CN111157226A - Method and device for measuring point spread function of microscope - Google Patents

Method and device for measuring point spread function of microscope Download PDF

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CN111157226A
CN111157226A CN202010146246.5A CN202010146246A CN111157226A CN 111157226 A CN111157226 A CN 111157226A CN 202010146246 A CN202010146246 A CN 202010146246A CN 111157226 A CN111157226 A CN 111157226A
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microscope
position coordinate
determining
point spread
target
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毛帅
王军涛
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Shandong University of Technology
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Shandong University of Technology
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Abstract

The invention provides a method and a device for measuring a point spread function of a microscope, which relate to the technical field of optical microscopic measurement and comprise the following steps: determining a first position coordinate of the optical fiber laser head so that the first linearly polarized light is emitted into a first detector, and a unit direction vector of the first linearly polarized light detected by the first detector is a preset unit direction vector; acquiring a second position coordinate set sent by a second detector and acquiring a light spot image on an image surface of the microscope; based on the light spot image, presetting a unit direction vector and a second position coordinate set, and determining a microscopic magnification array of the microscope; the point spread function group is determined by combining the normalization function and the microscopic magnification array, the technical problem that the longitudinal object plane perpendicular to the optical axis of the microscope cannot be accurately determined in the existing microscope point spread function measurement technology is solved, and the three-dimensional point spread function measurement on the longitudinal object plane perpendicular to the optical axis of the microscope is realized.

Description

Method and device for measuring point spread function of microscope
Technical Field
The invention relates to the technical field of optical microscopic measurement, in particular to a method and a device for measuring a point spread function of a microscope.
Background
After an ideal point light source passes through an optical system, the light field distribution of its image is called the Point Spread Function (PSF) of the system. The point spread function describes the resolving power of the optical system to the point source, and is a main parameter index for evaluating various microscopic imaging systems. Therefore, it is indispensable to accurately measure the system point spread function. There are generally two ways to estimate the point spread function, numerical computation and physical measurement. The numerical calculation usually uses a lens theoretical point spread function model, and because the pupil function is difficult to be accurately estimated, the theoretical model cannot reflect an actual imaging system, so that accurate physical experimental measurement of the point spread function needs to be performed on each set of specific microscopic imaging device. At present, the point spread function measuring method of the microscopic imaging system includes a star point detection method, a knife edge method, a fluorescent microsphere measuring method and the like. For a microscope system, point spread functions on object planes with different longitudinal heights along the optical axis direction in the depth of field range are different, although the point spread functions can be measured by the method, the method cannot determine which layer of object plane the obtained point spread functions are located in the depth of field range of the microscope imaging, namely the method cannot determine the longitudinal object plane perpendicular to the optical axis of the microscope, and cannot really measure the three-dimensional point spread functions.
No effective solution has been proposed to the above problems.
Disclosure of Invention
In view of the above, the present invention is directed to a method and an apparatus for measuring a point spread function of a microscope, so as to alleviate the technical problem that the point spread function corresponding to each height of an objective lens of the microscope cannot be accurately determined in the prior art.
In a first aspect, an embodiment of the present invention provides a method for measuring a point spread function of a microscope, including: determining a first position coordinate of the optical fiber laser head so that first linearly polarized light is emitted into a first detector, wherein a unit direction vector of the first linearly polarized light detected by the first detector is a preset unit direction vector, and the first linearly polarized light is linearly polarized light which is emitted by the optical fiber laser head at the first position coordinate and is refracted by a refractor; acquiring a second position coordinate set sent by a second detector and acquiring a light spot image on the image surface of the microscope, wherein the second position coordinate set comprises a plurality of second position coordinates, the second position coordinates are light spot position coordinates formed by nano fluorescent particles on the image surface of the microscope, the second position coordinates are used for representing the height of the object surface of the microscope, and the light spot image is used for representing the moving track of the nano fluorescent particles on the image surface of the microscope in the process that the displacement table moves in the preset direction with the minimum step length; determining a microscopic magnification array of the microscope based on the spot image, the preset unit direction vector and the second position coordinate set, wherein the microscopic magnification array comprises a plurality of microscopic magnification factors, and the object plane height value of one microscope corresponds to one microscopic magnification factor; and determining a point diffusion function group by combining the normalization function and the microscopic magnification power group, wherein the point diffusion function group comprises a plurality of point diffusion functions, and the object plane height value of one microscope corresponds to one point diffusion function.
