The phase recovery problem has also been solved. SBMIR methodology generally involves fixing a CCD camera on a precision stage and adopts a mechanical stepping mode. This easily causes the experimental image to have problems that result from shaking equipment, thereby reducing image resolution and quality. Furthermore, this technique usually requires that 10-20 diffractive faces be collected and recorded, which introduces the issue of oversampling defects. The above problems lead to difficulty repeating experiments and cause the technology to be less useful in real-world applications.

相干衍射成像(Coherent Diffraction Imaging，CDI)，是一種無透鏡衍射成像技術[1-3]，從提出至今快速發(fā)展并應用于自適應成像、X射線成像等相關領域[4-8]。CDI的實現(xiàn)方法有基于全息術[9-10]、波前檢測重建[11]和多個衍射信息面的Gerchberg-Saxton(GS)算法等[12-13]。通常，單步衍射成像因為只記錄一幅衍射圖像，無法適用于復振幅的恢復重建，所以基于此類相位恢復重建的問題，通常采用改進型的GS算法[14-15]、隨機二元純相位調制[16]、旋轉相位調制[17]、單光束多強度波前重建(SBMIR)等技術方案[18-21]。然而，大部分方法都只局限于利用計算機進行數(shù)值模擬，具體的光學成像實驗并未實現(xiàn)，也沒有提出具體的實驗方案。所以方法的實用性及實驗的可重復性需要進一步驗證。傳統(tǒng)的SBMIR技術對數(shù)值模擬分析和具體實驗都進行了研究，相位恢復問題得到了解決。但是，傳統(tǒng)的SBMIR技術大多是將圖像傳感器CCD固定于精密平移臺上，采用機械移動的步進方式，導致實驗圖像有抖動問題。從而降低了成像分辨率和質量，而且此技術通常需采集記錄10～20個衍射面，有過采樣的缺陷，上述問題及缺陷導致實驗重復性較差，不利于技術方案的實際應用。

In order to solve and avoid the above issues, a three-step coherent diffraction imaging system based on parallel plates is proposed. The position of the CCD camera and the sample is fixed and two parallel plates are inserted in or extracted from the system. By doing so, three intensity information diffraction planes are quickly obtained and the sample pattern is eventually reconstructed by the recovery algorithm. The results of computer numerical simulation and actual optical experiments show that the system effectively avoids and solves the problem with shaking and the oversampling defects that exist in the traditional technical solutions. The proposed method is simple, quick to perform and repeatable while also producing images that are of significantly higher quality

為了解決和避免上述問題及缺陷，本文提出一種基于平行平晶的三步相干衍射成像系統(tǒng)，圖像傳感器CDD和樣品的位置固定不變，采用依次在系統(tǒng)中插入或抽出2塊平行平晶的方法，快速獲得3幅強度信息衍射圖，通過恢復算法最終重建樣品圖像。計算機數(shù)值模擬和實際的光學實驗結果表明：該系統(tǒng)有效解決了傳統(tǒng)技術方案的抖動問題與過采樣的缺陷，最重要的是系統(tǒng)的成像效果顯著提升，且具有實驗可重復性高，操作簡單快捷的特點。

2 Imaging System Structure and Method Principle Analysis

成像系統(tǒng)結構及方法原理分析

2.1 Traditional SBMIR Technology and System Implementation

傳統(tǒng)SBMIR技術及系統(tǒng)實現(xiàn)

Before introducing the three-step coherent diffraction imaging system based on parallel plates, a brief discussion on the single-beam multi-strength reconstruction(SBMIR) technology scheme using a precision mobile platform will be presented. A typical SBMIR optical imaging system is shown in Fig.1(a). The CCD camera is fixed on a motorized precision stage where the rotation of a motor causes the precision stage to move along its track. The CCD camera records the diffraction intensity informationINof the object every time the precision stage moves by a distance of Δz. Anther scheme will be done by moving the position of the sample. Let the square of the intensity of the CCD acquisition recorded and the amplitude of the Fourier transform of the object be:

