CN111880389A - A method for eliminating zero-order diffraction of infrared digital holography - Google Patents

A method for eliminating zero-order diffraction of infrared digital holography Download PDF

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CN111880389A
CN111880389A CN202010608319.8A CN202010608319A CN111880389A CN 111880389 A CN111880389 A CN 111880389A CN 202010608319 A CN202010608319 A CN 202010608319A CN 111880389 A CN111880389 A CN 111880389A
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刘宁
刘志佳
刘宇昕
许吉
刘尧振
吴杨康
彭杰
曹海杰
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Nanjing University of Posts and Telecommunications
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Abstract

本发明公开了一种消除红外数字全息零级衍射的方法,包括以下步骤:获取原始全息图;对原始全息图进行FFT以获取原始全息图的频率和相位信息;采用高斯核函数和相位补偿因子对原始全息图的频率、相位信息进行滤波处理以去除零级衍射;对滤波处理获得的频率、相位信息进行FFT逆变换后,重建得到还原的目标图像。本发明的方法只需要采集到一帧全息图即可以完成计算,在连续视频拍摄时不会出现丢帧、漏帧现象,不会造成重建对比度的降低,由于该方法是在红外数字全息术的单发方式下工作的,而且不需要特殊的光学器件或设备。本发明方法简单、实用性强,具有广阔的应用前景。

Figure 202010608319

The invention discloses a method for eliminating zero-order diffraction of infrared digital holography, comprising the following steps: obtaining an original hologram; performing FFT on the original hologram to obtain frequency and phase information of the original hologram; using a Gaussian kernel function and a phase compensation factor The frequency and phase information of the original hologram is filtered to remove zero-order diffraction; the frequency and phase information obtained by the filtering process are subjected to inverse FFT transformation to reconstruct the restored target image. The method of the present invention only needs to collect one frame of hologram to complete the calculation, and there will be no frame loss or missing frame phenomenon during continuous video shooting, and will not cause the reduction of reconstruction contrast, because the method is based on infrared digital holography. Operates in single shot mode and requires no special optics or equipment. The method of the invention is simple, has strong practicability, and has broad application prospects.

Figure 202010608319

Description

一种消除红外数字全息零级衍射的方法A method for eliminating zero-order diffraction of infrared digital holography

技术领域technical field

本发明涉及一种消除红外数字全息零级衍射的方法,属于数字全息技术领域。The invention relates to a method for eliminating zero-order diffraction of infrared digital holography, and belongs to the technical field of digital holography.

背景技术Background technique

数字全息技术是古德曼和劳伦斯于1967年发明的。数字全息术的基本原理是用电子装置代替普通的照相板记录全息图,并用数字计算重新显示被记录的物体。数字全息技术在许多科学研究中(例如小尺度三维测量、显微检验、监测、颗粒测量等),都得到了极大的改进和应用。然而,零级衍射是一个位于全息图中心的大亮点,降低了被记录物再现的细节。因此,消除零级衍射是提高再现全息图对比度的关键。Digital holography was invented by Goodman and Lawrence in 1967. The basic principle of digital holography is to use electronic devices to replace ordinary photographic plates to record holograms, and to re-display the recorded objects with digital calculations. Digital holography technology has been greatly improved and applied in many scientific researches (such as small-scale three-dimensional measurement, microscopic inspection, monitoring, particle measurement, etc.). However, zero-order diffraction is a large bright spot in the center of the hologram, reducing the detail reproduced by the recorded material. Therefore, eliminating the zero-order diffraction is the key to improving the contrast ratio of reproduced holograms.

如何消除零级衍射一直是研究的热点,目前消除零级衍射最常用的方法有以下几类:How to eliminate zero-order diffraction has always been a research hotspot. At present, the most commonly used methods for eliminating zero-order diffraction are as follows:

1.相移法,通过改变记录相位来记录一个或多个全息图,相移法需要特殊的实验装置,并且在调整设置上耗费太多时间,相移法在静态测量中表现良好,但在动态测量中表现不佳。1. The phase-shift method, which records one or more holograms by changing the recording phase, the phase-shift method requires a special experimental setup and takes too much time to adjust the settings, the phase-shift method performs well in static measurements, but in Poor performance in dynamic measurements.

2.空间滤波方法,先对全息图进行快速傅里叶变换(FFT),得到全息图的空间频率分布,然后利用特定的滤波窗口同时识别出共轭像和零级衍射,最后用滤波后的光谱重建出目标。但空间滤波法仍有一定的局限性:例如,不同的目标具有不同的光谱分布,为了适应目标的光谱,必须选择合适的滤波窗口大小和形状,否则会降低重建过程的质量,会导致共轭像(即目标)在重建时出现频率缺失,这样的缺失则会导致目标重建时不是缺少对比度亮度,就是缺少清晰度和细节。另外,过滤器窗口必须最大限度地包含对象的所有信息,对于所有记录的全息图,很难找到一个通用的滤波窗口,如果滤波窗口不够合适,零级衍射就不能消除。2. Spatial filtering method, first perform fast Fourier transform (FFT) on the hologram to obtain the spatial frequency distribution of the hologram, then use a specific filtering window to identify the conjugate image and zero-order diffraction at the same time, and finally use the filtered The spectrum reconstructs the target. However, the spatial filtering method still has certain limitations: for example, different targets have different spectral distributions, in order to adapt to the target spectrum, an appropriate filter window size and shape must be selected, otherwise the quality of the reconstruction process will be degraded, resulting in conjugation Like (i.e. objects) are reconstructed with a frequency loss, such a loss will result in either a lack of contrast brightness or a lack of clarity and detail when the object is reconstructed. In addition, the filter window must contain all the information of the object to the maximum extent. It is difficult to find a universal filter window for all recorded holograms. If the filter window is not suitable enough, zero-order diffraction cannot be eliminated.

