CN107101974B - A Novel Three-Step Lensless Coherent Diffraction Imaging Method - Google Patents

Abstract

A novel three-step lensless method for coherent diffraction imaging. Use the collimated and expanded laser beam to illuminate the object to be tested, and record three diffraction patterns without parallel flat crystals, one parallel flat crystal and two parallel flat crystals at the front end of the CCD respectively; The algorithm combining filtering and coherent diffraction diffraction imaging processes the collected three diffraction patterns to reconstruct the complex amplitude image of the sample to be tested. The invention effectively solves the bottleneck problem of the traditional coherent diffraction imaging method that needs to move the CCD or the sample to be tested many times, and also solves the random error in the moving process and the operability of the experiment. The invention has simple and fast experimental operation, strong operability, and effective combination of coherent diffraction imaging algorithm and filtering, which improves the convergence speed and the recovery effect of the sample.

Description

A Novel Three-Step Lensless Coherent Diffraction Imaging Method

technical field

The invention relates to the technical field of optical diffraction imaging, in particular to a novel three-step lensless coherent diffraction imaging method.

Background technique

There have been many developments in lensless coherent diffraction imaging in recent years, and this method generally adopts an iterative algorithm. The complex amplitude information of the object can be reconstructed from the diffraction intensity pattern of the object without the need for reference light. See (Opt. Lett. 31, 3095-3097 (2006); J. Opt. Soc. Am. A25, 416-422 (2008); Nat. Phys., 4, 394-398 (2008); Appl. Opt. 21, 2758-2769 (1982); J. Opt. Soc. Am. A 23, 1179-1200 (2006)) After irradiating the sample with a beam of coherent light, the diffraction pattern produced by the sample was received on the CCD. In order to obtain more accurate amplitude and phase information, more diffraction patterns with different diffraction distances can be obtained by continuously changing the relative distance between the CCD and the sample. See (Opt.Lett.30(8), 833-5(2005)), but these technical solutions have the following technical defects: it is necessary to obtain a plurality of diffractive surfaces with different distances, and during the implementation process, a moving sample or CCD is used. This method needs to repeatedly change the position of the sample or CCD, which requires a lot of repeated work. At the same time, it introduces random errors that directly affect the experimental results. The obtained sampling pattern is not accurate, and requires Oversampling, long experimental operation period and weak operability, and poor timeliness of imaging.

SUMMARY OF THE INVENTION

In order to overcome the above problems of the prior art, the purpose of the present invention is to provide a novel three-step lensless coherent diffraction imaging method. The invention improves the timeliness and operability of the imaging system, simplifies the steps of implementing operations, improves the method that needs to change the relative distance between the CCD or the sample by changing the placement position, and overcomes the repetition of a large number of changes in the relative distance. It can reduce the random error caused by the experimental operation, avoid oversampling, and can restore and reconstruct the complex amplitude object quickly and with good imaging quality, so that the specific experimental operation is simple and easy to implement.

The object of the present invention can be achieved through the following technical solutions, a novel three-step lensless coherent diffraction imaging method, comprising the following steps:

1) Build the optical path of the three-step lensless coherent diffraction imaging system, and add the sample to be tested;

2) Irradiate the sample to be tested with a visible parallel beam, and use the CCD to collect the first diffraction pattern;

3) Add the first parallel flat crystal between the sample to be tested and the CCD, and use the CCD to collect the second diffraction pattern;

4) Add a second parallel flat crystal between the sample to be tested and the CCD, and use the CCD to collect the third diffraction pattern;

5) Using the three diffraction patterns at different distances obtained in steps 2) to 4), the image amplitude and phase of the sample to be tested are restored and reconstructed by an effective fusion method of coherent diffraction algorithm and filtering, and a lensless coherent diffraction imaging image is obtained ;

Wherein, in the effective fusion method of the coherent diffraction algorithm and filtering in the step 5), the initial complex amplitude distribution on the object plane is an arbitrary complex amplitude distribution of g ⁰ (x ₀ , y ₀ ).

