CN117348308A - Adjustable liquid crystal lens, spectrum imaging method and system based on adjustable liquid crystal lens - Google Patents
Adjustable liquid crystal lens, spectrum imaging method and system based on adjustable liquid crystal lens Download PDFInfo
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- G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
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Abstract
The invention belongs to the technical field of micro-nano optics, and discloses an adjustable liquid crystal lens, a spectrum imaging method and a spectrum imaging system based on the adjustable liquid crystal lens. The invention breaks through the limitation that the traditional lens can only realize space information recording, can greatly improve the information quantity obtained by optical detection, develops a multi-dimensional planar imaging device with compact structure and high efficiency, and provides a spectrum imaging method and a spectrum imaging system realized by utilizing a single adjustable liquid crystal lens.
Description
Technical Field
The invention belongs to the technical field of micro-nano optics, and particularly relates to an adjustable liquid crystal lens, a spectrum imaging method based on the adjustable liquid crystal lens and a system.
Background
While conventional optical imaging techniques based on lenses can only obtain spatial and temporal dimensional information of a target, spectral imaging can break the limitations of conventional optical imaging techniques while obtaining a data cube containing spatio-temporal information and spectral information of the measured target. Currently available commercial spectral cameras are based on a direct expansion of the spectrometer or imaging system, which requires scanning in the spatial or spectral domain, has a limited data acquisition rate and is bulky in the system. However, the micro spectrometer based on quantum dots, photonic crystals, nanowires, super surfaces and the like lacks a phase regulation function and cannot realize imaging, so that the micro spectrometer needs to be combined with an achromatic lens to realize imaging and spectrum detection simultaneously.
Disclosure of Invention
The invention provides an adjustable liquid crystal lens, a spectrum imaging method and a system based on the adjustable liquid crystal lens, and solves the problems that the traditional lens in the prior art can only realize space information recording and cannot realize spectrum imaging by utilizing a single lens.
In a first aspect, the present invention provides a spectroscopic imaging method based on an adjustable liquid crystal lens, comprising the steps of:
step 1, constructing a spectrum imaging system model, wherein the spectrum imaging system model is expressed as follows:
O m (x,y,λ)＝O g (x,y,λ)*PSF(x,y,λ)
in the formula, LC i (lambda) is the spectral response of the tunable liquid crystal lens at different external voltages, O m (x, y, lambda) is the actual image of the object under test, I i (x, y) is intensity information obtained by the corresponding camera of the adjustable liquid crystal lens under different external voltages, Λ is a set wavelength range, O g (x, y, lambda) is an ideal image of the measured object, and PSF (x, y, lambda) is a point spread function of the adjustable liquid crystal lens;
step 2, converting the geometric phase distribution of the adjustable liquid crystal lens into an in-plane orientation angle of the adjustable liquid crystal lensDistribution; changing the out-of-plane orientation angle of the tunable liquid crystal lens by applying different external voltages to LC in a set wavelength range i Calibrating (lambda);
step 3, recording and LC i (lambda) one-to-one I i (x,y)；
Step 4, based on the obtained multiple groups of LC i (lambda) and corresponding I i (x, y) representing the relationship between the two in matrix form as follows:
I＝LC·X
wherein I is an intensity information matrix, LC is a spectral response matrix, and X is a matrix to be solved;
solving X by adopting an optimization algorithm, and recovering the actual image O of the detected object m (x,y,λ)；
Step 5, obtaining point spread functions PSF (x, y, lambda) under different wavelengths;
step 6, based on O m (x, y, lambda) and PSF (x, y, lambda), calculating by adopting an optimization algorithm, and reconstructing to obtain an ideal image O of the measured object g (x,y,λ)。
Preferably, the adjustable liquid crystal lens has a five-layer structure, and the adjustable liquid crystal lens sequentially comprises, from top to bottom: the first conductive glass layer, the first photo-alignment layer, the nematic liquid crystal layer, the second photo-alignment layer and the second conductive glass layer.
Preferably, the tunable liquid crystal lens has a geometrical phase of even aspherical surface, expressed as follows:
wherein r is the radius of the circle where any point (x, y) on the adjustable liquid crystal lens is located, phi (r) is the geometric phase of the adjustable liquid crystal lens at the radius r, k r For wave vector at r, f 0 R is the focal length of the adjustable liquid crystal lens 0 Is the radius lambda of the adjustable liquid crystal lens min And lambda (lambda) max The minimum wavelength and the maximum wavelength of the tunable liquid crystal lens in each zone are respectively.
Preferably, in the step 2, the geometric phase distribution of the adjustable liquid crystal lens is converted into the in-plane orientation angle distribution of the adjustable liquid crystal lens based on the relationship that the reverse circularly polarized light passing through the adjustable liquid crystal lens carries a phase adjustment amount of 2 times of the in-plane orientation angle when the circularly polarized light is incident.
