CN111880389A - Method for eliminating infrared digital holographic zero-order diffraction - Google Patents

Method for eliminating infrared digital holographic zero-order diffraction 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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order diffraction
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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

The invention discloses a method for eliminating infrared digital holographic zero-order diffraction, which comprises 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. The method can complete calculation only by collecting a frame of hologram, and can not cause frame loss and frame leakage during continuous video shooting, thereby not causing reduction of reconstruction contrast. The method is simple, strong in practicability and wide in application prospect.

Description

Method for eliminating infrared digital holographic zero-order diffraction
Technical Field
The invention relates to a method for eliminating infrared digital holographic zero-order diffraction, belonging to the technical field of digital holography.
Background
Digital holography was invented in 1967 by Goodman and Lorentz. The basic principle of digital holography is to record a hologram with electronic means instead of a conventional photographic plate and to redisplay the recorded object with digital calculations. Digital holography has been greatly improved and applied in many scientific studies (e.g., small-scale three-dimensional measurements, microscopic examination, monitoring, particle measurement, etc.). However, the zero-order diffraction is a large bright spot in the center of the hologram, reducing the detail of the recorded matter reproduction. Therefore, elimination of the zeroth order diffraction is key to improving the contrast of the reconstructed hologram.
How to eliminate the zero-order diffraction has been a hot point of research, and the most common methods for eliminating the zero-order diffraction at present are as follows:
1. phase shift methods, which record one or more holograms by changing the recording phase, require special experimental equipment and take too much time in adjusting the settings, perform well in static measurements but do not perform well in dynamic measurements.
2. The spatial filtering method comprises the steps of firstly carrying out Fast Fourier Transform (FFT) on a hologram to obtain spatial frequency distribution of the hologram, then simultaneously identifying a conjugate image and zero-order diffraction by utilizing a specific filtering window, and finally reconstructing a target by using a spectrum after filtering. However, the spatial filtering method still has certain limitations: for example, different targets have different spectral distributions, and in order to adapt to the spectrum of the target, the size and shape of the filtering window must be selected, otherwise the quality of the reconstruction process is reduced, and the conjugate image (i.e., the target) is subjected to frequency loss during reconstruction, and such loss causes the target to be reconstructed with either lack of contrast brightness or lack of definition and detail. In addition, the filter window must contain all the information of the object to the maximum, it is difficult to find a common filter window for all the recorded holograms, and if the filter window is not adequate, the zero-order diffraction cannot be eliminated.
3. Averaging, which attempts to eliminate the zero-order diffraction by calculating the average value of each pixel of the capture device, directly subtracting the direct current component of the hologram. However, this method is only applicable to the case where the amplitude distribution of the reference wave is uniform. In addition, the subtraction results in a reduction in the amplitude of the real image reconstruction, thereby reducing the contrast of the image.
In recent years, infrared digital holography is more easily applied to the industrial field, and the application range of digital holography is widened, so that the infrared digital holography is gradually paid extensive attention and researched by scholars at home and abroad. However, the infrared digital holography also has the problem of zero-order diffraction effect, and in the infrared digital holography, the elimination of the zero-order diffraction is more complicated than the influence factor of the common digital holography. For example, thermal imagers or microbolometers have lower pixel resolution than ordinary CCD or CMOS devices; due to the long infrared digital holography wavelength of the laser light source, the recorded object is much larger than the object used in ordinary digital holography. The space bandwidth product of the infrared digital hologram is not enough to be completely filtered, and zero-order diffraction is often overlapped with a real image and a conjugate image and is more difficult to eliminate. Therefore, a method for eliminating infrared digital holography zero-order diffraction, which can be used for efficiently measuring dynamic conditions and has high universality, needs to be designed.
Disclosure of Invention
The invention aims to overcome the defect of low efficiency of a method for eliminating infrared digital holographic zero-order diffraction in the prior art, and provides a method for eliminating infrared digital holographic zero-order diffraction, which has the following technical scheme:
a method for eliminating infrared digital holographic zero-order diffraction comprises 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.
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
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) The propagation distance between the target surface and the holographic surface is d, k represents the wave number, | O (x)0,y0) I and exp [ j phi (x, y)]Respectively representing the amplitude and phase of the object wave.