3.平均法,平均法试图通过计算捕获装置每个像素的平均值,直接减去全息图的直流分量来消除零级衍射。然而,此方法只适用于参考波振幅分布均匀的情况。此外,减法会导致真实图像重建的振幅降低,从而降低图像的对比度。3. The averaging method, which attempts to eliminate zero-order diffraction by calculating the average value of each pixel of the capture device and directly subtracting the DC component of the hologram. However, this method is only applicable when the amplitude distribution of the reference wave is uniform. In addition, subtraction results in a reduction in the amplitude of the reconstruction of the real image, thereby reducing the contrast of the image.

近年来,由于红外数字全息术更易应用于工业领域,拓宽了数字全息术的应用范围,因而逐渐得到国内外学者的广泛关注和研究。然而,红外数字全息术也存在零级衍射效应的问题,而且在红外数字全息术中,要消除零级衍射比普通数字全息术的影响因素更为复杂。例如,热像仪或微测辐射热计的像素分辨率比普通的CCD或CMOS器件低;由于激光光源的红外数字全息术波长较长,所以记录的物体比普通数字全息术中使用的物体要大得多。红外数字全息图的空间带宽积不足以完全滤除,零级衍射往往与真实像和共轭像重叠,更加难以消除。因此,需要设计一种能够高效的、测量动态情况下、通用性较高的消除红外数字全息零级衍射的方法。In recent years, because infrared digital holography is easier to be applied in the industrial field, which broadens the application scope of digital holography, it has gradually attracted extensive attention and research by scholars at home and abroad. However, infrared digital holography also has the problem of zero-order diffraction effect, and in infrared digital holography, it is more complicated to eliminate the influence factors of zero-order diffraction than ordinary digital holography. For example, thermal imaging cameras or microbolometers have lower pixel resolution than ordinary CCD or CMOS devices; due to the longer wavelengths of infrared digital holography of laser light sources, the recorded objects are smaller than those used in ordinary digital holography much bigger. The spatial bandwidth product of the infrared digital hologram is not enough to completely filter out, and the zero-order diffraction often overlaps with the real image and the conjugate image, which is more difficult to eliminate. Therefore, it is necessary to design a method that can eliminate the zero-order diffraction of infrared digital holography with high efficiency, high versatility under dynamic measurement conditions.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于克服现有技术中的消除红外数字全息零级衍射的方法效率低不足,提供一种消除红外数字全息零级衍射的方法,技术方案如下:The object of the present invention is to overcome the low efficiency of the method for eliminating the zero-order diffraction of infrared digital holography in the prior art, and a method for eliminating the zero-order diffraction of infrared digital holography is provided, and the technical scheme is as follows:

一种消除红外数字全息零级衍射的方法,包括以下步骤:A method for eliminating zero-order diffraction of infrared digital holography, comprising the following steps:

获取原始全息图;Get the original hologram;

对原始全息图进行FFT以获取原始全息图的频率和相位信息;Perform FFT on the original hologram to obtain the frequency and phase information of the original hologram;

采用高斯核函数和相位补偿因子对原始全息图的频率、相位信息进行滤波处理以去除零级衍射;Using Gaussian kernel function and phase compensation factor to filter the frequency and phase information of the original hologram to remove zero-order diffraction;

对滤波处理获得的频率、相位信息进行FFT逆变换后,重建得到还原的目标图像。After inverse FFT transformation is performed on the frequency and phase information obtained by filtering, the restored target image is reconstructed.

进一步地,还包括根据菲涅耳衍射,可以将物光波在XY平面上的实际振幅O(x,y)分布计算为公式:Further, according to Fresnel diffraction, the actual amplitude O(x,y) distribution of the object light wave on the XY plane can be calculated as the formula:

Figure BDA0002559877130000031
Figure BDA0002559877130000031

式(1)中,x0y0面为目标面,XY为全息面,x’y’为像面,假设物体波在x0y0上的复振幅分布为O(x0,y0),目标面与全息面之间的传播距离为d,k表示波数,|O(x0,y0)|和exp[jφ(x,y)]分别表示物光波的振幅和相位。In formula (1), the x 0 y 0 surface is the target surface, XY is the holographic surface, and x'y' is the image surface. It is assumed that the complex amplitude distribution of the object wave on x 0 y 0 is O(x 0 , y 0 ) , the propagation distance between the target surface and the holographic surface is d, k represents the wave number, |O(x 0 , y 0 )| and exp[jφ(x, y)] represent the amplitude and phase of the object light wave, respectively.

