CN110987927A - Rotating object imaging system based on Laguerre Gaussian transformation - Google Patents

Rotating object imaging system based on Laguerre Gaussian transformation Download PDF

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CN110987927A
CN110987927A CN201911117320.4A CN201911117320A CN110987927A CN 110987927 A CN110987927 A CN 110987927A CN 201911117320 A CN201911117320 A CN 201911117320A CN 110987927 A CN110987927 A CN 110987927A
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rotating object
dimensional array
array detector
laser
laguerre
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CN110987927B (en
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魏丹
王天新
马剑涛
徐钏
张勇
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Nanjing University
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Abstract

The invention discloses a rotating object imaging system based on Laguerre Gaussian transformation, which comprises a laser, a beam expanding system, an imaging lens and a one-dimensional array detector, wherein the beam expanding system is positioned behind a laser output port of the laser, the imaging lens and the one-dimensional array detector are sequentially positioned on a light path output by the beam expanding system, a target rotating object is positioned on the light path between the beam expanding system and the imaging lens, a light beam emitted by the laser is expanded by the beam expanding system and then is irradiated on the target rotating object, the light beam is imaged on a plane where the one-dimensional array detector is positioned through the imaging lens, and the one-dimensional array detector extracts a Laguerre Gaussian spectrum from a received image optical signal and reconstructs a target rotating object image by adopting Laguerre Gaussian transformation. The invention has more convenient image processing.