Preferably, in the step 2, as the applied external voltage increases, the out-of-plane orientation angle of the tunable liquid crystal lens gradually rotates from 0 to pi/2; by simulating the out-of-plane orientation angle of the adjustable liquid crystal lens to be [0, pi/2]Spectral response when the working wavelength range of the liquid crystal is the set wavelength range, realizing LC i Calibration of (lambda).
Preferably, step 3 gives I i (x, y) further includes a pair I i (x, y) adding random noise to obtain intensity information after adding noise, and marking the intensity information as I i_noise (x, y); in the step 4, based on the obtained multiple LC groups i (lambda) and corresponding I i_noise (x, y) representing the relationship between the two in the form of a matrix.
Preferably, in the step 6, if the point spread function of the tunable lc lens at a certain wavelength is PSF (x, y), the ideal image of the measured object is O g (x, y) the actual image of the measured object is O m (x, y), the noise is n (x, y), then O m (x,y)＝O g (x,y)*PSF(x,y)+n(x,y)；
Based on O m (x, y) and PSF (x, y), and performing wiener filter deconvolution to obtain O g (x, y) as follows:
in the method, in the process of the invention,f (u, v), H (u, v) and G (u, v) are each O g (x, y), PSF (x, y) and O m (x, y) spectrum, H * (u, v) is the conjugate of H (u, v), P f (u, v) and P n (u, v) is the power spectral density of the actual image and the power spectral density of the actual image noise, respectively;
based on the method, the method is to O m Recovering the image at each wavelength to obtain O g (x,y,λ)。
In a second aspect, the present invention provides an adjustable liquid crystal lens, wherein the adjustable liquid crystal lens has a five-layer structure, and the structure sequentially comprises, from top to bottom: the first conductive glass layer, the first photo-alignment layer, the nematic liquid crystal layer, the second photo-alignment layer and the second conductive glass layer;
the adjustable liquid crystal lens has geometrical phases of even-order aspheric surfaces, and is expressed as follows:
wherein r is the radius of the circle where any point (x, y) on the adjustable liquid crystal lens is located, phi (r) is the geometric phase of the adjustable liquid crystal lens at the radius r, k r For wave vector at r, f 0 R is the focal length of the adjustable liquid crystal lens 0 Is the radius lambda of the adjustable liquid crystal lens min And lambda (lambda) max The minimum wavelength and the maximum wavelength of the adjustable liquid crystal lens in each annular zoneA large wavelength;
the adjustable liquid crystal lens can realize phase regulation and spectrum regulation simultaneously by changing the in-plane orientation angle and the out-of-plane orientation angle.
Preferably, when the circularly polarized light is incident, the reverse circularly polarized light passing through the adjustable liquid crystal lens carries a phase regulation quantity of 2 times of in-plane orientation angle; as the applied external voltage increases, the out-of-plane orientation angle of the tunable liquid crystal lens gradually rotates from 0 to pi/2.
In a third aspect, the present invention provides a spectroscopic imaging system based on an adjustable liquid crystal lens, comprising: an adjustable liquid crystal lens, a camera and a reconstruction unit; light emitted or reflected by the measured object is imaged on the camera after passing through the adjustable liquid crystal lens;
the reconstruction unit stores a spectral imaging system model, which is expressed as follows:
O m (x,y,λ)＝O g (x,y,λ)*PSF(x,y,λ)
in the formula, LC i (lambda) is the spectral response of the tunable liquid crystal lens at different external voltages, O m (x, y, lambda) is the actual image of the object under test, I i (x, y) is intensity information obtained by the corresponding camera of the adjustable liquid crystal lens under different external voltages, Λ is a set wavelength range, O g (x, y, lambda) is an ideal image of the measured object, and PSF (x, y, lambda) is a point spread function of the adjustable liquid crystal lens;
the reconstruction unit is used for reconstructing and obtaining an ideal image of the measured object based on the spectral imaging system model, the spectral response of the adjustable liquid crystal lens under different external voltages, the intensity information obtained by the camera corresponding to the adjustable liquid crystal lens under different external voltages and the point spread function of the adjustable liquid crystal lens.
One or more technical schemes provided by the invention have at least the following technical effects or advantages:
the invention is based on the characteristics of optical anisotropy and electro-optic regulation, and realizes phase regulation and spectrum regulation simultaneously by changing the in-plane orientation angle and the out-of-plane orientation angle of the liquid crystal molecules, and particularly provides a spectrum imaging method based on an adjustable liquid crystal lens, which can simultaneously image and spectrum detect a measured target based on calculation spectrum imaging of a dynamic adjustable liquid crystal lens, breaks the limitation that the traditional lens can only image, can greatly improve the information quantity obtained by optical imaging, and correspondingly, the invention also provides a novel multi-dimensional plane imaging device with compact structure and high efficiency, namely an adjustable liquid crystal lens, can greatly improve the information quantity obtained by optical imaging, and in addition, the invention also provides a spectrum imaging system based on the adjustable liquid crystal lens, which corresponds to the spectrum imaging method based on the adjustable liquid crystal lens. The invention can realize the simultaneous imaging and spectrum detection of the measured object by using only a single lens, and the two functions are mutually independent and do not affect each other, thereby breaking the limitation that the traditional lens can only perform imaging. Compared with the traditional optical material, the liquid crystal has the advantages of high efficiency, adjustable spectral response and the like, can be prepared in a large scale and at low cost by combining a mature liquid crystal material processing technology, is easy to be compatible with other systems, has high integration degree, and can be suitable for the development of future multifunctional devices, so that the device provided by the invention has the advantages of low cost, easy preparation and integration.