在介紹基于平行平晶的三步衍射成像系統(tǒng)之前，先簡要討論采用精密移動平臺完成SBMIR技術方案。典型的SBMIR光學成像系統(tǒng)如圖1(a)所示。圖像傳感器CCD固定在精密的機械移動平臺上，通過電機轉動使平移臺沿著軌道方向移動，平移臺每移動一段距離Δz，CCD就記錄一次物體的衍射強度信息IN。另一種方案則是通過移動樣品位置來實現(xiàn)。設CCD采集記錄的強度信息與物體傅里葉變換的幅度成平方關系為：

IN=[F(ON)RZ+ΔZ]2, (1)

WhereFdenotes the Fourier transform operator,INis the object plane andRZ+ΔZis the diffraction distance. Typically, an SBMIR system requires that at least 3 diffraction intensity maps be recorded for wavefront reconstruction of the completed sample but often as many as 10-20 are used.

式中，F(xiàn)表示傅里葉變換算子，IN為物平面，RZ+ΔZ為衍射距離。通常情況下，典型的SBMIR系統(tǒng)需要采集記錄的衍射強度圖不少于3幅，一般為10～20幅，并以此完成的樣品的波前重建工作。

2.2 Three-step Coherent Diffraction Imaging System Based on Parallel Plates

基于平行平晶的三步衍射成像系統(tǒng)

The proposed three-step coherent diffraction imaging system based on parallel plates is shown in Fig.1(b). The relative position of the object and the CCD camera is fixed. P1 and P2 represent two parallel flat crystal plates, which are illuminated by coherent light. The monochromatic plane wave in the system is vertically irradiated to the object plane after being collimated by a pinhole filter and a lens. It then reaches the CCD camera which records the surface after a diffraction of distancez. The system can complete the imaging processing in three steps:For the first step, after constructing and fixing the system device, the CCD camera is directly used to record the intensity informationI1of the first diffractive surface; In the second step, with the relative position of the CCD camera and the object unchanged, a parallel crystal plane P1 is inserted at any position between them. The CCD camera then collects and records the intensity informationI2of the second diffractive surface; In the third step, without disturbing the setup from the second step, another parallel flat crystal P2 is inserted in an arbitrary position between the object and the CCD camera, then the CCD camera is once again used to record the intensity informationI3of the third diffraction plane. After completing these three steps, the diffractive surface intensity information ofI1,I2,I3are each known. The positions of the object and CCD camera do not need to be moved or changed throughout the entire process and the completion time of the entire experiment is about 30 s. It does not involve the use of a precision stage, has no shaking in its system, no accuracy problems and has a simple experimental procedure that does not suffer from issues caused by oversampling.

研究提出的基于平行平晶的三步衍射成像系統(tǒng)如圖1(b)所示,物體與圖像傳感器CDD的相對位置是固定不變的，P1和P2表示兩塊平行平晶，采用相干光照明，系統(tǒng)中的單色平面波，經針孔濾波器與透鏡組合成的準直擴束系統(tǒng)后，垂直照射到物體平面，經過一段衍射距離z后到達圖像傳感器CDD記錄面。系統(tǒng)經過3個步驟完成成像過程：第一步，搭建與固定好系統(tǒng)器件后，直接用CCD采集記錄得到第一衍射面的強度信息I1；第二步，保持CCD與物體的位置不變，在它們之間的任意位置插入一塊平行平晶P1，CCD采集記錄后得到第二衍射面的強度信息I2；第三步，在第二步系統(tǒng)結構位置不變的基礎上，在物體與CCD之間任意位置插入另一塊平行平晶P2，CCD再次記錄下第三幅衍射圖的強度信息I3。最終，一共得到3個不同衍射面的強度信息I1,I2,I3。整個過程中，物體和CCD的位置是不需要移動及改變的，完成整個實驗約需30 s。該系統(tǒng)不使用精度平移臺，沒有系統(tǒng)抖動、精度問題，也無過采樣的復雜實驗過程。

Fig.1 Structural comparison and principle analysis of proposed system 圖1 系統(tǒng)結構比較及原理分析

