CN109883993B - Hartmann ray tracing-based non-uniform medium field measuring method - Google Patents
Hartmann ray tracing-based non-uniform medium field measuring method Download PDFInfo
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Abstract
The invention discloses a method for measuring a non-uniform medium field based on Hartmann ray tracing, which comprises the steps of calculating an image by adopting a color three-step phase shifting method and obtaining phase information, and calculating by adopting an inverse integral curve three-dimensional reconstruction algorithm to obtain the change data of the refractive index of a liquid-liquid mixed medium existing in a measuring space; according to the invention, a color three-step phase shifting method is adopted, a three-dimensional reconstruction algorithm of an inverse integral curve of a three-dimensional inhomogeneous medium field is combined, and accurate tracking of the measured light of the inhomogeneous medium field and measurement of the transient refraction characteristic of the refractive index of a three-dimensional space are realized through the combined arrangement of a projection screen and a telecentric optical system, so that the measurement accuracy and efficiency are greatly improved; and the measurement system of the inhomogeneous medium field based on Hartmann ray tracing has precise overall design, high measurement precision, lower cost and wide application range, has important theoretical significance and engineering application value, and is suitable for popularization and application.
Description
Technical Field
The invention relates to a measuring method, in particular to a Hartmann ray tracing-based non-uniform medium field measuring method, wherein the non-uniform medium field refers to a spatial field with non-uniform space physical characteristics formed by non-uniform spatial distribution of factors such as pressure, speed, temperature, density, substances and the like, and comprises a non-uniform medium field formed by temperature, pressure and flow and a non-uniform medium field formed by a liquid-liquid mixed medium, a gas-liquid mixed medium and a gas medium.
Background
The nonuniform medium field refers to a spatial field with nonuniform spatial physical characteristics formed by nonuniform spatial distribution of factors such as pressure, speed, temperature, density, substances and the like, and the reproduction of physical quantities such as temperature, pressure, air flow and the like can be realized through the measurement of the nonuniform medium field. Therefore, the method has very important scientific significance and wide application prospect in scientific research such as fluid mechanics, heat transfer science and the like and in various industries such as energy, environment, power, chemical industry and the like for three-dimensional measurement of the inhomogeneous medium field.
Chemical reaction flow, laminar flow, turbulent flow, rarefied flow, low-temperature flow, high-temperature gas dynamics, supersonic speed and hypersonic flow, wind tunnel experiment and water tunnel flow field are typical heterogeneous medium fields, detection of the heterogeneous medium fields is accurately achieved, effective parameters can be provided for chemical reaction processes such as combustion and the like, design and control of aerodynamic equipment and the like, optimal control strategies are achieved, and the method is widely applied to the fields of industrial boilers, power plant coal, gas turbines, aviation, automobile engine combustion, ship propellers, spraying operation and the like. For example, when the method is applied to monitoring a combustion temperature field of a boiler, unreasonable combustion conditions of a hearth are main factors causing operation accidents of the boiler, and the reasonableness and the unreasonable combustion states directly influence the heat efficiency of the boiler and the proportion of power supply and fuel loss. Therefore, in order to keep the combustion field of the hearth to operate uniformly and stably and improve the combustion efficiency, the on-line monitoring of the temperature distribution of the combustion field in the hearth is realized, and the on-line monitoring is a necessary measure for regulating and controlling the combustion state; the method can also provide basic measurement data for the design and improvement of aerodynamic equipment, for example, the measurement of a feather-like jet plume ejected by a rocket engine in a high and vacuum state, the plume flow pattern defect can cause the swinging, the thrust weakening, the unstable flight and the incapability of flying according to a preset orbit of the aircraft, and finally the aircraft is probably not capable of reaching a preset height and area in the flying process; and the data of a real-time mixed flow field, such as the proportion of oil, water and gas in the process of oil and gas extraction, can be provided for the extraction of oil and gas, and the strategy relates to the strategy of oil and gas extraction, and is the basis of the oil and gas extraction.
At present, the general measurement method for the inhomogeneous medium field is mainly realized by measuring the change of the refractive index of the inhomogeneous medium field. When light penetrates through the refractive index field of the inhomogeneous medium, two changes occur, namely light deviates from the original direction, and light generates relative phase change and phase shift. The refractive index method determines the refractive index based on these two characteristics. The refractive index method has the irreplaceable advantages of other methods, has no interference to an original field, belongs to non-insertion measurement, has high time resolution, can be used for researching a very quick transient process, and even can track the process of space inhomogeneous medium field change; the spatial resolution is high, and the method can be used for researching non-uniform medium fields of the space with extremely small temperature gradient, such as shock waves, small flames and the like; the device can simultaneously provide measurement of a spatially inhomogeneous medium field, but not point measurement, and has a large amount of information. Other major methods include schlieren, shadow, optical, holographic, moire, laser speckle photography, laser speckle shearing involving talbot interference, and the like. The shadow method and the schlieren method are measured according to the deflection effect of light; the optical interference method and the holographic interference method directly measure the phase change, and assume that the light rays are not deflected; moire deflection, laser speckle photography, laser speckle shearing interference and the like relate to the deflection angle of light rays directly measured by Taibo interference.