Drawings
Fig. 1 is a schematic diagram of a spectral imaging system model constructed in a spectral imaging method based on an adjustable liquid crystal lens according to embodiment 1 of the present invention;
fig. 2 is a schematic structural diagram of an adjustable liquid crystal lens used in a spectral imaging method based on an adjustable liquid crystal lens according to embodiment 1 of the present invention;
FIG. 3 is a graph showing the in-plane orientation angle of a tunable liquid crystal lens;
FIG. 4 is a spectral response of a tunable liquid crystal lens;
FIG. 5 is a schematic diagram showing the comparison of a restored image and an actual image of a partially selected region; wherein (a) in fig. 5 is an actual image, and (b) in fig. 5 is a restored image;
FIG. 6 is a diagram showing the comparison of the recovered spectrum of a portion of the selected region with the actual spectrum;
FIG. 7 is a schematic diagram of the point spread function of the tunable liquid crystal lens at different wavelengths obtained by simulation;
FIG. 8 is a schematic illustration of the effect of convolving simulated broadband imaging with a point spread function at different wavelengths;
FIG. 9 is a schematic diagram showing the effect of a blurred image after wiener filtering deconvolution; where (a) in fig. 9 is an actual image, (b) in fig. 9 is a blurred image, and (c) in fig. 9 is a wiener filtered deblurred image.
Detailed Description
In order to better understand the above technical solutions, the following detailed description will refer to the accompanying drawings and specific embodiments.
Example 1:
embodiment 1 provides a spectral imaging method based on an adjustable liquid crystal lens, comprising the steps of:
and 1, constructing a spectrum imaging system model.
The spectral imaging system model is represented as follows:
O m (x,y,λ)＝O g (x,y,λ)*PSF(x,y,λ)
in the formula, LC i (lambda) is the spectral response of the tunable liquid crystal lens at different external voltages, O m (x, y, lambda) is the actual image of the object under test, I i (x, y) is intensity information obtained by the corresponding camera of the adjustable liquid crystal lens under different external voltages, Λ is a set wavelength range, O g (x, y, lambda) is the ideal image of the object under test, and PSF (x, y, lambda) is the point spread function of the tunable liquid crystal lens.
Step 2, converting the geometric phase distribution of the adjustable liquid crystal lens into the phase distributionAn in-plane orientation angle distribution of the tunable liquid crystal lens; changing the out-of-plane orientation angle of the tunable liquid crystal lens by applying different external voltages to LC in a set wavelength range i Calibration is performed (lambda).
Wherein, adjustable liquid crystal lens is five-layer structure, from top to bottom in proper order: the first conductive glass layer, the first photo-alignment layer, the nematic liquid crystal layer, the second photo-alignment layer and the second conductive glass layer.
The adjustable liquid crystal lens has geometrical phases of even-order aspheric surfaces, and is expressed as follows:
wherein r is the radius of the circle where any point (x, y) on the adjustable liquid crystal lens is located, phi (r) is the geometric phase of the adjustable liquid crystal lens at the radius r, k r For wave vector at r, f 0 R is the focal length of the adjustable liquid crystal lens 0 Is the radius lambda of the adjustable liquid crystal lens min And lambda (lambda) max The minimum wavelength and the maximum wavelength of the tunable liquid crystal lens in each zone are respectively.
Specifically, based on the relationship that the reverse circularly polarized light passing through the adjustable liquid crystal lens carries a phase adjustment amount of 2 times of in-plane orientation angle when circularly polarized light is incident, the geometric phase distribution of the adjustable liquid crystal lens is converted into the in-plane orientation angle distribution of the adjustable liquid crystal lens.
The out-of-plane orientation angle of the tunable liquid crystal lens gradually rotates from 0 to pi/2 as the applied external voltage increases; by simulating the out-of-plane orientation angle of the adjustable liquid crystal lens to be [0, pi/2]Spectral response when the working wavelength range of the liquid crystal is the set wavelength range, realizing LC i Calibration of (lambda).
Step 3, recording and LC i (lambda) one-to-one I i (x,y)。
Step 4, based on the obtained multiple groups of LC i (lambda) and corresponding I i (x, y) representing the relationship between the two in matrix form as follows:
I＝LC·X
wherein I is an intensity information matrix, LC is a spectral response matrix, and X is a matrix to be solved;
solving X by adopting an optimization algorithm, and recovering the actual image O of the detected object m (x,y,λ)。
In a preferred embodiment, step 3 provides step I i (x, y) further includes a pair I i (x, y) adding random noise to obtain intensity information after adding noise, and marking the intensity information as I i_noise (x, y); in the step 4, based on the obtained multiple LC groups i (lambda) and corresponding I i_noise (x, y) representing the relationship between the two in the form of a matrix.
