CN109212749A - A kind of filter plate and its design method for realizing edge enhancing imaging - Google Patents

Abstract

The invention relates to the technical field of edge enhancement imaging, and discloses a filter for realizing edge enhancement imaging and a design method thereof. The method includes: superposing four Gaussian functions to obtain a point spread function of the filter function; The point spread function is reversely calculated to obtain the filter function. The invention combines the modulation effect of amplitude and phase on edge enhancement imaging, obtains the point spread function by superposing four Gaussian functions, and satisfies that there are no redundant side lobes around the main lobe, and uses Fourier transform to inverse the point spread function. This method is based on Hilbert transformation, and reinterprets the imaging theory of edge enhancement from the theory of convolution, and can achieve high-resolution and isotropic edge-enhanced imaging. .

Description

A filter for realizing edge-enhanced imaging and its design method

technical field

The present invention relates to the technical field of edge-enhanced imaging, in particular to a filter for realizing edge-enhanced imaging and a design method thereof.

Background technique

Edge-enhanced imaging technology has a great application in the field of imaging. In 1942, Zernike first realized phase-contrast imaging. Since then, a lot of work has been used to study this technology. Marr and Torre et al. Imaging makes a big contribution. At present, the techniques commonly used to achieve edge-enhanced imaging mainly include (1) numerical spatial differential imaging (2) differential interference contrast imaging (3) Hilbert transform filtering imaging.

In 2018, Zhu Tengfeng used the surface plasmon structure to realize the edge-enhanced imaging of spatial differentiation in the experiment, but this digital imaging technology cannot realize the phase pair well when the object has no obvious features. Differential interference contrast imaging is relatively simple to implement. Spatial light modulators can be used to simplify the optical path to complete the imaging operation, but the imaging results of this technique are anisotropic. The Hilbert transform filtering imaging uses the idea of spatial filtering, adding a filter to the spectral surface of the 4f system to achieve edge-enhanced imaging. To achieve Hilbert transform, the most practical method is to use the spiral Phase plate.

In the field of optical microwaves, helical phase plates are widely used to reconstruct the amplitude and phase information at the edges of biological specimens. With the development of technology, direction-selective edge-enhanced imaging can be achieved by vector optics filters, fractional-order vortex filters, and phase-shift vortex filters. At the same time, the vortex lens also has great application value in edge-enhanced imaging. However, we found that due to the existence of a large number of redundant side lobes on both sides of the main lobe of the point spread function of the traditional vortex phase plate, this phenomenon will cause diffraction noise at the edges of the imaging results, making the results non-uniform, and this effect will becomes severe as the topological sum increases. To solve this problem and improve imaging quality, Laguerre Gaussian filters, Bessel filters, and Airy helical phase filters are designed to suppress unwanted sidelobes, resulting in uniform, high-resolution edge imaging result. At present, edge-enhanced imaging technology has great application prospects in the fields of infrared illumination, biological imaging, astronomical observation, fingerprint identification and long-distance remote sensing.

SUMMARY OF THE INVENTION

In view of the deficiencies of the prior art, the purpose of the present invention is to provide a filter for realizing edge-enhanced imaging. The following technical solutions are adopted:

A filter for realizing edge-enhanced imaging, its filter function for:

(in, represents the radial coordinates of the spectral plane, FT represents the Fourier transform, Represents a circular hole with radius R, h(x,y) is the filter function The point spread function of , which is obtained by the superposition of four Gaussian functions, (x, y) represents the coordinates of the imaging plane, ω ₀ is the Gaussian beam waist, and d ₀ is an arbitrary constant).

The second purpose of the present invention is to provide a design method of a filter for realizing edge-enhanced imaging. The following technical solutions are adopted:

A design method of a filter for realizing edge-enhanced imaging, comprising:

The point spread function of the filter function is obtained by superimposing the four Gaussian functions;

Using Fourier transform, the point spread function is reversely calculated to obtain a filter function.