The schlieren method utilizes the phenomenon that deflection can be generated when light propagates in media with different internal densities, and the deflected light is shielded by using a knife edge device, so that the throughput of the light is changed, and the light and shade change can be observed on a receiving surface such as a light screen or a camera to realize refractive index measurement. In addition to the conventional schlieren method, the schlieren method commonly used at present includes a focus schlieren method, a background schlieren method, a rainbow schlieren method, and the like. The principle of the shadow method is the same as that of the schlieren method, but the measurement of the refractive index is realized by recording the displacement of a point on a projection screen caused by the deflection of light. The experimental principle and the system structure of the schlieren method and the shadow method are simple, but the precision of the shadow method is relatively low, the traditional schlieren method is easily influenced by the background brightness, the displacement of each point cannot be accurately determined by the background schlieren method, and the measurement precision is limited.
In general, a mach-zehnder interferometer, a double-mirror interferometer, a michelson interferometer, a raman interferometer, a schlieren interferometer, or the like is used as the optical interference method. The light emitted by the same light source is divided into two beams, one beam is coherent with the other beam of reference light after passing through the measuring area, and the measurement of the spatial refractive index and the non-uniform medium field information of the reaction space are realized by analyzing the phase change of the light penetrating through the measuring area. The mach-zehnder interferometer, the double-mirror interferometer, the michelson interferometer, the raman interferometer, and the like all employ an amplitude spectroscopy, and the schlieren interferometer employs a polarization spectroscopy. The holographic interference method is similar to common optical interference method in principle, but it adopts time light splitting method to record the same light beam on the same holographic plate at different time, then makes these wave fronts produce interference again, and utilizes the analysis of phase change of light passed through the measuring region to implement measurement of space refractive index and reflect the nonuniform medium field information of space. Interferometry is currently widely used in heat transfer, combustion and aerodynamic research, and is also the most basic and classical method of thermophysical measurements.
The moire deflection method realizes the measurement of refractive index in the inhomogeneous medium field through moire interference phenomenon, the light that the light source sent places the grating around two, form two grating fringe superimposed moire fringes, under general conditions, moire fringe is parallel or according to the regular orderly distribution of setting for, when measuring space is inhomogeneous medium field, light can be because the change of refractive index takes place the deflection, moire fringe can produce deformation or displacement, the displacement of this fringe of analysis can obtain the deflection angle of light, thereby calculate the distribution of space inhomogeneous medium field. The moire deflexion method reduces the requirements of the interference method on mechanical, optical components and environmental control, has wider application range, but the diffraction phenomenon in the moire deflexion method reduces the contrast ratio and the spatial resolution of the fringes.
The talbot interference is measured using the talbot effect. When parallel light perpendicularly irradiates a grating with a period d, an identical image of the grating appears on a certain plane behind the grating, which is called self-imaging, namely a Talbot effect, and an imaging plane is called a Talbot surface. And another identical grating is placed on the stage-surface of the former grating, the latter grating is parallel to and coaxial with the former grating, the two gratings are positioned in the direction of a vertical axis identically, and a zero light field is observed behind the latter grating at the moment. When a non-uniform medium field of a phase object is inserted between the two gratings, light is disturbed, the self-imaging of the first grating generates distortion, the distorted self-imaging interacts with the second grating, interference fringes can be observed on an observation screen behind the second grating, and the interference fringes can be examined to obtain information of a light deflection angle, namely the Bobby interference. The Talbot interference is mostly used for optical instruments and parameter measurement, and has been developed for measurement of inhomogeneous medium fields. However, the processing precision requirement of the manufacturing of the above interferometric measuring devices is very high, and the adjustment of the devices is time-consuming and labor-consuming, so that the devices are generally expensive.
In laser speckle photography, laser beams with good coherence are diffusely reflected on the surface of an object to generate countless tiny point light sources, coherent light emitted by the point light sources is spread in space and is coherent with each other, bright spots and dark spots with different distributions are generated on projection equipment at different positions, when the laser beams penetrate through a space non-uniform medium field, patterns generated on the projection equipment move according to a certain rule, the motion information of the patterns is tracked, the displacement of each scattered spot is obtained, and the change of the refractive index of the space non-uniform medium field can be calculated in an inversion mode. The technique is insensitive to vibrations and does not require prior knowledge of the gradient direction of the inhomogeneous medium field. The point-by-point analysis of speckle photography is time consuming and cumbersome and requires correction for the fringe width due to the halo effect.