Preferably, the plane wave is used as a 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)
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)。
further, the discrete intensity distribution of the original hologram is calculated by equation (4):
Figure BDA0002559877130000032
wherein m and n are integers, and following the rule-Nx/2 ≧ m ≦ Nx/2, — Ny/2 ≧ n ≦ Ny/2, the size of the infrared planar array is lxxnly, the pixel number is Nx × Ny, Δ x, Δ y are the pixel size;
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 BDA0002559877130000041
wherein d' represents a reconstruction distance; when the reconstruction distance d' is equal to the recording distance, the object can be clearly reconstructed.
And further, analyzing and designing a Gaussian low-pass filter and a phase averaging filter according to the hologram image spectrogram, calculating parameters of a Gaussian kernel function g and a phase factor C, and filtering the original hologram by adopting the Gaussian low-pass filter and the phase averaging filter.
Preferably, the gaussian kernel function g and the phase factor C are calculated by the following formula:
Figure BDA0002559877130000042
Figure BDA0002559877130000043
further, the original hologram is acquired based on off-axis interferometry.
Preferably, the original hologram is acquired by a microbolometer based on mach-zehnder interferometry.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a new method for eliminating hologram reproduction zero-order diffraction. 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 the two cross bars of the reconstruction. The method of the invention does not cause a reduction in the reconstructed contrast. The method works in the single-shot mode of the infrared digital holography, and special optical devices or equipment are not needed in the process. The conventional method does not consider that the spectrum and phase of a conjugate image appear in pairs during fourier transform. Therefore, the main objective of the design of the invention is to correct the zero-order diffraction in two aspects of frequency spectrum and phase by designing the Gaussian kernel function filter and the phase factor, compensate the frequency spectrum and phase information of the occupied conjugate image position, and then remove the zero-order diffraction, so that the brightness, the contrast and the definition of the reconstructed target cannot be lost.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is an optical setup used in experiments of the present invention;
FIG. 3 is an off-axis digital holographic recording and reconstruction scheme;
FIG. 4 is an infrared digital hologram with strong zero-order diffraction:
(a) a captured original hologram;
(b) processing results of the post-FFT hologram;
(c) the three-dimensional grid result of FIG. 4 (b);
FIG. 5 is a process of the method of the present invention:
(a) and (b) is the original reconstruction of the hologram;
(c) and (d) σ ═ 2, the result of the filtering of the hologram;
(e) and (f) σ ═ 1, the result of the filtering of the hologram;
(g) and (h) σ ═ 0.7, the result of filtering of the hologram.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
Description of related terms:
BS is Beam Splitter; m1 Mirror 1, Mirror number one; m2 Mirror No. 2, Mirror No. two; m3 Mirror No. 3, Mirror No. three; m4 Mirror No. 4, Mirror No. four; VA is variable attenuator; l1 Lens 1, Lens number one; l2 Lens 2, Lens number II; l3 Lens No. 3 Lens No. III; microbolometer: a microbolometer.
Example 1
As shown in fig. 1 to 5, a method for eliminating zero-order diffraction of an infrared digital hologram includes the following steps:
and 1, capturing the original hologram based on a Mach-Zehnder interference method. The experimental setup used in this example is shown in FIG. 2. The experimental device comprises a laser, a BS, an M1, an M2, an M3, an M4, a VA, an L1, an L2, an L3 and a microbolometer, wherein laser emitted by the laser is divided into two light beams after passing through the BS, the first light beam sequentially passes through the M1, the M2 and the L3 and then irradiates a target object, and the first light beam enters the microbolometer after being reflected from the target object;
the second beam is reflected to the microbolometer after sequentially passing through M3, VA, L1, L2 and M4;
the microbolometer obtains the original hologram by integrating the information of the two beams.
And 2, performing FFT (fast Fourier transform) on the original hologram to acquire frequency and phase information of the original hologram, namely acquiring a holographic image spectrogram. The original hologram is subjected to fast fourier transform (i.e., FFT) by formula (1) and formula (5), resulting in a spatial frequency distribution of the hologram.