And 5, obtaining point spread functions PSF (x, y, lambda) under different wavelengths.
Specifically, PSF (x, y, λ) can be experimentally measured.
Step 6, based on O m (x, y, lambda) and PSF (x, y, lambda), calculating by adopting an optimization algorithm, and reconstructing to obtain an ideal image O of the measured object g (x,y,λ)。
Specifically, the point spread function of the adjustable liquid crystal lens under a certain wavelength is set as PSF (x, y), and the ideal image of the measured object is O g (x, y) the actual image of the measured object is O m (x, y), the noise is n (x, y), then O m (x,y)＝O g (x,y)*PSF(x,y)+n(x,y)；
Based on O m (x, y) and PSF (x, y), and performing wiener filter deconvolution to obtain O g (x, y) as follows:
in the method, in the process of the invention,f (u, v), H (u, v) and H (u, v) are each O g (x, y), PSF (x, y) and O m (x, y) spectrum, H * (u, v) is the conjugate of H (u, v), P f (u, v) and P n (u, v) is the power spectral density of the actual image and the power spectral density of the actual image noise, respectively;
based on the method, the method is to O m Recovering the image at each wavelength to obtain O g (x,y,λ)。
Example 2:
embodiment 2 provides an adjustable liquid crystal lens, the adjustable liquid crystal lens is five-layer structure, from top to bottom: the first conductive glass layer, the first photo-alignment layer, the nematic liquid crystal layer, the second photo-alignment layer and the second conductive glass layer.
The adjustable liquid crystal lens has geometrical phases of even-order aspheric surfaces, and is expressed as follows:
wherein r is the radius of the circle where any point (x, y) on the adjustable liquid crystal lens is located, phi (r) is the geometric phase of the adjustable liquid crystal lens at the radius r, k r For wave vector at r, f 0 R is the focal length of the adjustable liquid crystal lens 0 Is the radius lambda of the adjustable liquid crystal lens min And lambda (lambda) max The minimum wavelength and the maximum wavelength of the tunable liquid crystal lens in each zone are respectively.
The adjustable liquid crystal lens can realize phase regulation and spectrum regulation simultaneously by changing the in-plane orientation angle and the out-of-plane orientation angle.
Specifically, when circularly polarized light is incident, reverse circularly polarized light passing through the adjustable liquid crystal lens carries a phase regulation quantity of 2 times of in-plane orientation angle; as the applied external voltage increases, the out-of-plane orientation angle of the tunable liquid crystal lens gradually rotates from 0 to pi/2.
The tunable liquid crystal lens provided in example 2 was used to realize the tunable liquid crystal lens-based spectral imaging method as provided in example 1.
Example 3:
embodiment 3 provides a spectral imaging system based on an adjustable liquid crystal lens, mainly comprising: an adjustable liquid crystal lens, a camera and a reconstruction unit; light emitted or reflected by the measured object is imaged on the camera after passing through the adjustable liquid crystal lens.
The reconstruction unit stores a spectral imaging system model, which is expressed as follows:
O m (x,y,λ)＝O g (x,y,λ)*PSF(x,y,λ)
in the formula, LC i (lambda) is the spectral response of the tunable liquid crystal lens at different external voltages, O m (x, y, lambda) is the actual image of the object under test, I i (x, y) is intensity information obtained by the corresponding camera of the adjustable liquid crystal lens under different external voltages, Λ is a set wavelength range, O g (x, y, lambda) is the ideal image of the object under test, and PSF (x, y, lambda) is the point spread function of the tunable liquid crystal lens.
The reconstruction unit is used for reconstructing and obtaining an ideal image of the measured object based on the spectral imaging system model, the spectral response of the adjustable liquid crystal lens under different external voltages, the intensity information obtained by the camera corresponding to the adjustable liquid crystal lens under different external voltages and the point spread function of the adjustable liquid crystal lens.
The spectrum imaging system based on the adjustable liquid crystal lens provided in embodiment 3 corresponds to the spectrum imaging method based on the adjustable liquid crystal lens provided in embodiment 1, and the functions of each component in the system can be understood by referring to embodiment 1, and are not described herein.
In addition, in the spectral imaging system based on the tunable liquid crystal lens provided in embodiment 3, related devices such as a collimation device, an imaging lens, a driving power supply and the like may be further set according to application requirements.
The present invention is further described below.
