CN105404128B - Multiframe phase-shifted digital holographic method and device - Google Patents
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Abstract
The invention discloses a kind of multiframe phase-shifted digital holographic method and device, correlation technique to include：Low frequency heterodyne is produced using the corresponding modulation object lights of two acousto-optic modulator AOM and reference light, and is detected using high frame frequency planar array detector, obtains multiframe Phase Shifting Holographic figure；Time-domain spectral conversion is carried out to the signal of each pixel in the multiframe Phase Shifting Holographic figure respectively, and extracts the amplitude and phase of spectrum value at heterodyne frequency；Target amplitude and target phase are extracted from the amplitude of spectrum value at the heterodyne frequency and phase, so as to fulfill holographic reconstruction.By using scheme provided by the invention, the influence of twin image can be not only eliminated, more can effectively mitigate the interference of random noise, improves imaging precision and environmental suitability.
Description
Technical Field
The invention relates to the technical field of digital holography, in particular to a multi-frame phase shift digital holography method and a device.
Background
The holographic technique utilizes interferometric recording and diffractive reconstruction to obtain amplitude and phase information of a target, thereby realizing three-dimensional imaging of the target. Digital holography techniques utilize digital equipment to achieve holographic recording and reconstruction. Compared with other three-dimensional imaging technologies, the digital holographic technology has the advantages of non-contact, non-scanning, non-dyeing, quantification and the like, and can be applied to imaging and measurement in the fields of biology and micro electro mechanical systems. There are two main problems in digital holography: one is the twin image problem and one is the random noise problem (mechanical vibrations, airflow disturbances, etc.). These problems affect the imaging accuracy of digital holography and limit the range of applications. The phase shift digital holography technology can obtain a hologram with a certain phase shift amount (usually 4 frames) by introducing a phase shift between object light and reference light, and can eliminate twin image interference after digital processing and reduce the influence of random noise to a certain extent.
At present, several phase shift holographic devices and corresponding processing algorithms exist, but due to the problems of phase shift nonlinearity, limited detection frame number, limited noise immunity of the processing algorithms and the like, the systems have the defect of low noise immunity, influence the imaging precision and limit the applicable field.
Disclosure of Invention
The invention aims to provide a multi-frame phase shift digital holography method and a device, which can eliminate the influence of twin images, effectively reduce the interference of random noise and improve the imaging precision and environmental adaptability.
The purpose of the invention is realized by the following technical scheme:
a multi-frame phase-shifting digital holography method comprising:
the method comprises the steps that low-frequency heterodyne is generated by modulating object light and reference light which respectively correspond to two acousto-optic modulators AOM, and a high-frame frequency area array detector is used for detecting to obtain a multi-frame phase shift hologram;
respectively carrying out time domain spectrum transformation on signals of each pixel point in the multi-frame phase shift hologram, and extracting the amplitude and the phase of a frequency spectrum value at the heterodyne frequency;
and extracting a target amplitude and a target phase from the amplitude and the phase of the spectral value at the heterodyne frequency, thereby realizing holographic reconstruction.
Further, the obtaining a multi-frame phase shift hologram includes:
obtaining object light U reaching high frame frequency area array detectorOAnd a reference light UR：
Wherein, t is a time,aO,ωO,the amplitude, angular frequency and phase of the object light respectively; a isR,ωR,Amplitude, angular frequency and phase of the reference light, respectively;
an ideal noise-free hologram s generated by the interference of object light and reference light is represented as:
in the formula, ωHFor heterodyne angular frequency, fHFor the heterodyne frequencies of two AOMs, the relationship is:
ωH＝ωO-ωR＝2πfH；
including random noiseThe total signal of the multi-frame phase-shift hologram is:
thereby obtaining a plurality of frames of phase-shifted holograms stotal(t (n)), where n is each frame number, and t (n) is the sampling time corresponding to the nth frame numberN is 1,2total，NtotalThe total number of frames for the obtained hologram.
Further, the performing time-domain spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram, and extracting the amplitude and the phase of the spectrum value at the heterodyne frequency includes:
and respectively carrying out time domain spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram by using Fast Fourier Transform (FFT) to obtain a time domain spectrum S (omega):
in the formula, ω represents the heterodyne angular frequency, stotalFor multi-frame phase shift hologram total signal, N is each frame number, t (N) is sampling time corresponding to nth frame number, NtotalTotal number of frames for the obtained hologram;
extracting time domain frequency spectrum S (omega) at heterodyne angular frequency omegaHProcessing value S (omega)H)：
Wherein σ is a standard deviation;
thereby obtaining the amplitude of the spectral values of the time-domain spectrum S (omega) at the heterodyne frequenciesAnd phase
Further, extracting a target amplitude and a target phase from the amplitude and the phase of the spectrum value at the heterodyne frequency, thereby implementing holographic reconstruction and obtaining complete information of a target, which includes:
amplitude of vibrationInAs a constant, after normalization processing, the normalized amplitude a of the target is obtainednorm：
In the formula, max and min represent data distributed in two dimensions respectivelyTaking a maximum value and a minimum value;
the position of the reference light path lens is symmetrical to that of the object light path lens, so that the phase of the object light is not included when the target is not includedIs equal toPhase of the targetExpressed as:
and, obtaining target complete information O according to the obtained target amplitude and target phaseresultIt is expressed as:
a multi-frame phase-shifting digital holographic device, comprising: presetting a light path, a high frame frequency area array detector and a data processor; wherein:
the preset light path comprises two acousto-optic modulators AOM which are used for respectively modulating object light and reference light to generate low-frequency heterodyne;
the high-frame frequency area array detector detects light in an imaging mirror with a preset light path to obtain a multi-frame phase shift hologram, and transmits the multi-frame phase shift hologram to the data processor;
the data processor respectively carries out time domain frequency spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram, and extracts the amplitude and the phase of the frequency spectrum value at the heterodyne frequency; and extracting a target amplitude and a target phase from the amplitude and the phase of the frequency spectrum value at the heterodyne frequency, thereby realizing holographic reconstruction.