The laser speckle shearing interference images speckles on a CCD of a camera through double holes, and a crystal oscillation plane of the CCD is slightly deviated from a conjugate image plane, so that the speckles passing through the double holes form a slightly defocused image on the CCD, namely shearing, and the speckles are coherent to form a stripe pattern, namely the speckle shearing interference. The laser speckle shearing interference method measures the deflection angle of light, and the formed coherent fringes are equal displacement gradient lines of the light and represent the distribution condition of spatial nonuniformity, so that the laser speckle shearing interference method can perform online visual measurement on a spatial nonuniform medium field. Laser speckle shear interferometry is commonly used for the measurement of strain, tilt, bending and other mechanical parameters, and is also being developed for the measurement of inhomogeneous media fields. The method reduces the calculation amount of point-by-point analysis in laser speckle photography, but still needs to correct the width of the halo effect stripe.
The spatial measurement methods for the inhomogeneous medium field have advantages and disadvantages, the interference method has high requirements on equipment processing and mounting precision, so that the cost is higher, and the measurement precision of the schlieren method and the shadow method is lower. Therefore, the invention provides a low-cost and high-precision three-dimensional refractive index measuring method, which is based on the Hartmann ray tracing principle and realizes accurate tracing of measuring rays through the combined arrangement of a projection screen and a telecentric optical system, thereby realizing the measurement of the refractive index in a three-dimensional space.
Disclosure of Invention
The invention solves the technical problem of overcoming the defects of the prior art and provides a Hartmann ray tracing-based non-uniform medium field measuring method which realizes accurate tracing of measuring rays and measurement of three-dimensional space refractive index through the combined arrangement of a projection screen and a telecentric optical system.
In order to solve the technical problem, the invention is solved by the following technical scheme:
the method for measuring the inhomogeneous medium field based on Hartmann ray tracing comprises the following specific contents:
each light spot on the projection screen is taken as a point light source to emit spherical incident light to the measurement space, wherein one spherical incident light which forms a deflection angle theta with the optical axis penetrates through a non-uniform medium field in the measurement space to be refracted to form deflection light parallel to the optical axis; deducing and obtaining the angle corresponding relation between incident light and refracted light through a formula (A), and deducing and obtaining the relation between a deflection angle theta and image position deviation shown in a formula (B) according to the formula (A), so that the relation between the integral of the refractive index gradient of the liquid-liquid mixed medium and the image displacement shown in the formula (C) is obtained through the formula (A) and the formula (B); calculating the image by adopting a color three-step phase shifting method to obtain phase information, and determining the optical refraction characteristics and the corresponding relation of the image generated after the light spot on the projection screen is refracted by the liquid-liquid mixed medium according to the phase information so as to realize light ray tracing; calculating to obtain the change data of the refractive index of the liquid-liquid mixed medium existing in the measuring space by adopting an inverse integral curve three-dimensional reconstruction algorithm; wherein, formula (A), formula (B) and formula (C) are respectively as follows:
wherein z is the direction of the optical axis,
the amount of change in the X, Y, Z axis, n is the spatial index of refraction,
is the change of space refractive index, F is the focal length of the lens, delta is the displacement of the pixel point of the image on the imaging screen of the CCD camera, S1The distance between the image space focus of the object space telecentric diaphragm and the imaging screen of the CCD camera is L, and the distance between the projection screen and the emitting end of the measuring space is L.
Preferably, the liquid-liquid mixed medium flowing in the measuring space generates a temperature field and/or a pressure field, so that the measurement of the liquid-liquid mixed medium formed by temperature, pressure and flow is realized. Wherein the liquid-liquid mixed medium is an oil-water mixed liquid, and the pressure field is generated by the flow of the liquid-liquid mixed medium; the measuring space is provided with a temperature adjusting device for adjusting a temperature field in the measuring space, the temperature adjusting device comprises a heating temperature control system and a constant temperature control system, and the constant temperature field is provided by the temperature adjusting device.
Preferably, the color three-step phase shifting method is based on a three-step phase shifting method, and comprises the following specific contents:
information I to be modulated1、I2、I3、I4、I5、I6The color RGB light source is respectively modulated into R, G, B three different channels of color RGB through brightness subareas, so that R, G, B three different channels of color RGB on a projection screen and a CCD camera respectively output and collect three phase images in the transverse direction and the longitudinal direction and obtain three phase information, and the CCD camera transmits the three phase information to the projection screen; calculating RGB three-channel information M (RGB) acquired by CCD camera by formula (D)]', RGB three-channel information M and actual RGB three-channel information N ═ RGB]' transformation matrix A and background matrix M0＝[R0G0B0]' conversion is achieved by equation (E); finally, measuring transient refraction characteristics according to the actual RGB three-channel information N obtained through calculation; wherein the projection screen displays modulation information I of three cosine waves with different phase shifts, and three cosine waves with different phase shifts in the transverse direction and the longitudinal direction respectively1、I2、I3、I4、I5、I6Respectively obtained by calculation through a formula (F) and a formula (G); calculating three phase images collected by a CCD camera through a formula (H) and a formula (I) respectively to obtain phase information of each pixel, and comparing the obtained phase information of each pixel with three cosine wave stripes with different phase shifts displayed on a projection screen, so that the optical refraction characteristic and the corresponding relation of the images generated after light spots on the projection screen are refracted through an uneven medium field are determined, and light ray tracing is realized; the formulas (D), (E), (F), (G), (H), (I) are shown below:
M＝A·N+M0 (E)，
wherein I' (x, y) is a background gray value and I "(x, y) is a modulation gray value;
wherein phi is1(x,y)、φ2And (x, y) are phase information.
