CN111474188B - Single exposure wavefront reconstruction and phase imaging device and method based on dynamic modulation - Google Patents
Single exposure wavefront reconstruction and phase imaging device and method based on dynamic modulation Download PDFInfo
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Abstract
A single exposure wave front reconstruction and phase imaging device and method based on dynamic modulation are disclosed, wherein after a light beam to be detected passes through a specially designed wave front modulator, diffraction spots of the light beam to be detected have separability, meanwhile, the frequency spectrum of the wave front modulator also has separability, equivalently, the light beam to be detected passes through a plurality of different wave front modulators to obtain a plurality of diffraction spots, and by utilizing a matching iterative algorithm, complex amplitude distribution of the wave front to be detected can be rapidly reconstructed, and finally wave front reconstruction and phase imaging under single exposure are realized.
Description
Technical Field
The invention relates to wavefront phase recovery, in particular to a single-exposure wavefront reconstruction and phase imaging device and method based on dynamic modulation.
Background
The phase information measurement has an extremely important role in the fields of Imaging, measurement and the like, but the phase distribution cannot be directly measured at present, so that the measurement can be realized only by an indirect measurement mode, and the recorded diffraction spot intensity information and Coherent Diffraction Imaging (CDI) (j.m. rodenburg, "ptychographing and correlated diffraction Imaging Methods," advanced in Imaging and Electron Physics, Hawkes, ed. (essence, 2008), pp.87-184.) can be used for obtaining lost phase information through iterative calculation and reconstruction, so as to realize phase recovery of diffraction spots, and further obtain complete complex amplitude distribution of wave front by combining the recorded intensity information, so as to realize wave front reconstruction, and further obtain complex amplitude distribution of any plane by using diffraction theory calculation, so as to realize phase Imaging of a specific plane. The method has simple structure, can theoretically reach diffraction limit resolution as a non-lens imaging technology, particularly in the field of X-ray and electron beam imaging, is extremely restricted in resolution of the traditional direct imaging method because a high-quality imaging lens is difficult to process, is an extremely important imaging technology because a CDI technology does not need the high-quality lens, and has wide application in other wave bands. However, convergence is a key problem faced by CDI algorithm, and poor convergence directly causes imaging failure, so additional constraint condition needs to be added for achieving fast convergence, and the ptychographic algorithm (h.m.l.fault kner and j.m.rodenburg, "movableAperture less Transmission Microscopy: ANovel Phase reeval Algorithm," Physical Review Letters 93,023903 (2004)) records a series of diffraction spots by translating a sample in a plane perpendicular to an optical axis, well solves convergence problem by utilizing redundant information introduced in two adjacent translations, has very high convergence speed and anti-interference capability, and is verified and widely applied in the fields of visible light, X-ray and electron beam. However, in many cases, the application conditions determine that multiple scans cannot be performed, such as online measurement of pulsed laser or imaging of biological samples vulnerable to X-ray damage, and the multiple scanning mode is not applicable, so that single exposure measurement still has a broad demand base, and there is a strong need to develop a single exposure phase recovery device and algorithm with fast convergence capability.
Disclosure of Invention
Aiming at the defects of the prior art in the field of single-exposure wavefront reconstruction and phase imaging, the invention provides a simple and effective single-exposure wavefront reconstruction device and algorithm, a specially designed wavefront modulator is utilized to realize phase recovery under single exposure, the modulator can be equivalent to a plurality of different sub-wavefront modulators through spectral decomposition, meanwhile, sub-diffraction spots corresponding to the sub-wavefront modulators can also be effectively divided, the dynamic modulation effect under single exposure is realized, and the constraint force is enhanced by increasing the modulation times, so that the rapid wavefront reconstruction under single exposure is realized.