优选地,平面波作为参考波,参考波的复振幅分布可以写成公式:Preferably, the plane wave is used as the reference wave, and the complex amplitude distribution of the reference wave can be written as the formula:

R(x,y)=Aexp[jk(xcosθx+ycosθy)] (2)R(x,y)=Aexp[jk(xcosθ x +ycosθ y )] (2)

其中A表示强度,θx和θy分别表示参考波与x、y方向之间的角度;当物光波和参考波之间发生干涉时,全息面上的强度分布可以写成公式:where A represents the intensity, θ x and θ y represent the angles between the reference wave and the x and y directions, respectively; when interference occurs between the object light wave and the reference wave, the intensity distribution on the holographic surface can be written as the formula:

I(x,y)=A2+|O(x,y)|2+2A|O(x,y)|·cos[φ(x,y)-kxcosθx-kycosθy] (3)。I(x,y)=A 2 +|O(x,y)| 2 +2A|O(x,y)|·cos[φ( x , y )-kxcosθx-kycosθy] (3).

进一步地,原始全息图的离散强度分布通过公式(4)计算:Further, the discrete intensity distribution of the original hologram is calculated by formula (4):

Figure BDA0002559877130000032
Figure BDA0002559877130000032

其中m和n是整数,并遵循规则﹣Nx/2≧m≦Nx/2,﹣Ny/2≧n≦Ny/2,红外平面阵列的尺寸设为Lx×Ly,像素号是Nx×Ny,Δx,Δy是像素尺寸;where m and n are integers and follow the rules ﹣Nx/2≧m≦Nx/2,﹣Ny/2≧n≦Ny/2, the size of the infrared plane array is set to Lx×Ly, the pixel number is Nx×Ny, Δx, Δy is the pixel size;

以单位复振幅平面波为再现波,对原始全息图进行照明,再现物体时,像面上的复振幅分布为公式(5):Taking the unit complex amplitude plane wave as the reproduced wave, the original hologram is illuminated, and when the object is reproduced, the complex amplitude distribution on the image plane is formula (5):

Figure BDA0002559877130000041
Figure BDA0002559877130000041

其中d′表示重建距离;当重建距离d′等于记录距离时,对象能被清楚的重建。where d' represents the reconstruction distance; when the reconstruction distance d' is equal to the recording distance, the object can be clearly reconstructed.

进一步地,还包括根据全息图像频谱图,分析设计高斯低通滤波器和相位平均滤波器,并计算参数高斯核函数g和相位因子C,采用高斯低通滤波器和相位平均滤波器对原始全息图进行滤波。Further, it also includes analyzing and designing a Gaussian low-pass filter and a phase averaging filter according to the holographic image spectrogram, and calculating the parameter Gaussian kernel function g and phase factor C, and using the Gaussian low-pass filter and phase averaging filter to the original holographic filter. filter the image.

优选地,高斯核函数g和相位因子C通过以下公式计算得到:Preferably, the Gaussian kernel function g and the phase factor C are calculated by the following formulas:

Figure BDA0002559877130000042
Figure BDA0002559877130000042

Figure BDA0002559877130000043
Figure BDA0002559877130000043

进一步地,基于离轴干涉法获取原始全息图。Further, the original hologram is obtained based on off-axis interferometry.

优选地,基于马赫-赞德干涉法通过微测辐射热计获取原始全息图。Preferably, the raw hologram is acquired by a microbolometer based on Mach-Zander interferometry.

与现有技术相比,本发明所达到的有益效果:Compared with the prior art, the beneficial effects achieved by the present invention:

本发明提出了一种消除全息图再现零级衍射的新方法。该方法基于高斯低通滤波器和高通相位平均滤波器。两个滤波器一起工作可以消除零级衍射和重建的两个交叉条。本发明的方法不会造成重建对比度的降低。由于该方法是在红外数字全息术的单发方式下工作的,而且在这一过程中不需要特殊的光学器件或设备,本发明方法简单、实用性强,具有广阔的应用前景。传统方法没有考虑到的部分就是在傅里叶变换时,一个共轭像的频谱和相位是成对出现的。因此,本发明设计的主要目标就是通过设计高斯核函数滤波器和相位因子,在频谱和相位两个方面同时对零级衍射进行修正,补偿掉其所占据的共轭像位置的频谱和相位信息后再进行零级衍射去除,这样就不会丢失重建目标的亮度、对比度和清晰度。The invention proposes a new method for eliminating zero-order diffraction of hologram reproduction. The method is based on a Gaussian low-pass filter and a high-pass phase averaging filter. The two filters work together to eliminate the zero-order diffraction and reconstruct the two cross bars. The method of the present invention does not cause a reduction in reconstructed contrast. Since the method works in the single-shot mode of infrared digital holography, and no special optical device or equipment is required in the process, the method of the invention is simple, has strong practicability, and has broad application prospects. The part that the traditional method does not take into account is that in the Fourier transform, the spectrum and phase of a conjugate image appear in pairs. Therefore, the main goal of the design of the present invention is to correct the zero-order diffraction in both spectrum and phase by designing a Gaussian kernel function filter and a phase factor to compensate for the spectrum and phase information of the conjugate image position occupied by it. This is followed by zero-order diffraction removal so that the brightness, contrast and clarity of the reconstructed target are not lost.

