CN105607453A - Optical scanning holographic technique without mechanical motion scanning - Google Patents

Abstract

The invention discloses an optical scanning holographic technique without mechanical motion scanning and belongs to the field of optical imaging. The optical scanning holographic technique is used for improving the traditional optical scanning holographic system. According to the optical scanning holographic technique, a digital micro-mirror device is used for replacing a two-dimensional mechanical scanning device in the traditional system and a compressing sensitive technique is applied to the two key links of data recording and plural hologram reconstruction, so that the problems caused by the factors, such as, precision and jittering of mechanical motion scanning in the traditional system are solved, the volume of to-be-recorded data of the system is extremely reduced, and the technique also can be used for reconstructing images with acceptable quality even under the condition of lower sampling rate.

Description

Optical scanning holographic technology without mechanical motion scanning

Technical Field

The invention belongs to the field of optical holographic imaging, and particularly relates to an optical scanning holographic imaging method.

Background

Optical scanning holography is a non-conventional digital holography technique proposed by professor Poon et al in the united states (t. — c. Poon, "scanning holographia and two dimensional imaging processing byacousto-optical-pulpyynthesis," j.opt. soc. am. a2, 621-627,1985). Unlike the traditional way of recording holographic information by object light reference light interference, the technology adopts active optical heterodyne scanning to acquire holographic data information (including amplitude and phase) of a three-dimensional object on the basis of a double-pupil optical system. The working process is that only one-time two-dimensional plane scanning is carried out, and the single-pixel detector can record the intensity information of each layer of the object distributed along the longitudinal direction to a plurality of holographyIn the drawingsI.e. directly recording the three-dimensional information of the object in the transverse and longitudinal directions in digital form. The technology effectively avoids the problems of zero-order spots, twin images and the like in the traditional holography, can acquire all data of the measured object at one time, and then acquires the data as requiredLine partData reconstruction, and thus has great advantages in data acquisition speed. The method is particularly suitable for occasions which cannot adopt an area array imaging device and separate signal detection and information reconstruction due to the limitation of a detection device, for example, the method can have great application potential in the fields of biomedical imaging, remote sensing space detection and the like, and has the advantages of reducing the volume of a detection system, reducing the cost of the system and the like.

FIG. 1 shows a schematic view of aConventional optical scanning holographic imaging system principle proposed by Poon et alDrawing (A)Diffraction by superimposing two light wavesDrawing (A)A three-dimensional object is scanned (time-varying fresnel zone plate). Theoretical analysis shows that the scanning recording process can be equivalent to the light transmittance of a scanning light field and the light transmittance of a scanned objectThe convolution operation process of the function, the output of the system is complex holographyDrawing (A)In the form of (1). In the system, the two-dimensional plane scanning is usually performed in a mechanical scanning mode, and the transverse resolution effect of the reconstructed image of the system is limited to a great extent by the scanning precision. If a highly precise mechanical scanning device is used, the system cost will be increased. In addition, the mechanical scanning process mainly depends on controlling the starting and stopping movement of the stepping motor, and the caused inevitable micro jitter can cause the holographyDrawing (A)The recording of (2) is deviated, thereby influencing the reconstruction effect of the object image.

Disclosure of Invention

In order to eliminate the adverse effect of mechanical scanning device on the holographic information record of object, the invention provides an optical scanning holographic technique without mechanical motion scanning.

Structural principle of the inventionDrawing (A)Similar to the traditional optical scanning holographic system, the optical scanning holographic system is based on a double-pupil optical system taking a Mach-Zehnder interferometer as a basic framework. The difference is that the invention adopts digital micro-mirror device (DMD) to replace two-dimensional mechanical scanning device; in addition, the direct data recorded by the present invention is not a complex hologram of the object to be measuredDrawing (A)It is also necessary to apply the compressive sensing theory to reconstruct and recover the complex holography of the object from the recorded direct dataDrawing (A). From complex holograms of the objectDrawing (A)The invention is completely the same as the traditional optical scanning holographic method when the image of the object is reconstructed.