Further, the preset optical path includes:
the device comprises a laser, a half-wave plate, three polarization beam splitting prisms, two reflectors, two acousto-optic modulators AOM, two diaphragms, a spatial filter, two 1/4 wave plates, two micro-objectives, a reference reflector and an imaging mirror; wherein:
laser emitted by the laser is divided into two beams of polarized light of object light and reference light through a half-wave plate and a polarization beam splitter prism 1, wherein the object light is polarized light in a p direction, and the reference light is polarized light in an s direction;
the object light passes through the reflector 1, the-1 level light and the 0 level light emitted after entering the acousto-optic modulator AOM 1 are shielded by the diaphragm 1, the emitted +1 diffraction light enters the spatial filter through the polarization beam splitter prism 2, and the filtered light beam sequentially passes through the polarization beam splitter prism 3, the 1/4 wave plate 1 and the microobjective 1 and then irradiates on a target; reflected light carrying target information sequentially passes through a microscope objective 1 and an 1/4 wave plate 1 and then is changed into s-direction polarized light, and the s-direction polarized light passes through a polarization beam splitter prism 3 and a polarizing film arranged at an angle of 45 degrees and then is emitted into an imaging mirror;
the-1 level light and the 0 level light emitted after the reference light enters the AOM 2 are shielded by the diaphragm 2, the +1 level diffracted light emitted enters the spatial filter after passing through the reflector 2 and the polarization beam splitter prism 2, and the filtered light beam sequentially passes through the polarization beam splitter prism 3, the 1/4 wave plate 2 and the microscope objective lens 2 and then irradiates the reference reflector; the reflected light is changed into p-direction polarized light after sequentially passing through the microscope objective lens 2 and the 1/4 wave plate 2, and then passes through the polarization beam splitter prism 3 and the polarizing plate arranged at an angle of 45 degrees and then is emitted into the imaging lens.
Further, the preset optical path includes:
the device comprises a laser, a half-wave plate, three polarization beam splitting prisms, two reflectors, two acousto-optic modulators AOM, two diaphragms, a spatial filter, a beam splitting prism, two 1/4 wave plates, a microscope objective, a reference reflector and an imaging mirror; wherein:
laser emitted by the laser is divided into two beams of polarized light of object light and reference light through a half-wave plate and a polarization beam splitter prism 1, wherein the object light is polarized light in a p direction, and the reference light is polarized light in an s direction;
the object light passes through the reflector 1, the-1 level light and the 0 level light emitted after entering the acousto-optic modulator AOM 1 are shielded by the diaphragm 1, the emitted +1 diffraction light enters the spatial filter through the polarization beam splitter prism 2, and the filtered light beam sequentially passes through the beam splitter prism, the microscope objective, the polarization beam splitter prism 3 and the 1/4 wave plate 1 and then irradiates on a target; the reflected light carrying the target information is changed into s-direction polarized light after passing through 1/4 wave plate 1, and then is transmitted into the imaging lens after sequentially passing through the polarization beam splitter prism 3, the microscope objective, the beam splitter prism and the polarizing plate arranged at an angle of 45 degrees;
the-1 level light and the 0 level light emitted after the reference light enters the AOM 2 are shielded by the diaphragm 2, the +1 level diffracted light emitted enters the spatial filter after passing through the reflector 2 and the polarization beam splitter prism 2, and the filtered light beam sequentially passes through the beam splitter prism, the microscope objective, the polarization beam splitter prism 3 and the 1/4 wave plate 2 and then irradiates the reference reflector; the reflected light is changed into p-direction polarized light after passing through 1/4 wave plate 2, and then passes through polarization beam splitter prism 3, microscope objective, beam splitter prism and polarizing plate placed at 45 degree angle in turn to be injected into the imaging lens.
Further, the preset optical path includes:
the device comprises a laser, two half-wave plates, a polarization beam splitting prism, two reflectors, two acousto-optic modulators AOM, two diaphragms, two spatial filters, a beam combining prism and an imaging mirror; wherein:
laser emitted by the laser is divided into two beams of polarized light of object light and reference light through a half-wave plate 1 and a polarization beam splitter prism, wherein the object light is polarized light in a p direction, and the reference light is polarized light in an s direction;
the object light sequentially passes through a half-wave plate 2 and a reflector 1, emergent-1-level light and 0-level light are shielded by a diaphragm 1 after entering an acousto-optic modulator AOM 1, emergent +1 diffracted light enters a spatial filter 1, and filtered light beams sequentially pass through a beam combining prism and a microobjective and then irradiate on a target; reflected light carrying target information sequentially passes through the microscope objective and the beam combining prism and then is incident into the imaging lens;
the-1 level light and the 0 level light emitted after the reference light enters the AOM 2 are shielded by the diaphragm 2, the +1 level diffracted light emitted enters the spatial filter 2 after passing through the reflector 2, and the filtered light beam enters the imaging mirror after passing through the beam-combining prism.