The invention uses the adjustable liquid crystal lens to simultaneously image and spectrum detect the object O (x, y, lambda) to obtain the data cube O containing the spatial information and the spectral information m (x, y, λ), see fig. 1, the system model is:
I i (x,y)＝∫ Λ LC i (λ)×[O g (x,y,λ)*PSF(x,y,λ)]dλ (1)
because the liquid crystal molecules of the adjustable liquid crystal lens have optical anisotropy and electrooptical regulation and control characteristics, LC is realized under different voltages i (lambda) different responses I measured by a camera (e.g. CMOS camera) i (x, y) in combination with an optimization algorithm to recover the image O of the object O (x, y, λ) m (x, y, λ). And O again m (x,y,λ)＝O g (x, y, lambda) PSF (x, y, lambda), by measuring the point spread function PSF (x, y, lambda) at different wavelengths, deconvoluting, the ideal image O of the object can be reconstructed g (x,y,λ)。
Several main parts of the present invention are described below.
(1) And (3) designing an adjustable liquid crystal lens.
As shown in fig. 2, from top to bottom, the steps are as follows: a first conductive glass layer 210, a first photoalignment layer 220, a nematic liquid crystal layer 230, a second photoalignment layer 240, and a second conductive glass layer 250; namely, ITO (Indium Tin Oxide) conductive glass comprising a top layer and a bottom layer, nematic liquid crystal comprising an intermediate layer, and a packageA photoalignment layer wrapped around the nematic liquid crystal. For a single liquid crystal molecule, it can be equivalent to a variable wave plate, its Jones matrix J (lambda 0 θ, α) can be expressed as:
wherein lambda is 0 The operating wavelength of the variable wave plate is represented by θ, the in-plane orientation angle of the tunable liquid crystal lens (i.e., liquid crystal molecules), α, the out-of-plane orientation angle of the liquid crystal molecules, and δ, the phase retardation between the fast and slow axes of the liquid crystal molecules.
Jones matrix E for outgoing light after passing through liquid crystal molecules under incidence of a beam of circularly polarized light out (λ 0 θ, α) can be expressed as:
where p is the amplitude of the outgoing light in the same direction as the incoming light, and q is the amplitude of the outgoing light in the opposite direction to the incoming light.
It can be seen that after passing through the liquid crystal, the output field is divided into two parts, one part is circularly polarized light with the same rotation direction as the incident light, the other part is circularly polarized light with the opposite rotation direction to the incident light, the part carries a phase adjustment quantity which is twice the in-plane orientation angle of the liquid crystal molecules, and the modes of p and q represent the amplitudes of the two parts of circularly polarized light respectively.
For the geometric phase design of the tunable liquid crystal lens, at the operating wavelength lambda 0 Under the design, the liquid crystal lens with the following even-order aspheric phase is designed, and the focal length is f 0 Radius r 0 The expression is as follows:
the phase comprehensively considers the characteristics of point spread functions (point spread function, PSF) under different wavelengths, and ensures that modulation transfer functions (Modulation Transfer Function, MTF) under different wavelengths are not cut off in a certain range.
According to the phase regulation quantity relationship that the reverse circularly polarized light carries 2 times of the in-plane orientation angle of the liquid crystal molecules after passing through the liquid crystal when the circularly polarized light is incident, the phase distribution of the liquid crystal lens can be converted into the in-plane orientation angle distribution of the liquid crystal molecules. The in-plane alignment angle distribution of the liquid crystal molecules is shown in fig. 3.
(2) Calibration of the spectral response of the tunable liquid crystal lens.
When no external power is applied, the out-of-plane alignment angle α=0 of the liquid crystal molecules, at which time the phase is retarded δ (λ 0 α) can be expressed as:
wherein n is e And n o Respectively representing refractive index, lambda of liquid crystal molecules in the direction of the fast and slow axes 0 D is the thickness of the nematic liquid crystal layer for the wavelength of the incident light. With the introduction of the applied voltage, the liquid crystal molecules rotate out of plane along with the increase of the applied voltage, and the refractive index of the liquid crystal molecules in the fast axis direction changes due to the rotation of the liquid crystal molecules in the vertical and plane directions because the propagation direction of the incident light is kept unchanged, and the equivalent refractive index n of the liquid crystal molecules in the fast axis direction eff Can be expressed as:
equation (6) is further rewritten as:
it is noted that as the applied voltage increases, the out-of-plane alignment angle α of the liquid crystal molecules gradually rotates from 0 to pi/2, and accordingly, the liquid crystal molecules rapidly rotate, etcThe effective refractive index is also from n e Gradually change to n o At this time, the liquid crystal molecules no longer have anisotropy, but become an isotropic structure, and the continuous increase of the applied voltage will not affect the out-of-plane alignment angle of the liquid crystal molecules.
By combining the formula (2) and the formula (3), the polarization conversion efficiency of the liquid crystal molecules is:
which is in accordance with the operating wavelength lambda 0 Since the out-of-plane alignment angle α of the liquid crystal molecules is related, the polarization conversion efficiency of the liquid crystal molecules varies with the operating wavelength and the applied voltage.