Further, determining a microscopic magnification array of the microscope based on the spot image, the preset unit direction vector and the second position coordinate, includes: determining a target light spot image and a target second position coordinate, wherein the target light spot image is the light spot image on the image surface of the microscope after the displacement platform moves for n minimum step lengths in the preset direction, and the target second position coordinate is the second position coordinate sent by the second detector after the displacement platform moves for n minimum step lengths in the preset direction; determining the space attitude compensation quantity of the displacement platform after the displacement platform moves n minimum step lengths in the preset direction based on the light spot image, the preset unit direction vector and the second position coordinate; determining the space attitude compensation quantity of the point spread function calibration equipment after the displacement platform moves n minimum step lengths in the preset direction based on the light spot image, the preset unit direction vector and the second position coordinate; and after the spatial attitude compensation of the point spread function calibration equipment is completed, determining the target light spot image as the microscopic magnification of the microscope after the displacement platform moves n minimum step lengths in the preset direction.
Further, determining, based on the light spot image, the preset unit direction vector and the second position coordinate, that the target light spot image is a spatial attitude compensation amount of the displacement table after the displacement table moves n minimum step lengths in a preset direction, including: determining a target unit direction vector corresponding to the target second position coordinate, wherein the target unit direction vector is a unit direction vector of the first linearly polarized light detected by the first detector after the displacement table moves n minimum step lengths in a preset direction; determining a space attitude compensation quantity of the displacement table by using the target unit direction vector and a preset position direction vector, wherein the space attitude compensation quantity comprises at least one of the following components: a pitch angle compensation amount and a yaw angle compensation amount; and compensating the spatial attitude of the displacement table based on the spatial attitude compensation amount so that the target second position coordinate is changed into an initial second position coordinate after the displacement table completes the spatial attitude compensation, wherein the initial second position coordinate is a second position coordinate sent by the second detector before the displacement table moves in a preset direction.
Further, determining, based on the light spot image, the preset unit direction vector and the second position coordinate, that the target light spot image is a spatial attitude compensation amount of the point spread function calibration device after the displacement stage moves n minimum step lengths in a preset direction, includes: performing Gaussian surface fitting on the target light spot image to obtain a Gaussian surface fitting image; performing full-width half-maximum difference calculation on the Gaussian surface fitting image to obtain a difference value of the Gaussian surface fitting image, and performing absolute value calculation on the difference value to obtain an absolute value of the difference value of the Gaussian surface fitting image; determining the space attitude compensation quantity of the point spread function calibration equipment based on the absolute value; and performing spatial attitude compensation on the point spread function calibration equipment based on the spatial attitude compensation amount of the point spread function calibration equipment, so that the target second position coordinate is changed into the initial second position coordinate after the point spread function calibration equipment completes the spatial attitude compensation.
Further, after the compensation of the spatial attitude of the point spread function calibration device is completed, determining that the target light spot image is the microscopic magnification of the microscope after the displacement stage moves n minimum step lengths in a preset direction, including: acquiring a translation distance sent by the first detector, wherein the translation distance is the translation distance of the first polarized light on the first detector; and determining the ratio of the moving distance to the translation distance as the microscopic magnification, wherein the moving distance is the distance between the light spot after the displacement table moves n minimum steps in the preset direction and the light spot after the displacement table moves n-1 minimum steps in the preset direction.
Further, determining a set of point spread functions in combination with a normalization function and the set of microscopic magnification factors, comprising: substituting the microscopic magnification factor and the position coordinates of the light spots after the displacement table moves n minimum step lengths in the preset direction into the normalization function to obtain an objective function, wherein the objective function is
Figure BDA0002400175740000041
D is the particle diameter of the spherical nano fluorescent particles with known particle diameter, FHeight(xi,yi) Is the normalized Gaussian surface fitting distribution of the light spot image at the object plane height i, MHeightIs the microscopic magnification, IHeight(xi,yi) Is the point spread function of the microscope when the height of the object plane is i; and carrying out minimum solving on the target function to obtain a point spread function of the microscope when the height of the object plane is i.
