Multi-spectral imaging method for ultraweak photon emission and system thereof

Abstract

An ultra-weak light multispectral imaging method and an ultra-weak light multispectral imaging system, which can realize multispectral two-dimensional imaging of an ultra-weak light object by constituting a linear array from single-photon detectors of all response wavelengths and combining it with light-splitting technology. The ultra-weak light multispectral two-dimensional imaging system realizes high-resolution optical modulation by adopting the compressive sensing (CS) theory and the digital light processing (DLP) technology and using a linear array single-photon detector as a detection element; the ultra-weak light multispectral two-dimensional imaging system comprises a light filter, a first lens (1), a DMD control system, a second lens, a spectrophotometer, a linear array single-photon detector consisting of a plurality of single-photon detectors with different response wavelengths, and a central processing unit; and the sensitivity of the system can reach the single-photon level. The invention can be widely applied in the fields of biological self-illumination, medical diagnosis, nondestructive material analysis, astronomical observation, national defense and military, spectral measurement, quantum electronics and the like.

Claims

1. A two-dimensional imaging method for high-resolution optical modulation by compressive sensing and digital light processing and using a linear array single-photon detector as a detection element, said method comprising: 1) compressive sampling by a digital micro-mirror device (DMD) control system, a first lens and a second lens, to convert two-dimensional image data into a one-dimensional data sequence to complete compressive sampling of signals to be measured, wherein the compressive sampling includes filtering stray light by a light filter, imaging the light at the DMD control system through the first lens, controlling reflecting photons to the second lens by the DMD control system controlling focusing of the photons by the second lens; and imaging the light with different wavelengths by the linear array single-photon detector; and 2) completing a sparse reconstruction by a combination of a central processing unit and the linear array single-photon detector to reconstruct the two-dimensional image data and obtain a two-dimensional photon density image, wherein i) the compressive sampling further includes mapping the signals to be measured from high-dimensional signals to low-dimensional signals where, where xεR.sup.n is data to be measured, yεR.sup.k is observation data, ΦεR.sup.k×n is a measurement matrix (k<<n) and e εR.sup.k is measurement noise, the compressive sample precess is
y=Φx+e  (1) ii) where a value of measurement times is k, a number of pixels in the two-dimensional image is n, a measurement matrix in formula (1) is Φ={Φ.sub.1, . . . , Φ.sub.i, . . . , Φ.sub.k wherein Φ.sub.1 is an i.sup.th row of Φ wherein columns of the two-dimensional images of size √{square root over (n)}×√{square root over (n)} are connected end to end to form an nx1 one-dimensional column vector, and corresponding to x in formula (1), each element of the nx1 one-dimensional column vector represents a photon density at a corresponding position; in the DMD control system, each micro-mirror has a same resolution and columns of the micro-mirrors of the DMD control system are connected end to end to form a 1xn one-dimensional row vector, which corresponds to a row in the measurement matrix Φ, wherein each element indicates whether the photon at a corresponding position is transmitted to the second lens; iii) where a measurement period is T and during this period the DMD control system is kept unchanged, light with certain wavelength directly projected onto the linear array single-photon detector with a corresponding wavelength; where a number of the photons detected by the linear array single-photon detector corresponding to a certain wavelength in the linear array single photon detector is N, then N/T is equivalent to an inner product value of the photon density image and measurement number array Φ on the DMD control system, corresponding to an element $y_i=\underset{j=1}{\overset{n}{.Math.}}{\Phi }_{i,j}{x}_j$  of an observation vector y in formula (1), wherein Φ.sub.i,j and x.sub.j are j.sup.th elements of Φ.sub.i and x respectively; according to the measurement matrix Φ, the DMD control system is modified each time, repeat k times of the measurement procedure, and the whole observation data y; and iv) the sparse reconstruction solves x in formula (1) using the observation data y and measurement matrix Φ determined in steps ii) and iii) above, and x is equal to: $\begin{array}{cc}\min \left(\frac{1}{2}{.Math.y-{\mathrm{\Phi \Psi }}^{-1}\vartheta .Math.}_2^2+\tau {.Math.{\Psi }^{-1}\vartheta .Math.}_1\right)& \left(4\right)\end{array}$ where, Ψ is a wavelet transform matrix, θ is a Gaussian random matrix, and τ is a weight.

