CN111948296A - Method for improving axial resolution of photoacoustic microscopic imaging system based on axial modulation - Google Patents

Method for improving axial resolution of photoacoustic microscopic imaging system based on axial modulation Download PDF

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CN111948296A
CN111948296A CN202010699786.6A CN202010699786A CN111948296A CN 111948296 A CN111948296 A CN 111948296A CN 202010699786 A CN202010699786 A CN 202010699786A CN 111948296 A CN111948296 A CN 111948296A
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宋贤林
杨孝全
骆清铭
王玉皞
魏剑霜
宋玲芳
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Abstract

A method for improving axial resolution of a photoacoustic microscopic imaging system based on axial modulation comprises the steps of firstly irradiating a sample with axial structured light with the spatial frequency of k to modulate a photoacoustic signal, wherein frequency spectrum information of the photoacoustic signal received by an ultrasonic transducer with the narrow bandwidth comprises three parts of information of fundamental frequency, sum frequency and difference frequency. And acquiring photoacoustic signals of three phases excited by axial structure light of the space frequency, separating the three parts of spectrum information by a three-phase separation method, and then shifting the information to shift the dislocated high-frequency information to a correct position. And (3) gradually increasing the axial structure light space frequency to obtain photoacoustic signals of different frequency bands, and performing inverse Fourier transform to obtain a high-resolution image. The highest axial resolution achievable is determined by the axial structured light spatial frequency that can be produced. The method can improve the axial resolution to the optical diffraction limit, realizes the isotropy of the three-dimensional spatial resolution, and enables the obtained photoacoustic image to reflect the real structure of the biological tissue more truly.

Description

Method for improving axial resolution of photoacoustic microscopic imaging system based on axial modulation
Technical Field
The invention relates to the field of photoacoustic microscopic imaging, in particular to a method for improving the axial resolution of a photoacoustic microscopic imaging system based on axial modulation.
Background
In photoacoustic microscopy, since imaging is usually a point-scan method, the lateral resolution is determined by the size of the optical focus together with the size of the acoustic focus. However, in the axial direction of photoacoustic microscopy, regardless of the size of the optical focus, the spatial resolution is determined by the bandwidth of the ultrasound transducer for detection. This is because although the size of the optical focus can be reduced by increasing the numerical aperture of the light focusing in the axial direction, a time-resolved method is used instead of a point detection method when detecting the ultrasonic signal, so that the bandwidth of the ultrasonic transducer determines the width of the axial spatial unit impulse response, i.e., the axial resolution. The problem is particularly prominent in an optical resolution photoacoustic microscopic imaging system, in the optical resolution photoacoustic microscopic imaging, the transverse resolution can often reach the resolution of an optical diffraction limit (hundreds of nanometers), but the axial resolution is difficult to be better than 10 microns, so that the result of three-dimensional imaging is often anisotropic and cannot reflect the real structure of biological tissues.
In order to improve the axial resolution of the system, in recent years, research groups of all countries of the world respectively perform some research on two aspects of ultrasonic detection and optical laser. There are researchers in acoustically resolved photoacoustic microscopy systems in off-axis detection mode that promote spatial isotropy while promoting lateral and axial resolution by using two ultrasonic transducers placed orthogonally. The axial resolution is improved to 7.6 microns using a higher bandwidth piezoelectric ultrasound probe in conjunction with wiener deconvolution. Researchers have also used the Lucy-Richardson deconvolution method to improve the spatial resolution of the ultrasound propagation direction. Reducing the speed of sound with silicone oil instead of water as the coupling medium raises the axial resolution to 5.8 microns. However, on one hand, the bandwidth is difficult to continue to increase due to the manufacturing method of the ultrasonic transducer, and on the other hand, the resolution is only improved by the deconvolution method, so that research for improving axial resolution by using an optical method has been carried out in recent years. Compared with a commonly used piezoelectric ultrasonic transducer for ultrasonic detection, the photoacoustic signal is detected in an optical detection mode, which is beneficial to simplifying a system and improving the axial resolution, and typical optical detection devices comprise a micro-ring, a Fabry-Perot sensor and the like. The micro-ring has larger bandwidth and lower noise compared with traditional transducers such as piezoelectric ceramics, so that the axial resolution of the obtained photoacoustic imaging reaches 2.21 microns, the resolution reaches the optical resolution level, the isotropy of the three-dimensional resolution of the micro-ring has important significance for biological research, and the three-dimensional structure can be accurately revealed. Since the