As a further improvement of the present invention, the point spread function is:

(where, (x, y) represents the coordinates of the imaging plane, ω ₀ is the Gaussian beam waist, and d ₀ is an arbitrary constant);

The filter function is:

(in, represents the radial coordinates of the spectral plane, FT represents the Fourier transform, represents a circular hole of radius R).

Beneficial effects of the present invention:

The invention discloses a filter and a design method thereof. Combined with the modulation effect of amplitude and phase on edge-enhanced imaging, a point spread function is obtained by superposing four Gaussian functions to satisfy the requirement that there are no redundant side lobes around the main lobe. Fourier transform, reverse calculation of the point spread function to obtain the filter function of the filter, this method is based on the Hilbert transform, and reinterprets the imaging theory of edge enhancement from the theory of convolution, which can achieve High-resolution and isotropic edge-enhanced imaging.

The above description is only an overview of the technical solution of the present invention, in order to be able to understand the technical means of the present invention more clearly, it can be implemented according to the content of the description, and in order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand. , the following specific preferred embodiments, and in conjunction with the accompanying drawings, are described in detail as follows.

Description of drawings

1 is a schematic diagram of a 4f system in an embodiment of the present invention;

Figures 2(a) and 2(b) are respectively the filter functions in the embodiment of the present invention The two-dimensional plane distribution of the real part of the point spread function (vortex function) and the cross-sectional distribution of the radial value in the radial direction; Figures 2(c) and 2(d) are the filter functions in the embodiment of the present invention respectively The two-dimensional plane distribution of the imaginary part of the point spread function of the (vortex function) and the cross-sectional distribution of the radial value in the radial direction;

Figures 3(a) and 3(b) are respectively the filter functions in the embodiment of the present invention Two-dimensional plane distribution of the imaginary part of the point spread function (Bessel function) and cross-sectional distribution of radial values in the radial direction;

Figures 4(a) and 4(b) are respectively the filter functions in the embodiment of the present invention The two-dimensional plane distribution of the real part of the point spread function and the cross-sectional distribution of the radial value in the radial direction; Figures 4(c) and 4(d) are the filter functions in the embodiment of the present invention, respectively. The two-dimensional plane distribution of the imaginary part of the point spread function and the cross-sectional distribution of the radial value in the radial direction;

Fig. 5 is the theoretical and experimental comparison diagram of the amplitude object in the embodiment of the present invention;

FIG. 6 is a theoretical and experimental comparison diagram of a phase object in an embodiment of the present invention.

Detailed ways

The present invention is further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

As shown in FIG. 1 , which is a schematic diagram of the 4f system in this embodiment, the 4f system is the theoretical basis of the filter for realizing edge-enhanced imaging and the design method thereof in the present invention. L1 and L2 are Fourier thin lenses, both of which have a focal length of f. In Figure 1, (x ₀ , y ₀ ), (u, v) and (x, y) represent the Cartesian coordinates of the incident surface, the spectral surface and the imaging surface, respectively. Here, it is assumed that the complex amplitude of the object on the incident surface is g(x ₀ , y ₀ ), the function of the filter on the spectral surface is H(u, v), and the complex amplitude of the outgoing light field on the imaging surface is According to the optical path calculation of the 4f system, we can describe the exit field as follows:

where h(x,y) is the Fourier transform of the filter function H(u,v), the symbol stands for convolution operator). According to the theory of convolution, it can be obtained: if you want to achieve edge-enhanced imaging, the filter function needs two main properties, one is to darken the interior of the object, and the other is to brighten the edge of the object. In general, in order to satisfy the first property, the filter function needs to satisfy the following conditions:

Some constant terms are omitted from this formula, from which it follows that the center of the object can be darkened as long as the center of the filter function is equal to zero. The other property is more difficult to satisfy, so we first separately analyze the influence of the phase and amplitude of the filter function on the imaging results. For this reason, we find a pure phase filter function (vortex function) and a pure amplitude filter function (Bessel function), their expressions are:

in, represents the radial coordinates of the spectral surface, represents the diameter of a circular hole with radius R, J _l represents the Bessel function of the first kind of the lth order, and k _r is the mode constant. Through Fourier transform, the point spread functions of the two filter functions can be approximately expressed as follows:

Among them, (r, θ) represents the radial coordinate of the imaging plane, λ represents the wavelength, and J ₀ represents the 0th-order first-type Bessel function.