FIG. 3 shows an off-axis digital holographic recording and reconstruction scheme, as shown in FIG. 3, x0y0The surface is a target surface, XY is a holographic surface, and x 'y' is an image surface. Suppose that the object wave is at x0y0Has a complex amplitude distribution of O (x)0,y0) The propagation distance between the target surface and the holographic surface is d, and the actual amplitude O (x, y) distribution of the object light wave on the XY plane can be calculated as a formula according to Fresnel diffraction:
Figure BDA0002559877130000071
in the formula (1), k represents a wave number, | O (x)0,y0) I and exp [ j phi (x, y)]The amplitude and phase of the object beam are respectively shown, and when the holographic experiment is carried out, the plane where the target is located is assumed to be called a target surface, and the plane where the interference light is received is assumed to be called an image surface. Each point of the upper surface is given with a two-dimensional coordinate system, and the coordinate of the target surface is (x)0,y0) And the coordinates of the image plane are (x, y).
As can be seen from fig. 3, unlike the conventional method in which a plane wave is used as a reference wave in the present embodiment, the complex amplitude distribution of the reference wave can be written as the formula:
R(x,y)＝Aexp[jk(xcosθx+ycosθy)](2)
wherein A represents intensity, θxAnd thetayRepresenting the angle between the reference wave and the x, y direction, respectively. 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)
as can be seen from equation (3), the intensity on the holographic surface contains three components: first item A2And a second term | O (x, y) & gtdoes not phosphor2Representing zero-order diffraction, the third portion 2A | O (x, y) |. cos [ phi (x, y) -kxcos thetax-kycosθy]Representing a real image and a conjugate image, both of which appear in pairs, are included in the third portion, with the difference in sign that the difference in sign forms a centrosymmetric relationship. We see the sign of the absolute value in the third part, usually the value inside the absolute value, with a positive sign representing the real image and a negative sign representing the conjugate image.
The hologram is digitally recorded with a microbolometer, and the size of the infrared planar array is set to lxxny, the pixel number is Nx × Ny, and Δ x, Δ y are the pixel size. Ignoring the pixel distance, the discrete intensity distribution of the infrared digital hologram after spatial sampling can be calculated as:
Figure BDA0002559877130000081
wherein m and n are integers, and obey the rule-Nx/2 ≧ m ≧ Nx/2, and-Ny/2 ≧ n ≦ Ny/2.
When the hologram is illuminated by using the unit complex amplitude plane wave as a reconstruction wave, the complex amplitude distribution on the image surface can be written into a formula when an object is reconstructed:
Figure BDA0002559877130000082
where d' denotes the reconstruction distance, which means the distance of the holographic surface to the reconstruction plane. When the reconstruction distance d' is equal to the recording distance, the object can be clearly reconstructed.
Step 3, adopting a Gaussian kernel function and a phase compensation factor to filter frequency and phase information of the original hologram to remove zero-order diffraction; filtering the original hologram of the original hologram image:
and analyzing and designing a Gaussian low-pass filter according to the spectrogram of the holographic image. According to equation (3), the zero-order diffraction consists mainly of the energy of the hologram. In the Fresnel diffraction region, the light intensity distribution | O (x, y) & gtdistribution2The amplitude distribution | O (x, y) | and the phase distribution φ (x, y) on the infrared focal plane array vary slowly with (x, y).
Since the first part of equation (3) is contributed by the reference edge on the infrared focal plane array, A is ideally the same2Is a pure numerical constant. The second part is the contribution of the object light wave on the infrared focal plane array, and near a certain pixel point, this part can be considered as almost stationary. The third component is in the interference intensity distribution of the object wave and the reference wave on the infrared focal plane array, and it will follow k (xcos theta)x+ycosθy) Is varied. In view of the spatial filtering methods commonly used in the spectral domain, the present invention uses a window with a certain size in both dimensions to select the spectrum of the real image or the conjugate image. Therefore, a Gaussian low-pass filter is designed, a two-dimensional Gaussian function has the advantages of symmetry and low-pass, and a Gaussian kernel function formula is as follows:
Figure BDA0002559877130000083
when applied to a hologram, only the low frequency portion is left, so that the zero order diffraction region can be approximately resolved. Where σ represents the filtering effect of the kernel and is a constant. The sigma can control the window size of the Gaussian kernel function of the formula (6) in actual operation, and the value of the sigma can be adjusted according to different zero-order diffraction intensity degrees to change the filtering effect. x is the number ofcAnd ycIs the coordinate of the center pixel in the 3 x 3 gaussian filter window. The cut-off frequency is controlled by the vertical difference σ. cos [ phi (m-1, n-1) -psi (m-1, n-1)]M and n each represent a phase coordinate of a certain point in the phase distribution obtained after fourier transform, and m and n are integers.