The technical solution of the invention is as follows:
a single-exposure wavefront reconstruction and phase imaging apparatus based on dynamic modulation, characterized in that it comprises: the device comprises a light beam to be detected, a wavefront modulator and a light spot detector, wherein the light beam to be detected is coherent light or partially coherent light; the wave front modulator is an amplitude type, phase type or amplitude phase type wave front modulation plate, the facula detector is positioned on a Fraunhofer diffraction surface of the wave front modulator, and the wave front modulator has the following characteristics: according to the distribution of the spectrum intensity of the wave front modulator, the spectrum can be divided into a plurality of sub-spectrums which are close in energy and relatively independent in space, each sub-spectrum has certain discontinuity in space, the intensity distribution among the sub-spectrums is different under the condition that the space translation among the sub-spectrums is not considered, after each sub-spectrum is independently cut out, inverse Fourier transform can be carried out to obtain a plurality of different wave front modulators, namely the wave front modulator is provided with spectrum space divisibility, and a plurality of sub-wave front modulators with different complex amplitude transmittances can be decomposed through division in the spectrum space.
The wave-front modulator is an amplitude type, phase type or amplitude phase type wave-front modulation plate obtained based on a binary optical design theory. The single-exposure wavefront reconstruction and phase imaging method based on dynamic modulation is characterized by comprising the following steps of:
1) the transmittance function H of the wave front modulator is subjected to Fourier transform to obtain
FFT { } denotes the Fourier transform, according to
Dividing n sub-spectra according to distribution characteristics
1,2, … n, inverse fourier transform yielding n sub-wavefront modulators
FFT-1{ } denotes an inverse fourier transform.
2) After the light beam to be measured passes through the wavefront modulator, a diffraction light spot I is recorded by the light spot detector, and the light spot detector is positioned on a Fraunhofer diffraction surface, so that I is distributed and summed
The intensity distribution trends are similar according to
The splitting scheme of (1) equally splitting the diffraction spot I to obtain n sub-diffraction spots Ii，i＝1,2,…n。
3) The initial guess of the distribution of the light beam to be measured is G0Thereafter, the kth iteration process is described as the following process, where the subscripts denote the number of iterations:
computing the first sub-wavefront modulator H1(i ═ 1) corresponding diffraction spots were obtained
Representing the diffraction process from the wavefront modulator to the spot detector;
② to E obtained by calculation1Performing amplitude update to obtain
I denotes amplitude taking, inverse propagation
To the plane of the wave front modulator, and calculating according to the following formula to obtain updated illumination light
Wherein represents a conjugation, α β is a self-selected constant,
indicating reverse propagation.
③ will
As the 2 nd sub-wavefront modulator H2Guessing by using the sub-diffraction spots I2(corresponding to i-2) repeating the steps of (i) - (c) and obtaining the updated
Fourthly, will
Guessing and repeating the first step and the third step as the illuminating light of the next sub wavefront modulator until n self-diffraction light spots are obtained and obtaining updated illuminating light
Calculating the diffraction spot error without considering the division
Wherein M is the number of pixels of the calculation matrix.
Sixthly, the
And (3) as an initial guess of the (k + 1) th iteration, repeating the steps (i) - (v) until the RMS has small change, completing the iteration process to obtain the complex amplitude distribution G of the light beam to be detected, and transmitting the complex amplitude distribution G to a required plane to complete wavefront reconstruction or realize the phase imaging process.
The invention has the technical effects that:
1) the device has simple structure, and only one wave front modulator and one light spot detector are arranged in the core part.
2) Although only one wave front modulator is provided, the wave front modulator can be decomposed into a plurality of different wave front modulators through specific optical path arrangement and algorithm, so that only one diffraction spot is recorded, but the wave front modulators have higher convergence speed due to the strong constraint action of a plurality of equivalent wave front modulators, and single exposure measurement can be realized.
3) By utilizing the design idea of binary optics, the wavefront modulator described by the invention is easy to design and process, has wide flexibility and can be designed into a pure amplitude type, a pure phase type or an amplitude phase type.
3) As one of CDI algorithms, the diffraction limit resolution can be theoretically achieved, and wavefront reconstruction and phase reconstruction in visible light, X-rays, electron beams and other wavebands and fields can be extended.
