CN113487637A - Multi-direction edge detection method based on superimposed spiral phase filter - Google Patents
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Abstract
The invention provides a multi-direction edge detection method based on a superimposed spiral phase filter, which is characterized in that Gaussian light of a laser is collimated and expanded and then irradiates an object to be detected, the object to be detected is placed on an object plane of a 4f imaging system, the 4f imaging system comprises a Fourier lens L3, a Fourier lens L4 and a superimposed spiral phase filter, the focal lengths of the Fourier lens L3 and the Fourier lens L4 are the same, the distance is 2f, the superimposed spiral phase filter is placed on a back focal plane of the Fourier lens L3 and used for filtering edge information in a plurality of different directions, and multi-direction edge detection information of the object to be detected can be recovered on the back focal plane of the Fourier lens L4. The method has the advantages of flexibly carrying out multidirectional edge detection in real time, and simultaneously filtering edge information in a plurality of different directions according to actual requirements, thereby achieving the effect of emphasizing the information in certain directions.
Description
Technical Field
The invention relates to a multi-direction edge detection method based on a superimposed spiral phase filter, and relates to the field of spiral phase contrast imaging.
Background
Helical phase contrast (SPC) imaging has received great attention in recent years as an edge detection method in optics. In many imaging applications it is sufficient to detect the contour of an object, called the object edge, which will significantly reduce the resources needed for imaging. Edge detection identifies object edges primarily from some significant change in transmittance or reflectance of the object. Nowadays, edge detection has been widely applied in the fields of object recognition, security inspection, earth observation, and the like. Helical phase contrast imaging is an important edge detection means, which obtains edge information of an object by performing radial hilbert transform on the object. Compared with a classical edge detection operator which can only detect an intensity object, the spiral phase contrast imaging has the advantage of good edge detection capability on both the intensity object and the phase object. This has led to the earliest application of helical phase contrast imaging to microscopes for observing biological cells, since biological cells are generally only phase sensitive.
In 2005, F ü rhatter et al showed that phase-hopping resolution of phase-only objects could be improved by several orders of magnitude with the helical phase method, and that the first combination of SPC techniques with microscopy demonstrated that the edge-enhanced brightness and contrast of SPC methods are much better than conventional dark-field imaging. In 2006, Bernet et al further quantitatively reconstructed the phase and amplitude information of biological samples with SPC images of different orientations of the helical phase filter. In 2013, Lauterbach et al proposed an optical design that allowed the direct implementation of phase contrast channels in stimulated emission depletion microscopy (STED) in a wide field of view and scanning mode. In recent years, researchers have also proposed a new nonlinear filter that equivalently prints a helical phase plate on a potassium titanium phosphate crystal using Second Harmonic Generation (SHG), enabling simple and efficient SPC imaging, and visible edge enhancement under invisible light. In order to further improve the contrast of edge enhancement, researchers have proposed several improved spiral phase filters, such as Laguerre-Gaussian spatial filter and Airy spiral phase filter.
Due to the odd symmetry of the helical phase, both the phase gradient and the intensity gradient of the object will increase isotropically, independent of their local orientation. However, in practical applications, when it is desired to emphasize certain edges of an object (e.g., detecting crystal dislocations of low phase contrast biological samples), it is desirable to achieve anisotropic edge enhancement. To solve this problem, many selective edge enhancement methods based on spiral phase filtering have been proposed. In 2005, Jesacher et al achieved the shadow effect in SPC microscopy by changing the phase distribution in the central region of the helical phase hologram. Fractional order helical phase filters are also used to achieve edge-enhanced anisotropy effects by breaking the symmetry of the filtering process. 2011, Sharma et al proposed an anisotropic vortex phase mask that utilizes a sinusoidal function to introduce anisotropy in a conventional vortex mask and selective edge enhancement for amplitude objects. By varying the power and offset angle of the sinusoidal function, the anisotropy can achieve edge enhancement in selected regions and desired directions. Subsequently, in 2014, Sharma proposed a new directional edge enhancement filter. The filter can be regarded as the superposition of two radial Hilbert filters with opposite topological charge values, and directional edge detection can also be realized.
However, the existing anisotropic edge detection method still remains to be perfected. One of them is that, although the existing solutions implement directional edge detection through different principles, only the edges in the same direction can be filtered. For the purpose of filtering edge information in multiple directions simultaneously, a simple and efficient method is lacked.
The above-mentioned problem is a problem that should be considered and solved in the edge detection process.