micro-ring is unfocused, it is sensitive to sound pressure, but has a low quality of detected images relative to the use of a piezoelectric ultrasound probe. And the micro-ring is not convenient for researchers to realize commercialization. The Fabry-Perot sensor is applied to the detection of photoacoustic signals, and the axial resolution is better than 8 microns. In recent years, studies have been made to improve axial resolution from the viewpoint of photoacoustic signal excitation using an optical method. Researchers utilize the nonlinear effect of optical bleaching to subtract signals excited by two continuous pulses, and the axial resolution of 400 nanometers is realized. The photoacoustic signal is generated using two-photon excitation, and like a two-photon microscope, the ultrasonic signal is generated only in a small area due to the area limitation of two-photon absorption, thereby realizing the photoacoustic axial resolving power of optical resolution. The property that the thermo-ultrasonic conversion efficiency changes with local temperature changes is also used to improve the axial resolution, two photo-acoustic excitations are performed with two laser pulses with a very short time interval (about 100 nanoseconds), and an axial resolution of 2.3 microns is obtained by the difference between the two excitations. However, most methods using optical focusing utilize nonlinear optics to achieve axial optical resolution, require high intensity light focusing (phototoxicity), and the nonlinear absorption photoacoustic signal is relatively weak, so that these methods limit the use of optical resolution photoacoustic microscopy imaging systems.
Aiming at the problem, an axial modulation-based method is provided to greatly improve the axial resolution. Through the modulation of the structural light with the space frequency changing in the axial direction, the frequency spectrum information of the photoacoustic signal gradually falls into the frequency spectrum response range of the ultrasonic transducer, and then the frequency spectrum is restored to the correct position, so that the frequency spectrum response range of the system is widened, and the axial resolution is improved. The method can simultaneously realize the acquisition of the high-frequency photoacoustic frequency spectrum by using the low-frequency ultrasonic probe.
Disclosure of Invention
The invention aims to solve the technical problem of poor axial resolution in a photoacoustic microscopic imaging system in the prior art. The technology is capable of obtaining high-frequency photoacoustic frequency spectrum by using the low-frequency ultrasonic transducer, further improving the axial expansion function and further improving the axial resolution to the optical diffraction limit.
The invention solves the technical problems through the following technical scheme, and an axial modulation technology for improving the axial resolution of a photoacoustic microscopic imaging system comprises the following steps:
s1: the axial structured light with the spatial frequency k illuminates the sample, and due to the moire effect, the axial structured light modulates the photoacoustic signal.
S2: the spectrum information of the photoacoustic signal received by the narrow-bandwidth ultrasonic transducer comprises three parts of information of fundamental frequency DN, sum frequency DP and difference frequency DS, and three phases excited by axial structure light of the space frequency are obtained
Figure BDA0002592595730000031
Figure BDA0002592595730000032
The three parts of spectrum information are separated by a three-phase separation method.
S3: information shift is performed to shift the high frequency information (sum frequency and difference frequency) of the misalignment to the correct position.
S4: and (3) as the cutoff frequency of an object used for exciting the photoacoustic signal is far higher than the bandwidth of the ultrasonic transducer, increasing the light modulation frequency of the structure and repeating the steps until the cutoff frequency of the objective lens.
S5: and finally, combining the obtained photoacoustic signals of different frequency bands in a frequency domain through wiener filtering, and obtaining a high-resolution image after inverse Fourier transform.
The axial structured light in the S1 refers to a light spot whose light intensity changes in cosine in the detection direction of the ultrasonic probe:
Figure BDA0002592595730000033
I0is the average intensity of the cosine-varying axial structured light,
Figure BDA0002592595730000034
initial phase, k, of axially structured light which varies as a cosine0The spatial frequency of the axial cosine structured light, and m is the modulation degree of the structured light. The photoacoustic signal spectrum information obtained by the axial structure light modulation can be represented by the following formula:
Figure BDA0002592595730000041
wherein eta is the conversion efficiency of heat energy,
Figure BDA0002592595730000042
is a Fourier transform of mu (z),
Figure BDA0002592595730000043
for fourier transformation of the acquired photoacoustic signal pa (z),
Figure BDA0002592595730000044
is the spectral response of the entire system. The fundamental frequencies DN, difference frequency DP and sum frequency DS are
Figure BDA0002592595730000045
Figure BDA0002592595730000046
Figure BDA0002592595730000047
Figure BDA0002592595730000048
For the spectrum of photoacoustic signals obtained under uniform light illumination, the other two terms are
Figure BDA0002592595730000049
Respectively shifted to k in the frequency domain0，-k0A signal at a location.