Drawings
Fig. 1 is a schematic structural diagram of a single-exposure wavefront reconstruction and phase imaging device based on dynamic modulation.
Fig. 2 is a schematic diagram of the structural distribution and the spectral distribution of the wavefront modulator in embodiment 1.
Fig. 3 is a schematic diagram of the structural distribution and the spectral distribution of the wavefront modulator according to embodiment 2.
Fig. 4 is a schematic diagram of the structural distribution and the spectral distribution of the wavefront modulator according to embodiment 3.
Fig. 5 is a schematic diagram of the structural distribution and the spectral distribution of the wavefront modulator according to embodiment 4.
Fig. 6 is a schematic diagram of the structural distribution and the spectral distribution of the wavefront modulator according to embodiment 5.
Fig. 7 is a schematic diagram of the structural distribution and the spectral distribution of the wavefront modulator according to embodiment 6.
Fig. 8 is a schematic diagram of the structural distribution and the spectral distribution of the wavefront modulator according to embodiment 7.
Fig. 9 is a schematic diagram of the structural distribution and the spectral distribution of the wavefront modulator according to embodiment 8.
Fig. 10 is a schematic diagram of the structural distribution and the spectral distribution of the wavefront modulator according to embodiment 9.
Fig. 11 is a schematic diagram of the structural distribution and the spectral distribution of the wavefront modulator according to embodiment 10.
Fig. 12 is a schematic diagram of the structural distribution and the spectral distribution of the wavefront modulator of embodiment 11.
Fig. 13 is a schematic diagram of the structural distribution and the spectral distribution of the wavefront modulator according to embodiment 12.
Fig. 14 is a schematic diagram of the structural distribution, the spectral distribution and the distribution of corresponding diffraction spots of the wavefront modulator of the embodiment 13.
Fig. 15 is a schematic diagram of a single-exposure wavefront reconstruction optical path corresponding to embodiment 13.
Fig. 16 is a schematic diagram of a sample phase imaging optical path.
FIG. 17 is a schematic diagram of a single-exposure wavefront reconstruction path that can be used in the short wavelength band of X-rays and the like.
In the figure: 1-light beam to be measured, 2-wavefront modulator, 3-light spot detector, 4-convergent lens, 5-incident parallel light and 6-sample to be measured.
Detailed Description
Example 1
One design of the wavefront modulator, as shown in fig. 2, is a phase-only binary wavefront modulator, with an amplitude transmittance of 1, a phase retardation of 0 or pi, and a minimum cell size of 1 micrometer × 1 micrometer, and the spectral distribution has a divisibility and can be divided into a plurality of different sub-spectra.
Example 2
One design of the wavefront modulator, as shown in fig. 3, is a phase-only binary wavefront modulator, with an amplitude transmittance of 1, a phase retardation of 0 or pi/4, and a minimum cell size of 5 micrometers × 5 micrometers, and its spectral distribution has a divisibility and can be divided into a plurality of different sub-spectra.
Example 3
One design of the wavefront modulator, as shown in fig. 4, is an amplitude-phase binary wavefront modulator, the amplitude transmittance is 1 or 0, the phase retardation is 0 or pi, the minimum element size of the amplitude and the phase is 2 micrometers × 2 micrometers, and the spectral distribution has separability and can be divided into a plurality of different sub-spectra.
Example 4
One design of the wavefront modulator, as shown in fig. 5, is an amplitude-phase binary wavefront modulator, the amplitude transmittance is 1 or 0, the phase retardation is 0 or pi/3, the minimum element size of the amplitude and the phase is 10 micrometers × 10 micrometers, the spectral distribution has separability, and the wavefront modulator can be separated into a plurality of different sub-spectrums.