Disclosure of Invention
The invention aims to provide a multi-direction edge detection method based on a superimposed spiral phase filter, which solves the problems that in the prior art, only edges in the same direction can be filtered, and how to simply and efficiently filter edge information in multiple directions simultaneously is realized.
The technical solution of the invention is as follows:
the utility model provides a multi-direction edge detection method based on superimposed spiral phase filter, after the gaussian light with the laser instrument is collimated, expand the beam and handle, shine and detect on the object, detect that the object is placed on the object plane of a 4f imaging system, 4f imaging system includes Fourier lens L3, Fourier lens L4 and superimposed spiral phase filter, Fourier lens L3 is the same with Fourier lens L4's focal length and beam transmission distance is 2f, on Fourier lens L3's back focal plane, place superimposed spiral phase filter, be used for the marginal information of a plurality of not equidirectionals of filtering, can resume the multi-direction edge detection information of detecting the object at Fourier lens L4's back focal plane.
Further, the method specifically comprises the following steps,
s1, collimating the Gaussian light from the laser, and irradiating the collimated laser onto an object to be detected after the collimated laser is expanded by a group of lenses L1 and L2;
s2, placing an object to be detected on an object plane of a 4f imaging system, wherein the object plane is a front focal plane of the Fourier lens L3; the transmitted beam carrying the object information s (r, phi) is Fourier-transformed by Fourier lens L3, and the spectral information of the object is obtained in the back focal plane of Fourier lens L3
Wherein F represents the Fourier transform, (r, phi) and
polar coordinates representing real domain and fourier planes, respectively;
s3, transmitting the light beam carrying the object spectrum information through the superposition spiral phase filter, so that the object spectrum information is filtered by the superposition spiral phase filter, and the filtered light beam carries the spectrum information obtained by detecting the multidirectional edge of the object to be detected;
s4, the light beam carrying the edge frequency spectrum information passes through a Fourier lens L4, the light field information is subjected to inverse Fourier transform, and the multi-direction edge information is converted from a frequency domain back to a real domain, so that the multi-direction edge detection information of the object is recovered on a back focal plane of the Fourier lens L4 and is received by a CCD camera.
Further, in step S3, the superimposed helical phase filter formula is:
where angle represents the phase distribution of the function, i represents the imaginary unit,
representing the angle of polarization of the fourier plane,
and
respectively representing the topological charge value
And-1, the phase of the helical wavefront, the angular parameter θjRepresenting the direction of selective disappearance of the edge by adjusting the number j of superpositions and the corresponding angular parameter thetajAnd selectively filtering the edge information of the object to be detected in any multiple directions.
Further, in step S4, the light beam carrying the edge spectrum information passes through the fourier lens L4, and undergoes an inverse fourier transform:
wherein e (r, phi) represents the multi-directional edge detection result, h (r, phi) represents the inverse fourier transform of the superimposed helical phase filter, and (r, phi) represents the real-domain polar coordinates, as can be seen from equation (4), the edge detection result is given by the convolution between the input object and the fourier transform of the filter; according to the convolution theorem, the gray value of each image point is multiplied by h (r, phi); then, the light field of the image flat area, namely the non-edge area is completely offset by summing the multiplied results; in contrast, the boundaries between regions of different intensity or phase may be highlighted.
The invention has the beneficial effects that: the multi-direction edge detection method based on the superimposed spiral phase filter has the advantages of being capable of flexibly performing multi-direction edge detection in real time, and capable of filtering edge information in a plurality of different directions simultaneously according to actual requirements, so that the effect of emphasizing information in certain directions is achieved, and the designed filter is simple in structure, and therefore has a huge application prospect.
Drawings
FIG. 1 is a flow chart of a multi-directional edge detection method based on a superimposed helical phase filter according to an embodiment of the present invention;
FIG. 2 is an explanatory diagram of the 4f imaging system in the embodiment;
FIG. 3 is a holographic grating schematic of a superimposed helical phase filter designed according to an embodiment;
wherein fig. 3(a) - (d) represent the cases where j is 1, θ is 0 °, 45 °, 90 °, 135 ° (corresponding to horizontal, diagonal, vertical and anti-diagonal directions, respectively); fig. 3(e) represents j ═ 2, θ1＝45°，θ2135 °; fig. 3(f) represents j ═ 3, θ1＝0°，θ2＝45°，θ3135 °; fig. 3(g) represents j ═ 3, θ1＝45°，θ2＝90°，θ3135 ° case; fig. 3(h) represents j ═ 4, θ1＝0°，θ2＝45°，θ3＝90°，θ4135 °;
FIG. 4 is a diagram of simulation results of a multi-directional edge detection method based on a superimposed helical phase filter according to an embodiment;
fig. 4(a) shows an original, and fig. 4(b) - (i) are schematic diagrams of simulation results of multi-directional edge detection in which the holographic gratings in fig. 3(a) - (h) are loaded on the SLM, respectively.