The principle of the three-step coherent diffraction imaging system based on parallel plates is shown in Fig.1(c). The object is illuminated by a monochromatic coherent wave, and the object plane is diffracted by distancez0to meet a Fresnel plane, which is the first step of the system. The image then travels the distancez1to a second Fresnel plane, which is the second step of the system. Finally, it then continues to travel the distancez2to meet a third Fresnel plane, being the third step of the system. The above process is not completed by moving the CCD camera or the object through the precision stage, but instead by inserting parallel flat crystals between the CCD camera and the object, allowing the information to be reconstructed using the multiple intensities of the single beam. Of course, it should be pointed out that the above steps can be implemented in reverse, meaning that all the parallel flat crystals can be inserted first and then sequentially removed.

基于平行平晶的三步衍射成像系統(tǒng)的原理分析如圖1(c)所示，用單色相干平面波照射物體，物體經過距離z0的衍射后得到第一衍射面，即前文所述的第一步；繼續(xù)傳播距離z1后得到第二衍射面，即前文所述的第二步；再繼續(xù)傳播距離z2后得到第三衍射面，即前文所述的第三步。以上過程不是通過精密平移臺移動CCD或物體來實現(xiàn)的，而是采用在CCD與物體之間插入平行平晶得到單光束多強度的信息重建。當然，需要指出的是此系統(tǒng)上述步驟可以反向實施，即可先將所有的平行平晶插入，再每次抽取一塊完成實驗研究過程。

3 Key Algorithms and Numerical Simulation Analysis

關鍵算法及數(shù)值模擬分析

3.1 Key Algorithm Methodology

關鍵算法步驟

The algorithm of the three-step coherent diffraction imaging system based on parallel plates is based on the GS algorithm. The original diffraction plane is increased to three diffraction planes with different diffraction distances to recover and reconstruct the sample. It is through this method that the accuracy of the iterative algorithm and the convergence speed and recovery reconstruction effects are improved. An added benefit of the three-step coherent diffraction imaging system is that it has the ability to recover and reconstruct complex amplitude objects.

基于平行平晶的三步衍射成像系統(tǒng)的關鍵算法是以G-S算法為基礎，由原來的一幅衍射圖樣增加為3幅不同衍射距離的衍射圖樣，以實現(xiàn)對樣品的恢復重建，從而提高迭代算法的計算精確程度，及收斂速度和恢復重建效果。同時，三步衍射成像系統(tǒng)方法的一個最大優(yōu)勢在于可以對復振幅型的物體進行恢復重建。

The algorithm key steps are shown in Fig.2, assuming

Fig.2 Block diagram of the key algorithm 圖2 關鍵算法框圖

關鍵算法步驟如圖2所示，設

g(k)(x0，y0)=|g(k)(x0,y0)|·

exp[kφ0(x0,y0)] , (2)

(1)From the object plane positive to the first diffractive surface:

從物平面正向到第一衍射面：

(3)

(2)From the first diffractive surface positive to the second diffractive surface:

第一衍射面正向到第二衍射面：

(4)

(3)From the second diffractive surface positive to the third diffractive surface:

第二衍射面正向到第三衍射面：

(5)

(4)Reverse from the third diffractive surface to the second diffractive surface:

第三衍射面逆向到第二衍射面：

(6)

(5)Reverse from the second diffractive surface to the first diffractive surface:

第二衍射面逆向到第一衍射面：

(7)

(6)Reverse from the first diffractive surface to the object plane:

第一衍射面逆向到物平面：

(8)

When the sample is a pure amplitude type object, there is:

當樣品為純振幅型物體時，則有

g(k+1)(x0,y0)=|g(k)′(x0,y0)| ， (9)

When the sample is a complex amplitude type object, there is:

樣品為復振幅型物體時，則有

g(k+1)(x0,y0)=g(k)′(x0,y0) . (10)