The optical scanning holographic technique without mechanical motion scanning comprises the following steps:

(1) placing the three-dimensional object to be measured at a position which is away from the rear side of the DMD by a distance z, changing a configuration matrix of the DMD to modulate the light field projected on the measured object, and recording data corresponding to the total light intensity after the light field modulated by the DMD exits from the measured object each time;

(2) by using a compressed sensing algorithm, the system can be applied,calculating complex holography of measured object from recorded dataDrawing (A)Or encoding stage hologramDrawing (A))H_c(x,y,z_i)；

(3) Placing a point object (pinhole) at the back side of DMD by a distance z_dAt the position of the point element object, changing the configuration matrix of the DMD to modulate the light field projected on the point element object, and recording data corresponding to the total light intensity after the light field modulated by the DMD exits from the point element object each time;

(4) deducing point element object complex holography from recorded data by using compressed sensing algorithmDrawing (A)Or decoding stage hologramDrawing (A))H_d(x,y,z_d)；

(5) Complex holograms recorded by encoding and decoding stagesFIG. H _c(x,y,z_i) And H_d(x,y,z_d) Convolution operation is carried out on a computer to obtain the information of the reconstructed section image

The specific implementation process of the step (1) is as follows:

(1a) the laser outputs a light beam with frequency omega, and the light beam is divided into two paths after passing through the beam splitter, wherein one path is subjected to frequency shift into omega + omega after passing through the acousto-optic frequency shifter, so that the two paths of light waves present frequency difference omega; and the other path of light wave passes through the DMD and is modulated by the DMD, then is combined with the other path of light wave at the beam combining mirror, and is projected onto the three-dimensional object.

(1b) Collecting a light field emitted from a three-dimensional object on a photoelectric detector to obtain an optical heterodyne response current i (t); constantly and randomly changing the configuration matrix of the DMD, thereby randomly modulating the light field projected on the three-dimensional object; for each change, the detector outputs a corresponding optical heterodyne current i (t).

(1c) The output current i (t) contains DC component and AC component with frequency omega, and passes through band-pass filter (BPF) with central frequency omega to filter DC component and high-frequency interferenceAfter the components are combined, a heterodyne alternating current signal i is obtained_Ω(t)：

$\begin{array}{c}{i}_{\mathrm{\Ω}}\left(t\right)=\mathrm{Re}\[\underset{D}{\∫\∫}\{m(x,y)*h(x,y;z)\}{\left|\mathrm{\γ}(x,y;z)\right|}^{2}dxdy\exp \left(j\mathrm{\Ω}t\right)\]\\ =\left|i_{{\mathrm{\Ω}}_p}\right|\cos (\mathrm{\Ω}t+{\mathrm{\φ}}_p)\end{array}---\left(1\right)$

Wherein

Re[.]Representing the real part, D the pupil size, γ (x, y; z) the transmittance distribution of the object, "+" the convolution, m (x, y) the modulated light field exiting the DMD, h (x, y; z) the impulse response function with a transmission distance z,and phi_pRespectively representThe phase of the amplitude of (a).

(1d)i_Ω(t) is divided into two paths and input into a phase-locked amplifier, the two paths of signals are respectively mixed with two paths of single-frequency signals cos (omega t) and sin (omega t) which are orthogonal to each other, and then the in-phase component is extracted by a Low Pass Filter (LPF)And the orthogonal componentI.e., the real and imaginary components of equation (2).

(1e) The two paths of component signals i which are orthogonal to each other are processed_CAnd i_SRespectively carrying out analog-to-digital conversion, recording the converted digital information in a computer, and completing one measurement corresponding to a certain m (x, y); then randomly changing the value of the DMD configuration matrix to correspondingly obtain another distribution of the modulated light field m (x, y), and further obtaining another group i_CAnd i_sAnd recording the digital information; this was repeated M times for the change and recording.

(1f) The above process can also be represented as discretized

$\begin{array}{c}{i}_{{\mathrm{\Ω}}_p}=\underset{D}{\∫\∫}\[m(x,y)*h(x,y,z)\]{\left|\mathrm{\γ}(x,y,z)\right|}^{2}dxdy\\ =\underset{D}{\∫\∫}\[{\left|\mathrm{\γ}(x,y,z)\right|}^2*h(x,y,z)\]m(x,y)dxdy\\ \∝\underset{j=1}{\overset{N}{\mathrm{\Σ}}}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}m(x_i,y_j)l(x_i,y_j;z)\end{array}---\left(3\right)$

Where N is the number of sample points in a single-dimensional coordinate, x_i,y_jDiscretization of the coordinates x, y, l (x)_i,y_j(ii) a z) is then a discretized representation of the fresnel diffraction profile of the light field after passing through the object, i.e.:

l(x,y；z)＝|γ(x,y,z)|²*h(x_i,y_j,z)(4)

a two-dimensional matrix m (x)_i,y_j) And l (x)_i,y_j(ii) a z) separately vectorized to obtain an N²The row vector m and one N of the dimensions²A column vector l of dimensions, then equation (3) can be written as:

i_Ω＝ml(5)

equation (5) can be regarded as a measurement value of the compressed sensing recording process, and if the DMD configuration matrix is continuously changed for M times, M measurement values M are obtained₁,m₂,...m_MThey form a column vector of dimension M × 1, and the result can be expressed as:

$i_{{\mathrm{\Ω}}_p}^{M\×1}=m^{M\×N^2}l---\left(6\right)$

whereinThe M × 1 column vector is shown,represents by m₁,m₂,...m_MM × N composed of these vectors²A matrix of (a); thus, by step (1), it is recorded that M sets of heterodyne AC signals i are stored in the computer_Ω(t) corresponding numerical quantities, which contain i_Ω(t) amplitude and phase information.

