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

Abstract

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.

Description

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

technical field

The invention relates to a method for eliminating zero-order diffraction of infrared digital holography, and belongs to the technical field of digital holography.

Background technique

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.

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. 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. 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. 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.

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.

SUMMARY OF THE INVENTION

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:

A method for eliminating zero-order diffraction of infrared digital holography, comprising the following steps:

Get the original hologram;

Perform FFT on the original hologram to obtain the frequency and phase information of the original hologram;

Using Gaussian kernel function and phase compensation factor to filter the frequency and phase information of the original hologram to remove zero-order diffraction;

After inverse FFT transformation is performed on the frequency and phase information obtained by filtering, the restored target image is reconstructed.

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:

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.

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(xcosθ _x +ycosθ _y )] (2)

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)=A ² +|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 formula (4):

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;

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):

where d' represents the reconstruction distance; when the reconstruction distance d' is equal to the recording distance, the object can be clearly reconstructed.

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.

Preferably, the Gaussian kernel function g and the phase factor C are calculated by the following formulas:

Further, the original hologram is obtained based on off-axis interferometry.

Preferably, the raw hologram is acquired by a microbolometer based on Mach-Zander interferometry.

Compared with the prior art, the beneficial effects achieved by the present invention:

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.

Description of drawings

Fig. 1 is the flow chart of the method of the present invention;

Fig. 2 is the optical device used in the experiment of the present invention;

Figure 3 is an off-axis digital holographic recording and reconstruction scheme;

Figure 4 is an infrared digital hologram with strong zero-order diffraction:

(a) Raw hologram captured;

(b) The processing result of the hologram after FFT;

(c) is the 3D mesh result of Fig. 4(b);

Fig. 5 is the process of the method of the present invention:

(a) and (b) are original reproductions of the hologram;

(c) and (d) σ=2, the filtering results of the hologram;

(e) and (f) σ=1, the filtering result of the hologram;

(g) and (h) σ=0.7, filtered results of holograms.

Detailed ways

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.

Description of related terms:

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.

Example 1

As shown in Figure 1 to Figure 5, a method for eliminating zero-order diffraction of infrared digital holography, comprising the following steps:

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;

The second beam is also reflected on the microbolometer after passing through M3, VA, L1, L2, and M4 in sequence;

The microbolometer obtains the original hologram by integrating the information from the two beams.

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.

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:

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).

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(xcosθ _x +ycosθ _y )] (2)

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)=A ² +|O(x,y)| ² +2A|O(x,y)|·cos[φ(x,y)-kxcosθ _x -kycosθ _y ] (3)

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.

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:

where m and n are integers and follow the rules ﹣Nx/2≧m≦Nx/2,﹣Ny/2≧n≦Ny/2.

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:

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.

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:

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.

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:

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.

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.

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:

in,

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

So C cannot be equal to 1.

The original hologram was filtered with a Gaussian low-pass filter and a phase averaging filter.

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.

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.

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.

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.

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:

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(xcosθ_x+ycosθ_y)](2)

wherein A represents intensity, θ_xAnd theta_yRespectively 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)-kxcosθ_x-kycosθ_y](3)。

4. the method of claim 1, wherein the discrete intensity distribution of the original hologram is calculated by equation (4):

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):

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:

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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