3.2 Numerical Simulation Analysis

數(shù)值模擬分析

In order to further demonstrate the feasibility of the method using the three-step coherent diffraction imaging system, a numerical simulation analysis of the computer was first carried out, with the results shown in Fig.3. The single-step coherent diffraction image is calculated and analyzed is shown in Fig.3(a), the two-step diffraction imaging is shown in Fig.3(b) and the three-step diffraction imaging is shown in Fig.3(c). For convenience of comparison, the number of algorithm iterations is set to 200 times, the commonly used image evaluation function correlation coefficientCois used to judge the effect of restoration and reconstruction, and the range is generally [0,1]. The closer theCovalue is to 1, the closer the reconstruction is to the real object. If the value is smaller, the recovery quality is worse. Furthermore, the higher the deviation from the real object, the worse the imaging effect, affecting the iterative break and selection algorithm's number of iterations. For a pure amplitude type object, since there is no phase, the calculation is relatively simple and its detailed numerical simulation results are omitted. However, it should be pointed out that the convergence speed is very fast and theCovalue of the amplitude can quickly reach 1.

為了進一步論證三步衍射成像系統(tǒng)方法的可行性，首先進行了計算機數(shù)值模擬分析，結果如圖3所示。分別計算了單步衍射成像(圖3(a))，兩步衍射成像(圖3(b))、三步衍射成像(圖3(c))。為方便比較，特將算法的迭代次數(shù)都設置為200次，采用常用圖像評價函數(shù)相關系數(shù)Co來判斷恢復重建效果，其取值范圍一般為[0，1]。Co值越接近1說明恢復重建的物體越接近真實的物體。其值越小說明恢復質量越差，越偏離真實物體，成像效果越差，并以此來判斷和選擇算法的迭代停止條件。對于純振幅型的物體而言，由于沒有相位，所以較為簡單。就不在給出其詳細的數(shù)值模擬結果，但需要指出的是其收斂速度非常的快，且振幅的Co值能快速達到1。

In the process of computationally calculated numerical simulation, the sample pattern used is a grayscale image with a size of 256 pixel×256 pixel, the CCD camera′s pixel size is 6.45×10-6m/pixel, the laser′s wavelength is 632.8×10-9m. The sample is of the complex amplitude type, its phase distribution range is set to [-π,π], and the diffraction distances are set toz0=100 mm,z1=10 mm,z2=10 mm. The reconstruction of the complex amplitude of the sample is completed, and the correlationCocoefficient′s value is represented for the amplitude distribution and the phase distribution, respectively. In the simulated results, the black solid line is the value of the amplitude part correlation coefficient change, and the blue dotted line is the value of the phase part correlation coefficient change. In order to mark the value ofCoat a desired point in Fig.3 (a), the cursor included with the Matlab software package is used.

在進行計算機數(shù)值模擬分析過程中，使用的樣品圖樣為灰度圖，尺寸大小為256 pixel×256 pixel，圖像傳感器CCD的像素尺寸為6.45×10-6m/pixel，激光波長為632.8×10-9m，且樣品為復振幅型，其相位分布范圍設為[-π,π]，將衍射距離設為z0=100 mm,z1=10 mm,z2=10 mm，完成對樣品復振幅的恢復重建。對振幅分布與相位分布分別用相關系數(shù)Co值表示。在數(shù)值模擬結果中，其中實線為振幅部分相關系數(shù)變化值，藍色點線為相位部分相關系數(shù)變化值。為了標注Co在某點的數(shù)值大小，在圖3(a)中，使用了Matlab軟件中自帶的游標。

From the simulation results shown in Fig.3(a), under the same conditions, theCovalue range of the amplitude and phase fractions of the single-step diffraction imaging recovery reconstruction is less than 0.5. It is shown that only obtaining a single coherent diffraction intensity map is impossible to recover and reconstruct a complex amplitude object, which is why the method of single-step coherent diffraction imaging is not applicable to such objects. However, with the addition of a diffraction plane that has a distance ofz0+z1, the recovery and reconstruction effect resulting from two-step diffraction imaging is significantly improved, theCovalues of the amplitude and phase are higher than 0.5 and there is a tendency to converge. Nevertheless, late in the algorithm iteration, there is a slight decrease in morphology so a comprehensive evaluation shows that it cannot achieve the desired result. These results are shown in Fig.3(b). In contrast, the three-step coherent diffraction imaging process starts to converge when the algorithm passes 60 iterations and completely converges after about 70 iterations without any subsequent regression. Moreover, final convergenceCovalue of the recovery results, either the amplitude portion or the phase portion, reaches 1. These results show that the imaging quality of the system is continuously improved from one diffraction plane to three diffractions, that the algorithm completely converges to the third image, and that theCovalue reaches the optimal ideal value.