Detailed Description
Preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
Examples
A multi-direction edge detection method based on a superimposed spiral phase filter is disclosed, as shown in fig. 1 and fig. 2, Gaussian light of a laser is collimated and expanded to irradiate an object to be detected, the object to be detected is placed on an object plane of a 4f imaging system, the 4f imaging system comprises a Fourier lens L3, a Fourier lens L4 and the superimposed spiral phase filter, the focal lengths of the Fourier lens L3 and the Fourier lens L4 are the same, the light beam transmission distance is 2f, a Spatial Light Modulator (SLM) is placed on a back focal plane of the Fourier lens L3, the SLM loads a holographic grating to represent the superimposed spiral phase filter and is used for filtering edge information in multiple different directions, and multi-direction edge detection information of the object to be detected can be recovered on the back focal plane of the Fourier lens L4.
The multi-direction edge detection method based on the superimposed spiral phase filter has the advantages of being capable of flexibly performing multi-direction edge detection in real time, and capable of filtering edge information in a plurality of different directions simultaneously according to actual requirements, so that the effect of emphasizing information in certain directions is achieved, and the designed filter is simple in structure, and therefore has a huge application prospect.
The multi-direction edge detection method based on the superimposed helical phase filter specifically comprises the following steps,
s1, collimating the Gaussian light from the laser, and irradiating the collimated laser onto an object to be detected after the collimated laser is expanded by a group of lenses L1 and L2;
s2, placing an object to be detected on an object plane of a 4f imaging system, wherein the object plane is a front focal plane of the Fourier lens L3; the transmitted beam carrying the object information s (r, phi) is Fourier-transformed by Fourier lens L3, and the spectral information of the object is obtained in the back focal plane of Fourier lens L3
Wherein F represents the Fourier transform, (r, phi) and
polar coordinates representing real domain and fourier planes, respectively;
s3, irradiating the light beam carrying object spectrum information onto the SLM so that the object spectrum information is filtered by the superposition spiral phase filter, and carrying the spectrum information obtained by multi-direction edge detection of the object to be detected by the light beam reflected by the SLM;
in step S3, the superimposed helical phase filter has the formula:
where angle represents the phase distribution of the function, i represents the imaginary unit,
representing the angle of polarization of the fourier plane,
and
respectively representing the topological charge value
And-1, the phase of the helical wavefront, the angular parameter θjRepresenting the direction of selective disappearance of the edge by adjusting the number j of superpositions and the corresponding angular parameter thetajAnd selectively filtering the edge information of the object to be detected in any multiple directions.
S4, the light beam carrying the edge frequency spectrum information passes through a Fourier lens L4, the light field information is subjected to inverse Fourier transform, and the multi-direction edge information is converted from a frequency domain back to a real domain, so that the multi-direction edge detection information of the object is recovered on a back focal plane of the Fourier lens L4 and is received by a CCD camera.
In step S4, the light beam carrying the edge spectrum information is subjected to inverse fourier transform by the fourier lens L4:
wherein e (r, phi) represents the multi-directional edge detection result, h (r, phi) represents the inverse fourier transform of the superimposed helical phase filter, and (r, phi) represents the real-domain polar coordinates, as can be seen from equation (4), the edge detection result is given by the convolution between the input object and the fourier transform of the filter; according to the convolution theorem, the gray value of each image point is multiplied by h (r, phi); then, the light field of the image flat area, namely the non-edge area is completely offset by summing the multiplied results; in contrast, the boundaries between regions of different intensity or phase may be highlighted. The multi-direction edge detection method based on the superimposed spiral phase filter is used for a spiral phase contrast imaging system by designing the superimposed spiral phase filter, and multi-direction edge information of an object is obtained.