Further, the obtaining a multi-frame phase shift hologram includes:
obtaining object light U reaching high frame frequency area array detectorOAnd a reference light UR：
Wherein, t is a time,aO,ωO,the amplitude, angular frequency and phase of the object light respectively; a isR,ωR,Amplitude, angular frequency and phase of the reference light, respectively;
an ideal noise-free hologram s generated by the interference of object light and reference light is represented as:
in the formula, ωHFor heterodyne angular frequency, fHFor the heterodyne frequencies of two AOMs, the relationship is:
ωH＝ωO-ωR＝2πfH；
including random noiseThe total signal of the multi-frame phase-shift hologram is:
thereby obtaining a plurality of frames of phase-shifted holograms stotal(t (N)), where N is each frame number, t (N) is the sampling time corresponding to the nth frame number, and N is 1,2total，NtotalTotal number of frames for the obtained hologram;
the data processor respectively performs time domain spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram, and extracts the amplitude and the phase of the spectrum value at the heterodyne frequency, including:
and respectively carrying out time domain spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram by using Fast Fourier Transform (FFT) to obtain a time domain spectrum S (omega):
in the formula, ω represents the heterodyne angular frequency, stotal(t (N)) is multi-frame phase shift hologram, N is each frame number, t (N) is sampling time corresponding to nth frame number, NtotalTotal number of frames for the obtained hologram;
extracting time domain frequency spectrum S (omega) at heterodyne angular frequency omegaHProcessing value S (omega)H)：
Wherein σ is a standard deviation;
thereby obtaining the amplitude of the spectral values of the time-domain spectrum S (omega) at the heterodyne frequenciesAnd phase
Further, extracting a target amplitude and a target phase from the amplitude and the phase of the spectrum value at the heterodyne frequency, thereby implementing holographic reconstruction and obtaining complete information of a target, which includes:
amplitude of vibrationInAs a constant, after normalization processing, the normalized amplitude a of the target is obtainednorm：
In the formula, max and min represent data distributed in two dimensions respectivelyTaking a maximum value and a minimum value;
the position of the reference light path lens is symmetrical to that of the object light path lens, so that the phase of the object light is not included when the target is not includedIs equal toPhase of the targetExpressed as:
obtaining target complete information O according to the obtained target amplitude and target phaseresultIt is expressed as:
according to the technical scheme provided by the invention, two acousto-optic modulators (AOMs) are adopted to modulate object light and reference light to generate low-frequency heterodyne, and a high-frame-frequency area array detector is used for detecting, so that hundreds or even thousands of frames of accurate linear phase-shifted holograms are acquired in a short time. And different from the traditional 4-step holographic algorithm, the multi-frame phase shift holographic algorithm is adopted to extract the target amplitude and phase information, so that the interference of twin images and random noise can be effectively removed, and the clear and accurate three-dimensional reconstruction image of the target can be obtained.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
FIG. 1 is a flow chart of a multi-frame phase-shift digital holography method according to an embodiment of the present invention;
FIG. 2a is a schematic diagram of a three-dimensional matrix formed by multiple frames of phase-shifted holograms according to an embodiment of the present invention;
FIG. 2b is a schematic diagram of a time-domain sampling signal at a certain point according to an embodiment of the present invention;
FIG. 3a is a schematic structural diagram of a multi-frame phase-shifting digital holographic device according to an embodiment of the present invention;
FIG. 3b is a schematic structural diagram of another multi-frame phase-shifting digital holographic device according to an embodiment of the present invention;
FIG. 3c is a schematic structural diagram of another multi-frame phase-shifting digital holographic device according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a time domain spectrum obtained by processing the signal with FFT according to an embodiment of the present invention;
fig. 5 is a schematic diagram of a three-dimensional image according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a flowchart of a multi-frame phase-shift digital holography method according to an embodiment of the present invention. As shown in fig. 1, it mainly includes the following steps:
and 11, adopting two acousto-optic modulators AOM to respectively generate low-frequency heterodyne on the modulated object light and the reference light, and detecting by using a high-frame-frequency area array detector to obtain a multi-frame phase-shift hologram.
In two embodiments of the present invention, the obtaining a multi-frame phase shift hologram includes:
obtaining object light U reaching high frame frequency area array detectorOAnd a reference light UR：
Wherein, t is a time,aO,ωO,the amplitude, angular frequency and phase of the object light respectively; a isR,ωR,Amplitude, angular frequency and phase of the reference light, respectively;
andthe relationship of (1) is:
wherein,the phase of the object light wave is not included,the phase of the object light wave is changed after the target is placed.
An ideal noise-free hologram s generated by the interference of object light and reference light is represented as:
in the formula, ωHFor heterodyne angular frequency, fHFor the heterodyne frequencies of two AOMs, the relationship is:
ωH＝ωO-ωR＝2πfH； (5)
including random noiseThe total signal of the multi-frame phase-shift hologram is:
as can be seen from the above, the amplitude and phase information of the object is recorded by modulation in the third item at a modulation angular frequency ofωHTwin images are recorded in the second term with different modulation angular frequencies-omegaH。
In the embodiment of the invention, heterodyne frequency fHFrame frequency f of detectorDEach frame number n, each frame corresponding to a sampling time t (n), recording the total time ttotalObtaining the total frame number N of the hologramtotalNumber of phase shift cycles NperiodNumber of phase shift steps N per cyclestepThe relationship of (1) is:
Nperiod＝fHttotal(7)
Ntotal＝fDttotal＝NperiodNstep(9)
for example, if a 10Hz heterodyne frequency and a 200Hz acquisition frame frequency are used, a 200 × 3 — 600 frame hologram can be obtained in 3 seconds, comprising 10 × 3 — 30 periods with 200/10 — 20 phase shifts per period, and a sampling time interval 1/200 — 0.005s for each frame.
Thereby obtaining a multi-frame phase-shifted hologram stotal(t(n))，n＝1,2,...,Ntotal。
And step 12, respectively carrying out time domain frequency spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram, and extracting the amplitude and the phase of the frequency spectrum value at the heterodyne frequency.
Obtained multiframe phase shift hologram stotal(t (N)) forming a data matrix M [ r, c, N ] in a computertotal]. The matrix includes two dimensions of space and one dimension of time. r is the detector row pixel number, c is the detector column pixel number, NtotalIs made ofTotal number of frames of the information map. Therefore, for any pixel point (x, y) of the detector, the detection signal M [ x, y,1: N ] of the point can be obtainedtotal]The number of samples is equal to the total number of frames Ntotal. As shown in fig. 2, fig. 2a is a three-dimensional matrix formed by multiple frames of phase-shifted holograms, and fig. 2b is a time-domain sampling signal at a certain point.
