CN107014784B - A kind of measuring device and method of scattering medium vector transmission matrix - Google Patents
A kind of measuring device and method of scattering medium vector transmission matrix Download PDFInfo
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Abstract
The invention discloses a kind of measuring devices of scattering medium vector transmission matrix, including vector space light-modulating cell, fourier lense, Mach to increase Dare interference system, imaging sensor and calculate equipment;The vector space light-modulating cell is made of transmissive spatial light modulator and low-angle birefringent polarizing optical splitter;Light is divided into two-way using the first Amici prism through the light of vector space light-modulating cell and fourier lense and enters in Mach increasing Dare interference system, and then reaches the recording surface of imaging sensor;The light beam for reaching recording surface interferes to form binary channels angular multiplexing polarization holograms;Equipment utilization binary channels angular multiplexing polarization holograms are calculated, obtain the complex amplitude and polarization information of sample scattered optical field, and then calculate vector transmission matrix.Based on the present invention, vector transmission matrix can be quickly and accurately measured.
Description
Technical Field
The invention relates to digital holographic imaging, in particular to a measuring device for a vector transmission matrix of a scattering medium.
Background
The transmission of light through a Scattering Medium (SM) is a fundamental problem in physics. Especially in the field of wavefront measurement and imaging research, such as deep tissue imaging, optical focusing through turbid media, and fiber-optic imaging, the scattering effect of light by scattering media when the amplitude and phase information of the wavefront of an optical wave passes through the scattering media can bring great difficulty to the recovery and acquisition of image information. One effective way to overcome this difficulty is to eliminate the effect of the SM on the imaging by using a Transmission Matrix (TM) that characterizes the determined relationship between the input light field and the scattered light field transmitted through the SM. In recent years, a large number of research results show that based on a transmission matrix, effective optical information can be recovered from an optical field disturbed by multiple scattering, and wavefront regulation and focusing through a scattering medium can be realized. In these applications, however, a critical issue is how to accurately measure the TM. In 2010, Popoff et al successfully measured the TM of the SM with the aid of an SLM and a common-path interference device. In the following years, more methods have been proposed for measuring TM under different experimental conditions. However, most methods do not take into account the polarization properties of the scattering medium. Although some of these work proposed methods of measuring Vector Transmission Matrices (VTMs), these measurement methods all require relatively complex experimental equipment and involve rotation control of the phase shifting and polarizing devices during the measurement process.
In summary, how to adopt a simple method and device to quickly and accurately measure a vector transmission matrix is still a problem to be solved urgently in the technical field.
Disclosure of Invention
In order to solve the above problems, the present invention provides an apparatus for measuring a Vector Transmission Matrix (VTM) of a Scattering Medium (SM). In the device, a vector spatial light modulator consisting of a Spatial Light Modulator (SLM) and a small-angle birefringence polarization beam splitter (BBS) is established to realize point-by-point control on the amplitude and the phase of two orthogonal polarization components of an input light field; meanwhile, the synchronous measurement of two orthogonal polarization components of a scattering light field penetrating through a scattering medium is completed by introducing a dual-channel angle division multiplexing polarization holographic recording light path.
In order to achieve the purpose, the invention adopts the following technical scheme:
a scattering medium vector transmission matrix measurement apparatus, comprising: the device comprises a vector spatial light modulation unit, a Fourier lens, a Mach-Zehnder interference system, an image sensor and a computing device;
the vector spatial light modulation unit is arranged on the front focal plane of the Fourier lens, consists of a spatial light modulator and a small-angle birefringence polarization beam splitter and is illuminated by a collimated laser beam; light penetrating through the vector spatial light modulation unit and the Fourier lens is divided into two paths through the first beam splitter prism and enters the Mach-Zehnder interference system, and then reaches the recording surface of the image sensor; the beams reaching the recording surface interfere to form a dual-channel angle division multiplexing polarization hologram; the computing equipment obtains the complex amplitude and the polarization information of the scattered light field of the measured sample by utilizing the dual-channel angular multiplexing polarization hologram, and then computes a vector transmission matrix.
In the mach-zehnder interferometer system: one path of light passes through the first reflector and then passes through the single-hole filter screen to generate a vector light field with programmable complex amplitude and polarization distribution, the vector light field is coupled to a measured sample through the first lens and the first objective lens, and scattered light penetrating through the measured sample reaches a recording surface of the image sensor through the second objective lens and the second beam splitter prism; the other path of light passes through a double-hole filter screen to generate two reference lights with orthogonal linear polarization states, and the reference lights reach the recording surface of the image sensor through a second lens, a second reflecting mirror and a second beam splitting prism.