In the method of the embodiment, considering the problem that the traditional spiral phase contrast imaging scheme can only obtain isotropic edge information of an object or can only filter the edge information in the same direction when performing direction selective edge detection, the method proposes to perform superposition operation on the traditional directional edge detection filter based on the spiral phase, and sets different angle parameters theta for each filter before superpositionjAnd then, a plurality of filters are superposed together by utilizing the SLM to obtain a superposed spiral phase filter, and the superposed spiral phase filter is used as a new filter to replace a common filter in the traditional spiral phase contrast imaging for edge detection, so that the aim of simultaneously filtering edge information in a plurality of directions is fulfilled, and the multidirectional edge detection of the object is realized.
The principle of the multi-direction edge detection method based on the superimposed spiral phase filter is described as follows: the common spiral phase filter is realized by using a spiral phase plate with a topological charge value of 1, and the superposed spiral phase filter designed by the invention is obtained by superposing a group of spiral phase plates with opposite topological charge values
At this moment, although the filter can realize directional edge detection, the filter can only filter edges in the same direction, and further adds an arbitrary angle theta to the filter, wherein the angle corresponds to the direction of the edge to be filtered, so as to obtain the directional edge detection
By further superposing the filters, the filter is obtained
The method can obtain the edge information of the object, selectively filter edges in multiple directions and reserve some edge information which is required to be emphasized. By combining the characteristic that the SLM can conveniently generate the computer holographic grating in real time and selecting the computer holographic grating to realize the superposition of spiral phases, the required filter can be quickly and conveniently generated according to actual requirements, so that the multi-direction edge detection information of the object to be detected can be obtained in real time without post-processing.
Fig. 2 shows a schematic diagram of a multi-directional edge detection method based on a superimposed helical phase filter. The lenses L1, L2 used in fig. 2 are for expanding the laser beam, L3, L4 are a set of fourier lenses, have the same focal length (f 50cm), and constitute a 4f imaging system. An object is placed on an object plane of a 4f system, after laser light irradiates the object, a light field carries spectrum information of the object through a lens L3, an SLM is placed on a Fourier plane of the 4f system, a corresponding holographic grating is loaded to represent a superposition spiral phase filter designed by the invention, a light beam carrying the spectrum information of the object irradiates the SLM, the light field information is filtered by the filter, then the light beam penetrates through the lens L4, the light field is restored to a real field from a frequency domain, and a result of multi-direction edge detection of the object is obtained on a CCD camera.
The embodiment method is characterized in that firstly, the Gaussian light emitted by the laser is collimated and irradiated on an object to be detected after being expanded. The object is placed in the object plane of a 4f imaging system, after the light beam is transmitted (reflected) through the object, the light beam carrying the spatial position information of the object is further transmitted through the fourier lens L3, and the spectral information of the object is obtained in the back focal plane of the fourier lens L3. In the back focal plane of the fourier lens L3, a Spatial Light Modulator (SLM) is placed. The SLM is loaded with a designed holographic grating to represent a superimposed helical phase filter, and a light beam carrying object spectrum information is irradiated onto the SLM so that the object spectrum information is filtered by the superimposed helical phase filter. Thus, the light beam reflected by the SLM carries the edge spectrum information obtained after the object is subjected to multi-directional edge detection. The light beam carrying the edge spectrum information passes through a Fourier lens L4, inverse Fourier transform is carried out, the object edge information is converted from a frequency domain back to a real domain, multi-direction edge detection information of the object is recovered in a back focal plane of the Fourier lens L4, and the multi-direction edge detection information is received by a CCD camera.
According to the multi-direction edge detection method based on the superimposed spiral phase filter, the brand-new superimposed spiral phase filter is designed to replace the traditional spiral phase contrast imaging method, and only the isotropic edge-enhanced spiral phase filter can be realized, so that multi-direction edge detection is realized. The method designs a filter based on superimposed helical phase, and the superimposed helical phase filter is obtained by superimposing a plurality of helical phase plates (SPPs) with opposite topological charges and changing the phase among the SPPs, so that multi-directional edge detection is realized, and the problem that only isotropic edge enhancement can be realized is effectively solved.
FIG. 3 shows holographic gratings, partially used to represent superimposed helical phase filters, based on different number of superpositions j and angle parameter θjThe design is derived and represents a superimposed helical phase filter by loading onto the SLM. In fig. 3(a) - (d), j is 1, θ is 0 °, 45 °, 90 °, 135 ° (corresponding to horizontal, diagonal, vertical and anti-diagonal directions, respectively); fig. 3(e), representing j 2, θ1＝45°，θ2135 °; fig. 3(f), representing j as 3, θ1＝0°，θ2＝45°，θ3135 °; fig. 3(g), representing j 3, θ1＝45°，θ2＝90°，θ3135 ° case; fig. 3(h), representing j 4, θ1＝0°，θ2＝45°，θ3＝90°，θ4In the case of 135 °.