Preferably, the inverse integral curve three-dimensional reconstruction algorithm comprises the following specific contents: establishing a ill-conditioned matrix with the refractive index distribution of the liquid-liquid mixed medium as a variable, and then solving the ill-conditioned matrix, thereby converting the reconstruction problem into a solution problem of the ill-conditioned matrix; wherein, the ill-conditioned matrix shown in formula (J) is obtained by deforming and dispersing formula (C):
T＝WDS2 (J)，
wherein T is a displacement information matrix of image pixels, represents the displacement of the measuring light compared with the uniform medium field through the liquid-liquid mixed medium, and is directly obtained from the corresponding relation of the image; w is a model coefficient matrix, the matrix is obtained by a model coefficient calculation method under a direct body reconstruction strategy, a Monte Carlo method is adopted, the Monte Carlo method is regarded as the method for solving the probability that any point in a voxel space falls in a light beam, a large number of random samples can be directly carried out in the voxel space, the probability that a sampling point in a sample space falls in the light beam is further calculated according to the spatial position relation of the sampling point and the light beam, and when the number of samples is large enough, the probability value is regarded as a model coefficient; d is a refractive index change vector matrix to be solved; s2Is a projection matrix, and traces in three dimensionsProjected onto an offset of the distance; the calculation method of the formula (J) can specifically adopt an additive algebra reconstruction, a multiplicative algebra reconstruction or a filtering back projection reconstruction algorithm to solve, so as to realize the reconstruction of the three-dimensional inhomogeneous medium field.
The invention relates to a method for measuring a nonuniform medium field based on Hartmann ray tracing, which is realized by a measuring system of the nonuniform medium field based on Hartmann ray tracing, wherein the measuring system of the nonuniform medium field based on Hartmann ray tracing comprises a measuring space in which the nonuniform medium field exists, a projection screen for emitting spherical incident rays to the measuring space, and an object-side telecentric optical system for refracting the spherical incident rays emitted by light spots on the projection screen through the nonuniform medium field in the measuring space to form deflection rays parallel to an optical axis, screening and converging the deflection rays into an image, wherein the measuring space is positioned between the projection screen and the object-side telecentric optical system; calculating the image by adopting a color three-step phase shifting method, obtaining phase information, and determining the optical refraction characteristic and the corresponding relation of the image according to the phase information; calculating to obtain the change data of the refractive index of the liquid-liquid mixed medium existing in the measuring space by adopting an inverse integral curve three-dimensional reconstruction algorithm; the basic measurement principle of the liquid-liquid mixed medium measurement system based on Hartmann ray tracing is as follows: each light spot on the projection screen is taken as a point light source to emit spherical incident light rays to the measuring space, wherein one of the spherical incident light rays which form a deflection angle theta with the optical axis penetrates through a non-uniform medium field in the measuring space to be refracted to form deflection light rays parallel to the optical axis, the deflection light rays which are emitted from the measuring space and are parallel to the optical axis are emitted to the object-side telecentric optical system, and the object-side telecentric optical system screens the deflection light rays and converges the deflection light rays into an image; calculating the image by adopting a color three-step phase shifting method, obtaining phase information, and determining the optical refraction characteristic and the corresponding relation of the image according to the phase information so as to realize light ray tracing; calculating to obtain the change data of the refractive index of the liquid-liquid mixed medium flowing in the measuring space by adopting an inverse integral curve three-dimensional reconstruction algorithm, thereby realizing the real-time measurement of the refractive index of the liquid-liquid mixed medium flowing in the measuring space; the invention adopts a color three-step phase-shifting method, combines a three-dimensional reconstruction algorithm of a reverse integral curve of a three-dimensional inhomogeneous medium field, and realizes accurate tracking of measured light of a liquid-liquid mixed medium and transient refraction characteristic measurement of a three-dimensional space refractive index by the combined arrangement of a projection screen and a telecentric optical system, thereby greatly improving the measurement accuracy and efficiency; the system has the advantages of precise overall design, high measurement precision, lower cost and wide application range, has important theoretical significance and engineering application value, and is suitable for popularization and application.