2. A two-dimensional imaging method of realizing high- resolution optical modulation by compressive sensing and digital light processing and using a linear array single-photon detector as a detection element, said method comprising: 1) compressive sampling by a digital micro-mirror device (DMD) control system, a first lens and a second lens, to convert two-dimensional image data into a one-dimensional data sequence to complete compressive sampling of signals to be measured, wherein the compressive sampling includes filtering stray light in an light by a light filter, imaging the light at the DMD control system through the first lens, controlling reflecting photons to the second lens by the DMD control system controlling focusing of the photons by the second lens; and imaging the light with different wavelengths by the linear array single-photon detector; and 2) completing a sparse reconstruction by a combination of a central processing unit and the linear array single-photon detector to reconstruct the two-dimensional image data and obtain a photon density image, wherein x is the data to be measured, and x is solved by a sparse reconstruction with discrete wavelet transform (SpaRSA-DWT) algorithm, the estimated value of the next iteration is obtained by performing discrete wavelet transform (DWT) on an estimated value of a current iteration, performing threshold-processing on transform coefficients and performing inverse DWT on threshold-processed coefficients, wherein a step factor is calculated in each iteration; where the threshold-processing function is , S(u,v)=sigh(u)max{|u|−v,0}, the SpaRSA-DWT algorithm is $x^{t+1}={\Psi }^{-1}.Math.S\left(\Psi \left(x^t-\frac{1}{\alpha }▽f\left(x^t\right)\right),\frac{\tau }{\alpha }\right)$ wherein α.sub.tchanges with each iteration according to:
α.sub.t(x.sup.t-x.sup.t−1)=∇f(x.sup.t)−∇f(x.sup.t−1) and the formula is solved by using a least square method, obtaining ${\alpha }_t=\frac{{.Math.\Phi \left(x^t-x^{t-1}\right).Math.}_2^2}{{.Math.x^t-x^{t-1}.Math.}_2^2}.$ wherein S(u,v) is the threshold-processing function; sign (u) is the signum function of a real number u defined as follows: $\mathrm{sign}\left(u\right):=\{\begin{array}{cc}-1,& \mathrm{if}u<0\\ 0,& \mathrm{if}u=0\\ 1,& \mathrm{if}u>0\end{array};$ Φis the measurement matrix; Ψis a wavelet transform matrix; t means in tth iteration; and τis a weight.

Description

DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a structural diagram of a system provided by the invention.

(2) FIG. 2(a)-2(l) are simulation result diagrams of reconstructing a color image by adopting a SpaRSA-DWT algorithm,

(3) TABLE-US-00001 Reference signs 1 first lens 2 second lens 3 spectrophotometer 4 linear array 5 central processing single-photon unit detector 6 light filter 7 DMD control system

DETAILED DESCRIPTION OF EMBODIMENTS

(4) The invention is further illustrated in details in conjunction with the drawings.

(5) In FIG. 1, the stray light in an ultra-weak light emitted by an observation object is filtered by a light filter 6, after which the ultra-weak light is imaged at a DMD through a first lens 1. The DMD control system 7 controls the probability that photons are reflected to a second lens 2, and then the photons are converged by the second lens 2. If the detector is a counting type single-photon detector, the photons are counted during a certain period of time, and the resulted value is converted into the probability of detecting photons, as a measured value; and if the detector is a single-photon detector with the resolution capability of photon number, then the amplitude of the output electrical signals can be used as the measured value of photon density. Finally, a photon density image is reconstructed by a computer 5 according to the measured value and a measurement matrix on the DMD control system 7 through adopting an optimization algorithm.