In the embodiment of the present invention, a fast fourier transform FFT is used to perform time-domain spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram, so as to obtain a time-domain spectrum S (ω):
where ω represents the heterodyne angular frequency. Then extracting the time domain frequency spectrum S (omega) at the out-of-tolerance angular frequency omegaHProcessing value S (omega)H) When the frame frequency f is in accordance with the Nyquist-Shannon sampling lawDSatisfying heterodyne frequency fHAt 2 times or more than 2 times, the target spectrum and the twin image spectrum are separated. Heterodyne frequency point ω in the time domain spectrumHExtracting s corresponding to the pixel pointtotal(t) target information on the third term in the expression (equation 6) as shown in the above-described S (ω) expression. Since only the spectral point omega is extractedHAvoiding the spectrum point-omega where the twin image is locatedHSo that the effect of the twin image can be eliminated, as follows:
when the number of sampling frames NtotalWhen it is positive infinity, the accumulated partial factor in the above formula isThe mathematical expectation of (a) is as follows:
typically, random noise is complex, including random vibrations, airflow disturbances, and the like. If the statistical distribution of the noise satisfies a normal (gaussian) distribution and the expectation value μ is 0, the probability density function p and the feature function F are as shown in equations (14) (15), where σ is a standard deviation.
The result of equation (13) is equal to the value when k is 1 in equation (15), as shown in equation (16).
By deriving the above equations (13), (14), (15) and (16), the result of equation (12) can be obtained, as shown in equation (17):
when the sampling frame number is infinite, the statistic value of random noise is a constant, and the extracted target information is not influenced by noise. In practice, the number of sampling frames N is increasedtotalThe closer equation (17) is to the equation, the less the influence of random noise is, and the higher reconstruction accuracy is.
Therefore, by extracting the target information in the time-frequency domain, the influence of the twin image can be effectively removed. Moreover, because the calculation is carried out by obtaining enough holograms of a plurality of frames, the statistical value of the random noise can be close to a constant, thereby reducing the influence of the random noise. For noise with different magnitudes, corresponding heterodyne frequency and sampling frame number can be set, so that the required holographic imaging precision is met.
From equation (17), the time domain spectrum S (ω) is at the heterodyne angular frequency point ωHThe value S (ω) ofH) Has an amplitude value ofPhase value of
And step 13, extracting target amplitude and target phase from the amplitude and phase of the spectrum value at the heterodyne frequency, thereby realizing holographic reconstruction.
Amplitude of vibrationInAs a constant, after normalization processing, the normalized amplitude a of the target is obtainednorm：
In the formula, max and min represent data distributed in two dimensions respectivelyTaking a maximum value and a minimum value;
in the embodiment of the invention, the reference light path lens and the object light path lens are arranged symmetrically, so that the phase of the object light is not included when the target is not includedIs equal toPhase of the targetExpressed as:
and because the detector is arranged at the image surface position of the lens, the detector is arranged at the image surface position of the lensEqual to the target reconstruction phase, and does not need to be diffracted and reconstructed.
Thereby obtaining a normalized amplitude a of the targetnormPhase reconstructionAnd realizing holographic reconstruction.
In addition, target complete information O is obtained according to the obtained target amplitude and target phaseresultIt is expressed as:
in another embodiment of the present invention, a multi-frame phase shift digital holographic device is further provided, which mainly includes: presetting a light path, a high frame frequency area array detector and a data processor; wherein:
the preset light path comprises two acousto-optic modulators AOM which are used for respectively modulating object light and reference light to generate low-frequency heterodyne;
the high-frame frequency area array detector detects light in an imaging mirror with a preset light path to obtain a multi-frame phase shift hologram, and transmits the multi-frame phase shift hologram to the data processor;
the data processor respectively carries out time domain frequency spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram, and extracts the amplitude and the phase of the frequency spectrum value at the heterodyne frequency; and extracting a target amplitude and a target phase from the amplitude and the phase of the frequency spectrum value at the heterodyne frequency, thereby realizing holographic reconstruction.
In the embodiment of the invention, the preset light path has various structural forms. As shown in fig. 3a-3c, three light paths with different structural forms are shown, and the light paths shown at the same time, the high frame frequency area array detector and the data processor together form a multi-frame phase-shift digital holographic device. The following description is directed primarily to the optical path of fig. 3a-3c, excluding the high frame rate area array detector and data processor.
As shown in fig. 3a, it mainly includes: the device comprises a laser, a half-wave plate, three polarization beam splitting prisms, two reflectors, two acousto-optic modulators AOM, two diaphragms, a spatial filter, two 1/4 wave plates, two micro-objectives, a reference reflector and an imaging mirror; wherein:
laser emitted by the laser is divided into two beams of polarized light of object light and reference light through a half-wave plate and a polarization beam splitter prism 1, wherein the object light is polarized light in a p direction, and the reference light is polarized light in an s direction;
the object light passes through the reflector 1, the-1 level light and the 0 level light emitted after entering the acousto-optic modulator AOM 1 are shielded by the diaphragm 1, the emitted +1 diffraction light enters the spatial filter through the polarization beam splitter prism 2, and the filtered light beam sequentially passes through the polarization beam splitter prism 3, the 1/4 wave plate 1 and the microobjective 1 and then irradiates on a target; reflected light carrying target information sequentially passes through a microscope objective 1 and an 1/4 wave plate 1 and then is changed into s-direction polarized light, and the s-direction polarized light passes through a polarization beam splitter prism 3 and a polarizing film arranged at an angle of 45 degrees and then is emitted into an imaging mirror;
the-1 level light and the 0 level light emitted after the reference light enters the AOM 2 are shielded by the diaphragm 2, the +1 level diffracted light emitted enters the spatial filter after passing through the reflector 2 and the polarization beam splitter prism 2, and the filtered light beam sequentially passes through the polarization beam splitter prism 3, the 1/4 wave plate 2 and the microscope objective lens 2 and then irradiates the reference reflector; the reflected light is changed into p-direction polarized light after sequentially passing through the microscope objective lens 2 and the 1/4 wave plate 2, and then passes through the polarization beam splitter prism 3 and the polarizing plate arranged at an angle of 45 degrees and then is emitted into the imaging lens.