Description

Rotating object imaging system based on Laguerre Gaussian transformation
Technical Field
The invention relates to an imaging technology, in particular to a rotating object imaging system based on Laguerre Gaussian transformation.
Background
The fourier transform decomposes the signal into constituent frequencies because many linear operations, including differentiation and convolution, are easily manipulated in the frequency domain, such as signal processing, differential formulation analysis, fourier transform spectroscopy. An important branch is fourier optics, and the transformation of an optical image into its spatial spectrum can be achieved with only one lens. Image processing technologies such as image edge enhancement, spatial filtering, image reconstruction, computer holography, image compression and the like are developed on the basis of Fourier optics. However, there is an important application scenario that imaging monitoring is required for rotating objects such as an aircraft engine, an energy storage flywheel, a high-speed centrifuge and the like. Optical fourier transform techniques are difficult to work with at this time because the components of the fourier spectrum change during rotation of the optical field, and fourier transform-based imaging becomes chaotic and complex.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides a rotating object imaging system based on Laguerre-Gaussian (LG) spectrum, and the components of the Laguerre-Gaussian (LG) spectrum can not change along with the rotation of a light field, so the imaging of the invention is simpler and the image processing is more convenient.
The technical scheme is as follows: the rotating object imaging system based on the Laguerre Gaussian transformation comprises a laser, a beam expanding system, an imaging lens and a one-dimensional array detector, wherein the beam expanding system is positioned behind a laser output port of the laser, the imaging lens and the one-dimensional array detector are sequentially positioned on a light path output by the beam expanding system, a target rotating object is positioned on the light path between the beam expanding system and the imaging lens, a light beam emitted by the laser is expanded by the beam expanding system and then is irradiated on the target rotating object, the light beam is imaged on a plane where the one-dimensional array detector is positioned through the imaging lens, and the one-dimensional array detector extracts the Laguerre Gaussian spectrum from a received image optical signal and reconstructs a target rotating object image by adopting the Laguerre Gaussian transformation.
Further, the one-dimensional array detector is located at the radius of the imaging surface of the imaging lens, and the pixels cover the center and the edge of the image.
Further, the beam expanding system is composed of two lenses, and the lens positioned at the rear is a multiple of the focal length of the lens positioned at the front.
Further, the reconstructing the target rotating object image is realized by loading a program in the one-dimensional array detector, and the program when executed realizes the following steps:
A. performing time Fourier transform on an image optical signal received by the one-dimensional array detector according to the following formula to obtain a transformed signal:
Figure BDA0002274421470000021
in the formula, bl(r) represents the Fourier transformed signal, r represents the light field radius, T represents the rotation period of the target rotating object, l represents the angular coefficient, phi0The representation represents the azimuth angle, E (r), of a one-dimensional array detectorn,φ0T) represents the image optical signal received by the one-dimensional array detector,
Figure BDA0002274421470000022
B. calculating the following formula according to the signals after Fourier transformation to obtain a Laguerre Gaussian mode coefficient:
Figure BDA0002274421470000023
in the formula, Ap,lCoefficient, LG, representing a Laguerre Gaussian mode with an angular coefficient of l and a radial coefficient of pp,l(r) represents a radial distribution of Laguerre Gaussian modes, and
Figure BDA0002274421470000024
ω0the waist of the beam is shown,
Figure BDA0002274421470000025
represents a laguerre polynomial;
C. reconstructing the target rotating object image according to the Laguerre Gaussian mode coefficient according to the following formula:
Figure BDA0002274421470000026
in the formula, E (r, phi) represents the reconstructed target rotating object image,
Figure BDA0002274421470000027
phi denotes the attitude.
Further, the laser is a 1064nm laser.
Has the advantages that: compared with the prior art, the invention has the following remarkable advantages: the invention extracts the LG spectrum from the optical signal measured by the linear array detector at one time, reconstructs images with different precision at different ranges by using the spectrums in different ranges, and the components of the LG spectrum can not change along with the rotation of the light field, so the system of the invention has simpler imaging and more convenient image processing.
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FIG. 1 is a block diagram of one embodiment of the present invention;
FIG. 2 is a diagram illustrating the weight and phase of an image LG spectrum;
in fig. 3, (a) - (d) are 1/16, 1/4, 9/16 and full range spectra, respectively, and (e) - (h) are graphs reconstructed from (a) - (d) range spectra, respectively.
Detailed Description
The embodiment provides a rotating object imaging system based on laguerre gaussian transformation, as shown in fig. 1, including laser 1, beam expanding system 2, imaging lens 4 and one-dimensional array detector 5, beam expanding system 2 is located behind the laser output port of laser 1, imaging lens 4 and one-dimensional array detector 5 are located the light path of beam expanding system 1 output in proper order, and target rotating object 3 is located the light path between beam expanding system 2 and imaging lens 4. Laser instrument 1 is 808nm laser instrument, and beam expanding system 2 comprises for two lenses of 50mm and 500mm focus, and the distance of two lenses is 550mm, can expand 10 times with the 808nm light beam of 1 outgoing of laser instrument, and the rotatory object 3 rotation cycle of target is 50ms, and imaging lens 4's focus is 200mm, and object distance and image distance are all for 200mmIs 400 mm. The one-dimensional array detector 5 is located at a radius, i.e., +, of the imaging plane of the imaging lens0At 0 radius, the refresh rate is 22KHz, the pixels are overlaid to the center and edges of the image. When the device works, light beams emitted by the laser 1 are expanded by the beam expanding system 2 and then reach a target rotating object 3, the light beams are imaged on a plane where the one-dimensional array detector 5 is located through the imaging lens 4, the one-dimensional array detector 5 extracts a Laguerre Gauss spectrum from received image optical signals and reconstructs a target rotating object image by adopting Laguerre Gauss transformation.
To extract the LG spectrum from the resulting optical signal, the theoretical analysis is as follows:
the expression for the laguerre gaussian mode is as follows:
Figure BDA0002274421470000031
according to the principle of digital helical imaging, a graph of amplitude type can be decomposed into a superposition of LG modes:
Figure BDA0002274421470000032
where r denotes the radius,. phi.p,lIs a coefficient of LG mode, is complex, and
Figure BDA0002274421470000033
definition of
Figure BDA0002274421470000034
Wherein b islAnd (r) represents an orbital angular momentum spectrum transformed along with the radius of the light field, and is formed by superposing LG modes of the same angular coefficient l and different radial coefficients p.
Figure BDA0002274421470000035
Representing the radial distribution of the LG mode. Therefore, it is not only easy to use
Figure BDA0002274421470000036
When the object rotates at the rotation speed of Ω, according to the rotating doppler effect, the orbital angular momentum mode with topological charge of l will generate a frequency shift of l Ω t, so the rotating optical field can be represented again as:
Figure BDA0002274421470000041
rotating the one-dimensional array detector to the azimuth angle phi of the light field E (r, phi, t)0At the radial position of (a). The light field E (r, phi) to be obtained0T) performing a fourier transform in time:
Figure BDA0002274421470000042
wherein
Figure BDA0002274421470000043
Representing the period of rotation. Spatial distribution LG of LG modes at any beam waistp,l(r) is known, and we can fit the coefficients A for each LG mode according to equation (3)p,l. From the obtained LG spectrum Ap,lThe light field can be synthesized by equation (2).
Therefore, through the above analysis, it is possible to load a program in a one-dimensional array detector to realize the reconstruction of an image of a target rotating object, and the program when executed realizes the following steps:
A. performing time Fourier transform on an image optical signal received by the one-dimensional array detector according to the following formula to obtain a transformed signal:
Figure BDA0002274421470000044
in the formula, bl(r) represents the Fourier transformed signal, r represents the light field radius, T represents the rotation period of the target rotating object, l represents the angular coefficient, phi0The representation represents the azimuth angle, E (r), of a one-dimensional array detectorn,φ0And t) represents oneThe image optical signal received by the dimension array detector,
Figure BDA0002274421470000045
B. calculating the following formula according to the signals after Fourier transformation to obtain a Laguerre Gaussian mode coefficient:
Figure BDA0002274421470000046
in the formula, Ap,lCoefficient, LG, representing a Laguerre Gaussian mode with an angular coefficient of l and a radial coefficient of pp,l(r) represents a radial distribution of Laguerre Gaussian modes, and
Figure BDA0002274421470000047
ω0the waist of the beam is shown,
Figure BDA0002274421470000048
represents a laguerre polynomial; fig. 2(a) and (b) are weight and phase of the LG spectrum, respectively.
C. Reconstructing the target rotating object image according to the Laguerre Gaussian mode coefficient according to the following formula:
Figure BDA0002274421470000051
in the formula, E (r, phi) represents the reconstructed target rotating object image,
Figure BDA0002274421470000052
phi denotes the attitude. In fig. 3 (a) - (d) correspond to the coverage of LG spectra 1/16, 1/4, 9/16, 1, respectively. (e) - (h) spectral reconstruction plots corresponding to the ranges (a) - (d), respectively.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.