In order to restore the spectral image of the object to be measured, the spectral response of the liquid crystal lens, that is, the polarization conversion efficiency, is calibrated by the formula (1). By combining the formula (5), the formula (7) and the formula (8), the invention adopts Matlab to simulate that the out-of-plane alignment angle range of liquid crystal molecules is [0, pi/2 ]]Spectral response LC of adjustable liquid crystal lens with working wavelength of 450-650 nm i (lambda) as shown in figure 4.
(3) And recovering the actual image of the measured object.
For the image O, i.e. the object O (X, y, λ), its spatial information S (X, y) and spectral information X (λ) are known, the object under test being at a point (X 0 ,y 0 ) The spectrum at X 0 (lambda) in combination with the simulated spectral response data LC of the tunable liquid crystal lens i And (lambda), simulating the modulation effect of the adjustable liquid crystal lens on the image O under different voltages by adopting Matlab, and obtaining the modulation intensity (namely the intensity information obtained by a camera) under different external voltages as follows:
I i (x 0 ,y 0 )＝∑LC i (λ)X 0 (λ) (9)
operating each point of the image O to obtain I i (x, y), i.e. record the response of the CMOS camera at different voltages: i i ＝∑LC i (λ)X(λ)。
Pair I i (x, y) adding random noise to simulate realityNoise existing in the measuring process, and the result after adding the noise is I i_noise (x, y). In consideration of the calculation amount, a part of the area in the image is selected for calculation.
I i_noise (x 0 ,y 0 )＝∑LC i (λ)X(λ) (10)
X (lambda) is (X) 0 ,y 0 ) A recovered spectrum.
Multiple sets of LC are obtained by multiple measurements i (lambda) and corresponding I i_noise (x, y) to obtain matrices I and LC, writing the above summation into a matrix form:
I＝LC·X (11)
solving the optimization problem by adopting a CVX (i.e. CVX toolbox in Matlab) optimization algorithm to obtain X, namely O m (x 0 ,y 0 Lambda) of the image, and operating on each point of the obtained image to obtain O m (x,y,λ)。
FIG. 5 is a schematic diagram showing the comparison of a restored image and an actual image of a partially selected region; wherein (a) in fig. 5 is an actual image (i.e., an actual image of the object to be measured), and (b) in fig. 5 is a restored image (i.e., an ideal image of the object to be measured); FIG. 6 is a diagram showing the comparison of the recovered spectrum of a portion of the selected region with the actual spectrum; wherein the solid line is the actual spectrum and the dotted line is the recovered spectrum. Based on fig. 5 and 6, it can be seen that the restored image and the actual image have a restored spectrum that matches well with the actual spectrum.
(4) Obtaining a point spread function.
The object is placed in front of the lens with a distance d 0 Is input plane x of (2) 0 y 0 At a distance d after the lens i Is the conjugate plane x of (2) i y i And (5) observing imaging conditions. Assuming that the complex amplitude distribution immediately after the object is U 0 (x 0 ′,y 0 ′)，(x 0 ′,y 0 The unit pulse emitted at the') point is delta (x) 0 -x 0 ′,y 0 -y 0 ') calculating the field distribution on three specific planes face by face along the propagation direction of the light wave: the field distribution dU in two planes immediately before and after the lens 1 And dU 1 ' field distribution h on viewing planeThus, the input-output relation of a point source can be finally derived. The fresnel formula is used:
wherein dU is 1 (x 0 ′,y 0 'A'; x, y) is the light field distribution immediately in front of the lens and k is the wave vector.
Due to (x) 0 ′,y 0 ') point is arbitrary, for writing convenience, after omitting the constant phase factor, the above formula can be written as:
after the light wave passes through a lens with aperture function P (x, y) and phase distribution phi (r), the complex amplitude dU 1 ′(x 0 ,y 0 The method comprises the steps of carrying out a first treatment on the surface of the x, y) is:
dU 1 ′(x 0 ,y 0 ；x,y)＝P(x,y)φ(r)dU 1 (x 0 ,y 0 ；x,y) (14)
the propagation of the optical field from the rear surface of the lens to the viewing surface satisfies fresnel diffraction, so the complex amplitude distribution caused by the unit pulses on the object plane on the viewing surface, i.e. the point spread function, can be written as:
the point spread function of the lens at different wavelengths was thus obtained using Matlab simulation, as shown in fig. 7.
(5) And (3) the ideal reconstruction of the measured object.
In the process of recovering the data cube O for obtaining the actual image of the measured object m On the basis of (x, y, λ), in order to obtain its ideal image, image restoration, i.e. deconvolution with a point spread function, is required. In the process of image restoration, if the adjustable liquid crystal lens is at the wavelength lambda 0 The point spread function is PSF (x, y), the object to be measuredIs conceivable as O g (x, y), the actual image obtained is O m (x, y), the noise is n (x, y), then
O m (x,y)＝O g (x,y)*PSF(x,y)+n(x,y) (16)
O obtained from the foregoing m (x, y) and experimentally measured PSF (x, y), wiener filter deconvolution was performed:
wherein P is f (u, v) and P n (u, v) is typically calculated using a constant estimate.