In order to see the influence of the filter function on the imaging results more intuitively, the point spread function distribution diagram of the filter function is drawn through numerical simulation.

As shown in Figure 2, Figures 2(a) and 2(b) are the filter functions respectively The two-dimensional plane distribution of the real part of the point spread function (vortex function) and the cross-sectional distribution of the radial value in the radial direction; Figures 2(c) and 2(d) are the filter functions, respectively The two-dimensional plane distribution of the imaginary part of the point spread function (vortex function) and the cross-sectional distribution of the radial value in the radial direction; where R=700mm, f=400mm, and PSF represents the point spread function.

As shown in Figure 3, Figures 3(a) and 3(b) are the filter functions respectively Two-dimensional planar distribution of the imaginary part of the point spread function (Bessel function) and cross-sectional distribution of radial values in the radial direction; where l=1, k _r =1.1 mm ⁻¹ .

Through Figure 2 and Figure 3, combined with the imaging theory of convolution, we find that in the filter function There is a main maximum lobe and a main minimum lobe in the real and imaginary parts of the point spread function of the (vortex function), and there will be many redundant side lobes around the main maximum lobe and the main minimum lobe. So we can predict using the filter function Edge-enhanced imaging (vortex function) can be achieved in all directions, but some smears will appear at the edges of the image, making the edge imaging non-uniform. And for the filter function (Bessel function), its point spread function has only the imaginary part, it has two main maximum lobes and one main minimum lobe, and the two main maximum lobes and one main minimum lobe are obviously different, but in the main There are only some very tiny side lobes next to the maximum lobe and the main minimum lobe, and the diffraction noise is well suppressed, so for the filter function (Bessel function), its edge imaging can also be achieved in all directions, the quality of the imaging results is better, and it is isotropic, but there will be two edge images at the edge.

Through the previous analysis, we found that both the pure phase filter function and the pure amplitude filter function can achieve edge-enhanced imaging, but there are some defects in edge-enhanced imaging, which shows that the amplitude and phase of the filter function have the same effect on edge-enhanced imaging. certain influence.

Therefore, in order to obtain better imaging quality, to eliminate the imaging defects of the pure phase filter function and pure amplitude filter function, and to combine the modulation effect of phase and amplitude on edge enhancement imaging, the point spread function of the filter function is calculated to ensure the point spread function. The real and imaginary parts satisfy that there is only one main maximum lobe and one main minimum lobe, and the redundant side lobes around the main maximum lobe and the main minimum lobe can be completely suppressed, then the filter corresponding to the point spread function The function is able to achieve high-resolution and isotropic edge-enhanced imaging, which can simultaneously modulate amplitude and phase. The design method of the filter proposed in this embodiment includes the following steps:

Step 1. Superimpose four Gaussian functions to obtain the point spread function of the filter function; specifically, the point spread function h(x, y) is:

(where, (x, y) represents the coordinates of the imaging plane, ω ₀ is the Gaussian beam waist, and d ₀ is an arbitrary constant);

Since the Gaussian function is the simplest filtering function, a Gaussian function has only one extreme value, and the superposition of two Gaussian beams will have a maximum value and a minimum value. Therefore, by combining two pure real Gaussian functions with two pure The superposition of the imaginary part of the Gaussian function can ensure that there is only one main maximum lobe and one main minimum lobe for the real and imaginary parts of the point spread function.

Step 2. Using Fourier transform, reverse calculation is performed on the point spread function to obtain a filter function.

The filter function is:

(in, represents the radial coordinates of the spectral plane, FT represents the Fourier transform, represents a circular hole with radius R on the spectral surface).