The object space telecentric optical system comprises a lens for refracting the deflection light rays emitted from the measuring space, a CCD camera for shooting the converged deflection light rays and obtaining an image, and an object space telecentric diaphragm for converging the deflection light rays emitted from the lens on the CCD camera, wherein the lens is positioned between the measuring space and the object space telecentric diaphragm, the object space telecentric diaphragm is positioned between the lens and the CCD camera, and the projection screen, the measuring space, the lens, the object space telecentric diaphragm and the CCD camera are arranged in a manner of being opposite to each other in sequence by taking an optical axis as a central axis. In the invention, each light spot on a projection screen is taken as a point light source to emit spherical incident light to a measurement space, wherein one spherical incident light which forms a deflection angle theta with an optical axis penetrates through a non-uniform medium field in the measurement space to be refracted to form deflection light parallel to the optical axis, the deflection light parallel to the optical axis emitted from the measurement space is emitted to a lens, the lens refracts the deflection light parallel to the optical axis again, the deflection light after the secondary refraction is screened by an object-side telecentric diaphragm and converged on a CCD camera, and the CCD camera shoots the converged deflection light and obtains an image, namely: the incident light rays emitted by the light spot on the projection screen pass through the measuring space in sequence and are refracted twice by the lens, the deflected light rays are screened by the object space telecentric stop and are converged on the CCD camera, so that the CCD camera shoots the converged deflected light rays and obtains an image.
The measuring system of the inhomogeneous medium field based on the Hartmann ray tracing also comprises a measuring ring, a projection screen and a lens are both arranged on the inner wall of the measuring ring, the measuring space is a circular area concentrically arranged with the measuring ring, the radius of the circular area is smaller than that of the measuring ring, an optical axis passes through the measuring ring and the circle center of the circular area, and the projection screen and the lens are symmetrically arranged by taking the circle center as the center. The measuring ring and the circular area which are concentrically arranged further improve the accuracy and the efficiency of measurement.
The invention relates to a projection screen, a lens, an object space telecentric diaphragm and a CCD camera, which are composed of 4-8 groups, wherein the 4-8 groups of projection screen, lens, object space telecentric diaphragm and CCD camera are uniformly distributed along the 360-degree annular direction of a measuring ring to form a plurality of groups of rear projection Hartmann systems and the cross parts of measuring light sections thereof, each group of rear projection Hartmann systems measures and obtains the linear displacement of light rays generated in the measuring direction according to the light ray tracing, and calculates and obtains the change data of the refractive index of a liquid-liquid mixed medium in the measured three-dimensional space by combining with a corresponding inverse integral curve three-dimensional reconstruction algorithm according to the light ray tracing result in a plurality of measuring directions, thereby further improving the measuring accuracy and efficiency.
In the invention, the angle corresponding relation between the incident light and the refracted light is obtained by derivation through the formula (A), and the relation between the deflection angle theta and the image position deviation shown in the formula (B) is obtained by derivation according to the formula (A), so that the relation between the integral of the gradient of the refractive index of the liquid-liquid mixed medium and the image displacement shown in the formula (C) is obtained through the formula (A) and the formula (B).
In the invention, the CCD camera is connected with the projection screen, the CCD camera transmits the shot and obtained image to the projection screen, and the image is displayed on the projection screen.
According to the invention, the liquid-liquid mixed medium flowing in the measuring space generates a temperature field and/or a pressure field, and the measuring space is provided with a temperature adjusting device for adjusting the temperature field existing in the measuring space, so that the liquid-liquid mixed medium formed by temperature, pressure and flow can be measured. Wherein the liquid-liquid mixed medium is an oil-water mixed liquid, and the pressure field is generated by the flow of the liquid-liquid mixed medium; the temperature regulating device comprises a heating temperature control system and a constant temperature control system, and a constant temperature field is provided by the temperature regulating device.
Due to the adoption of the technical scheme, the invention has the remarkable technical effects that: by adopting a color three-step phase shifting method, combining a three-dimensional reconstruction algorithm of a reverse integral curve of a three-dimensional inhomogeneous medium field and combining a projection screen and a telecentric optical system, accurate tracking of measured light of a liquid-liquid mixed medium and measurement of transient refraction characteristics of refractive indexes of three-dimensional spaces are realized, and the measurement accuracy and efficiency are greatly improved; the system has the advantages of precise overall design, high measurement precision, lower cost and wide application range, has important theoretical significance and engineering application value, and is suitable for popularization and application.
Drawings
Fig. 1 is a schematic structural diagram of a measurement system using a conventional hartmann method.
FIG. 2 is a schematic structural diagram of a measurement principle embodiment of the Hartmann ray tracing-based inhomogeneous medium field measurement system of the present invention.
FIG. 3 is a schematic structural diagram of an embodiment of a rear projection Hartmann measuring system composed of 4 groups of projection screens, lenses, an object space telecentric diaphragm and a CCD camera.
FIG. 4 is a view showing a projection screen of the present invention showing a-2 π/3 phase image in the lateral direction.
Fig. 5 is a 0-phase image displayed in the lateral direction of the projection screen of the present invention.