Solving the optimization problem through an optimization algorithm to obtain O g (x, y) to obtain O g (x,y,λ 0 ) For O m Recovering the image at each wavelength (x, y, lambda) to obtain the final data cube O g (x,y,λ)。
The invention carries out simulation verification, firstly, the measured image under different wavelengths and the point spread function of the adjustable liquid crystal lens designed by the invention are convolved to simulate the wide-band imaging effect of the lens to obtain a blurred image, and the imaging effect of the simulated lens under 5 wavelengths is shown in fig. 8. Adding random noise to the blurred image, deconvoluting by wiener filtering, and fig. 9 is a schematic diagram of the effect of deconvolution of the blurred image by wiener filtering; where (a) in fig. 9 is an actual image, (b) in fig. 9 is a blurred image, and (c) in fig. 9 is a wiener filtered deblurred image (i.e., a restored image). It can be seen that the present invention can reconstruct a data cube, i.e. a spectral image of an object, containing both spatial information and spectral information of the object under test.
It should be noted that, although the optimization algorithm adopted in the spectrum recovery and the image restoration of the present invention is a CVX optimization algorithm, the present invention is not limited thereto; although the invention employs wiener filter deconvolution in a process that utilizes point spread function deconvolution to be ideal, it is not so limited.
In summary, the invention realizes imaging function by designing in-plane orientation angle of liquid crystal molecules, realizes spectrum information recording by changing out-of-plane orientation angle of liquid crystal molecules by applying external voltage, and further can simultaneously image and spectrum detect a measured object, namely, the invention adopts a single lens formed by liquid crystal materials with optical anisotropy and electro-optic regulation and control characteristics to simultaneously image and spectrum detect the measured object, and can reconstruct a data cube containing spatial information and spectrum information of the measured object, namely, a spectrum image of the object by recording images output by an adjustable liquid crystal lens under different voltages and then combining with spectrum response of the adjustable liquid crystal lens. The invention breaks through the limitation that the traditional lens can only realize space information recording, can greatly improve the information quantity obtained by optical detection, and develops a novel multi-dimensional planar imaging device with compact structure and high efficiency.
Finally, it should be noted that the above-mentioned embodiments are only for illustrating the technical solution of the present invention, and not for limiting the same, and although the present invention has been described in detail with reference to examples, it should be understood by those skilled in the art that modifications and equivalents may be made to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention, and all such modifications and equivalents are intended to be encompassed in the scope of the claims of the present invention.
Claims (10)
1. The spectrum imaging method based on the adjustable liquid crystal lens is characterized by comprising the following steps of:
step 1, constructing a spectrum imaging system model, wherein the spectrum imaging system model is expressed as follows:
I i (x,y)＝∫ΛLC i (λ)×O m (x,y,λ)dλ
O m (x,y,λ)＝O g (x,y,λ)*PSF(x,y,λ)
in the formula, LC i (lambda) is the spectral response of the tunable liquid crystal lens at different external voltages, O m (x, y, lambda) is the actual image of the object under test, I i (x, y) is intensity information obtained by the corresponding camera of the adjustable liquid crystal lens under different external voltages, Λ is a set wavelength range, O g (x, y, lambda) is an ideal image of the measured object, and PSF (x, y, lambda) is a point spread function of the adjustable liquid crystal lens;
step 2, adjustingThe geometric phase distribution of the liquid crystal lens is converted into an in-plane orientation angular distribution of the tunable liquid crystal lens; changing the out-of-plane orientation angle of the tunable liquid crystal lens by applying different external voltages to LC in a set wavelength range i Calibrating (lambda);
step 3, recording and LC i (lambda) one-to-one I i (x,y)；
Step 4, based on the obtained multiple groups of LC i (lambda) and corresponding I i (x, y) representing the relationship between the two in matrix form as follows:
I＝LC·X
wherein I is an intensity information matrix, LC is a spectral response matrix, and X is a matrix to be solved;
solving X by adopting an optimization algorithm, and recovering the actual image O of the detected object m (x,y,λ)；
Step 5, obtaining point spread functions PSF (x, y, lambda) under different wavelengths;
step 6, based on O m (x, y, lambda) and PSF (x, y, lambda), calculating by adopting an optimization algorithm, and reconstructing to obtain an ideal image O of the measured object g (x,y,λ)。
2. The spectroscopic imaging method based on an adjustable liquid crystal lens according to claim 1, wherein the adjustable liquid crystal lens has a five-layer structure, and the method is as follows, in order from top to bottom: the first conductive glass layer, the first photo-alignment layer, the nematic liquid crystal layer, the second photo-alignment layer and the second conductive glass layer.
3. The tunable lc lens-based spectroscopic imaging method of claim 1, wherein the tunable lc lens has an even aspherical geometric phase represented as follows:
wherein r is the radius of the circle where any point (x, y) on the adjustable liquid crystal lens is located, phi (r) is the geometric phase of the adjustable liquid crystal lens at the radius r, k r For wave vector at r, f 0 R is the focal length of the adjustable liquid crystal lens 0 Is the radius lambda of the adjustable liquid crystal lens min And lambda (lambda) max The minimum wavelength and the maximum wavelength of the tunable liquid crystal lens in each zone are respectively.