The sample to be tested is of pure amplitude type, and the complex amplitude distribution on the object plane after the k+1 iteration is shown in formula (10):

g ^(k+1) (x ₀ , y ₀ )=|g ^(k) (x ₀ , y ₀ )| (10).

The sample to be tested is of complex amplitude type, and the complex amplitude distribution on the object plane after the k+1 iteration is shown in formula (11):

g ^(k+1) (x ₀ , y ₀ )=g ^(k) (x ₀ , y ₀ ) (11).

The g ^(k) (x ₀ , y ₀ ) represents the complex amplitude distribution of the object function obtained by the k-th iteration, and g ^(k) (x ₀ , y ₀ ) is iteratively obtained by formula (1)-formula (9) :

分别为第1、第2、第3衍射平面上第k次迭代后的复振幅分布，|F₁(x₁,y₁)|、|F₂(x₂,y₂)|、|F₃(x₃,y₃)|分别为在第1、第2、第3衍射平面上实际测得的振幅分布，φ₁(x,y)、φ₂(x,y)、φ₃(x,y)分别表示第1、第2、第3衍射平面上第k次迭代后的相位分布，G₁ ^(k)'(x₁,y₁)、G₂ ^(k)'(x₂,y₂)、G₃ ^(k)'(x₃,y₃)分别为第1、第2、第3衍射平面上第k次迭代振幅部分经过校正的复振幅分布。其中(1)-(9)为一个循环，初始k＝0，随着迭代次数k的增加，直至输出理想的物体的复振幅重建图样。In the formula, FrT represents the forward transformation of Fresnel diffraction, IFrT represents the inverse transformation of Fresnel diffraction,

are the complex amplitude distributions after the k-th iteration on the 1st, 2nd, and 3rd diffraction planes, respectively, |F ₁ (x ₁ , y ₁ )|, |F ₂ (x ₂ , y ₂ )|, |F ₃ (x ₃ , y ₃ )| are the amplitude distributions actually measured on the first, second, and third diffraction planes, respectively, φ ₁ (x, y), φ ₂ (x, y), φ ₃ (x, y) represents the phase distribution after the k-th iteration on the 1st, 2nd, and 3rd diffraction planes, respectively, G ₁ ^(k) '(x ₁ , y ₁ ), G ₂ ^(k) '(x ₂ , y ₂ ) and G ₃ ^(k) '(x ₃ , y ₃ ) are the corrected complex amplitude distributions of the k-th iteration amplitude part on the first, second, and third diffraction planes, respectively. Among them (1)-(9) is a cycle, the initial k=0, with the increase of the number of iterations k, until the ideal complex amplitude reconstruction pattern of the object is output.

The optical path of the lensless coherent diffraction imaging system includes a helium-neon laser, a first parallel flat crystal and a second parallel flat crystal. After passing through the first diffraction plane where the sample to be tested is located, the second diffraction plane where the first parallel flat crystal is located, and the third diffraction plane where the second parallel planar crystal is located, the imaging image is recorded by the CCD image sensor, and the image is recorded by the CCD image sensor. The imaging image is transmitted to the computer, and the computer processes the imaging image recorded by the CCD image sensor.

The light source of the helium-neon laser produces red light with a wavelength of 632 nm.

Compared with the existing technical scheme, the present invention has the following beneficial effects:

1) The experimental operation method of “repeatedly moving the CCD or moving the relative distance of the sample to be tested” is fundamentally changed to obtain different diffraction patterns on the multi-distance diffraction surface, so that the experimental implementation can be qualitatively improved. improvement.

2) Diffraction patterns on diffractive surfaces at different distances are obtained by inserting parallel flat crystals to avoid random errors caused by the moving process, greatly improving the timeliness of experimental operations and enhancing the operability of experiments.

3) The filtering process is introduced into the algorithm, and the filtering and the coherent diffraction algorithm are effectively integrated, so that the convergence speed and accuracy are greatly improved during the image restoration process.