(6) In order to facilitate understanding, supposing the value of the measurement times is k, the measurement matrix in formula (1) is written as Φ={Φ.sub.1, . . . , Φ.sub.i, . . . , Φ.sub.k}, wherein Φ.sub.i is the i.sup.th row of Φ. The columns of the two-dimensional image of size √{square root over (n)}×√{square root over (n)} are connected end to end to form an n×1 one-dimension al column vector, and corresponding to x in formula (1), each element of the vector represents the photon density at a corresponding position; and in the DMD control system, each micro-minor has the same resolution and the columns of the DMD control system are also connected end to end to form a 1×n one-dimensional row vector, which corresponds to a row in the measurement matrix Φ, wherein each element represents the probability that the photon at a corresponding position is transmitted to the second lens 2. If the detector is a counting type single-photon detector, and if the measurement period is T and during this period, the DMD control system is kept unchanged and the number of the photons detected by the single-photon detector is N, then N/T is equivalent to the inner product value of the photon density image and the random number array on the DMD control system; and if the detector is a single-photon detector with the resolution capability of photon number, then the amplitude of the output electrical signals of the single-photon detector is equivalent to the inner product value of the photon density image and the random number array on the DMD control system 7.

(7) The inner product value corresponds to an element

(8) $y_i=\underset{j=1}{\overset{n}{.Math.}}{\Phi }_{i,j}{x}_j$
(Φ.sub.i,j and x.sub.j are the j.sup.th elements of Φ.sub.i and x respectively) of the observation vector y in formula (1). According to the measurement matrix, the DMD is modified each time, repeat k times of the measurement procedure, thereby the whole observation data y can be obtained, that is to say, the process of formula (1) is physically realized.

(9) According to photonics knowledge, in an elementary area dA, the probability p(r)dA of observing a photon at a point r at any moment is proportional to the light intensity at that point. Thus, the ultra-weak light image is simulated by a color image of a biochip in simulation experiments. The biochip is a typical ultra-weak light source, and can be conveniently observed mainly by a fluorescent labeling method at present. Actually, all organisms have self-illumination property, and a self-illumination spectrum contains much important information.

(10) In order to verify the feasibility and practicability of the system, the color image of a biochip is regarded as a combination of three primary colors R, G and B in a simulation experiment, for simulating spectral separation. Supposing that the original image is unknown, then it is recovered by adopting the method of the present invention. In the experiment, the resolution of the image is 64×64, and the result as shown in FIG. 2 is obtained by carrying out compressive sampling with a Gaussian matrix and adopting a SpaRSA-DWT sparse reconstruction algorithm, wherein FIG. 2(a) shows an original photon density color image; FIG. 2(b) shows a random matrix on the DMD in one-time measurement, wherein black points represent 0, white points represent 1, and gray points represent intermediate values; FIG. 2(c) shows a component R of the original image; FIG. 2(d) shows a component R reconstruction image of the SpaRSA-DWT algorithm; FIG. 2(e) shows a component R residual image of the SpaRSA-DWT algorithm; FIG. 2(f) shows a component G of the original image; FIG. 2(g) shows a component G reconstruction image of the SpaRSA-DWT algorithm; FIG. 2(h) shows a component G residual image of the SpaRSA-DWT algorithm; FIG. 2(i) shows a component B of the original image; FIG. 2(j) shows a component B reconstruction image of the SpaRSA-DWT algorithm; FIG. 2(k) shows a component B residual image of the SpaRSA-DWT algorithm; and FIG. 2(l) shows a reconstructed color image of the SpaRSA-DWT algorithm, wherein the correlation coefficient between the reconstructed color image and the original image is 0.9783, and the signal-to-noise ratio is 23.95 dB.

(11) Finally, it shall be noted that the embodiments are only used for illustrating the technical solution of the invention, not limitation thereto. While the invention is illustrated in details with reference to the embodiments, it shall be understood by those ordinary skilled in the art that modifications or equivalent replacements made to the technical solution of the invention do not depart from the spirit and scope of the technical solution of the invention and shall be encompassed in the scope of the claims of the invention.