In a second aspect, an embodiment of the present invention further provides a device for measuring a point spread function of a microscope, including: the device comprises a first determining unit, an obtaining unit, a second determining unit and a third determining unit, wherein the first determining unit is used for determining a first position coordinate of the optical fiber laser head so as to enable first linearly polarized light to enter a first detector, the first detector detects that a unit direction vector of the first linearly polarized light is a preset unit direction vector, and the first linearly polarized light is linearly polarized light which is emitted by the optical fiber laser head at the first position coordinate and refracted by a refractor; the acquiring unit is configured to acquire a second position coordinate set sent by a second detector and acquire a light spot image on an image plane of a microscope, where the second position coordinate set includes a plurality of second position coordinates, the second position coordinates are light spot position coordinates formed by nano fluorescent particles on the image plane of the microscope, the second position coordinates are used to represent an object plane height of the microscope, and the light spot image is used to represent a moving track of the nano fluorescent particles on the image plane of the microscope in a process that the displacement table moves in a preset direction with a minimum step length; the second determining unit is configured to determine a microscopic magnification array of the microscope based on the spot image, the preset unit direction vector, and the second position coordinate set, where the microscopic magnification array includes a plurality of microscopic magnifications, and an object plane height value of one microscope corresponds to one microscopic magnification; and the third determining unit is used for determining a point spread function set by combining the normalization function and the microscopic magnification power set, wherein the point spread function set comprises a plurality of point spread functions, and the object plane height value of one microscope corresponds to one point spread function.
Further, the second determination unit is configured to: determining the target light spot image as a space attitude compensation quantity of the displacement platform after the displacement platform moves n minimum step lengths in a preset direction based on the light spot image, the preset unit direction vector and the second position coordinate; determining the target light spot image as a space attitude compensation quantity of a point spread function calibration device after the displacement platform moves n minimum step lengths in a preset direction based on the light spot image, the preset unit direction vector and the second position coordinate; and after the spatial attitude compensation of the point spread function calibration equipment is completed, determining the target light spot image as the microscopic magnification of the microscope after the displacement platform moves n minimum step lengths in the preset direction.
Further, the second determination unit is configured to: determining a target light spot image and a target second position coordinate, wherein the target light spot image is the light spot image on the image surface of the microscope after the displacement platform moves for n minimum step lengths in the preset direction, and the target second position coordinate is the second position coordinate sent by the second detector after the displacement platform moves for n minimum step lengths in the preset direction; determining a target unit direction vector corresponding to the target second position coordinate, wherein the target unit direction vector is a unit direction vector of the first linearly polarized light detected by the first detector after the displacement table moves n minimum step lengths in a preset direction; determining a space attitude compensation quantity of the displacement table by using the target unit direction vector and a preset position direction vector, wherein the space attitude compensation quantity comprises at least one of the following components: a pitch angle compensation amount and a yaw angle compensation amount; and compensating the spatial attitude of the displacement table based on the spatial attitude compensation amount so that the target second position coordinate is changed into an initial second position coordinate after the displacement table completes the spatial attitude compensation, wherein the initial second position coordinate is a second position coordinate sent by the second detector before the displacement table moves in a preset direction.
In a third aspect, an embodiment of the present invention further provides a computer-readable medium having a non-volatile program code executable by a processor, where the program code causes the processor to execute the method for measuring a point spread function of a microscope according to the first aspect.
In the embodiment of the invention, firstly, a first position coordinate of the optical fiber laser head is determined so as to enable first linearly polarized light to be emitted into a first detector, and a unit direction vector of the first linearly polarized light detected by the first detector is a preset unit direction vector; then, acquiring a second position coordinate set sent by a second detector and acquiring a light spot image on an image surface of the microscope; then, based on the light spot image, presetting a unit direction vector and a second position coordinate set, and determining a microscopic magnification array of the microscope; and finally, determining a point diffusion function group by combining the normalization function and the microscopic magnification power group, wherein the point diffusion function group comprises a plurality of point diffusion functions, the height value of the object plane of a microscope corresponds to one point diffusion function, the purpose of determining the point diffusion function corresponding to the longitudinal object plane perpendicular to the optical axis of the microscope is achieved, the technical problem that the longitudinal object plane perpendicular to the optical axis of the microscope cannot be determined in the prior art is solved, the longitudinal object plane perpendicular to the optical axis of the microscope is determined, and the technical effect of measuring the three-dimensional point diffusion function on the longitudinal object plane perpendicular to the optical axis of the microscope is achieved.
Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and other drawings can be obtained by those skilled in the art without creative efforts.
FIG. 1 is a flow chart of a method for measuring a point spread function of a microscope according to an embodiment of the present invention;
FIG. 2 is a flow chart of a method for measuring microscopic magnification of a microscope according to an embodiment of the present invention;
FIG. 3 is a schematic diagram of a microscope point spread function measuring apparatus according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a light spot of a linearly polarized light beam according to an embodiment of the present invention;
fig. 5 is a schematic diagram of a microscope point spread function measurement device according to an embodiment of the present invention.