The three phases of axial structured light in S2 preferably have a phase difference of 2 pi/3. The three-phase separation method is that after structured light modulation, the obtained signal contains three parts of frequency spectrum information DN, DP and DS. And high frequency information of the signal is recovered to obtain a high resolution picture. This requires the separation of three parts of the spectral information. Three phases are respectively
Figure BDA00025925957300000410
The three A-line photoacoustic data obtained are PA1(z)、PA2(z)、PA3(z), thus forming a system of linear equations:
Figure BDA00025925957300000411
solving the equation can separate DN, DP and DS:
Figure BDA00025925957300000412
the information shift in S3 means that the separated three parts are separatedThe frequency spectrums DN, DP and DS carry out frequency spectrum frequency shift, and the accuracy of the frequency shift directly influences the accuracy of the reconstructed image. Inaccuracy in the shift of information can distort or artifact the reconstructed image. First through the spatial frequency k of the structured light0The magnitude of the spectral frequency shift is determined. Three parts of frequency spectrum information separated by the three-phase separation method are all in a frequency domain expression form, wherein DN is a fundamental frequency and does not need frequency shift, and DP and DS need frequency shift. k is a radical of0Usually, the frequency shift is not an integer, and in order to ensure the accuracy of the frequency shift, the shift characteristic of the fourier transform is used to perform the precise frequency shift. First, DP and DS are reversely converted into spatial domain expression, and then are multiplied by exp (+/-2 pi k)0r) and finally transformed into the frequency domain, the precise information shift can be completed, namely
CS1(k)＝DN(k)
Figure BDA0002592595730000051
Figure BDA0002592595730000052
Where FFT represents fourier transform and IFFT represents inverse fourier transform.
The step of increasing the spatial frequency of the structured light to the cut-off frequency of the objective lens in S4 means that the bandwidth k of the ultrasonic probe receiving the photoacoustic signal in the photoacoustic microscopy imaging system isusTypically only a few tens of mhz, which is well below the cut-off frequency k of the high numerical aperture objective lens used for exciting the photoacoustic signalsobjective(typically in the kilohertz range) so that the modulation frequency of the axial structured light is not affected by the ultrasound transducer and can far exceed the bandwidth of the ultrasound transducer.
The size of the light modulation frequency of the initially applied structure is set to be smaller than the bandwidth of the ultrasonic transducer, and the modulation frequency is gradually increased to the cut-off frequency of the objective lens. A photoacoustic signal spectrum segment is obtained at each light modulation frequency in accordance with steps S1-S3.
The photoacoustic signals of different frequency bands obtained by the above are combined in the frequency domain by wiener filtering in S5, as shown in the following formula:
Figure BDA0002592595730000061
wherein x represents a conjugate operation,
Figure BDA0002592595730000062
for the representation of the final reconstructed image in the frequency domain, N is the number of a-line data acquired under all types of structured light illumination. w is a small constant, the magnitude of which is typically set empirically to control the noise in the reconstructed image. A (k) is an apodization function for suppressing sidelobes in the reconstructed image due to frequency discontinuities at the edges during image reconstruction.
Figure BDA0002592595730000063
Is the nth order
Figure BDA0002592595730000064
The frequency shift of (2).
The invention has the advantages and beneficial effects that:
the invention realizes that the axial resolution in the photoacoustic microscopic imaging is obviously improved and reaches the optical diffraction limit. Through the axial modulation of the axial structure light, the ultra-high frequency photoacoustic signal frequency spectrum information can be obtained by using the low-frequency ultrasonic transducer, the axial point expansion function of the system is expanded, and the axial resolution is improved. The three-dimensional spatial resolution of the axial modulation is more uniform, and the acquired image can reflect the structural information of the biological tissue more truly. The scheme can also realize the acquisition of the information of the ultra-high frequency photoacoustic signals without craniotomy. Meanwhile, the acquisition of high-frequency information is helpful for the analysis work of the spectrum of the photoacoustic signal.