The invention has the beneficial effects that:
1. in the device, a vector spatial light modulator consisting of a Spatial Light Modulator (SLM) and a small-angle birefringence polarization beam splitter (BBS) is established to realize point-by-point control on the amplitude and the phase of two orthogonal polarization components of an input light field;
2. the synchronous measurement of two orthogonal polarization components of a scattered light field transmitted through a scattering medium is completed by introducing a two-channel angular multiplexing polarization holographic recording light path.
3. Since all polarization control required in measuring VTM is achieved based on the same SLM and BBS without the need for other polarizing elements such as polarizers and waveplates, the accuracy of the generated vector incident light field and the high extinction ratio required for orthogonally polarized reference light are ensured.
4. The method and the device based on the invention actually measure the VTM of a typical scattering medium and verify the accuracy of the measurement result and the stability of the system by realizing the experiment of focusing control of a vector beam through the scattering medium based on the measured VTM.
5. No experimental device is required to be moved in the whole polarization measurement process, so that the phase measurement errors of different polarization components of the measured VTM are greatly reduced.
Drawings
FIG. 1 is an experimental setup established by the present invention;
FIG. 2 is an example of a zinc oxide sample vector transmission matrix experimentally measured based on the method and apparatus of the present invention, (a) - (d) are amplitude distributions of four components in the measured vector transmission matrix; (e) - (h) is its corresponding phase distribution, the scale in the figure corresponding to a length of 300 μm;
fig. 3 shows the experimental results of focusing a vector beam through a scattering medium based on the measured VTM, where the scale bar corresponds to a length of 300 μm.
Detailed Description
The invention is further described with reference to the following figures and examples.
FIG. 1 shows an experimental setup established by the present invention.
The embodiment provides a measuring device for a medium vector transmission matrix, wherein the most important part of the system is a vector spatial light modulation unit (VSLM), and the unit structure is very simple and only consists of a traditional SLM and a small-angle birefringent polarizing beam splitter BBS. The VSLM is placed on the front focal plane of the fourier lens FL and is illuminated with a collimated laser beam. The light passing through the VSLM and the lens FL is split into two paths by the first beam splitter BS1 and enters the mach-zehnder interference system composed of the BS1, the second beam splitter BS2, the first reflector M1 and the second reflector M2, wherein the light path passing through the reflector M1 is an object light path, and the light path passing through the reflector M2 is a reference light path. In the reference optical path, two reference lights with orthogonal linear polarization states are generated by a double pinhole filter screen F2 placed on the back focal plane of the lens FL in cooperation with the VSLM. In the optical path of the object light, another single-hole filter screen F1 also placed on the back focal plane of the lens FL is used to generate a vector light field with programmable complex amplitude and polarization distribution in cooperation with the VSLM, and the vector light field is coupled to the sample to be measured through the first lens L1 and the first objective lens OL1 to serve as an illumination light source. The scattered light transmitted through the sample reaches the recording surface of the image sensor CCD through the second objective lens OL2 and the beam splitter prism BS2, and interferes with two orthogonally polarized reference lights reaching the recording surface from the reference light path via the second lens L2, the second mirror M2, and the BS2, forming a two-channel angle-division-multiplexed polarization hologram (AMPH). By using an angular multiplexing digital holographic reproduction method, the complex amplitude and polarization information of a scattered light field of a detected sample can be reproduced from AMPH recorded by a CCD.
The quantitative realization method of the experimental light path comprises the following steps:
the surface where the single-hole filter screen F1 is located is an input surface of the scattering medium to be detected, and the discrete coordinate of the input surface is (m △)i,n△i) The CCD recording surface is the output surface of the scattering medium and has discrete coordinate of (p △)o,q△o) Wherein, △iAnd △oSampling intervals corresponding to discrete coordinates of the input face and the output face, respectively; (m, n) and (p, q) areThe index value of the corresponding sample point. Let the Jones vector of the incident vector light field on the input face be
Wherein,andtwo orthogonal polarization components E of incident vector light field respectivelyin,xAnd Ein,yAmplitude and phase parameters. This vector light field can be realized by displaying a two-channel computed hologram (DC-CGH) output onto a spatial light modulator SLM, designed based on the following computed hologram encoding formula:
wherein (x)s,ys) Is the coordinates of the plane of the SLM,respectively two orthogonal polarization components E of the desired vector beamin,xAnd Ein,yInverse fourier transform of (d); parameter kα2 π sin α/λ, λ being the laser wavelength, α being the half-beam angle of the birefringent polarizing beamsplitter BBS, H0And a and b are three constants for adjusting the diffraction efficiency of the DC-CGH. Due to the polarization splitting property of BBS, the light field modulated by SLM and BBS is transformed by lens FL to be a diffraction light field on two back focal planes of FL
Wherein s isfFsin α, f is the focal length of lens L1 the first term in equation (3) corresponds to the zero-order diffraction term of DC-CGH, and the third term EfhIs a higher order diffraction term; and the second term is a vector beam of formula (1), wherein A0Is a constant related to the diffraction efficiency of the DC-CGH. To simplify the mathematical formula, the origin of coordinates of the input surface in formula (3) is translated to the center position of the second term. The inset to the upper left of FIG. 1 shows a schematic diagram of the light field distribution at the back focal plane of lens L1 corresponding to equation (3); the part marked by the dotted circle corresponds to the vector beam given by the second term of formula (3). The vector light beam can be irradiated to the input surface of the sample to be measured through the F1 by aligning the filter holes on the single-hole filter screen F1 with the area.