As shown in fig. 3b, it mainly includes: the device comprises a laser, a half-wave plate, three polarization beam splitting prisms, two reflectors, two acousto-optic modulators AOM, two diaphragms, a spatial filter, a beam splitting prism, two 1/4 wave plates, a microscope objective, a reference reflector and an imaging mirror; wherein:
laser emitted by the laser is divided into two beams of polarized light of object light and reference light through a half-wave plate and a polarization beam splitter prism 1, wherein the object light is polarized light in a p direction, and the reference light is polarized light in an s direction;
the object light passes through the reflector 1, the-1 level light and the 0 level light emitted after entering the acousto-optic modulator AOM 1 are shielded by the diaphragm 1, the emitted +1 diffraction light enters the spatial filter through the polarization beam splitter prism 2, and the filtered light beam sequentially passes through the beam splitter prism, the microscope objective, the polarization beam splitter prism 3 and the 1/4 wave plate 1 and then irradiates on a target; the reflected light carrying the target information is changed into s-direction polarized light after passing through 1/4 wave plate 1, and then is transmitted into the imaging lens after sequentially passing through the polarization beam splitter prism 3, the microscope objective, the beam splitter prism and the polarizing plate arranged at an angle of 45 degrees;
the-1 level light and the 0 level light emitted after the reference light enters the AOM 2 are shielded by the diaphragm 2, the +1 level diffracted light emitted enters the spatial filter after passing through the reflector 2 and the polarization beam splitter prism 2, and the filtered light beam sequentially passes through the beam splitter prism, the microscope objective, the polarization beam splitter prism 3 and the 1/4 wave plate 2 and then irradiates the reference reflector; the reflected light is changed into p-direction polarized light after passing through 1/4 wave plate 2, and then passes through polarization beam splitter prism 3, microscope objective, beam splitter prism and polarizing plate placed at 45 degree angle in turn to be injected into the imaging lens.
As shown in fig. 3c, it mainly includes: the device comprises a laser, two half-wave plates, a polarization beam splitting prism, two reflectors, two acousto-optic modulators AOM, two diaphragms, two spatial filters, a beam combining prism and an imaging mirror; wherein:
laser emitted by the laser is divided into two beams of polarized light of object light and reference light through a half-wave plate 1 and a polarization beam splitter prism, wherein the object light is polarized light in a p direction, and the reference light is polarized light in an s direction;
the object light sequentially passes through a half-wave plate 2 and a reflector 1, emergent-1-level light and 0-level light are shielded by a diaphragm 1 after entering an acousto-optic modulator AOM 1, emergent +1 diffracted light enters a spatial filter 1, and filtered light beams sequentially pass through a beam combining prism and a microobjective and then irradiate on a target; reflected light carrying target information sequentially passes through the microscope objective and the beam combining prism and then is incident into the imaging lens;
the-1 level light and the 0 level light emitted after the reference light enters the AOM 2 are shielded by the diaphragm 2, the +1 level diffracted light emitted enters the spatial filter 2 after passing through the reflector 2, and the filtered light beam enters the imaging mirror after passing through the beam-combining prism.
In the above-described optical path of fig. 3a, identical parameter micro objectives 1 and 2 are placed symmetrically in the object and reference optical paths to compensate for the phase change introduced by the micro objective 1. In the optical path apparatus of fig. 3b, the object light and the reference light pass through the same long working distance microscope objective to compensate for the phase change introduced by the object light passing through the microscope objective. In the optical path of fig. 3c, the reference light is parallel light. It is necessary to remove the phase changes introduced by the microscope objective during digital processing.
Further, the obtaining a multi-frame phase shift hologram includes:
obtaining object light U reaching high frame frequency area array detectorOAnd a reference light UR：
Wherein, t is a time,aO,ωO,the amplitude, angular frequency and phase of the object light respectively; a isR,ωR,Amplitude, angular frequency and phase of the reference light, respectively;
an ideal noise-free hologram s generated by the interference of object light and reference light is represented as:
in the formula, ωHFor heterodyne angular frequency, fHFor the heterodyne frequencies of two AOMs, the relationship is:
ωH＝ωO-ωR＝2πfH；
including random noiseThe total signal of the multi-frame phase-shift hologram is:
thereby obtaining a plurality of frames of phase-shifted holograms stotal(t (N)), where N is each frame number, t (N) is the sampling time corresponding to the nth frame number, and N is 1,2total，NtotalThe total number of frames for the obtained hologram.
Further, the data processor performs time-domain spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram, and extracts the amplitude and the phase of the spectrum value at the heterodyne frequency, including:
and respectively carrying out time domain spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram by using Fast Fourier Transform (FFT) to obtain a time domain spectrum S (omega):
in the formula, ω represents the heterodyne angular frequency, stotal(t (N)) is multi-frame phase shift hologram, N is each frame number, t (N) is sampling time corresponding to nth frame number, NtotalTotal number of frames for the obtained hologram;
extracting time domain frequency spectrum S (omega) at heterodyne angular frequency omegaHProcessing value S (omega)H)：
Wherein σ is a standard deviation;
thereby obtaining the amplitude of the spectral values of the time-domain spectrum S (omega) at the heterodyne frequenciesAnd phase
Further, the extracting a target amplitude and a target phase from the amplitude and the phase of the spectral value at the heterodyne frequency to realize the holographic reconstruction includes:
amplitude of vibrationInAs a constant, after normalization processing, the normalized amplitude a of the target is obtainednorm：
In the formula, max and min represent data distributed in two dimensions respectivelyTaking a maximum value and a minimum value;
the position of the reference light path lens is symmetrical to that of the object light path lens, so that the phase of the object light is not included when the target is not includedIs equal toPhase of the targetExpressed as:
further, target complete information O is obtained according to the obtained target amplitude and target phaseresultIt is expressed as:
it should be noted that, specific implementation manners of functions implemented by the functional modules included in the apparatus have been described in detail in the foregoing embodiments, and therefore, detailed descriptions thereof are omitted here.