4. The spectroscopic imaging method based on the tunable liquid crystal lens according to claim 1, wherein in the step 2, the geometric phase distribution of the tunable liquid crystal lens is converted into the in-plane orientation angle distribution of the tunable liquid crystal lens based on the relationship that the reverse circularly polarized light passing through the tunable liquid crystal lens carries a phase adjustment amount of 2 times of the in-plane orientation angle upon incidence of circularly polarized light.
5. The spectroscopic imaging method based on a tunable liquid crystal lens according to claim 1, wherein in the step 2, as the applied external voltage increases, the out-of-plane orientation angle of the tunable liquid crystal lens gradually rotates from 0 to pi/2; by simulating the out-of-plane orientation angle of the adjustable liquid crystal lens to be [0, pi/2]Spectral response when the working wavelength range of the liquid crystal is the set wavelength range, realizing LC i Calibration of (lambda).
6. The spectroscopic imaging method based on an adjustable liquid crystal lens as claimed in claim 1, wherein the step 3 is performed to obtain I i (x, y) further includes a pair I i (x, y) adding random noise to obtain intensity information after adding noise, and marking the intensity information as I i_noise (x, y); in the step 4, based on the obtained multiple LC groups i (lambda) and corresponding I i_noise (x, y) representing the relationship between the two in the form of a matrix.
7. The tunable lc lens-based spectral imaging of claim 1The imaging method is characterized in that in the step 6, if the point spread function of the adjustable liquid crystal lens at a certain wavelength is PSF (x, y), the ideal image of the measured object is O g (x, y) the actual image of the measured object is O m (x, y), the noise is n (x, y), then O m (x,y)＝O g (x,y)*PSF(x,y)+n(x,y)；
Based on O m (x, y) and PSF (x, y), and performing wiener filter deconvolution to obtain O g (x, y) as follows:
in the method, in the process of the invention,f (u, v), H (u, v) and G (u, v) are each O g (x, y), PSF (x, y) and O m (x, y) spectrum, H * (u, v) is the conjugate of H (u, v), P f (u, v) and P n (u, v) is the power spectral density of the actual image and the power spectral density of the actual image noise, respectively;
based on the method, the method is to O m Recovering the image at each wavelength to obtain O g (x,y,λ)。
8. The adjustable liquid crystal lens is characterized by comprising a five-layer structure, and the three layers of structures are sequentially arranged from top to bottom: the first conductive glass layer, the first photo-alignment layer, the nematic liquid crystal layer, the second photo-alignment layer and the second conductive glass layer;
the adjustable liquid crystal lens has geometrical phases of even-order aspheric surfaces, and is expressed as follows:
wherein r is the radius of the circle where any point (x, y) on the adjustable liquid crystal lens is located, phi (r) is the geometric phase of the adjustable liquid crystal lens at the radius r, k r For wave vector at r, f 0 R is the focal length of the adjustable liquid crystal lens 0 Is the radius lambda of the adjustable liquid crystal lens min And lambda (lambda) max The minimum wavelength and the maximum wavelength of the adjustable liquid crystal lens in each annular zone are respectively;
the adjustable liquid crystal lens can realize phase regulation and spectrum regulation simultaneously by changing the in-plane orientation angle and the out-of-plane orientation angle.
9. The tunable liquid crystal lens according to claim 8, wherein when circularly polarized light is incident, reverse circularly polarized light passing through the tunable liquid crystal lens carries a phase adjustment amount of 2 times of an in-plane orientation angle; as the applied external voltage increases, the out-of-plane orientation angle of the tunable liquid crystal lens gradually rotates from 0 to pi/2.
10. A spectroscopic imaging system based on an adjustable liquid crystal lens, comprising: an adjustable liquid crystal lens, a camera and a reconstruction unit; light emitted or reflected by the measured object is imaged on the camera after passing through the adjustable liquid crystal lens;
the reconstruction unit stores a spectral imaging system model, which is expressed as follows:
O m (x,y,λ)＝O g (x,y,λ)*PSF(x,y,λ)
in the formula, LC i (lambda) is the spectral response of the tunable liquid crystal lens at different external voltages, O m (x, y, lambda) is the actual image of the object under test, I i (x, y) is intensity information obtained by the corresponding camera of the adjustable liquid crystal lens under different external voltages, Λ is a set wavelength range, O g (x, y, lambda) is an ideal image of the measured object, and PSF (x, y, lambda) is a point spread function of the adjustable liquid crystal lens;
the reconstruction unit is used for reconstructing and obtaining an ideal image of the measured object based on the spectral imaging system model, the spectral response of the adjustable liquid crystal lens under different external voltages, the intensity information obtained by the camera corresponding to the adjustable liquid crystal lens under different external voltages and the point spread function of the adjustable liquid crystal lens.
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