4) The sample to be tested can be a pure amplitude sample or a complex amplitude sample, and the recovery effect of the complex amplitude sample is more advantageous.

Due to the method of adding parallel flat crystals in sequence proposed by the present invention, the random errors caused by human beings are reduced, no oversampling is required, and three diffraction patterns are used to complete the restoration and reconstruction of the pattern of the sample. The three-step lensless coherent diffraction imaging system greatly simplifies the experimental operation steps.

Description of drawings

1 is a schematic diagram of a novel three-step lensless coherent diffraction imaging method of the present invention;

2 is a schematic diagram of the optical path of the novel three-step lensless coherent diffraction imaging method of the present invention;

Fig. 3 is that the image collector CCD of the present invention receives the first diffraction pattern when there is no parallel flat crystal;

Fig. 4 is that after the present invention inserts a parallel flat crystal, the image collector CCD receives the second diffraction pattern;

Fig. 5 is that after the present invention inserts two parallel flat crystals, the image collector CCD receives the third diffraction pattern;

Fig. 6 is the simulation experiment series diagram of the present invention to pure amplitude type sample;

FIG. 7 is a series of diagrams of simulation experiments of the present invention on complex-amplitude type samples.

In the figure, 1 is a helium-neon laser; 2 is a collimated beam expansion system; 3 is a sample to be tested; 4 is a first parallel flat crystal; 5 is a second parallel flat crystal; 6 is a CCD image sensor; 7 is a computer.

Detailed ways

In order to better understand the specific content and implementation process of the present invention, the specific process of implementing the novel three-step lensless coherent diffraction imaging method will be described in detail below with reference to the accompanying drawings.

Referring to Figures 1 to 5, a new optical path system of a three-part lensless coherent diffraction imaging method includes a He-Ne laser, a first parallel flat crystal and a second parallel flat crystal. After the light source of the He-Ne laser generates laser light, the light passes After the collimating beam expanding system expands the beam, the parallel light passes through the first diffraction plane where the sample to be tested is located, the second diffraction plane where the first parallel flat crystal is located, and the third diffraction plane where the second parallel planar crystal is located. Then, the imaging image is recorded by the CCD image sensor, and the imaging image is transmitted to the computer, and the computer processes the imaging image recorded by the CCD image sensor.

Referring to Figure 2, build the experimental optical path diagram, use the red light with the wavelength of 632nm of the He-Ne laser, install the collimated beam expander system, and then place the sample to be tested, and prepare pure-amplitude and complex-amplitude samples separately for use in the experiment. A sample comparison can be formed, a CCD image sensor is placed after a distance Z ₀ , and the CCD image sensor is connected to the computer, and two parallel flat crystals required for the experiment are prepared for use in the experiment.

Referring to Figure 3, after building the optical path diagram, the first step is to open the image collector CCD to collect the first sample diffraction pattern and save it.

As shown in Figure 4, in the second step, insert a first parallel flat crystal at a distance Z ₁ from the sample, and the CCD collects the second diffraction pattern and saves it.

As shown in Figure 5, in the third step, insert a second parallel flat crystal at a distance Z ₂ from the parallel flat crystal, and the CCD collects the third diffraction pattern and saves it. The specific operation steps are implemented according to the above process, and then the collected patterns are processed by the computer.

分别为第1、第2、第3衍射平面上第k次迭代后的复振幅分布，|F₁(x₁,y₁)|、|F₂(x₂,y₂)|、|F₃(x₃,y₃)|分别为在第1、第2、第3衍射平面上实际测得的振幅分布，φ₁(x,y)、φ₂(x,y)、φ₃(x,y)分别表示第1、第2、第3衍射平面上第k次迭代后的相位分布，G₁ ^(k)'(x₁,y₁)、G₂ ^(k)'(x₂,y₂)、G₃ ^(k)'(x₃,y₃)分别为第1、第2、第3衍射平面上第k次迭代振幅部分经过校正的复振幅分布。其中(1)-(9)为一个循环，初始k＝0，随着迭代次数k的增加，直至输出理想的物体的复振幅重建图样：The algorithm used in the implementation of the present invention: let