附图说明Description of drawings

图1为本发明的方法的流程图;Fig. 1 is the flow chart of the method of the present invention;

图2为本发明的实验所用的光学装置;Fig. 2 is the optical device used in the experiment of the present invention;

图3为离轴数字全息记录与重建方案;Figure 3 is an off-axis digital holographic recording and reconstruction scheme;

图4为具有强零级衍射的红外数字全息图:Figure 4 is an infrared digital hologram with strong zero-order diffraction:

(a)捕获的原始全息图;(a) Raw hologram captured;

(b)FFT后全息图的处理结果;(b) The processing result of the hologram after FFT;

(c)为图4(b)的三维网格结果;(c) is the 3D mesh result of Fig. 4(b);

图5为本发明的方法的过程:Fig. 5 is the process of the method of the present invention:

(a)和(b)是全息图的原始再现;(a) and (b) are original reproductions of the hologram;

(c)和(d)σ=2,全息图的滤波结果;(c) and (d) σ=2, the filtering results of the hologram;

(e)和(f)σ=1,全息图的滤波结果;(e) and (f) σ=1, the filtering result of the hologram;

(g)和(h)σ=0.7,全息图的滤波结果。(g) and (h) σ=0.7, filtered results of holograms.

具体实施方式Detailed ways

下面结合附图对本发明作进一步描述。以下实施例仅用于更加清楚地说明本发明的技术方案,而不能以此来限制本发明的保护范围。The present invention will be further described below in conjunction with the accompanying drawings. The following examples are only used to illustrate the technical solutions of the present invention more clearly, and cannot be used to limit the protection scope of the present invention.

相关术语说明:Description of related terms:

BS:Beam Splitter,分光镜;M1:Mirror 1,一号反射镜;M2:Mirror 2,二号反射镜;M3:Mirror 3,三号反射镜;M4:Mirror 4,四号反射镜;VA:variable attenuator,消光衰减器;L1:Lens 1,一号透镜;L2:Lens 2,二号透镜;L3:Lens 3,三号透镜;microbolometer:微测辐射热计。BS: Beam Splitter, beam splitter; M1: Mirror 1, mirror 1; M2: Mirror 2, mirror 2; M3: Mirror 3, mirror 3; M4: Mirror 4, mirror 4; VA: variable attenuator, extinction attenuator; L1: Lens 1, No. 1 lens; L2: Lens 2, No. 2 lens; L3: Lens 3, No. 3 lens; microbolometer: Microbolometer.

实施例1Example 1

如图1至图5所示,一种消除红外数字全息零级衍射的方法,包括以下步骤:As shown in Figure 1 to Figure 5, a method for eliminating zero-order diffraction of infrared digital holography, comprising the following steps:

步骤1.基于马赫-赞德干涉法捕获得原始全息图。本实施例中所用的实验装置如图2所示。实验装置包括激光器、BS、M1、M2、M3、M4、VA、L1、L2、L3和微测辐射热计,激光器发出的激光经过BS后分为两条光束,第一条光束依次经过M1、M2和L3后照射到目标物体上,第一条光束从目标物体上反射后进入微测辐射热计;Step 1. Capture the original hologram based on Mach-Zander interferometry. The experimental setup used in this example is shown in FIG. 2 . The experimental device includes a laser, BS, M1, M2, M3, M4, VA, L1, L2, L3 and a microbolometer. The laser emitted by the laser is divided into two beams after passing through the BS. The first beam passes through M1, After M2 and L3 are irradiated on the target object, the first beam is reflected from the target object and then enters the microbolometer;

第二条光束依次经过M3、VA、L1、L2、M4后也反射到微测辐射热计上;The second beam is also reflected on the microbolometer after passing through M3, VA, L1, L2, and M4 in sequence;

微测辐射热计通过整合两条光束的信息后得到原始全息图。The microbolometer obtains the original hologram by integrating the information from the two beams.

步骤2.对原始全息图进行FFT以获取原始全息图的频率和相位信息,即获取全息图像频谱图。通过公式(1)和公式(5)对原始全息图进行快速傅里叶变换(即,FFT),得到全息图的空间频率分布。Step 2. Perform FFT on the original hologram to obtain the frequency and phase information of the original hologram, that is, obtain the holographic image spectrogram. Fast Fourier transform (ie, FFT) is performed on the original hologram by formula (1) and formula (5) to obtain the spatial frequency distribution of the hologram.