Claims (5)

1. A rotating object imaging system based on Laguerre Gaussian transform is characterized in that: the system comprises a laser, a beam expanding system, an imaging lens and a one-dimensional array detector, wherein the beam expanding system is positioned behind a laser output port of the laser, the imaging lens and the one-dimensional array detector are sequentially positioned on a light path output by the beam expanding system, a target rotating object is positioned on the light path between the beam expanding system and the imaging lens, light beams emitted by the laser are expanded by the beam expanding system and then impact on the target rotating object, the light beams are imaged on a plane where the one-dimensional array detector is positioned by the imaging lens, and the one-dimensional array detector extracts a Laguerre Gauss spectrum from received image optical signals and reconstructs a target rotating object image by adopting Laguerre Gauss transformation.
2. A laguerre gaussian based rotating object imaging system according to claim 1, wherein: the one-dimensional array detector is positioned at the radius of the imaging surface of the imaging lens, and pixels cover the center and the edge of an image.
3. A laguerre gaussian based rotating object imaging system according to claim 1, wherein: the beam expanding system consists of two lenses, the lens located behind being a multiple of the focal length of the lens located in front.
4. A laguerre gaussian based rotating object imaging system according to claim 1, wherein: the reconstruction of the target rotating object image is realized by loading a program in the one-dimensional array detector, and the program is specifically realized by the following steps when executed:
A. performing time Fourier transform on an image optical signal received by the one-dimensional array detector according to the following formula to obtain a transformed signal:
Figure FDA0002274421460000011
in the formula, bl(r) represents FourierThe signals after leaf transformation, r represents the radius of the light field, T represents the rotation period of the object rotating object, l represents the angular coefficient, phi0The representation represents the azimuth angle, E (r, phi), of a one-dimensional array detector0And t) is at phi0The image optical signal received by the one-dimensional array detector,
Figure FDA0002274421460000012
B. calculating the following formula according to the signals after Fourier transformation to obtain a Laguerre Gaussian mode coefficient:
Figure FDA0002274421460000013
in the formula, Ap,lCoefficient, LG, representing a Laguerre Gaussian mode with an angular coefficient of l and a radial coefficient of pp,l(r) represents a radial distribution of Laguerre Gaussian modes, and
Figure FDA0002274421460000014
ω0the waist of the beam is shown,
Figure FDA0002274421460000015
represents a laguerre polynomial;
C. reconstructing the target rotating object image according to the Laguerre Gaussian mode coefficient according to the following formula:
Figure FDA0002274421460000021
in the formula, E (r, phi) represents the reconstructed target rotating object image,
Figure FDA0002274421460000022
phi denotes the attitude.
5. A laguerre gaussian based rotating object imaging system according to claim 1, wherein: the laser is specifically a 808nm laser.
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