It will be clear to those skilled in the art that, for convenience and simplicity of description, the foregoing division of the functional modules is merely used as an example, and in practical applications, the above function distribution may be performed by different functional modules according to needs, that is, the internal structure of the device is divided into different functional modules to perform all or part of the above described functions.
In order to facilitate understanding of the present invention, experiments were conducted below in conjunction with the above-described examples.
In this experiment, the main devices used were: 532nm single-mode continuous laser, two AOMs with external difference of 10Hz, a lens with 10-fold microscope objective (NA 0.25), a high-frame-frequency area array detector (1280 1024pixels,500fps max) for detecting the frame frequency of 100Hz, and unstained mouse cells as targets.
Step 1:
with the above apparatus, 100 frames of phase shifted holograms were obtained in 1s, comprising 10 cycles with 10 steps of phase shift per cycle.
For clarity of display, a hologram of 120 by 120 pixel size may be truncated from 1280 by 1024pixels of full field of view.
And establishing a 120 x 100 three-dimensional data matrix by using 100 frames of holograms, wherein a certain pixel point (x, y) on the kth hologram corresponds to the (x, y, k) coordinate point data on the matrix. Thus, for a certain pixel point on the detector, we obtain 100 sampled data at that point. The sampled signal at a certain point is similar to that of fig. 2b above, and it can be seen that the phase shift is linear and accurate.
Step 2:
the signal is processed with FFT to obtain a time domain spectrum, as shown in fig. 4.
And step 3:
in the time domain spectrum, the frequency point where the twin image is located can be seen to be clearly separated from the target frequency point. At a heterodyne angular frequency omegaHAnd extracting amplitude and phase information at the corresponding heterodyne frequency of 10Hz, and performing normalization processing on the amplitude information to obtain the amplitude information of the target. And respectively carrying out the operations on each pixel point to obtain two-dimensional target amplitude and phase information.
And 4, step 4:
through the steps, the complete target information is obtained. The three-dimensional image is shown in fig. 5, and it can be seen that the reconstructed object is clear.
The experiment proves that the scheme is demonstrated, and the feasibility and the advantages of the scheme are proved.
The scheme provided by the embodiment of the invention adopts low-frequency heterodyne and high-frame frequency area array detection, and can obtain phase shift holograms with hundreds of frames or even thousands of frames. And then, obtaining the amplitude and phase information of each point by utilizing a time domain spectrum analysis algorithm, thereby obtaining a target three-dimensional image. Compared with the traditional technology, the technology has the main advantages that the influence of random noise can be effectively reduced, and therefore the technology is more accurate and has better environmental adaptability. Furthermore, under the condition of different intensity noises, heterodyne frequency and detection frame frequency can be flexibly designed, multi-frame phase shift holograms with different periods and different step numbers are obtained, and better noise resistance is obtained.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (10)
1. A multi-frame phase-shifting digital holography method, comprising:
the method comprises the steps that low-frequency heterodyne is generated by modulating object light and reference light which respectively correspond to two acousto-optic modulators AOM, and a high-frame frequency area array detector is used for detecting to obtain a multi-frame phase shift hologram;
respectively carrying out time domain spectrum transformation on signals of each pixel point in the multi-frame phase shift hologram, and extracting the amplitude and the phase of a frequency spectrum value at the heterodyne frequency;
and extracting a target amplitude and a target phase from the amplitude and the phase of the spectral value at the heterodyne frequency, thereby realizing holographic reconstruction.
2. The method of claim 1, wherein obtaining the multi-frame phase-shifted hologram comprises:
obtaining object light U reaching high frame frequency area array detectorOAnd a reference light UR：
Wherein, t is a time,aO,ωO,the amplitude, angular frequency and phase of the object light respectively; a isR,ωR,Amplitude, angular frequency and phase of the reference light, respectively;
an ideal noise-free hologram s generated by the interference of object light and reference light is represented as:
in the formula, ωHFor heterodyne angular frequency, fHFor the heterodyne frequencies of two AOMs, the relationship is:
ωH＝ωO-ωR＝2πfH；
including random noiseThe total signal of the multi-frame phase-shift hologram is:
thereby obtaining a plurality of frames of phase-shifted holograms stotal(t (N)), where N is each frame number, t (N) is the sampling time corresponding to the nth frame number, and N is 1,2total，NtotalThe total number of frames for the obtained hologram.