图3给出了离轴数字全息记录与重建方案,如图3所示,x0y0面为目标面,XY为全息面,x’y’为像面。假设物体波在x0y0上的复振幅分布为O(x0,y0),目标面与全息面之间的传播距离为d,根据菲涅耳衍射,可以将物光波在XY平面上的实际振幅O(x,y)分布计算为公式:Figure 3 shows the off-axis digital holographic recording and reconstruction scheme. As shown in Figure 3, the x 0 y 0 plane is the target plane, XY is the holographic plane, and x'y' is the image plane. Assuming that the complex amplitude distribution of the object wave on x 0 y 0 is O(x 0 , y 0 ), and the propagation distance between the target surface and the holographic surface is d, according to Fresnel diffraction, the object light wave can be placed on the XY plane The actual amplitude of the O(x,y) distribution is calculated as the formula:

Figure BDA0002559877130000071
Figure BDA0002559877130000071

式(1)中,k表示波数,|O(x0,y0)|和exp[jφ(x,y)]分别表示物光波的振幅和相位,在进行全息实验时,假设目标所在的平面叫做目标面,接收干涉光的平面叫做像面。分别用二维坐标系来给上面的每个点下坐标,目标面的坐标为(x0,y0),像面的坐标为(x,y)。In formula (1), k represents the wave number, |O(x 0 , y 0 )| and exp[jφ(x, y)] represent the amplitude and phase of the object light wave, respectively. When performing holographic experiments, it is assumed that the plane where the target is located It is called the target plane, and the plane that receives the interference light is called the image plane. Use a two-dimensional coordinate system to assign coordinates to each of the above points. The coordinates of the target surface are (x 0 , y 0 ), and the coordinates of the image surface are (x, y).

从图3可以看出,与常规方法的不同,本实施例中使用平面波作为参考波,参考波的复振幅分布可以写成公式:It can be seen from Fig. 3 that, different from the conventional method, the plane wave is used as the reference wave in this embodiment, and the complex amplitude distribution of the reference wave can be written as the formula:

R(x,y)=Aexp[jk(xcosθx+ycosθy)] (2)R(x,y)=Aexp[jk(xcosθ x +ycosθ y )] (2)

其中A表示强度,θx和θy分别表示参考波与x、y方向之间的角度。当物光波和参考波之间发生干涉时,全息面上的强度分布可以写成公式:where A is the intensity, and θ x and θ y are the angles between the reference wave and the x and y directions, respectively. When there is interference between the object light wave and the reference wave, the intensity distribution on the holographic surface can be written as the formula:

I(x,y)=A2+|O(x,y)|2+2A|O(x,y)|·cos[φ(x,y)-kxcosθx-kycosθy] (3)I(x,y)=A 2 +|O(x,y)| 2 +2A|O(x,y)|·cos[φ(x,y)-kxcosθ x -kycosθ y ] (3)

从式(3)可以看出,全息面上的强度包含三个部分:第一项A2和第二项|O(x,y)|2表示零级衍射,第三部分2A|O(x,y)|·cos[φ(x,y)-kxcosθx-kycosθy]表示实像和共轭像,实像和共轭像是成对出现的,都包含在第三部分中,区别在于符号,符号的不同就形成了中心对称关系。我们看到第三部分中有绝对值符号,通常情况下,绝对值里面的数值,正号表示实像,负号表示共轭像。It can be seen from equation (3) that the intensity on the holographic surface contains three parts: the first term A 2 and the second term |O(x,y)| 2 represent the zero-order diffraction, and the third part 2A|O(x ,y)|·cos[φ(x,y)-kxcosθ x -kycosθ y ] represents the real image and the conjugated image. The real image and the conjugated image appear in pairs and are included in the third part. The difference lies in the sign, The difference in symbols forms a central symmetry relationship. We see that there is an absolute value sign in the third part. Usually, the value in the absolute value, the positive sign represents the real image, and the negative sign represents the conjugate image.

用微测辐射热计数字记录全息图,把红外平面阵列的尺寸设为Lx×Ly,像素号是Nx×Ny,Δx,Δy是像素尺寸。忽略像素距离,在空间采样之后,红外数字全息图的离散强度分布可以计算为公式:The hologram was digitally recorded with a microbolometer, and the size of the infrared planar array was set as Lx×Ly, the pixel number was Nx×Ny, and Δx, Δy were the pixel dimensions. Ignoring the pixel distance, after spatial sampling, the discrete intensity distribution of the infrared digital hologram can be calculated as the formula:

Figure BDA0002559877130000081
Figure BDA0002559877130000081

其中m和n是整数,并遵循规则﹣Nx/2≧m≦Nx/2,﹣Ny/2≧n≦Ny/2。where m and n are integers and follow the rules ﹣Nx/2≧m≦Nx/2,﹣Ny/2≧n≦Ny/2.

以单位复振幅平面波为再现波,对全息图进行照明,再现物体时,像面上的复振幅分布可以写成公式:Taking the unit complex amplitude plane wave as the reproduced wave, the hologram is illuminated. When the object is reproduced, the complex amplitude distribution on the image plane can be written as the formula:

Figure BDA0002559877130000082
Figure BDA0002559877130000082

其中d′表示重建距离,重建距离d′指的是全息面到重建平面的距离。当重建距离d′等于记录距离时,对象能被清楚的重建。where d' represents the reconstruction distance, and the reconstruction distance d' refers to the distance from the holographic plane to the reconstruction plane. When the reconstruction distance d' is equal to the recording distance, the object can be clearly reconstructed.