And 4, analyzing and designing a phase averaging filter according to the holographic image spectrogram. When we perform FFT and fast FFT transformation on the hologram we can see two cross bars in the centre of the whole spectrum which must also be eliminated. Since the two lines occupy both the low and high frequency regions of the spectral domain, the gaussian filter can only resolve the relatively low frequency zero-order diffraction, but not both lines, and therefore a phase averaging filter is used to determine the two cross bars. Fig. 4(b) is formed by frequency components, and the frequency is lowest at the center of the graph, and the frequency is higher toward both sides, so that the white energy at the center is called low-frequency energy. According to fig. 4b, the real image and the conjugate image are a pair of image pairs which are inverted, and the invention removes the white bar which intersects horizontally and vertically in the center of the image and the low-frequency energy which is particularly bright in the center.
According to the analysis, the phase change is mainly composed of k (xcos θ)x+ycosθy) Therefore, from cos [ phi (m, n) -phi (m, n)]Where phi (m, n) ═ km Δ xcos θ x + kn Δ ycos θ y, we filter the hologram with a 3 × 3 unweighted phase averaging filter, which can be written as:
Figure BDA0002559877130000091
wherein,
Figure BDA0002559877130000101
in equation (7), the term average C represents an unweighted average. Since the pixel size, the wave number k and the angle between the object or reference wave and the optical axis are θxAnd thetayDetermined, C is therefore a constant. Considering off-axis digital holography, θxAnd thetayCannot be simultaneously
Figure BDA0002559877130000102
So C cannot be equal to 1.
The original hologram is filtered using a gaussian low pass filter and a phase averaging filter.
And 5, carrying out FFT inverse transformation on the frequency and phase information obtained by filtering, and reconstructing to obtain a restored target image. And processing the filtering result image, namely subtracting the original reconstruction of the hologram from the filtering result to obtain a non-interference result and only leaving clear real images and conjugate images.
The method for eliminating the infrared digital holographic zero-order diffraction has high measurement efficiency, can measure dynamic conditions, has no general filtering window, and is suitable for the condition that the amplitude distribution of the reference wave is not uniform.
Firstly, the method can complete calculation aiming at the hologram obtained by a single frame, does not need to carry out common calculation on front and back multiframe holograms, and improves the efficiency. Secondly, because the calculation is completed by a single frame, the method can well adapt to the real-time requirement when continuous video shooting recording is adopted, and the phenomena of frame leakage and frame loss can be avoided in the reconstruction process; third, the filtering process implemented in the present invention is an independent research and development, and is not a general filtering window. Fourthly, the reference wave refers to the fact that interference fringes are formed in the experimental process by means of a reflected light from an object and a reference light which is from the same light source and does not contain object information, and the interference fringes can be formed only by means of the two lights which are received at the same time. At this moment, the light intensity of the reference light can influence the recorded hologram in some experimental processes, which is mainly expressed in the fringe recording definition of the hologram, in the holographic reconstruction, the definition of the fringe is a very critical ring, and the quality of the fringe directly determines whether the reconstruction can obtain the final result, so that the invention can well resist the phenomenon of non-uniform amplitude (namely energy) of the reference light because of the double compensation process of the frequency spectrum and the phase and the final aim of eliminating zero-order diffraction with overlarge energy.
The invention aims to design a new algorithm, which can easily eliminate zero-order diffraction in single-lens digital holographic capture without adding a specific optical element. The invention relates to a novel method for eliminating zero-order diffraction, which is mainly used for preprocessing a hologram in a single shooting in a spatial domain, and a specific experimental device is not arranged on an optical path. The invention can effectively filter the hologram and can completely eliminate zero-order diffraction and two cross strips in a spectral domain. It is much easier than the conventional method, it can greatly reduce the computational complexity, and realize high-quality reconstruction of the hologram. The method is simple, the calculation can be completed only by collecting one frame of hologram, the phenomena of frame loss and frame leakage can not occur in the continuous video shooting, and compared with the current research progress, the method has the advantages of simple missing method, strong practicability and wide application prospect.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations 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 Holographic encoding method for regulating and controlling independent light wave field of multiple diffraction orders

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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 Holographic encoding method for regulating and controlling independent light wave field of multiple diffraction orders
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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