The step (2) is specifically realized as follows:

(2a) plural holograms of the object to be measuredFIG. H _c(x,y,z_i) Is actually l in the formula (5), which is N having a length of²And the length of the recording result obtained in step (1) is M. Since usually the signal l satisfies sparsity or compressibility, it is known from the compressive sensing theory that even at M<N²In the case of (2), the signal/can still be derived from the measured valueIs reconstructed out.

(2b) N available for signal l²× 1 vector group on basisNote that for simplicity, assuming the bases are orthogonal, then l can be used at N²×N²Set of bases of dimensional spaceThe linear combination is expressed as:

or l ═ Ψ s (7)

In which s is N²× 1, Ψ is N²×N²Of the matrix of (a). Obviously, l and s are equivalent representations of the same signal, where l is a representation in the time or space domain, s is a representation in the Ψ domain, and signal l is said to be K-sparse when it can be linearly represented by only K basis vectors.

(2c) Minimization of use l₁Norm method from random measurementsThe middle recovery signal l is only M ≧ O [ K.log (N) as known from compressed sensing theory²/K)]The K sparse vectors can be accurately reconstructed by secondary random measurement or the compressible vectors can be stably and approximately reconstructed. The larger M is, the better the effect of recovering the reconstructed signal l is, but the resource overhead is correspondingly increased, and in practice, M can be 0.1-0.5N²I.e. the sampling rate (M/N)²) 10 to 50 percent. Minimization of₁The norm algorithm satisfies the constraint of a linear equation, and can be implemented by programming, such as a common basis pursuit algorithm, or some other reconstruction algorithm based on greedy, statistical or variational ideas, and satisfies:

and is

The specific implementation of the step (3) is basically the same as that of the step (1), except that the object to be measured is replaced by a point element object (pinhole). The specific implementation of the step (4) is basically the same as that of the step (2), except that the complex holography of the point-element object is reconstructed by the compressed sensing algorithmDrawing (A)。

The specific implementation of said step (5) is exactly the same as the conventional optical scanning holographic method, by holographically recording the encoding and decoding phasesFIG. H _c(x,y,z_i) And H_d(x,y,z_d) Convolution operation is carried out on a computer to obtain the information of the reconstructed section image

Wherein "F" and "F" are^-1"denotes the Fourier and inverse Fourier operators, respectively, k₀Is wave number, k_xAnd k_yIs the spatial frequency, z_iFocusing a layer (satisfying z) for the position of a cross-sectional image of a layer in a three-dimensional object_i＝z_dCross-sectional layer) image output as

In practical applications, all z can be obtained in advance to meet the real-time requirement as much as possible_dDecoding stage complex holography corresponding to possible value positionsDrawing (A). Namely, the steps (3) and (4) are repeated by continuously changing the placing position of the point element object, so as to record the decoding complex number holography at different axial positionsDrawing (A)And storing the data in the computer for calling in the step (5).

Compared with the traditional optical scanning holographic technology, the invention has the following beneficial effects:

(1) a Digital Micromirror Device (DMD) is used for replacing a two-dimensional mechanical motion scanning device, so that the problem that the holographic image recording effect is influenced by jitter and the like caused by mechanical motion scanning is solved;

(2) by using the compressed sensing theory in the optical scanning holographic technique, complex holography can be recordedPicture frameThe required data volume is greatly reduced;

(3) can reconstruct a hologram according to the pairDrawing (A)The amount of data to be recorded in the experiment, if it is for a hologramDrawing (A)The quality requirement is not high, and the sampling rate can take a smaller value so as to save the cost of resources (time, calculated amount and the like).

Drawings

FIG. 1 of the drawingsThe principle of the method and the system of the inventionDrawing (A)。

FIG. 2 of the drawingsThe invention is the model of the object to be measured of the embodiment.