步骤3.采用高斯核函数和相位补偿因子对原始全息图的频率、相位信息进行滤波处理以去除零级衍射;对原始全息图像图原始全息图进行滤波处理:Step 3. Use the Gaussian kernel function and the phase compensation factor to filter the frequency and phase information of the original hologram to remove zero-order diffraction; filter the original hologram of the original hologram image:

根据全息图像频谱图,分析设计高斯低通滤波器。根据公式(3),零级衍射主要由全息图的能量构成。在菲涅耳衍射区,光强分布|O(x,y)|2,振幅分布|O(x,y)|和红外焦平面阵列上的相位分布φ(x,y)随(x,y)缓慢变化。According to the spectrogram of the holographic image, the Gaussian low-pass filter is analyzed and designed. According to formula (3), the zero-order diffraction is mainly composed of the energy of the hologram. In the Fresnel diffraction region, the intensity distribution |O(x,y)| 2 , the amplitude distribution |O(x,y)| and the phase distribution φ(x,y) on the infrared focal plane array vary with (x,y) ) changes slowly.

由于公式(3)的第一部分是由红外焦平面阵列上的参考波沿贡献的,所以在理想情况下A2是一个纯数值常数。第二部分是红外焦平面阵列上物光波的贡献,在某一像素点附近,这一部分可以被认为是几乎静止的。第三部分在红外焦平面阵列上物光波和参考波的干涉强度分布中,它将随k(xcosθx+ycosθy)的相位因子而变化。考虑到谱域中常用的空间滤波方法,本发明使用在两个维度上都有一定大小的窗口来选择真实图像或共轭图像的谱。于是设计高斯低通滤波器,二维高斯函数具有对称性和低通的优点,将高斯核函数公式:Since the first part of equation ( 3 ) is contributed by the reference edge on the infrared focal plane array, A2 is a purely numerical constant in the ideal case. The second part is the contribution of the object light wave on the infrared focal plane array, which can be considered to be almost static near a certain pixel point. The third part is in the interference intensity distribution of the object light wave and the reference wave on the infrared focal plane array, which will vary with the phase factor of k(xcosθ x +ycosθ y ). Considering the commonly used spatial filtering methods in the spectral domain, the present invention uses a window of a certain size in both dimensions to select the spectrum of the real image or the conjugated image. Therefore, a Gaussian low-pass filter is designed. The two-dimensional Gaussian function has the advantages of symmetry and low-pass. The Gaussian kernel function formula is:

Figure BDA0002559877130000083
Figure BDA0002559877130000083

应用于全息图时,只会留下低频部分,从而可以近似地分辨出零级衍射区域。其中σ表示内核的过滤效果,是一个常数。σ可以控制公式(6)的高斯核函数在实际工作中的窗口大小,根据不同的零级衍射强弱程度可以调整σ的值以改变滤波效果。xc和yc是3×3高斯滤波窗口中中心像素的坐标。由立差σ来控制截止频率。cos[φ(m-1,n-1)-ψ(m-1,n-1)],m,n分别表示在傅里叶变换后,获得的相位分布中,某一个点的相位坐标,m、n为整数。When applied to a hologram, only the low-frequency part is left, allowing the zero-order diffraction region to be approximately resolved. where σ represents the filtering effect of the kernel and is a constant. σ can control the window size of the Gaussian kernel function of formula (6) in practical work, and the value of σ can be adjusted to change the filtering effect according to different zero-order diffraction strengths. x c and y c are the coordinates of the center pixel in the 3×3 Gaussian filter window. The cutoff frequency is controlled by the standoff σ. cos[φ(m-1,n-1)-ψ(m-1,n-1)], m, n respectively represent the phase coordinates of a point in the phase distribution obtained after Fourier transform, m and n are integers.

步骤4.根据全息图像频谱图,分析设计相位平均滤波器。当我们对全息图进行FFT和快速FFT变换时,我们可以看到两个交叉条位于整个光谱的中心,这些交叉条也必须被消除。由于这两条线同时占据了谱域的低频和高频区域,高斯滤波器只能分辨出相对低频的零级衍射,而不能分辨出这两条线,因此使用相位平均滤波器来确定两个交叉条。图4(b)是频率分量形成的,这张图的正中央位置频率最低,越往两边走频率越高,因此中央的白色能量叫低频能量。根据图4b所示,真实像和共轭像是一对互为颠倒的像对,本发明要去除的是图片中央横竖交叉的白条以及中央特别亮的低频能量。Step 4. Analyze and design a phase averaging filter according to the holographic image spectrogram. When we FFT and fast FFT transform the hologram, we can see that two cross bars are located in the center of the whole spectrum, and these cross bars must also be eliminated. Since these two lines occupy the low and high frequency regions of the spectral domain at the same time, the Gaussian filter can only distinguish the zero-order diffraction at relatively low frequencies, but cannot distinguish these two lines. Therefore, the phase averaging filter is used to determine the two cross bar. Figure 4(b) is formed by frequency components. The center of this picture has the lowest frequency, and the frequency increases as it goes to both sides. Therefore, the white energy in the center is called low-frequency energy. As shown in Fig. 4b, the real image and the conjugate image are a pair of reversed images, and the present invention needs to remove the white bars that cross vertically and horizontally in the center of the image and the particularly bright low-frequency energy in the center.