are the complex amplitude distributions after the k-th iteration on the 1st, 2nd, and 3rd diffraction planes, respectively, |F ₁ (x ₁ , y ₁ )|, |F ₂ (x ₂ , y ₂ )|, |F ₃ (x ₃ , y ₃ )| are the amplitude distributions actually measured on the first, second, and third diffraction planes, respectively, φ ₁ (x, y), φ ₂ (x, y), φ ₃ (x, y) represents the phase distribution after the k-th iteration on the 1st, 2nd, and 3rd diffraction planes, respectively, G ₁ ^(k) '(x ₁ , y ₁ ), G ₂ ^(k) '(x ₂ , y ₂ ) and G ₃ ^(k) '(x ₃ , y ₃ ) are the corrected complex amplitude distributions of the k-th iteration amplitude part on the first, second, and third diffraction planes, respectively. Among them (1)-(9) is a cycle, the initial k=0, with the increase of the number of iterations k, until the complex amplitude reconstruction pattern of the ideal object is output:

If the object is of pure amplitude type, then g ^(k+1) (x _0, y ₀ )＝|g ^(k) (x _0, y ₀ )|, if the object is of complex amplitude type, then g ^(k+1) (x ₀ , y ₀ )=g ^(k) (x ₀ , y ₀ ).

After a laser beam passes through the collimating beam expander system, place the sample to be tested behind the probe, install the CCD at a distance from the sample, and then keep the distance between the CCD and the sample unchanged, step by step between the CCD and the sample to be tested Between the test samples, the technical method proposed by the present invention is adopted: two parallel flat crystals are added in sequence, and the first, second, third and three sample diffraction patterns are received on the CCD, and the sample is finally restored and reconstructed. .

Example 1

The imaging effect of the pure amplitude sample is shown in Figure 6. In the series of Figure 6, 6a is the pure amplitude pattern to be measured, 6b is the diffraction pattern on the first diffraction plane at a distance of 300mm from the sample, and 6c is the distance from the first diffraction pattern. 1 is the diffraction pattern on the second diffraction plane at a distance of 50 mm from the diffraction plane, 6d is the diffraction pattern on the third diffraction plane at a distance of 50 mm from the second diffraction plane, and 6e is the recovery result of 100 iterations of the three-step diffraction iterative algorithm. The correlation coefficient between 6a and 6e is 0.9991, indicating that this method can achieve good imaging effect for pure amplitude objects.

Example 2

The imaging effect of the complex amplitude type sample is shown in Figure 7. In the series of pictures in Figure 7, 7a is the amplitude part of the original complex amplitude type object, 7b is the phase part of the original complex amplitude type object, and 7c is the first 300mm away from the object. 1 The diffraction pattern on the diffraction plane, 7d is the diffraction pattern on the second diffraction plane at a distance of 50mm from the first diffraction plane, 7e is the diffraction pattern on the third diffraction plane at a distance of 50mm from the second diffraction plane, 7f and 7g are three steps respectively The coherent diffraction algorithm iterates 100 times the amplitude and phase components of the reconstruction. The correlation coefficient of 7a and 7f was 0.9982, and the correlation coefficient of 7b and 7g was 0.9763. It shows that this method can achieve good imaging effect for complex amplitude objects.

The above-mentioned methods and embodiments all use the novel three-step lensless coherent diffraction imaging method proposed by the present invention, and obtain three diffraction patterns at different distances by inserting parallel flat crystals in sequence, and finally realize the recovery of the amplitude and phase information of the sample to be tested. purpose of reconstruction. The practice of the present invention is not limited to the specific embodiments described above. As long as it is a diffraction imaging method, device, and system that obtains different diffraction distances by inserting a parallel flat crystal, the latter adopts the recovery algorithm proposed by the present invention, and belongs to the protection scope of the invention.