Due to the circular hole on the spectrum surface The effect of the filter function The actual point spread function in radial coordinates can be expressed as:

The filter for realizing edge-enhanced imaging in this embodiment is obtained by designing the above-mentioned design method, and its filter function is:

As shown in Figure 4, Figures 4(a) and 4(b) are the filter functions respectively The two-dimensional plane distribution of the real part of the point spread function and the cross-sectional distribution of the radial value in the radial direction; Figures 4(c) and 4(d) are the filter functions, respectively The two-dimensional plane distribution of the imaginary part of the point spread function and the cross-sectional distribution of the radial value in the radial direction; where ω ₀ =d ₀ =26mm.

Through Figure 4, it can be found that the filter function The extra sidelobes (diffraction noise) in the real and imaginary parts of the point spread function have been completely suppressed, so for the filter function For example, it can achieve edge-enhanced imaging in all directions in the 4f imaging system, and it is isotropic, with uniform imaging distribution, and its imaging quality is better than the filter function. (vortex function) and filter function (Bessel function) is much better, very well eliminates the defects in the imaging, and can get a better effect and higher resolution edge image.

As shown in FIG. 5 , it is a comparison diagram of theory and experiment of the amplitude object in the embodiment of the present invention. Among them, the amplitude object is a simple circular hole (radius is 7mm), the first row is the theoretical result, the second row is the experimental result, (a) and (e) are the photos of the object, (b) and (f) is through the filter (the filter function is ), (c) and (g) are after the filter (the filter function is ), (d) and (h) are filtered through filters (the filter function is ) after the image.

As shown in FIG. 6 , it is a theoretical and experimental comparison diagram of the phase object in the embodiment of the present invention. where the phase object is a panda (with a phase change of 0-π), the first row is the theoretical result, the second row is the experimental result, (a) and (e) are photographs of the object, (b) and (f) are After the filter (the filter function is ), (c) and (g) are after the filter (the filter function is ), (d) and (h) are filtered through filters (the filter function is ) after the image.

It can be found from Figures 5 and 6 that the filter function is The filter can modulate the amplitude and phase of the object at the same time, so as to achieve high-resolution and isotropic edge-enhanced imaging. Compared with the traditional filter, the imaging quality has been greatly improved and imaging defects have been eliminated. .

Beneficial effects of the present invention:

The invention discloses a filter and a design method thereof. Combined with the modulation effect of amplitude and phase on edge-enhanced imaging, a point spread function is obtained by superposing four Gaussian functions to satisfy the requirement that there are no redundant side lobes around the main lobe. Fourier transform, reverse calculation of the point spread function to obtain the filter function of the filter, this method is based on the Hilbert transform, and reinterprets the imaging theory of edge enhancement from the theory of convolution, which can achieve High-resolution and isotropic edge-enhanced imaging.

The above embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention is subject to the claims.

Claims (3)

1. A filter for realizing edge-enhanced imaging is characterized in that the filter function isComprises the following steps:

(wherein,represents the radial coordinates of the spectral plane, FT represents the fourier transform,representing a circular hole of radius R in the spectral plane, h (x, y) being the filter functionThe point spread function of (a) is obtained by superposing four Gaussian functions, (x, y) represents the coordinates of an imaging plane, and omega₀Is the Gaussian beam waist, d₀Is an arbitrary constant).

2. A design method of a filter for realizing edge enhanced imaging is characterized by comprising the following steps:

superposing the four Gaussian functions to obtain a point spread function of a filter function;

and performing inverse calculation on the point spread function by utilizing Fourier transform to obtain a filter function.

3. The method of claim 2, wherein the point spread function is:

(wherein, (x, y) represents coordinates of an imaging plane, ω₀Is the Gaussian beam waist, d₀Is an arbitrary constant);

the filter function is:

(wherein,represents the radial coordinates of the spectral plane, FT represents the fourier transform,representing a circular hole of radius R on the spectral plane).