FIG. 4 is a diagram of simulation results based in part on the multi-directional edge detection method. In the embodiment, a disc-shaped pattern is selected as a detection image, and j is 1,2. 3 and 4, and verifying the method by simulation. Where FIG. 4(a) shows the original, the holographic gratings of FIGS. 3(a) - (h) are loaded onto the SLM to show the multi-directional edge detection filter, and the multi-directional edge detection results shown in FIG. 4(b- (i) are obtained by simulation, it can be seen that the uniform annular edge effect due to the isotropic edge detection scheme is destroyed, instead, rings with different numbers (1-4) of notches are provided, and the positions of the notches exactly correspond to the angle parameter θ added to the holographic gratingj. By combining the analysis, the multidirectional edge detection filter designed by the invention can be flexibly adjusted according to actual requirements to carry out edge detection, so that a multidirectional edge detection result is obtained.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may occur to those skilled in the art without departing from the principle of the invention, and are considered to be within the scope of the invention.
Claims (4)
1. A multi-direction edge detection method based on a superimposed spiral phase filter irradiates an object to be detected after the alignment and beam expansion processing of Gaussian light of a laser, and the object to be detected is placed on an object plane of a 4f imaging system, and is characterized in that: the 4f imaging system comprises a Fourier lens L3, a Fourier lens L4 and a superposition spiral phase filter, the focal lengths of the Fourier lens L3 and the Fourier lens L4 are the same, the light beam transmission distance is 2f, the superposition spiral phase filter is placed on the back focal plane of the Fourier lens L3 and used for filtering edge information in a plurality of different directions, and multi-direction edge detection information of an object to be detected can be restored on the back focal plane of the Fourier lens L4.
2. The multi-directional edge detection method based on a superimposed helical phase filter of claim 1, wherein: the method specifically comprises the following steps of,
s1, collimating the Gaussian light from the laser, and irradiating the collimated laser onto an object to be detected after the collimated laser is expanded by a group of lenses L1 and L2;
s2, placing an object to be detected on an object plane of a 4f imaging system, wherein the object plane is a front focal plane of the Fourier lens L3; the transmitted beam carrying the object information s (r, phi) is Fourier-transformed by Fourier lens L3, and the spectral information of the object is obtained in the back focal plane of Fourier lens L3
Wherein F represents the Fourier transform, (r, phi) and
polar coordinates representing real domain and fourier planes, respectively;
s3, transmitting the light beam carrying the object spectrum information through the superposition spiral phase filter, so that the object spectrum information is filtered by the superposition spiral phase filter, and the filtered light beam carries the spectrum information obtained by detecting the multidirectional edge of the object to be detected;
s4, the light beam carrying the edge frequency spectrum information passes through a Fourier lens L4, the light field information is subjected to inverse Fourier transform, and the multi-direction edge information is converted from a frequency domain back to a real domain, so that the multi-direction edge detection information of the object is recovered on a back focal plane of the Fourier lens L4 and is received by a CCD camera.
3. The multi-directional edge detection method based on a superimposed helical phase filter according to claim 1 or 2, characterized in that: the superimposed helical phase filter has the formula:
where angle represents the phase distribution of the function, i represents the imaginary unit,
representing the angle of polarization of the fourier plane,
and
helical wavefront phase, angle parameter theta, representing the respective topological charge values l-1 and-1jRepresenting the direction of selective disappearance of the edge by adjusting the number j of superpositions and the corresponding angular parameter thetajAnd selectively filtering the edge information of the object to be detected in any multiple directions.
4. The multi-directional edge detection method based on a superimposed helical phase filter of claim 2, wherein: in step S4, the light beam carrying the edge spectrum information is subjected to inverse fourier transform by the fourier lens L4:
wherein e (r, phi) represents the multi-direction edge detection result, h (r, phi) represents the inverse Fourier transform of the superimposed helical phase filter, and (r, phi) represents the real-domain polar coordinates;
as can be seen from equation (4), the edge detection result is given by the convolution between the input object and the fourier transform of the filter; according to the convolution theorem, the gray value of each image point is multiplied by h (r, phi); then, the light field of the image flat area, namely the non-edge area is completely offset by summing the multiplied results; in contrast, the boundaries between regions of different intensity or phase may be highlighted.
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