Claims (5)

1. A novel three-step lensless coherent diffraction imaging method, comprising the following steps: 1) Build the optical path of the three-step lensless coherent diffraction imaging system, and add the sample to be tested; 2) Irradiate the sample to be tested with a visible parallel beam, and use the CCD to collect the first diffraction pattern; 3) Add the first parallel flat crystal between the sample to be tested and the CCD, and use the CCD to collect the second diffraction pattern; 4) Add a second parallel flat crystal between the sample to be tested and the CCD, and use the CCD to collect the third diffraction pattern; 5) Using the three diffraction patterns at different distances obtained in steps 2) to 4), the image amplitude and phase of the sample to be tested are restored and reconstructed by an effective fusion method of coherent diffraction algorithm and filtering, and a lensless coherent diffraction imaging image is obtained ; Wherein, in the effective fusion method of the coherent diffraction algorithm and filtering in the step 5), the initial complex amplitude distribution on the object plane is an arbitrary complex amplitude distribution of g ⁰ (x ₀ , y ₀ ). 2. The method for a novel three-step lensless coherent diffraction imaging according to claim 1, wherein g ^(k) (x ₀ , y ₀ ) represents the complex amplitude distribution on the object plane, which is arbitrarily selected by The initial complex amplitude distribution formula g ⁽⁰⁾ (x ₀ , y ₀ ) on the object plane is substituted into (1) to (9) after k iterations to obtain iteratively (initial iteration number k=0):

In the formula, FrT represents the forward transformation of Fresnel diffraction, IFrT represents the inverse transformation of Fresnel diffraction,

are the complex amplitude distributions after the k-th iteration on the 1st, 2nd, and 3rd diffraction planes, respectively, |F ₁ (x ₁ , y ₁ )|, |F ₂ (x ₂ , y ₂ )|, |F ₃ (x ₃ , y ₃ )| are the amplitude distributions actually measured on the first, second, and third diffraction planes, respectively, φ ₁ (x, y), φ ₂ (x, y), φ ₃ (x, y) represents the phase distribution after the k-th iteration on the 1st, 2nd, and 3rd diffraction planes, respectively, G ₁ ^(k) '(x ₁ , y ₁ ), G ₂ ^(k) '(x ₂ , y ₂ ) and G ₃ ^(k) '(x ₃ , y ₃ ) are the corrected complex amplitude distributions of the k-th iteration amplitude part on the first, second, and third diffraction planes, respectively. Among them (1)-(9) is a cycle, the initial k=0, with the increase of the number of iterations k, until the ideal complex amplitude reconstruction pattern of the object is output. 3. A novel three-step lensless coherent diffraction imaging method according to claim 2, wherein the sample to be tested is of pure amplitude type, and the complex amplitude distribution on the object plane after the k+1th iteration As shown in formula (10): g ^(k+1) (x ₀ , y ₀ )=|g ^(k) (x ₀ , y ₀ )| (10). 4 . A novel three-step lensless coherent diffraction imaging method according to claim 2 , wherein the sample to be tested is a complex amplitude type, and the complex amplitude on the object plane after the k+1 iteration The distribution is shown in formula (11): g ^(k+1) (x ₀ , y ₀ )=g ^(k) (x ₀ , y ₀ ) (11). 5. A novel three-step lensless coherent diffraction imaging method according to claim 1, wherein the optical path of the lensless coherent diffraction imaging system comprises a laser (1), a first parallel flat crystal (4). ) and the second parallel flat crystal (5), after the light source of the helium-neon laser (1) generates laser light, after the light is expanded by the collimating beam expanding system (2), the parallel light passes through the sample to be tested (3), the first After the parallel flat crystal (4) and the third diffraction plane where the second parallel flat crystal (5) is located, the imaging image is recorded by the CCD image sensor (6), and the imaging image is transmitted to the computer (7), and the computer (7 ) processes the imaged images recorded by the CCD image sensor (6).

Images