Fig.3 Numerical simulation analysis and comparison 圖3 數(shù)值模擬分析及比較

圖3(a)數(shù)值模擬結果表明，在相同的條件下，單步衍射成像恢復重建的振幅與相位部分的Co數(shù)值均低于0.5。說明僅有單幅衍射強度圖是無法對復振幅型的物體進行恢復重建的，單步相干衍射成像方法不適用于復振幅型物體。然而，在增加一幅距離為z0+z1的衍射圖后，兩步衍射成像的恢復重建效果得到了明顯提升，振幅及相位部分的Co值均高于0.5，且有收斂的趨勢，但算法迭代到后面則出現(xiàn)了輕微的降低趨勢。所以綜合評價沒有達到理想結果，結果如圖3(b)。相比之下，三步相干衍射成像在算法迭代到60次時開始收斂且到70次左右完全收斂，后續(xù)沒有任何下降的趨勢。并且，無論是振幅部分還是相位部分，最終收斂的Co值均達到1。結果說明由一幅衍射圖增加至三幅衍射的過程中，系統(tǒng)的成像質量不斷的提升，且到第三幅時算法完全收斂，Co值也達到最佳的理想值。

In order to illustrate the robustness of the three-step coherent diffraction imaging system, a numerical simulation of the system′s ability to combat noise is added, as shown in Fig.3(d). Thex-value indicates that the system gradually increases the noise from 0, and the step size increases by 2%. When the noise increases to 20%, theCovalue of the amplitude and phase continues to exceed 0.94 with only minor fluctuations. Numerical simulation results show that the three-step diffraction imaging can effectively combat noise.

為了分析三步相干衍射成像系統(tǒng)方案的魯棒性，對增加噪聲系統(tǒng)進行了的數(shù)值模擬計算，結果如圖3(d)所示。其中橫坐標表示加入的噪聲從0逐漸增加，增加步長為2%，當噪聲增加至20%時，振幅與相位的Co值繼續(xù)高于0.94，且變化幅度非常小。數(shù)值模擬結果表明，三步衍射成像對抗噪聲能力良好。

4 Experimental results and analysis

實驗結果及分析

4.1 Optical experiment results

光學實驗結果

In order to demonstrate the feasibility of the three-step coherent diffraction imaging system based on parallel plates, the actual optical system imaging and recovery reconstruction work was carried out, and the corresponding SBMIR experiment based on precision translation stage was completed. These system structures are shown in Fig.1(a) and Fig.1(b). The experiment uses the following parameters: the laser is a coherent light source of a single plane with a wavelength ofλ=632.8 nm. The CCD camera′s pixel size is 6.45 μm/pixel, the number of intensities recorded by the experiment is 3 and the image size is 800 pixel×800 pixel. The above parameters are identical for both experiments. The difference between these experiments is that the traditional SBMIR system uses a precision translation stage where the moving CCD camera obtains diffractive surfaces at different distances. The accuracy of the translation stage is 0.01 μm and the maximum movement range is 15 mm. The three-step coherent diffraction imaging system based on parallel plates uses three parallel flat crystals, which are sequentially inserted into the system to obtain different diffractive surfaces. To an extent, the size of the parallel flat crystals does not affect the experimental operation so there is no outlined requirement, which is an advantage of this method. For more diffractive surfaces, the number of parallel flat crystals can be increased and the system will not need to be modified. Furthermore, there is no issue with shaking equipment or error caused by movement.