FIG. 6 is a 2 π/3 phase image displayed in the transverse direction of the projection screen of the present invention.
FIG. 7 is a view showing a-2 π/3 phase image displayed in the longitudinal direction of the projection screen of the present invention.
Fig. 8 is a 0-phase image displayed in the longitudinal direction of the projection screen of the present invention.
FIG. 9 is a 2 π/3 phase image displayed in the longitudinal direction of the projection screen of the present invention.
Fig. 10 shows RGB color phase images synthesized from fig. 4, 5, 6, 7, 8 and 9 displayed on the projection screen according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
The method for measuring the inhomogeneous medium field based on Hartmann ray tracing, as shown in FIGS. 2 and 3, includes the following specific contents:
each light spot on the projection screen 2 is taken as a point light source to emit spherical incident light to the measuring space 3, wherein one spherical incident light which forms a deflection angle theta with the optical axis 1 penetrates through a non-uniform medium field in the measuring space 3 to be refracted to form deflection light parallel to the optical axis 1, the deflection light which is emitted from the measuring space 3 and is parallel to the optical axis 1 is emitted to the lens 4, the lens 4 refracts the deflection light parallel to the optical axis 1 again, the deflection light after the secondary refraction is screened through the object-side telecentric diaphragm 5 and converged on the CCD camera 6, and the CCD camera 6 shoots the converged deflection light and obtains an image; deducing and obtaining the angle corresponding relation between incident light and refracted light through a formula (A), and deducing and obtaining the relation between a deflection angle theta and image position deviation shown in a formula (B) according to the formula (A), so that the relation between the integral of the refractive index gradient of the liquid-liquid mixed medium and the image displacement shown in the formula (C) is obtained through the formula (A) and the formula (B); calculating the image by adopting a color three-step phase shifting method to obtain phase information, and determining the optical refraction characteristics and the corresponding relation of the image generated after the light spot on the projection screen 2 is refracted by the liquid-liquid mixed medium according to the phase information so as to realize light ray tracing; calculating to obtain the change data of the refractive index of the liquid-liquid mixed medium existing in the measuring space 3 by adopting an inverse integral curve three-dimensional reconstruction algorithm; wherein, formula (A), formula (B) and formula (C) are respectively as follows:
wherein z is the direction of the optical axis 1,
the amount of change in the X, Y, Z axis, n is the spatial index of refraction,
f is the focal length of the lens 4, and delta is the displacement of the pixel point of the image on the imaging screen of the CCD camera 6, S1Is the distance between the image-side focal point of the object-side telecentric diaphragm 5 and the imaging screen of the CCD camera 6, and L is the distance between the projection screen 2 and the emergent end of the measuring space 3.
In this embodiment, the liquid-liquid mixed medium flowing inside the measurement space 3 generates a temperature field and/or a pressure field.
In this embodiment, the color three-step phase shifting method includes the following specific contents:
information I to be modulated1、I2、I3、I4、I5、I6The images are respectively modulated into R, G, B three different channels of color RGB through brightness subareas, so that R, G, B three different channels of color RGB on the projection screen 2 and the CCD camera 6 respectively output and collect three phase images in the transverse direction and the longitudinal direction and obtain three phase information, and the CCD camera 6 transmits the three phase information to the projection screen 2; calculating RGB three-channel information M ═ RGB acquired by CCD camera 6 by formula (D)]', RGB three-channel information M and actual RGB three-channel information N ═ RGB]' transformation matrix A and background matrix M0＝[R0G0B0]' conversion is achieved by equation (E); finally, measuring transient refraction characteristics according to the actual RGB three-channel information N obtained through calculation; wherein the projection screen 2 displays modulation information I of three different phase-shifted cosine waves in the transverse and longitudinal directions1、I2、I3、I4、I5、I6Respectively calculated by formula (F) and formula (G) in the horizontal directionThree cosine waves with different phase shifts in the two directions of the longitudinal direction are respectively shown in fig. 4, 5, 6, 7, 8 and 9, and the RGB color phase image synthesized by the images of fig. 4, 5, 6, 7, 8 and 9 is a 2 pi/3 space phase image shown in fig. 10; calculating three phase images collected by the CCD camera 6 through a formula (H) and a formula (I) respectively to obtain phase information of each pixel, and comparing the obtained phase information of each pixel with three cosine wave stripes with different phase shifts displayed on the projection screen 2, so that the optical refraction characteristic and the corresponding relation of the images generated after the light spots on the projection screen 2 are refracted through the uneven medium field are determined, and the light ray tracing is realized; the formulas (D), (E), (F), (G), (H), (I) are shown below:
M＝A·N+M0 (E)，
wherein I' (x, y) is a background gray value and I "(x, y) is a modulation gray value;
wherein phi is1(x,y)、φ2And (x, y) are phase information.