The scattered light field at the output face of the light transmitted through the scattering medium sample is also typically a vector light field with spatially varying amplitude, phase and polarization, whose jones vector can be expressed as:
wherein,
vtm describing the vector scattering properties of the scattering medium for simplicity, the coordinate parameter (m △) in equation (5)i,n△i,p△o,q△o) Abbreviated to (m, n, p, q). In general, the four components M of the VTM11、M12、M21And M22Each is a complex spatial function of input coordinates (m, n) and output coordinates (p, q).
In the invention, the VSLM device unit capable of generating any vector light beam is combined with the dual-channel angle division multiplexing holographic polarization measurement light path, so that the VTM four parameters are realizedAnd (5) synchronous and quick measurement. In the measuring system, the polarization state and complex amplitude distribution of illumination light irradiated on the input surface of a sample can be regulated point by changing DC-CGH displayed on an SLM; meanwhile, the two orthogonally polarized reference lights required for recording the two-channel angle-division-multiplexed polarization hologram AMPH come from two zero-order diffraction terms with orthogonal polarization states generated by the VSLM unit (corresponding to the first term in equation (3)). The inset in the lower left corner of fig. 1 shows a schematic representation of the extraction of two zero-order diffraction terms with orthogonal polarization states in a diffracted light field using a two-pinhole filter F2, where the area marked by the two dashed circles corresponds to the location of the two filter pinholes on the filter F2. With this system, any input point (m) on the input surface is corresponded0,n0) Vector transmission matrix M (M)0,n0Four components M of p, q)11(m0,n0,p,q)、M12(m0,n0,p,q)、M21(m0,n0P, q) and M22(m0,n0P, q) can be obtained by the following two-step measurement procedure. First, at the input point (m) by SLM0,n0) A linearly polarized point source is generated, polarized along the x-axis (or horizontally), and the AMPH of the scattered light field obtained at the output face after the point source of illumination has passed through the scattering sample is recorded. Then, (m) by changing the DC-CGH output to the SLM0,n0) The point source of illumination at (a) becomes a linearly polarized point source polarized along the y-axis direction (or polarized in the vertical direction) and a second AMPH is recorded. The intensity distributions of the two AMPHs obtained above can be expressed as:
and
wherein R is||,R⊥Andrespectively representing the amplitude and wave vector of two orthogonal polarized reference lights reaching the recording surface through a double-pinhole filter screen F2, a lens L2, a reflector M2 and a beam splitter prism BS 2; deltain,x(m0,n0) And deltain,y(m0,n0) Indicating (m) on the input surface during measurement0,n0) Two point sources of illumination with orthogonal polarizations are produced. Corresponding to the input point (m) based on the conventional off-axis holographic reconstruction method0,n0) Vector transmission matrix M (M)0,n0The complex amplitude distribution of all four components of p, q) can be extracted from the two AMPHs shown in equations (6) and (7). By changing the position of the illumination point source and repeating the measurement process, the vector transmission matrix M (M, n, p, q) corresponding to all the input points can be finally measured.
And (3) experimental verification:
in the experimental setup built according to fig. 1, the light source is a He-Ne laser with a wavelength equal to 632.8 nm; the spatial light modulator SLM is a twisted nematic liquid crystal spatial light modulator (LC-SLM) with a pixel count of 1024 × 768 and a pixel size of 18um × 18 um; the birefringent polarizing beam splitter BBS is a wollaston prism having a polarizing beam splitting angle equal to 0.9 degrees. The scattering medium sample to be tested was a zinc oxide (ZnO) scattering film about 20 μm thick. The scattered light field transmitted through the sample is amplified by an objective lens OL2(60 ×, NA ═ 0.85) and reaches the CCD recording surface. The CCD camera recording the AMPH is a major factor limiting the size of the number of VTM samples measured. The number of pixels of the CCD used in our experiments was 1280 × 960 and the single pixel size was 2.2 um. Thus on the output face, the maximum number of samples of VTM we can measure is 1280 × 960. However, to avoid edge effects during holographic recording and reconstruction, we have only chosen 900 x 900 pixels in the center of the recording pattern as the number of valid samples of the measured VTM in the experiment. FIG. 2 shows an example of a transmission matrix of a zinc oxide sample vector measured based on the experiment of the method and apparatus of the present invention, wherein FIGS. 2(a-d) are the transmission matrices M of the measured vector(m0,n0P, q) and fig. 2(e-h) are their corresponding phase distributions. As can be seen from the VTM given in fig. 2, the ZnO scattering layer has a high polarization-sensitive characteristic.
