CN102920438B - High-resolution optical scanning holographic slice imaging method based on variable pupils - Google Patents

Abstract

The invention discloses a high-resolution optical scanning holographic slice imaging method based on a variable pupil, which belongs to the field of optical scanning and mainly solves the problem of relatively large defocus noise when reconstructing images of arbitrary two-dimensional slices in the prior art Defects. The present invention uses a two-dimensional scanning mirror to control the deflection of the first Fresnel zone plate, thereby realizing the first two-dimensional scanning of the object to be measured, and obtaining the first matrix equation; and controlling the second pupil after shifting the second pupil The deflection of the two Fresnel zone plates realizes the second two-dimensional scanning of the object to be measured, and obtains the second matrix equation; then combines the two matrix equations, and then introduces the conjugate gradient algorithm to realize slice imaging. Through the above solution, the present invention realizes high-precision slice imaging, greatly reduces defocus noise, and is applicable to various optical fields for obtaining slice imaging.

Description

A High-Resolution Optical Scanning Holographic Slice Imaging Method Based on Variable Pupil

technical field

The invention belongs to the field of optical scanning, and in particular relates to a high-resolution optical scanning holographic slice imaging method based on a variable pupil.

Background technique

Optical scanning holography, referred to as OSH, is a non-traditional imaging technology based on Fresnel zone plate scanning, which achieves high-resolution three-dimensional imaging of targets through two-dimensional optical scanning. It is used in biomedical imaging and fluorescent object imaging. , 3D holographic television system and optical remote sensing and other fields have broad application prospects.

The two-dimensional hologram obtained by optical scanning holography technology contains the complete three-dimensional information of the object. Therefore, an important analysis and processing step of the object hologram in optical scanning holography technology is the slice imaging of the object, that is, any two-dimensional section of the object image reconstruction. The difficulty in image reconstruction of any two-dimensional slice of an object is how to eliminate noise from other layers of the object, that is, defocus noise. Slice imaging is a typical inverse problem in image processing, and it is also an ill-posed problem.

The literature 'Optical Scanning Holography with MATLAB' proposes a traditional slice imaging method, that is, to perform convolution operation with the hologram of the object and the Fresnel zone plate conjugate at the slice to be reconstructed, so as to realize slice imaging, but Since isolation noise cannot be eliminated, its application is greatly restricted.

The literature 'Three-dimensional microscopy and sectional image reconstruction using optical scanning holography' introduces an inverse imaging algorithm. This iterative algorithm can achieve slice imaging with an axial resolution of about 1 mm, and can effectively suppress defocus noise, but its Good imaging cannot be achieved at smaller axial dimensions.

The document 'Depth resolution enhancement in optical scanning holography with a dual-wavelength laser source' proposed a method to improve the axial resolution of slice imaging by using a dual-wavelength laser. It uses lasers with output wavelengths of 632nm and 543nm respectively to obtain two sets of Object hologram, which in turn increases the axial resolution to about 2.5 microns, but its practicality is greatly limited due to the large noise introduced by the two different wavelengths working simultaneously in the optical system.

Contents of the invention

The purpose of the present invention is to reduce the defocus noise in slice imaging, and propose a high-resolution optical scanning holographic slice imaging method based on variable pupils, using two different Fresnel zone plates for the same object to be measured Scanning is performed to obtain two sets of holograms, so that more linear equations are introduced for the ill-posed inverse problem of slice imaging, and high-resolution slice imaging is realized.

The technical scheme that the present invention adopts is as follows:

A high-resolution optical scanning holographic slice imaging method based on a variable pupil, comprising the following steps:

(1) The first polarizing beam splitter divides the light emitted by the same light source into two beams. The first beam passes through the first pupil to form a plane wave, and the second beam passes through the acousto-optic modulator to generate After the translation, the spherical wave is formed through the second pupil, and the plane wave and the first spherical wave are condensed through the second polarizing beam splitter, and after polymerization, interference is generated on the object to be measured to form the first Fresnel zone plate;

(2) Use the two-dimensional scanning mirror to control the deflection of the first Fresnel zone plate, so as to realize the first two-dimensional scanning of the object to be measured, and obtain slice information The first matrix equation of ;

(3) Adjust the voltage of the spatial light modulator to shift the second pupil;

(4) The first polarizing beam splitter divides the light emitted by the same light source into two beams. The first beam passes through the first pupil to form a spherical wave, and the second beam is generated by the acousto-optic modulator. After the translation, the second spherical wave is formed through the shifted second pupil, the plane wave and the second spherical wave are condensed by the second polarizing beam splitter, and after polymerization, interference is generated on the object to be measured to form the second Fresnel Erbo belt plate;

(5) Use the two-dimensional scanning mirror to control the deflection of the second Fresnel zone plate, so as to realize the second two-dimensional scanning of the object to be measured, and obtain slice information The second matrix equation of ;

(6) Integrate the first matrix equation and the second matrix equation to convert the slice imaging process into a minimum linear equation, and solve the slice information according to the conjugate gradient algorithm .