3. The method according to claim 1 or 2, wherein the performing time-domain spectrum transformation on the signal of each pixel point in the multiple frames of phase-shift holograms and extracting the amplitude and phase of the spectral value at the heterodyne frequency respectively comprises:
and respectively carrying out time domain spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram by using Fast Fourier Transform (FFT) to obtain a time domain spectrum S (omega):
<mrow> <mi>S</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>N</mi> <mrow> <mi>t</mi> <mi>o</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mrow> <mi>t</mi> <mi>o</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> </munderover> <msub> <mi>S</mi> <mrow> <mi>t</mi> <mi>o</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> <mi>&omega;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mi>t</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </msup> <mo>;</mo> </mrow>
in the formula, ω represents the heterodyne angular frequency, stotalFor multi-frame phase shift hologram total signal, N is each frame number, t (N) is sampling time corresponding to nth frame number, NtotalTotal number of frames for the obtained hologram;
extracting a time domain frequency spectrum S (omega) at a heterodyne angular frequency point omegaHProcessing value S (omega)H)：
Wherein σ is a standard deviation;
thereby obtaining the amplitude of the spectral values of the time-domain spectrum S (omega) at the heterodyne frequenciesAnd phase
4. The method of claim 3, wherein extracting a target amplitude and a target phase from the amplitude and the phase of the spectral value at the heterodyne frequency to achieve holographic reconstruction and obtain complete information of a target comprises:
amplitude of vibrationInIs constant, go on toAfter normalization, the normalized amplitude a of the target is obtainednorm：
<mrow> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mn>2</mn> </mfrac> </mrow> </msup> <msub> <mi>a</mi> <mi>R</mi> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>-</mo> <mi>min</mi> <mrow> <mo>(</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mn>2</mn> </mfrac> </mrow> </msup> <msub> <mi>a</mi> <mi>R</mi> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>max</mi> <mrow> <mo>(</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mn>2</mn> </mfrac> </mrow> </msup> <msub> <mi>a</mi> <mi>R</mi> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>min</mi> <mrow> <mo>(</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mn>2</mn> </mfrac> </mrow> </msup> <msub> <mi>a</mi> <mi>R</mi> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>;</mo> </mrow>
In the formula, max and min represent data distributed in two dimensions respectivelyTaking a maximum value and a minimum value;
the position of the reference light path lens is symmetrical to that of the object light path lens, so that the phase of the object light is not included when the target is not includedIs equal toPhase of the targetExpressed as:
and, obtaining target complete information O according to the obtained target amplitude and target phaseresultIt is expressed as:
5. a multi-frame phase-shifting digital holographic device, comprising: presetting a light path, a high frame frequency area array detector and a data processor; wherein:
the preset light path comprises two acousto-optic modulators AOM which are used for respectively modulating object light and reference light to generate low-frequency heterodyne;
the high-frame frequency area array detector detects light in an imaging mirror with a preset light path to obtain a multi-frame phase shift hologram, and transmits the multi-frame phase shift hologram to the data processor;
the data processor respectively carries out time domain frequency spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram, and extracts the amplitude and the phase of the frequency spectrum value at the heterodyne frequency; and extracting a target amplitude and a target phase from the amplitude and the phase of the frequency spectrum value at the heterodyne frequency, thereby realizing holographic reconstruction.
6. The apparatus of claim 5, wherein the predetermined light path comprises:
the device comprises a laser, a half-wave plate, three polarization beam splitting prisms, two reflectors, two acousto-optic modulators AOM, two diaphragms, a spatial filter, two 1/4 wave plates, two micro-objectives, a reference reflector and an imaging mirror; wherein:
laser emitted by the laser is divided into two beams of polarized light of object light and reference light through a half-wave plate and a polarization beam splitter prism 1, wherein the object light is polarized light in a p direction, and the reference light is polarized light in an s direction;
the object light passes through the reflector 1, the-1 level light and the 0 level light emitted after entering the acousto-optic modulator AOM 1 are shielded by the diaphragm 1, the emitted +1 diffraction light enters the spatial filter through the polarization beam splitter prism 2, and the filtered light beam sequentially passes through the polarization beam splitter prism 3, the 1/4 wave plate 1 and the microobjective 1 and then irradiates on a target; reflected light carrying target information sequentially passes through a microscope objective 1 and an 1/4 wave plate 1 and then is changed into s-direction polarized light, and the s-direction polarized light passes through a polarization beam splitter prism 3 and a polarizing film arranged at an angle of 45 degrees and then is emitted into an imaging mirror;
the-1 level light and the 0 level light emitted after the reference light enters the AOM 2 are shielded by the diaphragm 2, the +1 level diffracted light emitted enters the spatial filter after passing through the reflector 2 and the polarization beam splitter prism 2, and the filtered light beam sequentially passes through the polarization beam splitter prism 3, the 1/4 wave plate 2 and the microscope objective lens 2 and then irradiates the reference reflector; the reflected light is changed into p-direction polarized light after sequentially passing through the microscope objective lens 2 and the 1/4 wave plate 2, and then passes through the polarization beam splitter prism 3 and the polarizing plate arranged at an angle of 45 degrees and then is emitted into the imaging lens.
7. The apparatus of claim 5, wherein the predetermined light path comprises:
the device comprises a laser, a half-wave plate, three polarization beam splitting prisms, two reflectors, two acousto-optic modulators AOM, two diaphragms, a spatial filter, a beam splitting prism, two 1/4 wave plates, a microscope objective, a reference reflector and an imaging mirror; wherein:
laser emitted by the laser is divided into two beams of polarized light of object light and reference light through a half-wave plate and a polarization beam splitter prism 1, wherein the object light is polarized light in a p direction, and the reference light is polarized light in an s direction;
the object light passes through the reflector 1, the-1 level light and the 0 level light emitted after entering the acousto-optic modulator AOM 1 are shielded by the diaphragm 1, the emitted +1 diffraction light enters the spatial filter through the polarization beam splitter prism 2, and the filtered light beam sequentially passes through the beam splitter prism, the microscope objective, the polarization beam splitter prism 3 and the 1/4 wave plate 1 and then irradiates on a target; the reflected light carrying the target information is changed into s-direction polarized light after passing through 1/4 wave plate 1, and then is transmitted into the imaging lens after sequentially passing through the polarization beam splitter prism 3, the microscope objective, the beam splitter prism and the polarizing plate arranged at an angle of 45 degrees;
the-1 level light and the 0 level light emitted after the reference light enters the AOM 2 are shielded by the diaphragm 2, the +1 level diffracted light emitted enters the spatial filter after passing through the reflector 2 and the polarization beam splitter prism 2, and the filtered light beam sequentially passes through the beam splitter prism, the microscope objective, the polarization beam splitter prism 3 and the 1/4 wave plate 2 and then irradiates the reference reflector; the reflected light is changed into p-direction polarized light after passing through 1/4 wave plate 2, and then passes through polarization beam splitter prism 3, microscope objective, beam splitter prism and polarizing plate placed at 45 degree angle in turn to be injected into the imaging lens.