FIG. 3(a) (b) and (c) are Fresnel holograms recorded by a conventional optical scanning holographic methodDrawing (A)Real part, imaginary part and reconstructed objectDrawing (A)。

FIG. 4(a) The Fresnel holography recorded at the sampling rates of 15% and 30% in the embodiment of the invention is represented by (b), (c) and (d), (e) and (f)Drawing (A)Real part, imaginary part and reconstructed objectDrawing (A)。

As described aboveIn the attached drawingsIs/are as followsIllustration of the drawingsThe reference numbers are:

1 spectroscope, 2 acousto-optic frequency shifter, 3 diaphragm, 4 reflector, 5 Digital Micromirror (DMD), 6 beam combiner, 7 object, 8 lens, 9 photoelectric detector, 10 band-pass filter, 11 analog multiplier, 12 low-pass filter, 13 computer

Detailed Description

Lower surface combinationDrawingsThe present invention will be further described with reference to a specific embodiment thereof.

In this embodiment, a solid-state laser with an output power of about 20mW is used as a light source, the wavelength of light is λ 532nm, the pupil size is D5 mm × 5mm (128 × 128pixels), the resolution of a Digital Micromirror Device (DMD) is 1920 × 1080, and the object to be measured is 1920As shown in fig. 2The 5mm × 5mm (128 × 128pixels) character image is shown, with the object under test and the point element object (pinhole) at a distance of 20cm from the DMD.

The whole experimental process is carried out according to the steps (1) to (5) described above. The DMD configuration matrix is a random matrix, each element of the matrix only has two values of 0 and 1, and the values are randomly determined according to the probability of 50 percent; 2500 random matrixes and 5000 random matrixes are respectively prepared for comparing the experimental effects under the conditions that the sampling rate is 15% and 30%; in the experiment, these random matrices are input to the DMD in turn, thereby modulating the light field output and projected on the object; corresponding to each modulated light field, collecting response by a photoelectric detector, filtering, phase-locked amplifying and other processing are carried out on the difference frequency electric signals, and finally 2500 and 5000 groups of data are obtained through analog-to-digital conversion and stored in a computer; then, a compressed sensing algorithm is utilized to reconstruct complex holography of the object to be measured from the stored dataDrawing (A)HolographicDrawing (A)Is also 128 × 128.

As shown in fig. 2、FIG. 3AndFIG. 4Respectively showing the actual image of the object to be measured and the contrast effect of image reconstruction by adopting the traditional optical scanning holographic method and the method of the inventionDrawing (A). Wherein,FIG. 2Is an actual image of the object to be measured,FIG. 3(a) (b) and (c) show the Fresnel holography of the traditional optical scanning holographic systemDrawing (A)The real part, the imaginary part and the reconstructed image,FIG. 4(a) (b), (c) andFIG. 4(d) The Fresnel holographic method shown in the (e) and the (f) respectively has the Fresnel holographic sampling rate of 15% and the Fresnel holographic sampling rate of 30%Drawing (A)The real part, the imaginary part and the reconstructed image, from the viewpoint of viewing effect,reconstructed Fresnel holographyDrawing (A)Almost the same as that of the conventional optical scanning holographic technique, the reconstructed object image effect is clearly visible although having a little difference from that of the conventional optical scanning holographic technique. It can be seen that the system employing the method of the present invention is functionally equivalent to a conventional optical scanning holographic system, yet effectively eliminates the effects of mechanical motion scanning.

Claims (2)

1. An optical scanning holographic technique without mechanical movement scan features that an optical scanning holographic system is used to obtain the holographic image of the object to be measuredDrawing (A)In the process of (1), including the following data recording, complex holographyDrawing (A)Two key steps of reconstruction:

(1) recording data; placing an object to be measured at a position with a distance z from the rear side of a Digital Micromirror Device (DMD), changing a configuration matrix of the DMD to modulate a light field projected on the object to be measured, and recording data corresponding to total light intensity after the light field modulated by the DMD exits from the object to be measured each time, wherein the specific steps are as follows:

(1a) the laser outputs a light beam with frequency omega, and the light beam is divided into two paths after passing through the beam splitter, wherein one path is subjected to frequency shift into omega + omega after passing through the acousto-optic frequency shifter, so that the two paths of light waves present frequency difference omega; and the other path of light wave passes through the DMD and is modulated by the DMD, then is combined with the other path of light wave at the beam combining mirror, and is projected onto the three-dimensional object.

(1b) Collecting a light field emitted from a three-dimensional object on a photoelectric detector to obtain an optical heterodyne response current i (t); constantly and randomly changing the configuration matrix of the DMD, thereby randomly modulating the light field projected on the three-dimensional object; for each change, the detector outputs a corresponding optical heterodyne current i (t).