Example 5
One design of the wavefront modulator, as shown in fig. 6, is an amplitude-phase binary wavefront modulator, the amplitude transmittance is 1 or 0, the phase retardation is 0 or pi/10, the minimum element size of the amplitude and the phase is 20 micrometers × 20 micrometers, the spectral distribution has separability, and the wavefront modulator can be separated into a plurality of different sub-spectrums.
Example 6
One design of the wavefront modulator, as shown in fig. 7, is an amplitude-phase binary wavefront modulator, the amplitude transmittance is 1 or 0.1, the phase retardation is 0 or pi/4, the phase and amplitude distribution has a certain correspondence, the minimum element size of the amplitude and the phase is 0.1 micrometer × 0.1 micrometer, the spectral distribution has divisibility, and the amplitude and the phase can be divided into a plurality of different sub-spectra.
Example 7
One design of the wavefront modulator, as shown in fig. 8, is an amplitude binary wavefront modulator, the amplitude transmittance is 1 or 0.5, the phase delay amount is constant, the minimum element size of the amplitude distribution is 0.1 micrometer × 0.1 micrometer, and the spectral distribution has separability and can be divided into a plurality of different sub-spectrums.
Example 8
One design of the wavefront modulator, as shown in fig. 9, is a phase binary wavefront modulator, where the amplitude transmittance is constant, the phase distribution has a certain randomness, the minimum element size is 6 micrometers × 12 micrometers, the phase delay is 0 or pi, the spectral distribution has divisibility, and can be divided into a plurality of different sub-spectra.
Example 9
One design of the wavefront modulator, as shown in fig. 10, is an amplitude binary wavefront modulator, the amplitude transmittance is 1 or 0, the phase distribution is constant, the minimum element size of the amplitude distribution is 3 micrometers × 3 micrometers, and the distribution is optimized by an algorithm so that the spectrum has more obvious separability and can be divided into a plurality of different sub-spectra.
Example 10
One design of the wavefront modulator is shown in fig. 11, which is a phase binary wavefront modulator, the amplitude transmittance is constant, the phase distribution is 0 or pi, the minimum element size of the phase distribution is 60 micrometers × 60 micrometers, and the distribution is optimized by an algorithm so that the spectrum has more obvious separability and can be divided into a plurality of different sub-spectrums.
Example 11
One design of the wavefront modulator, as shown in fig. 12, is an amplitude binary wavefront modulator, the amplitude transmittance is randomly 1 or 0, the phase distribution is constant, the minimum element size of the amplitude distribution is 7 micrometers × 7 micrometers, and the spectrum has separability and can be divided into a plurality of different sub-spectra.
Example 12
One design of the wavefront modulator, as shown in fig. 13, is a phase binary wavefront modulator, the amplitude transmittance is 1, the phase distribution is 0 or pi, the minimum element size of the phase distribution is 9 micrometers × 9 micrometers, and the spectrum has separability and can be divided into a plurality of different sub-spectra.
Example 13
One design of the wavefront modulator, as shown in fig. 14, is an amplitude binary wavefront modulator, the amplitude transmittance is 1 or 0, the phase distribution is constant, the minimum element size of the amplitude distribution is 3.5 micrometers × 3.5 micrometers, and the spectral distribution has separability and can be divided into a plurality of different sub-spectra.