Wherein, the first Fresnel zone plate in the step (1) is:

(1)

Among them, x , y , z represent space coordinates, k is the wave number of light, and z is the distance from the object to be measured to the two-dimensional scanning mirror.

Further, the object to be measured in the step (2) is a set of two discrete slices, and the axial positions of the two slices are respectively and , so the specific implementation of the first matrix equation is as follows:

(2a) Carry out the first two-dimensional scanning of the object to be measured to obtain the first two-dimensional hologram:

(2)

where the complex function is the amplitude information of the object to be measured, and * represents two-dimensional convolution;

(2b) Place the Fresnel zone plate on and The values at are converted to matrix and ;

(2c) Combine the first 2D hologram with the matrix and Combined to get the first matrix equation:

(3)

in is Gaussian white noise, the Gaussian white noise is of length A one-dimensional vector matrix of .

In order to obtain slice information accurately, after adjusting the voltage, the pupil offset distance is , so the second Fresnel zone plate is:

(4).

Furthermore, the specific implementation of obtaining the second matrix in step (5) is the same as the specific implementation of obtaining the first matrix in step (2), so the equation of the second matrix is as follows:

(5).

Furthermore, in the step (6), the slice information is obtained The method is as follows:

(6a) Integrating the first matrix equation and the second matrix equation, we get:

(6)

(6b) Transform the above formula into a minimized linear equation:

(7)

Where || || represents the second-order determinant norm, is a penalty coefficient and >0, C is the Laplacian operator, and the solution of the minimized linear equation is expressed as:

(8)

in for The conjugate transpose of ;

(4c) By introducing the conjugate gradient algorithm, the minimized linear equation can be solved to obtain the slice information value.

Compared with the prior art, the present invention has the following beneficial effects:

(1) The present invention uses optical scanning holography technology, that is, through the deflection of two Fresnel zone plates to realize two scans of the object to be measured, and obtain its high-resolution three-dimensional imaging, the application range of Fresnel zone plates Including biology, machinery, optics, electricity, etc., so the present invention is applicable to various fields and has a very wide range of applications;

(2) In the present invention, the position of the second pupil can be adjusted only by adjusting the voltage of the spatial light modulator When the second beam of light passes through the shifted pupil, a new spherical wave can be obtained, and the second Fresnel zone plate can be obtained. Compared with scanning only once, one more two-dimensional hologram can be obtained. , so more linear equations are introduced for the ill-posed inverse problem of slice imaging, so that when solving the slice information The obtained results further approximate the slice information The true value of , which is the reason for fundamentally improving the resolution of slice imaging;

(3) The invention does not need to move the object to be tested, but only needs to adjust the voltage of the spatial light modulator, which is easy to implement and has strong operability;

(4) The present invention combines the obtained first matrix equation with the second matrix equation, transforms it into a minimized linear equation, and combines the conjugate gradient algorithm to solve the high-precision slice information The value of , the entire calculation process is simple, the actual operation is easy, and the slice information is greatly simplified The solution process;

(5) The present invention accurately obtains slice information The process is simple to operate, easy to implement, has strong practicability and operability, and is suitable for popularization and use.

Description of drawings

Fig. 1 is a schematic diagram of the structure of the present invention.

Fig. 2 is a schematic diagram of a slice of a sample to be tested in an embodiment of the present invention.

Fig. 3 is different pupils among the present invention-embodiment The corresponding Fresnel zone plot.

Fig. 4 is a cosine hologram obtained by the first scan in the embodiment of the present invention.

Fig. 5 is a sinusoidal hologram obtained by the first scan in the embodiment of the present invention.

Fig. 6 is a cosine hologram obtained in the second scan in the embodiment of the present invention.

Fig. 7 is a sinusoidal hologram obtained in the second scan in the embodiment of the present invention.

Fig. 8 adopts different methods in the present invention-embodiment and Slice images obtained at .

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and examples, and the embodiments of the present invention include but not limited to the following examples.

Example

As shown in FIG. 2 , in order to simplify the problem, FIG. 2 is a schematic diagram of the object to be tested in the present invention, and the object to be tested only includes two slices of information. In the first optical scan, the axial positions of the two slices of the object are , , and The axial distance is 10nm, and each slice size is , the matrix size is , where the scanning process can be realized by following the steps shown below:

Step 1 Set the variable pupil to , to obtain the first Fresnel zone plate FZP ₁ , to scan the object for the first time

(1) As shown in Figure 1, the light with angular frequency ω emitted by the same light source is split into two beams by the first polarizing beam splitter BS1, where the first beam passes through the first pupil form a plane wave ; The first beam of light passes through the first pupil after passing through the acousto-optic modulator to produce a frequency shift of Ω , the second pupil It is a variable pupil, which is realized by a transmission-type spatial light modulator. When scanning the sample for the first time, the Set as , thus forming the first spherical wave. The central wavelength of the single-wavelength light source used therein is 632nm.