為了論證基于平行平晶的三步衍射成像系統(tǒng)的可行性，進行了實際的光學系統(tǒng)成像及恢復重建工作，并完成相對應的基于精密平移臺的SBMIR實驗，系統(tǒng)結構如圖1(a)和圖1(b)所示。實驗參數(shù)設置如下：激光器為單色平面波的相干光源，波長λ=632.8 nm,圖像傳感器CCD像素尺寸為6.45 μm/pixel,實驗所采集記錄的強度信息圖數(shù)量為3幅，采集圖像尺寸為800 pixel×800 pixel,兩個系統(tǒng)的實驗參數(shù)完全相同。不同的是，傳統(tǒng)的SBMIR采用的是精密平移臺，移動CCD得到不同距離的衍射面，平移臺的精度為0.01 μm,最大移動量程為15 mm。而基于平行平晶的三步衍射成像系統(tǒng)，使用的是三塊平行平晶，依次插入系統(tǒng)中，以此得到不同的衍射面。在不影響實驗操作的情況下，平行平晶的規(guī)格尺寸并沒有嚴格要求，這也是此系統(tǒng)的一個優(yōu)勢，具有一定的自由度。如果需要更多衍射面，則增加平行平晶數(shù)量即可，不需要改動系統(tǒng)，故沒有移動器件導致的系統(tǒng)抖動問題。

The experimental samples used were USAF 1951 resolution targets. The experimental results of recovery and reconstruction are shown in Fig.4. For the traditional SBMIR system, using a precision mobile platform requires that the CCD camera and sample be affixed to the platform, then, using movements of the platform, the CCD camera records the diffraction surface intensity information at different positions. In the experimental results given, in order to facilitate the comparison, the position of the sample to be tested and the CCD camera are fixed on the platform and the test was performed using moving steps of 3 mm. The translation stage is moved twice to create three steps and the CCD was allowed to record three experimental results. Finally, reconstruction was performed with the results shown in Fig.4(a).

實驗樣品均為USAF 1951分辨率板，恢復重建結果如圖4所示。傳統(tǒng)SBMIR系統(tǒng)使用了精密移動平臺，其將CCD或待測樣品固定于平臺上，然后移動平臺，CCD記錄不同位置處的衍射面強度信息圖。在給出的實驗結果中，為了便于比較，待測樣品位置固定不變，把CCD固定于平臺上移動，移動步長為Δz=3 mm，分3個步驟移動2次平移臺，CCD記錄3次實驗結果。最終恢復重建結果如圖4(a)所示。

Fig.4 Comparison of phase distribution after restoration and reconstruction 圖4 恢復重建后相位分布比較

In order to perform the three-step diffraction imaging system based on parallel plane, parallel flat crystals were inserted in three steps. The CCD camera recorded three experimental results which were eventually recovered and reconstructed. These results are shown in Fig.4(b).

基于平行平晶的三步衍射成像系統(tǒng)，使用平行平晶，分3個步驟兩次插入平行平晶，CCD記錄3次實驗結果，最終進行恢復重建，結果如圖4(b)所示。

Some areas in Figs.4(a) and (b) are highlighted in dotlines and then magnified. It can be clearly seen that the quality of (b) is better than that of (a), showing higher quality in experimental results given by the three-step coherent diffraction imaging system, when compared to the traditional SBMIR system method using a mobile platform.

圖4(a)和(b)中,將虛線圈標出的部分放大相同倍數(shù)進行觀察比較。通過對比可以明顯看出圖4(b)比圖4(a)的質量好。實驗結果表明：平行平晶的三步衍射成像系統(tǒng)比傳統(tǒng)的使用移動平臺的SBMIR系統(tǒng)實際成像效果好。

The experimental results also show that the phase distributions of some parts of the sample are reversed. The reason for this may be that the sample is tilted during the experiment, so that the parallel beam is inconsistent when it is irradiated onto the surface of the sample, causing errors in the reconstructed results.

同時實驗結果顯示，樣品某些部位的相位分布存在翻轉情況，原因可能是在實驗過程中，樣品有傾斜，使得平行光束照射到樣品表面時并不一致，所以記錄后重構結果有誤差。

In order to further illustrate the three-step coherent diffraction imaging system based on parallel flat crystals and how a complex amplitude type object can be imaged and restored, the experiment of using a biological slice as a sample was performed with results shown in Fig.5. The experimental parameters used were the same as the preceding experiment with only the test sample being different.