8. The apparatus of claim 5, wherein the predetermined light path comprises:
the device comprises a laser, two half-wave plates, a polarization beam splitting prism, two reflectors, two acousto-optic modulators AOM, two diaphragms, two spatial filters, a beam combining prism and an imaging mirror; wherein:
laser emitted by the laser is divided into two beams of polarized light of object light and reference light through a half-wave plate 1 and a polarization beam splitter prism, wherein the object light is polarized light in a p direction, and the reference light is polarized light in an s direction;
the object light sequentially passes through a half-wave plate 2 and a reflector 1, emergent-1-level light and 0-level light are shielded by a diaphragm 1 after entering an acousto-optic modulator AOM 1, emergent +1 diffracted light enters a spatial filter 1, and filtered light beams sequentially pass through a beam combining prism and a microobjective and then irradiate on a target; reflected light carrying target information sequentially passes through the microscope objective and the beam combining prism and then is incident into the imaging lens;
the-1 level light and the 0 level light emitted after the reference light enters the AOM 2 are shielded by the diaphragm 2, the +1 level diffracted light emitted enters the spatial filter 2 after passing through the reflector 2, and the filtered light beam enters the imaging mirror after passing through the beam-combining prism.
9. The apparatus of claim 5,
the obtaining a multi-frame phase-shift hologram includes:
obtaining object light U reaching high frame frequency area array detectorOAnd a reference light UR：
Wherein, t is a time,aO,ωO,the amplitude, angular frequency and phase of the object light respectively; a isR,ωR,Amplitude, angular frequency and phase of the reference light, respectively;
an ideal noise-free hologram s generated by the interference of object light and reference light is represented as:
in the formula, ωHFor heterodyne angular frequency, fHFor the heterodyne frequencies of two AOMs, the relationship is:
ωH＝ωO-ωR＝2πfH；
including random noiseThe total signal of the multi-frame phase-shift hologram is:
thereby obtaining a plurality of frames of phase-shifted holograms stotal(t (N)), where N is each frame number, t (N) is the sampling time corresponding to the nth frame number, and N is 1,2total，NtotalTotal number of frames for the obtained hologram;
the data processor respectively performs time domain spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram, and extracts the amplitude and the phase of the spectrum value at the heterodyne frequency, including:
and respectively carrying out time domain spectrum transformation on the signal of each pixel point in the multi-frame phase shift hologram by using Fast Fourier Transform (FFT) to obtain a time domain spectrum S (omega):
<mrow> <mi>S</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>N</mi> <mrow> <mi>t</mi> <mi>o</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> </mfrac> <munderover> <mo>&Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mrow> <mi>t</mi> <mi>o</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> </munderover> <msub> <mi>S</mi> <mrow> <mi>t</mi> <mi>o</mi> <mi>t</mi> <mi>a</mi> <mi>l</mi> </mrow> </msub> <mi>&omega;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> <mo>)</mo> </mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mi>t</mi> <mo>(</mo> <mi>n</mi> <mo>)</mo> <mo>)</mo> </mrow> </mrow> </msup> <mo>;</mo> </mrow>
in the formula, ω represents the heterodyne angular frequency, stotal(t (N)) is multi-frame phase shift hologram, N is each frame number, t (N) is sampling time corresponding to nth frame number, NtotalTotal number of frames for the obtained hologram;
extracting a time domain frequency spectrum S (omega) at a heterodyne angular frequency point omegaHProcessing value S (omega)H)：
Wherein σ is a standard deviation;
thereby obtaining the amplitude of the spectral values of the time-domain spectrum S (omega) at the heterodyne frequenciesAnd phase
10. The apparatus of claim 9, wherein extracting a target amplitude and a target phase from the amplitude and the phase of the spectral value at the heterodyne frequency to achieve holographic reconstruction and obtain complete information of a target comprises:
amplitude of vibrationInAs a constant, after normalization processing, the normalized amplitude a of the target is obtainednorm：
<mrow> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mi>o</mi> <mi>r</mi> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mn>2</mn> </mfrac> </mrow> </msup> <msub> <mi>a</mi> <mi>R</mi> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>-</mo> <mi>min</mi> <mrow> <mo>(</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mn>2</mn> </mfrac> </mrow> </msup> <msub> <mi>a</mi> <mi>R</mi> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mi>max</mi> <mrow> <mo>(</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mn>2</mn> </mfrac> </mrow> </msup> <msub> <mi>a</mi> <mi>R</mi> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mi>min</mi> <mrow> <mo>(</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mfrac> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mn>2</mn> </mfrac> </mrow> </msup> <msub> <mi>a</mi> <mi>R</mi> </msub> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>;</mo> </mrow>
In the formula, max and min represent data distributed in two dimensions respectivelyTaking a maximum value and a minimum value;
the position of the reference light path lens is symmetrical to that of the object light path lens, so that the phase of the object light is not included when the target is not includedIs equal toPhase of the targetExpressed as:
obtaining target complete information O according to the obtained target amplitude and target phaseresultIt is expressed as:
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| CN105204310A (en) * | 2015-10-19 | 2015-12-30 | 中国科学院上海光学精密机械研究所 | Complex amplitude object reconstruction device based on optical scanning holographic technique |
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| CN102920438A (en) * | 2012-10-30 | 2013-02-13 | 电子科技大学 | High-resolution optical scanning holographic slice imaging method based on variable pupils |
| CN105204310A (en) * | 2015-10-19 | 2015-12-30 | 中国科学院上海光学精密机械研究所 | Complex amplitude object reconstruction device based on optical scanning holographic technique |
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