(2) The two beams of processed light are combined by the second polarizing beam splitter BS2 to generate interference on the measured object to form the first Fresnel zone plate FZP ₁ , and then use the two-dimensional scanning mirror 2D Scanning Control the deflection of TD-FZP, so as to realize the first two-dimensional scanning of three-dimensional objects.

When the object to be measured is scanned, the photodetector receives the light wave propagating to the detection surface and generates a heterodyne current output. The photogenerated current undergoes electrical processing such as frequency mixing and amplification to generate demodulation information and store it in the computer.

The spatial impulse response of the optical scanning holographic system, that is, the first Fresnel zone plate can be expressed as:

(1)

in represent space coordinates, is the wavenumber of light. It can be seen from formula (1) that for a certain axial position , the first Fresnel wave zone plate is a about two-dimensional function.

Assuming a complex function Represents the amplitude information of the object, and the first two-dimensional hologram obtained after the object is scanned by the optical system can be expressed as:

(9)

Among them, * represents two-dimensional convolution. If the object is regarded as a collection of a series of discrete slices, the axial coordinate z can be discretized, expressed as , respectively representing the axial positions of different slices. Then the first two-dimensional hologram represented by formula (9) can be expressed as:

(10)

Since there are only two slices, the above formula can be simplified to the following form:

(2)

In order to simplify equation (2) into a set of linear equations for analysis, we will and respectively converted to a one-dimensional vector matrix and . Since the slice of the object to be measured is a matrix, and then the length is A one-dimensional vector matrix of . Likewise, a two-dimensional hologram of an object can also be transformed into a length of 1D vector matrix .

The convolution operation in (2) can be expressed as a matrix operation, so the first Fresnel zone plate is in and The values at the matrix and the matrix , respectively constructing two The two-dimensional matrix of and :

(11)

(12)

Then through (11) and (12) can be expressed as the first matrix equation:

(3)

in and Represents the white Gaussian noise of the system and is ^a one-dimensional vector matrix of length N2 .

_The so-called slice imaging means recovering the slice information from G1 This is an ill-posed inverse problem, so we use the second Fresnel zone plate to scan the same object to improve the axial resolution of slice imaging.

Step 2 Use the second Fresnel zone plate to scan the same object to be measured

adjust the voltage of the spatial light modulator, the Set as:

(13)

So as to obtain the spherical wave with center position offset, where and Represents the second pupil exist Spatial offset on axis. The second spherical wave and the plane wave are combined through the second polarization beam splitter to produce interference on the measured object to form the second Fresnel zone plate FZP ₂ .

Therefore, the spatial impulse response of the optical scanning holographic system, that is, the second Fresnel zone plate can be expressed as:

(4)

Comparing formula (4) with formula (1), we can see that by changing the second pupil , different Fresnel zone plates can be designed and realized by using the same optical system.

By scanning the same object to be measured, the hologram of the second object to be measured can be obtained, and the same process can be characterized as a matrix equation:

(5)

It can be seen from (6) that through the second scan we have obtained set of linear equations. In the two scans, the Fresnel zone plates that record the holographic information of the sample are different, namely , it can be seen that the linear equations obtained by using the second Fresnel zone plate to scan the same object to be measured are different. This way we add more efficient systems of linear equations to the solution of this ill-posed problem.

Step 3 Use the hologram obtained after two Fresnel zone plate scans to perform slice imaging.

The so-called slice imaging, even in the known In the case of , solve the slice information .

First, combine the first rectangular equation and the second matrix equation obtained by two 2D scans, expressed as:

(6)

The solution to this problem can be transformed into the following minimized linear equation, namely:

(7)

In (8), || || represents the second-order norm, λ>0 is the penalty coefficient, and C is the Laplacian operator. The solution to this minimization problem can be expressed as:

(8)

in for the matrix The conjugate transposition of . Equation (9) can be solved by introducing the conjugate gradient algorithm, and the convergence of the algorithm depends on the matrix . For an object containing two slices, the matrix can be expressed as:

(14)

It can be seen from formula (14) that the matrix is a positive definite symmetric matrix, and it is solved by the conjugate gradient algorithm to obtain the slice information , wherein the conjugate gradient algorithm is a prior art.

Fresnel zone diagrams obtained with different pupils in the two scans are shown in Figure 3. 4 is the cosine hologram of the first scan, FIG. 5 is the sine hologram of the first scan, FIG. 6 is the cosine hologram of the second scan, and FIG. 7 is the sine hologram of the second scan. It can be seen from Figures 4 to 7 that we cannot obtain any slice information of the sample to be tested from the hologram.