Drawings
Fig. 1 is a flow chart of a method for improving the axial resolution of a photoacoustic microscopy imaging system based on axial modulation according to the present invention.
FIG. 2 is a schematic diagram of a method for improving the axial resolution of a photoacoustic microscopy imaging system based on axial modulation according to the present invention.
The rectangular block in the figure is the pass frequency range of the system, the size of the structural light modulation frequency applied for the first time is set to be smaller than the bandwidth of the ultrasonic transducer, and the modulation frequency is gradually increased to the cut-off frequency of the objective lens. And acquiring photoacoustic signal spectrum fragments (various line segments in fig. 2) at each light modulation frequency according to a three-phase reconstruction algorithm, and finally fusing the photoacoustic spectrum fragments acquired by reconstruction under the structured light of each spatial frequency to acquire an expanded photoacoustic signal spectrum.
Detailed Description
To facilitate an understanding of the invention, the invention will now be described more fully with reference to the accompanying drawings. Preferred embodiments of the present invention are shown in the drawings. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.
Example 1
The invention provides a method for improving the axial resolution of a photoacoustic microscopic imaging system based on axial modulation, which is implemented as follows in a flow chart shown in figure 1:
photoacoustic imaging utilizes the photoacoustic effect to describe the light absorption distribution. The intensity of the photoacoustic signal is proportional to the amount of light energy absorbed. The photoacoustic imaging system is a linear translation invariant system, and the imaging process can be expressed by the following formula
Figure BDA0002592595730000071
Wherein z represents an axial spatial coordinate, P (z) is the systemDetermines the axial resolution of the system. I (z) is the axial luminous flux distribution, mu (z) is the axial absorption coefficient distribution, eta is the conversion efficiency of the thermal energy, PA (z) is the signal detected by the system through an ultrasonic transducer,
Figure BDA0002592595730000072
representing a convolution operation.
Using a spatial frequency k in the axial direction0The cosine structured light illuminates the sample, and the expression form of the axial cosine structured light is
Figure BDA0002592595730000073
I0Is the average intensity of the light of the cosine structure,
Figure BDA0002592595730000081
is the initial phase, k, of the cosine structured light0The spatial frequency of the cosine structured light, and m is the modulation degree of the structured light. Formula (1) can be written as
Figure BDA0002592595730000082
Fourier transform is carried out on the (3) to obtain photoacoustic signal frequency spectrum information subjected to structural light modulation
Figure BDA0002592595730000083
Wherein the content of the first and second substances,
Figure BDA0002592595730000084
is a Fourier transform of mu (z),
Figure BDA0002592595730000085
for fourier transformation of the acquired photoacoustic signal pa (z),
Figure BDA0002592595730000086
is the spectral response of the entire system. In the formula (4), the reaction mixture is,
Figure BDA0002592595730000087
for the spectrum of photoacoustic signals obtained under uniform light illumination, the other two terms are
Figure BDA0002592595730000088
Respectively shifted to k in the frequency domain0，-k0A signal at a location. For the convenience of description, we use the fundamental frequencies DN, difference frequencies DP, and sum frequencies DS to represent three parts of information, i.e.
Figure BDA0002592595730000089
Acquiring images corresponding to three phase structured light with the same spatial frequency, wherein the three phases are respectively
Figure BDA00025925957300000810
Figure BDA00025925957300000811
The three A-line data obtained are PA1(z)、PA2(z)、PA3(z), thus forming a system of linear equations:
Figure BDA00025925957300000812
suppose that
Figure BDA00025925957300000813
The DN, DP and DS can be separated by solving the equation:
Figure BDA0002592595730000091
and carrying out frequency spectrum frequency shift on the separated three frequency spectrums DN, DP and DS, wherein the accuracy of the frequency shift directly influences the accuracy of the reconstructed image. Inaccuracy of information shiftThe reconstructed image may be distorted or artifact-free. First through the spatial frequency k of the structured light0The magnitude of the spectral frequency shift is determined. Three parts of frequency spectrum information separated by the three-phase separation method are all in a frequency domain expression form, wherein DN is a fundamental frequency and does not need frequency shift, and DP and DS need frequency shift. k is a radical of0Usually not an integer, to ensure the accuracy of the frequency shift, we use the translation property of fourier transform to perform the precise frequency shift. First, DP and DS are reversely converted into spatial domain expression, and then are multiplied by exp (+/-2 pi k)0r) and finally transformed into the frequency domain, the precise information shift can be completed, namely
Figure BDA0002592595730000092
Where FFT represents fourier transform and IFFT represents inverse fourier transform.