The wavefront modulator shown in fig. 14 is placed in the optical path shown in fig. 15, the incident parallel light 5 is converged by the converging lens 4, and then passes through the wavefront modulator 2 to reach the spot detector 3, wherein the spot detector 3 is placed on the focal plane of the converging lens 4, that is, the spot detector is equivalently located on the fraunhofer diffraction surface of the wavefront modulator 2, and the recorded diffraction spots and the spectral distribution of the wavefront modulator have a certain correspondence, so that the light can be divided. The incident parallel light 5 is coherent parallel light with the wavelength of 632.8nm, the focal length of the converging lens 4 is 100 mm, the diameter of the light beam to be measured on the wavefront modulator 2 is about 2 mm, and the pixel size of the light spot detector is 9 microns multiplied by 9 microns. In order to overcome the defect that the dynamic range of the spot detector 3 is limited, the exposure time is adjusted to partially saturate the recorded diffraction spots, the frequency spectrum of the wavefront modulator 2 and the diffraction spots recorded by the spot detector 3 are divided as shown in fig. 14 to obtain 9 sub-frequency spectrums with the labels of 1-9 and 9 sub-diffraction spots, the 9 sub-frequency spectrums are taken out and subjected to inverse fourier transform to obtain 9 sub-wavefront modulators corresponding to the 9 sub-diffraction spots, and the specific iteration process is as follows:
1) the transmittance function H of the wave front modulator is subjected to Fourier transform to obtain
FFT { } denotes the Fourier transform, according to
Dividing n sub-spectra according to distribution characteristics
i is 1,2, … 9, and 9 sub-wavefront modulators are obtained by inverse Fourier transform
FFT-1{ } denotes an inverse fourier transform.
2) After the light beam to be measured passes through the wavefront modulator, a diffraction light spot I is recorded by the light spot detector, and the light spot detector is positioned on a Fraunhofer diffraction surface, so that I is distributed and summed
The intensity distribution trends are similar according to
The same division is carried out on the diffraction spots I to obtain 9 sub-diffraction spots Ii，i＝1,2,…9。
3) The initial guess of the distribution of the light beam to be measured is G0Thereafter, the kth iteration process is described as the following process, where the subscripts denote the number of iterations:
computing the first sub-wavefront modulator H1(i ═ 1) corresponding diffraction spots were obtained
Representing the diffraction process from the wavefront modulator to the spot detector;
② to E obtained by calculation1Performing amplitude update to obtain
Meanwhile, the light spot saturation area is not updated, | | represents that the amplitude is taken, and the reverse propagation is carried out
To the plane of the wave front modulator, and calculating according to the following formula to obtain updated illumination light
Wherein represents a conjugation, α β is a self-selected constant,
indicating reverse propagation.
③ will
As the 2 nd sub-wavefront modulator H2Guessing by using the sub-diffraction spots I2(corresponding to i-2) repeating the steps of (i) - (c) and obtaining the updated
Fourthly, will
Guessing and repeating the first step and the third step as the next sub wavefront modulator until 9 self-diffraction light spots and obtaining updated illuminating light
Calculating without considering divisionDiffraction spot error under the circumstances
Wherein M is the number of pixels of the calculation matrix.
Sixthly, the
And (3) as an initial guess of the (k + 1) th iteration, repeating the steps (i) - (v) until the RMS has small change, completing the iteration process to obtain the complex amplitude distribution G of the light beam to be detected, and transmitting the complex amplitude distribution G to a required plane to complete wavefront reconstruction or realize the phase imaging process.
Example 14
A typical measurement optical path is shown in fig. 16, an incident parallel light 5 is converged by a converging lens 4, and then sequentially passes through a sample 6 to be measured and a wavefront modulator 2, and then reaches a light spot detector 3, wherein the light spot detector 3 is placed on a focal plane of the converging lens 4, that is, the light spot detector is equivalently located on a fraunhofer diffraction surface of the wavefront modulator 2, and a recorded diffraction light spot and a spectral distribution of the wavefront modulator have a certain correspondence, so that the light can be divided. After the complex amplitude distribution of the illumination light of the wavefront modulator 2 is obtained by iterative computation reconstruction, the illumination light reversely propagates to the plane where the sample 6 to be measured is located, the wavefront distribution of the sample 6 to be measured in the presence and absence is respectively measured, and the difference between the two is the complex amplitude transmittance of the sample 6 to be measured.
Example 15
A typical measurement optical path is shown in fig. 17, a light beam 1 to be measured is emergent light of collimated X-rays passing through a sample 6 to be measured, after passing through a wavefront modulator 2, a light spot detector 3 located on a fraunhofer diffraction surface is used to record corresponding diffraction light spots, complex amplitude distribution of the light beam 1 to be measured can be obtained through iterative calculation, and the complex amplitude distribution reversely propagates to a plane where the sample 6 to be measured is located, so that an emergent wave function of the sample 6 to be measured is obtained.