Reference numerals: the device comprises an optical fiber laser head 1, a first adjusting frame 2, a linearly polarized light beam 3, a refractor 4, a double-spot light beam vector measuring device 5, a detector group 6, an intermediate linearly polarized light beam, a first mirror surface group 8, a first light splitting surface 9, a second light splitting surface 10, a right-angle inclined surface 11, a first angle cone 12, a first wave plate 13, a second wave plate 14, a glass slide 15, an optical filter 16, nano fluorescent particles 17, a microscope 18, a point spread function calibrating device 19, a displacement table 20, a plane light splitting mirror 21, a first detector 22, a second adjusting frame 23 and a second angle cone 24.
Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The first embodiment is as follows:
in accordance with an embodiment of the present invention, there is provided an embodiment of a method for measuring a point spread function of a microscope, it is noted that the steps illustrated in the flowchart of the drawings may be performed in a computer system such as a set of computer executable instructions and that, although a logical order is illustrated in the flowchart, in some cases the steps illustrated or described may be performed in an order different than here.
Fig. 1 is a method according to an embodiment of the invention, as shown in fig. 1, comprising the steps of:
step S102, determining a first position coordinate of the optical fiber laser head so as to enable first linearly polarized light to be emitted into a first detector, wherein the unit direction vector of the first linearly polarized light detected by the first detector is a preset unit direction vector, and the first linearly polarized light is linearly polarized light which is emitted by the optical fiber laser head at the first position coordinate and is refracted by a refractor;
it should be noted that the predetermined unit direction vector is generally (0,0, -1), and the first detector is a dual CCD detector.
Specifically, linearly polarized light output by the optical fiber laser head when the optical fiber laser head is located at a first position coordinate is reflected by a refractor with a fixed position and then enters a first detector, a direction vector in a coordinate system determined by the first detector is obtained through a spot position detected by the linearly polarized light beam on the first detector, and an optical fiber laser head adjusting frame is adjusted to enable a unit direction vector measured by the linearly polarized light beam in a double-spot light beam vector measuring unit to be (0,0, -1);
step S104, acquiring a second position coordinate set sent by a second detector and acquiring a light spot image on the image surface of the microscope, wherein the second position coordinate set comprises a plurality of second position coordinates, the second position coordinates are light spot position coordinates formed by the nano fluorescent particles on the image surface of the microscope, the second position coordinates are used for representing the height of the object surface of the microscope, and the light spot image is used for representing the moving track of the nano fluorescent particles on the image surface of the microscope in the process that the displacement table moves in the preset direction with the minimum step length;
it should be noted that the second detector is a longitudinal position measurement CCD detector, and the displacement stage is a six-degree-of-freedom displacement stage.
Step S106, determining a microscopic magnification array of the microscope based on the light spot image, the preset unit direction vector and the second position coordinate set, wherein the microscopic magnification array comprises a plurality of microscopic magnification factors, and the object plane height value of one microscope corresponds to one microscopic magnification factor;
and S108, determining a point spread function group by combining the normalization function and the microscopic magnification group, wherein the point spread function group comprises a plurality of point spread functions, and the object plane height value of one microscope corresponds to one point spread function.
In the embodiment of the invention, firstly, a first position coordinate of the optical fiber laser head is determined so as to enable first linearly polarized light to be emitted into a first detector, and a unit direction vector of the first linearly polarized light detected by the first detector is a preset unit direction vector; then, acquiring a second position coordinate set sent by a second detector and acquiring a light spot image on an image surface of the microscope; then, based on the light spot image, presetting a unit direction vector and a second position coordinate set, and determining a microscopic magnification array of the microscope; and finally, determining a point diffusion function group by combining the normalization function and the microscopic magnification power group, wherein the point diffusion function group comprises a plurality of point diffusion functions, the height value of the object plane of a microscope corresponds to one point diffusion function, the purpose of determining the point diffusion function corresponding to the longitudinal object plane perpendicular to the optical axis of the microscope is achieved, the technical problem that the longitudinal object plane perpendicular to the optical axis of the microscope cannot be determined in the prior art is solved, the longitudinal object plane perpendicular to the optical axis of the microscope is determined, and the technical effect of measuring the three-dimensional point diffusion function on the longitudinal object plane perpendicular to the optical axis of the microscope is achieved.