(1c) The output current i (t) comprises a direct current component and an alternating current component with the frequency of omega, and the heterodyne alternating current signal i is obtained after the direct current component and the high-frequency interference component are filtered by a band-pass filter (BPF) with the center frequency of omega_Ω(t)：

Wherein

Re[.]Representing the real part, D the pupil size, γ (x, y; z) the transmittance distribution of the object, "+" the convolution, m (x, y) the modulated light field exiting the DMD, h (x, y; z) the impulse response function with a transmission distance z,and phi_pRespectively representThe phase of the amplitude of (a).

(1d)i_Ω(t) is divided into two paths and input into a phase-locked amplifier, the two paths of signals are respectively mixed with two paths of single-frequency signals cos (omega t) and sin (omega t) which are orthogonal to each other, and then the in-phase component is extracted by a Low Pass Filter (LPF)And the orthogonal componentI.e., the real and imaginary components of equation (2).

(1e) The two paths of component signals i which are orthogonal to each other are processed_CAnd i_SRespectively carrying out analog-to-digital conversion, recording the converted digital information in a computer, and completing one measurement corresponding to a certain m (x, y); then randomly changing the value of the DMD configuration matrix to correspondingly obtain another distribution of the modulated light field m (x, y), and further obtaining another group i_CAnd i_sAnd recording the digital information; this was repeated M times for the change and recording.

(1f) The above process can also be represented as discretized

Where N is the number of sample points in a single-dimensional coordinate, x_i,y_jDiscretization of the coordinates x, y, l (x)_i,y_j(ii) a z) is then a discretized representation of the fresnel diffraction profile of the light field after passing through the object, i.e.:

l(x,y；z)＝|γ(x,y,z)|²*h(x_i,y_j,z)(4)

a two-dimensional matrix m (x)_i,y_j) And l (x)_i,y_j(ii) a z) separately vectorized to obtain an N²The row vector m and one N of the dimensions²A column vector l of dimensions, then equation (3) can be written as:

i_Ω＝ml(5)

equation (5) can be regarded as a measurement value of the compressed sensing recording process, and if the DMD configuration matrix is continuously changed for M times, M measurement values M are obtained₁,m₂,...m_MThey form a column vector of dimension M × 1, and the result can be expressed as:

whereinThe M × 1 column vector is shown,represents by m₁,m₂,...m_MM × N composed of these vectors²A matrix of (a); thus, through the data recording step, M sets of heterodyne AC signals i are stored in the computer_Ω(t) corresponding numerical quantities, which contain i_Ω(t) amplitude and phase information.

(2) Plural holographyDrawing (A)Reconstructing; reconstructing and recovering complex holography of the measured object from the recorded data by using a compressed sensing algorithmDrawing (A)；

(2a) Plural holograms of the object to be measuredFIG. H _c(x,y,z_i) Is actually l in the formula (5), which is N having a length of²And the resulting length per data recording step is M. Since usually the signal l satisfies sparsity or compressibility, it is known from the compressive sensing theory that even at M<N²In the case of (2), the signal/can still be derived from the measured valueIs reconstructed out.

(2b) N available for signal l²× 1 vector group on basisNote that for simplicity, assuming the bases are orthogonal, then l can be used at N²×N²Set of radix psi ═ psi in a dimensional space₁,ψ₂,...,ψ_N2The linear combination is expressed as:

or l ═Ψs(7)

In which s is N²× 1, Ψ is N²×N²Of the matrix of (a). Obviously, l and s are equivalent representations of the same signal, where l is a representation in the time or space domain, s is a representation in the Ψ domain, and signal l is said to be K-sparse when it can be linearly represented by only K basis vectors.

(2c) Minimization of use l₁Norm method from random measurementsThe middle recovery signal l is only M ≧ O [ K.log (N) as known from compressed sensing theory²/K)]The K sparse vectors can be accurately reconstructed by secondary random measurement or the compressible vectors can be stably and approximately reconstructed. The larger M is, the better the signal l effect of the restored reconstruction is, but the resource overhead is correspondingly increased, and in practice, M can be 0.1-0.5N²I.e. the sampling rate (M/N)²) 10 to 50 percent. Minimization of₁The norm algorithm satisfies the constraint of a linear equation, and can be implemented by programming, such as a common basis pursuit algorithm, or some other reconstruction algorithm based on greedy, statistical or variational ideas, and satisfies:

and is。

2.According to claim1 toNovelThe optical scanning holographic system without mechanical motion scanning is characterized in that a Digital Micromirror Device (DMD) is adopted to replace a two-dimensional mechanical motion scanning device in the traditional optical scanning system, and a Compressed Sensing (CS) algorithm is used for calculating and reconstructing a plurality of holograms from recorded dataDrawing (A)。