In this embodiment, the inverse integral curve three-dimensional reconstruction algorithm includes the following specific contents: establishing a ill-conditioned matrix with the refractive index distribution of the liquid-liquid mixed medium as a variable, and then solving the ill-conditioned matrix, thereby converting the reconstruction problem into a solution problem of the ill-conditioned matrix; wherein, the ill-conditioned matrix shown in formula (J) is obtained by deforming and dispersing formula (C):
T＝WDS2 (J)，
wherein T is the displacement information matrix of the image point, W is the model coefficient matrix, D is the refractive index change vector matrix to be solved, S2Is a projection matrix.
The measurement method of the inhomogeneous medium field based on Hartmann ray tracing in the embodiment is realized by a measurement system of the inhomogeneous medium field based on Hartmann ray tracing, and the measurement system of the inhomogeneous medium field based on Hartmann ray tracing, as shown in figures 2 and 3, comprises a measurement space 3 in which the inhomogeneous medium field exists, a projection screen 2 for emitting spherical incident rays to the measurement space 3, and an object-side telecentric optical system for refracting the spherical incident rays emitted from light spots on the projection screen 2 through the inhomogeneous medium field in the measurement space 3 to form deflected rays parallel to an optical axis 1 for screening and converging into an image, wherein the measurement space 3 is positioned between the projection screen 2 and the object-side telecentric optical system; calculating the image by adopting a color three-step phase shifting method, obtaining phase information, and determining the optical refraction characteristic and the corresponding relation of the image according to the phase information; and calculating to obtain the change data of the refractive index of the inhomogeneous medium field existing in the measuring space 3 by adopting an inverse integral curve three-dimensional reconstruction algorithm.
In this embodiment, the object-side telecentric optical system includes a lens 4 for refracting the deflected light rays emitted from the measurement space 3, a CCD camera 6 for shooting the converged deflected light rays and obtaining an image, and an object-side telecentric stop 5 for screening the deflected light rays emitted from the lens 4 and converging on the CCD camera 6, wherein the lens 4 is located between the measurement space 3 and the object-side telecentric stop 5, the object-side telecentric stop 5 is located between the lens 4 and the CCD camera 6, the projection screen 2, the measurement space 3, the lens 4, the object-side telecentric stop 5, and the CCD camera 6 all use the optical axis 1 as a central axis and are arranged in sequence. In the invention, each light spot on a projection screen is taken as a point light source to emit spherical incident light to a measurement space, wherein one spherical incident light which forms a deflection angle theta with an optical axis penetrates through a non-uniform medium field in the measurement space to be refracted to form deflection light parallel to the optical axis, the deflection light parallel to the optical axis emitted from the measurement space is emitted to a lens, the lens refracts the deflection light parallel to the optical axis again, the deflection light after the secondary refraction is screened by an object-side telecentric diaphragm and converged on a CCD camera, and the CCD camera shoots the converged deflection light and obtains an image, namely: compared with the traditional Hartmann method shown in figure 1, the Hartmann screen 8 is replaced by the optical design of the combination of the projection screen, the lens, the object space telecentric diaphragm and the CCD camera, the track of imaging light is limited, and the quick tracing of light is realized.
In this embodiment, the system for measuring a non-uniform medium field based on hartmann ray tracing further includes a measuring ring 7, the projection screen 2 and the lens 4 are both disposed on the inner wall of the measuring ring 7, the measuring space 3 is a circular region concentrically disposed with the measuring ring 7, the radius of the circular region is smaller than that of the measuring ring 7, the optical axis 1 passes through the centers of the measuring ring 7 and the circular region, and the projection screen 2 and the lens 4 are symmetrically disposed with the center of the circle as the center.
In this embodiment, the projection screen 2, the lens 4, the object space telecentric stop 5, and the CCD camera 6 are composed of 4 groups, and the 4 groups of the projection screen 2, the lens 4, the object space telecentric stop 5, and the CCD camera 6 are uniformly distributed along the 360-degree annular direction of the measurement ring 7.
In this embodiment, the angle correspondence between the incident light and the refracted light is obtained by derivation according to the formula (a), and the relationship between the deflection angle θ and the image position deviation shown in the formula (B) is obtained by derivation according to the formula (a), so that the relationship between the integral of the refractive index gradient of the liquid-liquid mixed medium and the image displacement shown in the formula (C) is obtained by the formula (a) and the formula (B).
In this embodiment, the CCD camera 6 is connected to the projection screen 2, and the CCD camera 6 transmits the image captured and obtained to the projection screen 2, and the image is displayed on the projection screen 2.
In this embodiment, the liquid-liquid mixed medium flowing in the measurement space generates a temperature field and/or a pressure field, and the measurement space is provided with a temperature adjusting device for adjusting the temperature field existing in the measurement space, so that the measurement of the liquid-liquid mixed medium formed by temperature, pressure and flow is realized. Wherein the liquid-liquid mixed medium is an oil-water mixed liquid, and the pressure field is generated by the flow of the liquid-liquid mixed medium; the temperature regulating device comprises a heating temperature control system and a constant temperature control system, and a constant temperature field is provided by the temperature regulating device.