根据分析,相位变化主要是由k(xcosθx+ycosθy),所以,由cos[φ(m,n)-ψ(m,n)],其中φ(m,n)=kmΔxcosθx+knΔycosθy,我们用3×3非加权相位平均滤波器对全息图滤波,可写成公式:According to the analysis, the phase change is mainly caused by k(xcosθ x +ycosθ y ), so, by cos[φ(m,n)-ψ(m,n)], where φ(m,n)=kmΔxcosθx+knΔycosθy, we The hologram is filtered with a 3×3 unweighted phase averaging filter, which can be written as:

Figure BDA0002559877130000091
Figure BDA0002559877130000091

其中,in,

Figure BDA0002559877130000101
Figure BDA0002559877130000101

在公式(7)中,术语平均值C表示未加权平均值。由于像素大小、波数k以及物光波或参考波与光轴之间的角度是θx和θy确定的,因此C是常数。考虑到离轴数字全息中,θx和θy不能同时为

Figure BDA0002559877130000102
因此C不能等于1。In formula (7), the term mean value C denotes an unweighted mean value. Since the pixel size, the wavenumber k, and the angle between the object light wave or the reference wave and the optical axis are determined by θx and θy , C is a constant. Considering that in off-axis digital holography, θ x and θ y cannot be simultaneously
Figure BDA0002559877130000102
So C cannot be equal to 1.

采用高斯低通滤波器和相位平均滤波器对原始全息图进行滤波。The original hologram was filtered with a Gaussian low-pass filter and a phase averaging filter.

步骤5.对滤波处理获得的频率、相位信息进行FFT逆变换后,重建得到还原的目标图像。对滤波结果图的处理,将全息图的原始重建和滤波结果相减,得到无干扰的结果,只留下清晰的实像和共轭像。Step 5. After performing inverse FFT transformation on the frequency and phase information obtained by the filtering process, reconstruct the restored target image. In the processing of the filtering result image, the original reconstruction and filtering results of the hologram are subtracted to obtain a result without interference, leaving only clear real and conjugate images.

本发明的消除红外数字全息零级衍射的方法测量效率高,能测量动态情况,无通用滤波窗口,可适用于参考波振幅分布不均匀的情况。The method for eliminating the zero-order diffraction of infrared digital holography of the invention has high measurement efficiency, can measure dynamic conditions, has no general filtering window, and can be applied to the uneven distribution of reference wave amplitudes.

首先本方法是针对单帧获取到的全息图即可以完成计算,不需要前后多帧全息图进行共同计算,提高了效率。其次,由于是单帧完成计算,因此可以很好的适应当采用连续视频拍摄记录时的实时性要求,保证重建过程不会出现漏帧和丢帧的现象;第三,本发明中实现的滤波过程是自主研发,并非通用滤波窗口。第四,参考波指的是在实验过程中要形成干涉条纹,需要一道来自物体的反射光以及一道来自相同光源的不含物体信息的参考光,两道光同时被接收才可以形成干涉条纹。此时,参考光的光强在一些实验过程中会对记录的全息图产生影响,主要表现在全息图的条纹记录清晰度上,全息重建中,条纹的清晰度是很关键的一环,条纹质量的好坏直接决定了能否重建得到最后的结果,因此,本发明因为存在频谱和相位的双补偿过程,并且最终目标是消除能量过大的零级衍射,因此最终能够很好的抵抗参考光振幅(即能量)不均匀的现象。First of all, the method can complete the calculation for the hologram obtained in a single frame, and does not need to perform joint calculation of multiple frames of holograms before and after, which improves the efficiency. Secondly, since the calculation is completed in a single frame, it can be well adapted to the real-time requirements when continuous video recording is used to ensure that there will be no frame leakage and frame loss during the reconstruction process. Third, the filtering implemented in the present invention The process is self-developed, not a general filter window. Fourth, the reference wave refers to the formation of interference fringes during the experiment, which requires a reflected light from an object and a reference light from the same light source that does not contain object information. The interference fringes can be formed only when the two lights are received at the same time. At this time, the intensity of the reference light will affect the recorded hologram in some experimental processes, which is mainly manifested in the fringe recording resolution of the hologram. The quality directly determines whether the final result can be obtained by reconstruction. Therefore, the present invention can resist the reference very well because of the double compensation process of spectrum and phase, and the ultimate goal is to eliminate the zero-order diffraction with excessive energy. A phenomenon in which the amplitude (ie, energy) of light is not uniform.