As a means for verifying the accuracy and reliability of the measurement of the vector transmission matrix VTM of the scattering medium based on the method and the device of the present invention, we further provide experimental results for achieving the focusing of vector beams through the scattering medium based on the measured VTM. FIG. 3(a) is an example of a design of a computed hologram that uses the measured VTM (input face sample number 40X 40) design to achieve focusing of a vector beam through a scattering medium. Fig. 3(b) and (c) show examples of experimental results for achieving focusing of a vector beam through a scattering medium based on a measured VTM, where fig. 3(b) is an example of focusing for linearly polarized light and fig. 3(c) is an example of focusing for circularly polarized light. By way of comparison, FIG. 3(d) shows the intensity distribution at the output face when a vector beam of light that is not modulated for incident light by the measured VTM passes directly through the scattering medium. The high efficiency focusing results shown in fig. 3(b) and (c) demonstrate the accuracy of the measured VTM and the stability of the measurement system.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.
Claims (5)
1. A measuring device for vector transmission matrix of scattering medium is characterized by comprising: the device comprises a vector spatial light modulation unit, a Fourier lens, a Mach-Zehnder interference system, an image sensor and a computing device;
the vector spatial light modulation unit is arranged on the front focal plane of the Fourier lens, consists of a spatial light modulator and a small-angle birefringence polarization beam splitter and is illuminated by a collimated laser beam; the light penetrating through the vector spatial light modulation unit and the Fourier lens is divided into two paths through the first beam splitter prism, enters a Mach-Zehnder interference system comprising a double-pinhole filter screen F2 and a single-pinhole filter screen F1 and further reaches a recording surface of the image sensor; the beams reaching the recording surface interfere to form a dual-channel angle division multiplexing polarization hologram; the computing equipment obtains the complex amplitude and the polarization information of the scattered light field of the measured sample by utilizing the dual-channel angular multiplexing polarization hologram, and then computes a vector transmission matrix.
2. The apparatus of claim 1, wherein after entering the mach-zehnder interferometer system, one of the two beams passes through the first mirror and the single-aperture filter to generate a vector light field with programmable complex amplitude and polarization distribution, the vector light field is coupled to the sample through the first lens and the first objective lens, and the scattered light transmitted through the sample reaches the recording surface of the image sensor through the second objective lens and the second beam splitter prism.
3. The apparatus of claim 1 or 2, wherein after the two beams of light enter the mach-zehnder interferometer system, one beam passes through a double-pinhole filter screen to generate two reference beams with orthogonal linear polarization states, and the reference beams reach the recording surface of the image sensor through the second lens, the second reflector and the second beam splitter prism.
4. The apparatus of claim 1, wherein the polarization state and complex amplitude distribution of the illumination light applied to the input surface of the sample are adjusted point by changing a two-channel computer hologram displayed on the spatial light modulator.
5. A measuring method using the device of claim 2, wherein the surface of the single-hole filter screen is the input surface of the scattering medium to be measured, the recording surface is the output surface of the scattering medium, and any input point (m) on the input surface0,n0) Vector transmission matrix M (M)0,n0,Four components M of p, q)11(m0,n0,p,q)、M12(m0,n0,p,q)、M21(m0,n0,p, q) and M22(m0,n0,p, q) is obtained by the following procedure:
first, at the input point (m) by means of a spatial light modulator0,n0) Generating a linear polarization point source polarized along the x-axis direction, and recording a two-channel angular multiplexing polarization hologram of a scattering light field obtained on an output surface after the linear polarization point source passes through a scattering sample;
then, the hologram is calculated by changing the two channels output to the spatial light modulator (m)0,n0) Changing the linear polarization point source into a linear polarization point source polarized along the y-axis direction, and recording a second two-channel angle division multiplexing polarization hologram;
extracting corresponding input points (m) from two dual-channel angle-division-multiplexed polarization holograms based on a conventional off-axis holographic reconstruction method0,n0) Vector transmission matrix M (M)0,n0,p, q), changing the position of linear polarized point source, repeating the above measurement process, and finally obtaining vector transmission matrix M (M, n) corresponding to all input points,p,q)。
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