為了進一步的說明基于平行平晶的三步衍射成像系統(tǒng)，能夠對復振幅型物體成像并恢復重建，完成了以生物切片為樣品的實驗，如圖5所示。所使用的實驗參數(shù)與上述相同，只更換待測樣品。

Fig.5 Experimental results of complex amplitude type samples 圖5 復振幅型樣品的實驗結果

Fig.5(a) is a microscopic photograph of an original bio-slice sample. Fig.5(b) shows the reconstructed phase distribution under ordinary coherent diffraction imaging and Fig.5(c) is the amplitude distribution of the sample resulting from the parallel crystal plate system. The amplitude distribution after recovery is restored under a three-step diffraction imaging system. Fig.5(d) is the distribution of the phase portion. Fig.5(b) shows the recovery reconstruction results under ordinary(single-step) diffraction imaging technology. Since there is only one diffractive surface, the information that can be obtained is extremely limited. There is no effective constraint on the phase recovery of the sample so it is impossible to effectively restore and reconstruct the complex amplitude type object. From the results of Fig.5(c) and (d), it is clear that the three-step coherent diffraction imaging system based on parallel flat crystals can effectively image and recover reconstruction of complex amplitude objects.

在圖5中，5(a)為原始生物切片樣品的顯微圖，5(b)為普通相干衍射成像恢復重建后的相位分布，5(c)為基于平行平晶的三步衍射成像系統(tǒng)下恢復重建后的振幅分布，5(d)為相位部分的分布。圖5(b)為普通(單步)衍射成像技術下的恢復重構結果。由于只有一個衍射面，所能夠獲得的信息極為有限，對樣品的相位恢復沒有有效的約束條件，所以無法對復振幅型的物體進行有效的恢復重建。圖5(c)、5(d)的結果說明，基于平行平晶的三步衍射成像系統(tǒng)能夠對復振幅型的物體進行有效的成像及恢復重建。

The experimental results show that the three-step coherent diffraction imaging system based on parallel plates in which flat crystals are simply inserted or extracted can decrease error resulting from system shaking and movement of a traditional SBMIR precision mobile platform. It can also effectively capture an image of amplitude and complex amplitude objects and restore them without oversampling. Furthermore, all of this is possible with high repeatability.

實驗結果表明，基于平行平晶的三步衍射成像系統(tǒng)，采用插入或抽取平行平晶的方法，使系統(tǒng)避免了因機械移動而產生的系統(tǒng)抖動。能有效對振幅型，復振幅型的物體進行成像并恢復重建，不需要過采樣，并且系統(tǒng)的重復性高。

A further benefit of the 3-step process is that it combats the problem where imaging systems often encounter field-of-view problems. Because the system's used sample size is generally much smaller than the size of the parallel flat crystals, and both are in the near-field range, the field of view of the system is unaffected by the flat crystals.

成像系統(tǒng)通常會涉及到視場問題，系統(tǒng)中由于使用的樣品尺寸遠小于平行平晶的尺寸，且都是在近場范圍成像，因此系統(tǒng)的視場不會受到平晶的影響。

4.2 Error Discussion

誤差討論

The experimental results show that the imaging system has a certain amount of error and that the reconstructed sample has some ripples. In response to these problems, error analysis is performed from the following few aspects.

實驗結果表明，成像系統(tǒng)有一定的誤差，恢復重構的樣品有一些波紋。針對這些問題，從以下幾個方面進行誤差分析。

Influence of optical component uniformity:The parallel crystal three-step coherent diffraction imaging system is influenced by the uniformity of the optical components of which it is comprised. In the process of manufacturing such optical components, the level and quality are not always ideal. One of the most important devices within this system is the parallel flat crystal. The light in the experiment was deviated after passing through the flat crystal, causing reconstruction results to be inaccurate and corrugated. Presumably, the lens of the system may also have this problem.