Claims (3)
1. A single-exposure wavefront reconstruction and phase imaging apparatus based on dynamic modulation, comprising: the device comprises a light beam (1) to be detected, a wavefront modulator (2) and a light spot detector (3), wherein the light beam (1) to be detected is coherent light or partially coherent light; the wavefront modulator (2) is an amplitude type, phase type or amplitude phase type wavefront modulation plate, the facula detector (3) is positioned on a Fraunhofer diffraction surface of the wavefront modulator (2), and the wavefront modulator (2) has the following characteristics: according to the distribution of the spectrum intensity of the wave-front modulator (2), the spectrum can be divided into a plurality of sub-spectrums which are close in energy and relatively independent in space, each sub-spectrum has certain discontinuity in space, the intensity distribution of each sub-spectrum is different under the condition that the space translation between each sub-spectrum is not considered, each sub-spectrum is independently cut out, then inverse Fourier transform is carried out, and a plurality of different wave-front modulators can be obtained, namely the wave-front modulator (2) has spectrum space divisibility, and a plurality of sub-wave-front modulators with different complex amplitude transmittances can be decomposed through division in the spectrum space.
2. A single exposure wavefront reconstruction and phase imaging apparatus based on dynamic modulation according to claim 1, characterized in that the wavefront modulator (2) is an amplitude-, phase-or amplitude-phase wavefront modulation plate based on binary optical design theory.
3. A method for a single exposure wavefront reconstruction and phase imaging apparatus based on dynamic modulation as claimed in claim 1, characterized in that the method comprises the steps of:
1) fourier transform is carried out on the transmittance function H of the wave front modulator (2) to obtain
FFT { } denotes the Fourier transform, according to
Dividing n sub-spectra according to distribution characteristics
1,2, … n, inverse fourier transform yielding n sub-wavefront modulators
FFT-1{ } denotes an inverse fourier transform;
2) after the light beam (1) to be detected passes through the wavefront modulator (2), a diffraction light spot I is recorded through the light spot detector (3), and the light spot detector (3) is located on a Fraunhofer diffraction surface, so that I is distributed and summed
The intensity distribution trends are similar according to
The splitting scheme of (1) equally splitting the diffraction spot I to obtain n sub-diffraction spots Ii，i＝1,2,…n；
3) The initial guess of the distribution of the light beam (1) to be measured is G0Thereafter, the kth iteration process is described as the following process, where the subscripts denote the number of iterations:
computing the first sub-wavefront modulator H1I is 1, the corresponding diffraction spot is obtained
Represents the diffraction process from the wavefront modulator (2) to the spot detector (3);
② to E obtained by calculation1Performing amplitude update to obtain
I denotes amplitude taking, inverse propagation
To the wavefront modulator (2)Plane and calculating to obtain updated illumination light according to the following formula
Wherein represents a conjugation, α β is a self-selected constant,
representing reverse propagation;
③ will
As the 2 nd sub-wavefront modulator H2Guessing by using the sub-diffraction spots I2Repeating the steps of the first step and the second step corresponding to the condition that the i is equal to 2, and obtaining the updated product
Fourthly, will
Guessing and repeating the steps of the first step and the third step as the illumination light of the next sub wavefront modulator until n sub diffraction light spots are obtained, and obtaining updated illumination light
Calculating the diffraction spot error without considering the division
Wherein M is the number of pixels of the calculation matrix;
sixthly, the
As an initial guess of the (k + 1) th iteration, repeating the steps (i) - (v) until the RMS changes little, completing the iteration process to obtain the complex amplitude distribution G of the light beam (1) to be detected, transmitting the complex amplitude distribution G to a required plane, and completing wavefront reconstruction or realizing phase imagingAnd (6) carrying out the process.
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