Comparison of three slice imaging methods: (1) traditional slice imaging method, that is, using the Fresnel zone plate conjugate function at the slice to convolve the sample hologram; (2) slice imaging based on a single scan with a fixed pupil Methods; (3) Slice imaging method based on two scans with variable pupil. Figure 8(a)-(f) shows the results of slice imaging using three different methods, respectively. It can be seen from Figure 8(a)-(b) that the traditional slice imaging method not only cannot distinguish between two slices, but also introduces large defocus noise; Although the slice imaging method of a single pupil scan can suppress the defocus noise to a certain extent, it cannot achieve a higher axial resolution of 10nm; while using the method of the present invention, it is possible to completely distinguish two images with an axial distance of 10nm. A depth slice, the results are shown in Figure 8(e)-(f), which means that the method of the present invention improves the axial resolution of optical scanning holography to 10nm.

According to the above-mentioned embodiments, the present invention can be well realized.

Claims (6)

1. the high-resolution optical scanning holography slice imaging method based on variable pupil, is characterized in that, comprises the following steps:

The light that (1) first polarization beam apparatus sends same light source is divided into two bundles, and light beam forms plane wave by the first pupil, and the second bundle light produces through acousto-optic modulator translation after by the second pupil, form the first spherical wave again, plane wave and the first spherical wave, by the second polarization beam apparatus optically focused, are produced after polymerization to interfere and form the first Fresnel plate on object under test;

(2) utilize two-dimensional scan mirror to control the deflection of the first Fresnel plate, thereby realize the two-dimensional scan for the first time to object under test, obtain comprising slice information the first matrix equation;

(3) regulate the voltage of spatial light modulator, make the second pupil produce skew;

The light that (4) first polarization beam apparatus send same light source is divided into two bundles, and light beam forms plane wave by the first pupil, and the second bundle light produces by acousto-optic modulator translation after by the second pupil after skew, form the second spherical wave again, plane wave and the second spherical wave, by the second polarization beam apparatus optically focused, are produced after polymerization to interfere and form the second Fresnel plate on object under test;

(5) utilize two-dimensional scan mirror to control the deflection of the second Fresnel plate, thereby realize the two-dimensional scan for the second time to object under test, obtain comprising slice information the second matrix equation;

(6) the first matrix equation and the second matrix equation are integrated, made slice imaging process be converted into a minimal linear equation, and according to conjugate gradient algorithms, solve slice information .

2. a kind of high-resolution optical scanning holography slice imaging method based on variable pupil according to claim 1, is characterized in that, described in described step (1), the first Fresnel plate is:

（1）

Wherein x, y, zrepresent space coordinates, kfor the wave number of light, zfor the distance of object under test to two-dimensional scan mirror.

3. a kind of high-resolution optical scanning holography slice imaging method based on variable pupil according to claim 2, is characterized in that, in described step (2), object under test is the set of two discrete slices, and the axial location of two sections is respectively with , the specific implementation that therefore obtains the first matrix equation is as follows:

(2a) object under test is carried out to two-dimensional scan for the first time, obtains the first two-dimensional hologram:

（2）

Complex function wherein for the amplitude information of this object under test, * represents two-dimensional convolution simultaneously;

(2b) the first Fresnel plate is existed with the value at place is converted to respectively matrix with ;

(2c) by the first two-dimensional hologram and matrix with combine and obtain the first matrix equation:

（3）

Wherein for white Gaussian noise, this white Gaussian noise is that length is one dimension vector matrix; represent axial distance z ₁the slice information at place, represent axial distance z ₂the slice information at place.

4. a kind of high-resolution optical scanning holography slice imaging method based on variable pupil according to claim 3, is characterized in that, after regulation voltage, the offset distance of the second pupil is , therefore the second Fresnel plate is:

（4）。

5. a kind of high-resolution optical scanning holography slice imaging method based on variable pupil according to claim 4, it is characterized in that, the specific implementation that obtains the second matrix in described step (5) is identical with the specific implementation that step (2) obtains the first matrix, and therefore the second matrix equation is following formula:

（5）；

represent the white Gaussian noise in the second matrix equation.

6. a kind of high-resolution optical scanning holography slice imaging method based on variable pupil according to claim 5, is characterized in that, described step solves slice information in (6) method as follows:

(6a) the first matrix equation and the second matrix equation are integrated, are obtained:

（6）

(6b) above formula is converted into and minimizes linear equation:

（7）

Wherein || || represent second order ranks norm, for penalty factor and > 0, cfor Laplace operator, this solution that minimizes linear equation is expressed as:

（8）

Wherein for conjugate transpose;

(6c) by introducing conjugate gradient algorithms, can minimize linear equation to this and solve, obtain slice information value.