Using a generalized wiener filter to fuse all the obtained frequency-shifted spectral slices, i.e.
Figure BDA0002592595730000093
Wherein x represents a conjugate operation,
Figure BDA0002592595730000094
for the representation of the final reconstructed image in the frequency domain, N is the number of a-line data acquired under all types of structured light illumination. w is a small constant, the magnitude of which is typically set empirically to control the noise in the reconstructed image. A (k) is an apodization function for suppressing sidelobes in the reconstructed image due to frequency discontinuities at the edges during image reconstruction.
Figure BDA0002592595730000095
Is the nth order
Figure BDA0002592595730000101
The frequency shift of (2).
Ultrasonic probe for receiving photoacoustic signal in photoacoustic microscopic imaging system and bandwidth k thereofusTypically only a few tens of mhz, which is well below the cut-off frequency k of the high numerical aperture objective lens used for exciting the photoacoustic signalsobjective(typically in the kilohertz range) so that the modulation frequency of the axial structured light is not affected by the ultrasound transducer and can far exceed the bandwidth of the ultrasound transducer. As shown in fig. 2, the first applied structured light modulation frequency is set to be smaller in magnitude than the bandwidth of the ultrasonic transducer, and the modulation frequency is gradually increased to the cutoff frequency of the objective lens. And obtaining photoacoustic signal spectrum segments (such as line segments in fig. 2) at each light modulation frequency according to the above method, finally fusing the photoacoustic spectrum segments obtained by reconstruction under the structured light of each spatial frequency, and performing inverse fourier transform to obtain an axial high-resolution image. The scheme can greatly expand the passband area of the system and greatly improve the axial resolution of the photoacoustic microscopic imaging system.
While the invention has been described with reference to a preferred embodiment, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the spirit and scope of the invention. The present invention is not to be limited by the specific embodiments disclosed herein, and other embodiments that fall within the scope of the claims of the present application are intended to be within the scope of the present invention.

Claims (6)

1. A method for improving the axial resolution of a photoacoustic microscopic imaging system based on axial modulation is characterized by comprising the following steps:
the method comprises the following steps:
s1: irradiating the sample by axial structural light with the spatial frequency of k, wherein the photoacoustic signals can be modulated by the axial structural light due to the Moire effect;
s2: the spectrum information of the photoacoustic signal received by the narrow-bandwidth ultrasonic transducer comprises three parts of information of fundamental frequency DN, sum frequency DP and difference frequency DS, and three phases excited by axial structure light of the space frequency are obtained
Figure FDA0002592595720000011
The three parts of spectrum information are separated by a three-phase separation method;
s3: shifting information to shift the high-frequency information (sum frequency DP and difference frequency DS) with dislocation to a correct position;
s4: the cut-off frequency of the objective lens used for exciting the photoacoustic signal is far higher than the bandwidth of the ultrasonic transducer, and the steps are repeated by increasing the light modulation frequency of the axial structure until the cut-off frequency of the objective lens is reached;
s5: photoacoustic signals of different frequency bands are obtained by combining wiener filtering in a frequency domain, and a high-resolution image can be obtained after inverse Fourier transform.