光學元件均勻性的影響，基于平行平晶的三步相干衍射成像系統(tǒng)，其中最重要的器件之一平行平晶，此類光學元件在加工制造過程中，工藝水平達不到理想要求，所以導致實驗中衍射光束通過平晶后出現(xiàn)偏差，最終恢復重建結果有誤差及波紋，當然系統(tǒng)中的透鏡也可能有此問題。

The influence of the tilt of the optics in the imaging system:The need to insert or extract flat crystals in sequence in this operation cannot completely guarantee perfect alignment. Even the sample may be tilted. These tilts will cause the distance from the diffraction plane to the CCD camera to be inconsistent, which may cause ripples and errors in the experimental results.

光學器件的傾斜的影響，在成像系統(tǒng)中，需要依次插入或抽取平晶，在進行此操作時，無法完全保證絕對的平直而沒有傾斜，同時樣品也有可能出現(xiàn)傾斜，這些傾斜則會導致樣品衍射到CCD記錄面的距離不一致，因此可能會導致實驗結果出現(xiàn)了波紋和誤差。

External force vibration and air disturbance effects: In these optical experiments, all instruments are exposed to the environment, so external forces may cause the optical platform to vibrate. Such air disturbances in the system will affect the CCD recorded results which also has an impact on restoration and reconstruction.

外力振動及空氣的擾動影響，進行光學實驗，基所有的儀器都裸露在外，因此外力因素可能導致光學平臺振動，系統(tǒng)周圍的空氣擾動，都會影響到CCD記錄的結果。這同樣對恢復重建的結果造成了一定的影響。

5 Conclusion

結 論

Based on the GS algorithm and the single-step diffraction lensless imaging method, a three-step coherent diffraction imaging system based on parallel flat crystals is proposed and compared with traditional SBMIR technology using a precision mobile platform. Using computerized numerical simulation and actual optical experimentation, it was demonstrated that a three-step coherent diffraction imaging system based on parallel flat crystals: is unlike the traditional SBMIR technology in that the required diffraction patterns are reduced from between 10 and 20 to merely 3; has no mechanical movement, or evidence of shaking in resulting imagery; does not suffer from reduced imaging resolution in photoelectric imaging systems resulting from movement; and is easily repeatable. As the system′s diffractive surfaces are added simply added to the system, the system succeeds in imaging and recovery reconstruction complex amplitude type objects and overcomes the hurdles that the single-step diffraction imaging cannot. At the same time, the proposed imaging system, being a lensless coherent diffraction imaging system, has no lens aberration problem. However, the parallel crystal plates used in the system, the required level of precision, as well as the tilt problem during plate insertion can have a negative impact on results. The three-step coherent diffraction imaging system based on parallel flat crystals proposed in this paper has a wide range of applications and a high value in the fields of diffraction imaging measurement, multi-wavelength imaging, biological microscopy, and optical information security.

在G-S算法和單步衍射無透鏡成像方法的基礎上，提出了基于平行平晶的三步衍射成像系統(tǒng)，并與使用精密移動平臺的傳統(tǒng)SBMIR技術進行比較，從計算機數(shù)值模擬和實際的光學實驗進行論證。與傳統(tǒng)SBMIR技術不同，基于平行平晶的三步衍射成像系統(tǒng)所需記錄的衍射圖由10～20幅，降低為3幅，更值得注意的是系統(tǒng)沒有機械移動，沒有圖像抖動導致光電成像系統(tǒng)的成像分辨率降低的問題，也不需考慮移動的精度問題，且實驗的重復性好；由單步衍射成像1個衍射面提升至3個衍射面，系統(tǒng)實現(xiàn)了對復振幅型物體的成像及恢復重建，有效克服了單步衍射成像對復振幅型物體無法恢復的缺陷。提出的成像系統(tǒng)，雖然是無透鏡的相干衍射成像系統(tǒng)，沒有透鏡的像差問題，但系統(tǒng)中使用的平行平晶光學器件，其工藝水平及精度，還有插入過程中的傾斜問題對實驗結果造成一定的影響。研究所提出的基于平行平晶的三步衍射成像系統(tǒng)，在衍射成像的測量，多波長成像，生物顯微，光學信息安全等領域具有廣泛的應用價值。