In summary, the above-mentioned embodiments are only preferred embodiments of the present invention, and all equivalent changes and modifications made in the claims of the present invention should be covered by the claims of the present invention.
Claims (2)
1. The method for measuring the inhomogeneous medium field based on Hartmann ray tracing is characterized by comprising the following steps: the method comprises the following specific contents:
each light spot on the projection screen (2) is taken as a point light source to emit spherical incident light rays to the measuring space (3), wherein one of the spherical incident light rays which form a deflection angle theta with the optical axis (1) penetrates through a non-uniform medium field in the measuring space (3) to be refracted to form a deflection light ray parallel to the optical axis (1), the deflection light ray parallel to the optical axis (1) emitted from the measuring space (3) is emitted to the lens (4), the lens (4) refracts the deflection light ray parallel to the optical axis (1) again, the deflection light ray after being refracted again is screened through the object space telecentric diaphragm (5) and converged on the CCD camera (6), and the CCD camera (6) shoots the converged deflection light ray and obtains an image; deducing and obtaining the angle corresponding relation between incident light and refracted light through a formula (A), and deducing and obtaining the relation between a deflection angle theta and image position deviation shown in a formula (B) according to the formula (A), so that the relation between the integral of the refractive index gradient of the liquid-liquid mixed medium and the image displacement shown in the formula (C) is obtained through the formula (A) and the formula (B); calculating the image by adopting a color three-step phase shifting method to obtain phase information, and determining the optical refraction characteristics and the corresponding relation of the image generated after the light spot on the projection screen (2) is refracted by the liquid-liquid mixed medium according to the phase information so as to realize light ray tracing; calculating to obtain the change data of the refractive index of the liquid-liquid mixed medium existing in the measuring space (3) by adopting an inverse integral curve three-dimensional reconstruction algorithm; wherein, formula (A), formula (B) and formula (C) are respectively as follows:
wherein z is the direction of the optical axis (1),
the amount of change in the X, Y, Z axis, n is the spatial index of refraction,
f is the focal length of the lens (4), delta is the displacement of the pixel point of the image on the imaging screen of the CCD camera (6), S is the change of the space refractive index1The distance between the image space focus of the object space telecentric diaphragm (5) and the imaging screen of the CCD camera (6) is L, and the distance between the projection screen (2) and the ejection end of the measurement space (3) is L;
the color three-step phase shifting method comprises the following specific contents:
information I to be modulated1、I2、I3、I4、I5、I6The three different channels of color RGB R, G, B on the projection screen (2) and CCD camera (6) are modulated into R, G, B different channels of color RGB by luminance division respectivelyRespectively outputting and collecting three phase images in the transverse direction and the longitudinal direction and obtaining three phase information, and transmitting the three phase information to a projection screen (2) by a CCD camera (6); RGB three-channel information M (RGB) acquired by CCD camera (6) is calculated through formula (D)]', RGB three-channel information M and actual RGB three-channel information N ═ RGB]' transformation matrix A and background matrix M0＝[R0G0B0]' conversion is achieved by equation (E); finally, measuring transient refraction characteristics according to the actual RGB three-channel information N obtained through calculation; wherein the projection screen (2) displays modulation information I of three differently phase shifted cosine waves in both the transverse and longitudinal directions1、I2、I3、I4、I5、I6Respectively obtained by calculation through a formula (F) and a formula (G); calculating three phase images collected by a CCD camera (6) through a formula (H) and a formula (I) respectively to obtain phase information of each pixel, and comparing the obtained phase information of each pixel with three cosine wave stripes with different phase shifts displayed on a projection screen (2), so that the optical refraction characteristic and the corresponding relation of the images generated after light spots on the projection screen (2) are refracted through an uneven medium field are determined, and light ray tracing is realized; the formulas (D), (E), (F), (G), (H), (I) are shown below:
M＝A·N+M0(E)，
wherein I' (x, y) is a background gray value and I "(x, y) is a modulation gray value;
wherein phi is1(x,y)、φ2(x, y) are phase information;
the inverse integral curve three-dimensional reconstruction algorithm comprises the following specific contents: establishing a ill-conditioned matrix with the refractive index distribution of the liquid-liquid mixed medium as a variable, and then solving the ill-conditioned matrix, thereby converting the reconstruction problem into a solution problem of the ill-conditioned matrix; wherein, the ill-conditioned matrix shown in formula (J) is obtained by deforming and dispersing formula (C):
T＝WDS2 (J)，
wherein T is the displacement information matrix of the image point, W is the model coefficient matrix, D is the refractive index change vector matrix to be solved, S2Is a projection matrix.
2. The Hartmann ray tracing based inhomogeneous medium field measurement method as set forth in claim 1, wherein: the liquid-liquid mixed medium flowing inside the measuring space (3) generates a temperature field and/or a pressure field.
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