2. The method for improving the axial resolution of the photoacoustic microscopy imaging system based on the axial modulation as claimed in claim 1, wherein:
the axial structured light in S1 refers to a light spot with cosine change of light intensity in the detection direction of the ultrasonic probe: satisfy the requirement of
Figure FDA0002592595720000012
I0Is the average intensity of the cosine-varying axial structured light,
Figure FDA0002592595720000013
initial phase, k, of axially structured light which varies as a cosine0The spatial frequency of cosine change of the axial structured light, m is the modulation degree of cosine change of the axial structured light, and the photoacoustic signal spectrum information obtained by the axial structured light modulation can be represented by the following formula:
Figure FDA0002592595720000021
wherein eta is the conversion efficiency of heat energy,
Figure FDA0002592595720000022
is a Fourier transform of mu (z),
Figure FDA0002592595720000023
for fourier transformation of the acquired photoacoustic signal pa (z),
Figure FDA0002592595720000024
for the spectral response of the whole system, the fundamental frequencies DN, the difference frequencies DP and the sum frequencies DS are
Figure FDA0002592595720000025
Figure FDA0002592595720000026
Figure FDA0002592595720000027
Figure FDA0002592595720000028
For the spectrum of photoacoustic signals obtained under uniform light illumination, the other two terms are
Figure FDA0002592595720000029
Respectively shifted to k in the frequency domain0，-k0A signal at a location.
3. The method for improving the axial resolution of the photoacoustic microscopy imaging system based on the axial modulation as claimed in claim 1, wherein:
the phase difference of the fundamental frequency DN, the sum frequency DP and the difference frequency DS in the S2 is 2 pi/3;
the three-phase separation method is that after structured light modulation, the obtained signal contains three parts of frequency spectrum information fundamental frequencies DN, sum frequency DP and difference frequency DS, and high-resolution images are obtainedTo recover the high frequency information of the signal, it is necessary to separate three parts of the spectrum information, three phases being
Figure FDA00025925957200000210
The three A-line photoacoustic data obtained are PA1(z)、PA2(z)、PA3(z), thus forming a system of linear equations:
Figure FDA00025925957200000211
solving the equation separates three parts of fundamental frequencies DN, sum frequency DP and difference frequency DS:
Figure FDA0002592595720000031
4. the method for improving the axial resolution of the photoacoustic microscopy imaging system based on the axial modulation as claimed in claim 1, wherein:
s3, the information shift is to perform frequency spectrum shift on separated fundamental frequencies DN, sum frequencies DP and difference frequencies DS, the accuracy of the frequency shift directly affects the accuracy of the reconstructed image, the inaccuracy of the information shift can lead the reconstructed image to generate deformation or artifacts, and the spatial frequency k of the structured light is firstly passed through0Determining the magnitude of frequency spectrum frequency shift, wherein three parts of frequency spectrum information separated by a three-phase separation method are all in the expression form of frequency domain, DN is base frequency without frequency shift, DP and DS need frequency shift, k is0Usually not integer, to ensure the accuracy of frequency shift, the shift property of Fourier transform is used to perform precise frequency shift, first DP, DS are inversely converted to spatial domain representation, and then multiplied by exp (+/-2 π k0r), and finally transforming to frequency domain to complete accurate information shift
CS1(k)＝DN(k)
Figure FDA0002592595720000032
Figure FDA0002592595720000033
Where FFT represents fourier transform and IFFT represents inverse fourier transform.
5. The method for improving the axial resolution of the photoacoustic microscopy imaging system based on the axial modulation as claimed in claim 1, wherein:
s4 step-wise increasing the axial structured light spatial frequency up to the cut-off frequency of the objective lens,
the size of the light modulation frequency of the initially applied structure is set to be smaller than the bandwidth of the ultrasonic transducer, the modulation frequency is gradually increased to the cut-off frequency of the objective lens, and the photoacoustic signal spectrum segment is obtained according to the steps S1-S3 at each light modulation frequency.
6. The method for improving the axial resolution of the photoacoustic microscopy imaging system based on the axial modulation as claimed in claim 1, wherein:
s5, the photoacoustic signals of different frequency bands obtained by the method are combined in the frequency domain through the wiener filtering, and the following conditions are met:
Figure FDA0002592595720000041
wherein x represents a conjugate operation,
Figure FDA0002592595720000042
for the representation of the final reconstructed image in the frequency domain, N is the number of A-line data acquired under all types of structured light illumination, w is a small constant whose size is generally empirically set to control the noise in the reconstructed image, and A (k) is an apodization function for suppressing image reconstructionThe process is limited by the frequency discontinuity at the edges, the side lobes that appear in the reconstructed image,
Figure FDA0002592595720000043
is the nth order
Figure FDA0002592595720000044
The frequency shift of (2).
CN202010699786.6A 2020-07-20 2020-07-20 Method for improving axial resolution of photoacoustic microscopic imaging system based on axial modulation Withdrawn CN111948296A (en)

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