本发明的目的是为了设计一种新的算法,在不增加特定光学元件的情况下,可以很容易地消除单镜头数字全息捕获中的零级衍射。本发明所述的一种消除零级衍射的新方法,该方法主要是在空间域内对全息图进行单次拍摄的预处理,在光路上没有具体的实验装置。本发明能有效地对全息图进行滤波,并能达到完全消除零级衍射和谱域中的两个交叉条。它比常用方法容易得多,它可以大大降低计算复杂度,实现全息图的高质量再现。本发明方法简单,只需要采集到一帧全息图即可以完成计算,在连续视频拍摄时不会出现丢帧、漏帧现象,相较目前的研究进展,缺失方法简单、实用性强,具有广阔的应用前景。The purpose of the present invention is to design a new algorithm that can easily eliminate zero-order diffraction in single-lens digital holographic capture without adding specific optical elements. A new method for eliminating zero-order diffraction described in the present invention is mainly to perform single-shot preprocessing on holograms in the spatial domain, and there is no specific experimental device on the optical path. The invention can effectively filter the hologram, and can completely eliminate the zero-order diffraction and two cross bars in the spectral domain. It is much easier than common methods, and it can greatly reduce the computational complexity and achieve high-quality reproduction of holograms. The method of the invention is simple, and only needs to collect one frame of hologram to complete the calculation, and the phenomenon of frame loss and frame leakage will not occur during continuous video shooting. Compared with the current research progress, the missing method is simple, has strong practicability, and has wide application prospects.

以上所述仅是本发明的优选实施方式,应当指出,对于本技术领域的普通技术人员来说,在不脱离本发明技术原理的前提下,还可以做出若干改进和变形,这些改进和变形也应视为本发明的保护范围。The above are only the preferred embodiments of the present invention. It should be pointed out that for those skilled in the art, without departing from the technical principles of the present invention, several improvements and modifications can be made. These improvements and modifications It should also be regarded as the protection scope of the present invention.

Claims (8)

1. A method for eliminating infrared digital holographic zero-order diffraction is characterized by comprising the following steps:
acquiring an original hologram;
performing FFT on the original hologram to acquire frequency and phase information of the original hologram;
filtering the frequency and phase information of the original hologram by adopting a Gaussian kernel function and a phase compensation factor to remove zero-order diffraction;
and performing FFT inverse transformation on the frequency and phase information obtained by filtering, and reconstructing to obtain a restored target image.
2. The method of claim 1, further comprising calculating the actual amplitude O (x, y) distribution of the object light wave in the XY plane as a formula according to fresnel diffraction:
Figure FDA0002559877120000011
in the formula (1), x0y0The surface is the target surface, XY is the holographic surface, x 'y' is the image surface, and the object wave is assumed to be in x0y0Has a complex amplitude distribution of O (x)0,y0) D is the propagation distance between the target surface and the holographic surface, k represents the wavenumber, j is the imaginary symbol unit, λ is the wavelength of the light, | O (x)0,y0) I and exp [ j phi (x, y)]Respectively, the amplitude and phase of the object wave, phi (x, y) referring to the total phase factor of the final wave.
3. The method of claim 2, wherein the plane wave is used as a reference wave, and the complex amplitude distribution of the reference wave can be written as the following formula:
R(x,y)=Aexp[jk(xcosθx+ycosθy)](2)
wherein A represents intensity, θxAnd thetayRespectively representing the angles between the reference wave and the x and y directions; when interference occurs between the object wave and the reference wave, the intensity distribution on the holographic surface can be written as the formula:
I(x,y)=A2+|O(x,y)|2+2A|O(x,y)|·cos[φ(x,y)-kxcosθx-kycosθy](3)。
4. the method of claim 1, wherein the discrete intensity distribution of the original hologram is calculated by equation (4):
Figure FDA0002559877120000021
wherein m and n are integers and follow the rule-Nx/2 ≧ m ≦ Nx/2, -Ny/2 ≧ n ≦ Ny/2, the size of the infrared planar array is set to lxxly, the pixel number is Nx × Ny, Δ x, Δ y are the pixel sizes;
when an original hologram is illuminated with a unit complex amplitude plane wave as a reconstruction wave, the complex amplitude distribution on the image plane when reconstructing an object is expressed by the following formula (5):
Figure FDA0002559877120000022
wherein d' represents a reconstruction distance; when the reconstruction distance d' is equal to the recording distance, the object can be clearly reconstructed.
5. The method of claim 1, further comprising analyzing and designing a gaussian low pass filter and a phase averaging filter based on the hologram spectrogram, and calculating parameters of a gaussian kernel function g and a phase factor C, wherein the gaussian low pass filter and the phase averaging filter are used for filtering the frequency and the phase of the original hologram.
6. The method of claim 5, wherein the Gaussian kernel function g and the phase factor C are calculated by the following formula:
Figure FDA0002559877120000023
Figure FDA0002559877120000024
Figure FDA0002559877120000031
7. the method of claim 1, wherein the original hologram is obtained based on off-axis interferometry.
8. The method of claim 7, wherein the original hologram is acquired by a microbolometer based on Mach-Zehnder interferometry.
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CN114355743A (en) * 2022-02-22 2022-04-15 北京理工大学 A holographic coding method for multi-diffraction-order independent optical wavefield control

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杨超: "红外数字全息图像增强关键技术研究", 《中国优秀硕士学位论文全文数据库信息科技辑》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114355743A (en) * 2022-02-22 2022-04-15 北京理工大学 A holographic coding method for multi-diffraction-order independent optical wavefield control
CN114355743B (en) * 2022-02-22 2022-11-22 北京理工大学 Holographic encoding method for regulating and controlling multiple diffraction-level independent light wave fields

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