In this embodiment of the present invention, as shown in fig. 2, the step S106 further includes the following steps:
step S11, determining a target light spot image and a target second position coordinate, wherein the target light spot image is the light spot image on the image plane of the microscope after the displacement table moves for n minimum steps in the preset direction, and the target second position coordinate is the second position coordinate sent by the second detector after the displacement table moves for n minimum steps in the preset direction;
step S12, based on the light spot image, the preset unit direction vector and the second position coordinate, determining the target light spot image as the space attitude compensation quantity of the displacement table after the displacement table moves n minimum step lengths in a preset direction;
step S13, based on the light spot image, the preset unit direction vector and the second position coordinate, determining the target light spot image as the space attitude compensation quantity of the point spread function calibration equipment after the displacement platform moves n minimum step lengths in the preset direction;
step S14, after completing the spatial attitude compensation of the point spread function calibration device, determining that the target light spot image is the microscopic magnification of the microscope after the displacement stage moves n minimum steps in the preset direction.
In the embodiment of the invention, the initial position coordinates of the nano fluorescent particles on the image surface are firstly determined, in order to determine that the initial position coordinates can be linearly displaced through the six-degree-of-freedom displacement table, the nano fluorescent particles are imaged in a microscope, the axial direction of the microscope objective lens is approximately vertical to the plane of the slide plate in a mode of judging the verticality through the posture displacement motion of the six-degree-of-freedom displacement table by naked eyes, and the position coordinates (namely the initial position coordinates) of light spots on the longitudinal position measurement CCD at the moment are recorded.
Then, a target spot image is determined from the spot image, and a target second position coordinate is determined from the second position coordinate set.
And finally, determining the target light spot image as the space attitude compensation quantity of the point spread function calibration equipment and the microscopic magnification of the microscope after the displacement platform moves n minimum step lengths in the preset direction through the target light spot image, the target second position coordinate and the preset unit direction vector.
It should be noted that the step S12 further includes the following steps:
step S121, determining a target unit direction vector corresponding to the target second position coordinate, wherein the target unit direction vector is the unit direction vector of the first linearly polarized light detected by the first detector after the displacement table moves n minimum step lengths in a preset direction;
step S122, determining a space attitude compensation quantity of the displacement table by using the target unit direction vector and a preset position direction vector, wherein the space attitude compensation quantity comprises at least one of the following components: a pitch angle compensation amount and a yaw angle compensation amount;
step S123, compensating the spatial attitude of the displacement stage based on the spatial attitude compensation amount, so that after the spatial attitude compensation of the displacement stage is completed, the target second position coordinate is changed into an initial second position coordinate, where the initial second position coordinate is a second position coordinate sent by the second detector before the displacement stage moves in a preset direction.
Step S13 further includes the steps of:
step S131, performing Gaussian surface fitting on the target light spot image to obtain a Gaussian surface fitting image;
step S132, performing full-width half-maximum difference calculation on the Gaussian surface fitting image to obtain a difference value of the Gaussian surface fitting image, and performing absolute value calculation on the difference value to obtain an absolute value of the difference value of the Gaussian surface fitting image;
step S133, determining the space attitude compensation quantity of the point spread function calibration equipment based on the absolute value;
step S134, performing spatial attitude compensation on the point spread function calibration device based on the spatial attitude compensation amount of the point spread function calibration device, so that the target second position coordinate is changed into the initial second position coordinate after the point spread function calibration device completes the spatial attitude compensation.
Step S14 further includes the steps of:
step S141, obtaining a translation distance sent by the first detector, where the translation distance is a translation distance of the first polarized light on the first detector;
step S142, determining a ratio between a moving distance and the translation distance as the microscopic magnification, where the moving distance is a distance between a light spot after the displacement stage moves n minimum steps in a preset direction and a light spot after the displacement stage moves n-1 minimum steps in the preset direction.
The above steps are described in detail with reference to fig. 1 to 4 as follows:
step one, linearly polarized light output by the optical fiber laser head is reflected by a refractor with a fixed position and then enters a double-spot light beam vector measuring device, the direction vector of the linearly polarized light beam in a coordinate system determined by the double-spot light beam vector measuring device is obtained through the spot position detected by the linearly polarized light beam on a detector group in the double-spot light beam vector measuring device, and an optical fiber laser head adjusting frame is adjusted to enable the unit direction vector of the linearly polarized light beam measured in the double-spot light beam vector measuring device to be (0,0, -1);
and secondly, imaging the nano fluorescent particles with known particle sizes in a microscope through linear displacement of the displacement table, enabling the axis direction of the microscope objective lens to be approximately vertical to the plane of the slide plate in a manner of judging the verticality through visual inspection by naked eyes through posture displacement movement of the displacement table, and recording the position coordinates of the light spots on the first detector at the moment.
Thirdly, continuously and integrally translating the point spread function calibration device by a displacement table along a certain linear direction with the minimum step length thereof, so that the light spot imaging of spherical nano fluorescent particles with known particle sizes in a microscope is carried out from one corner position of an image surface of the microscope to the opposite corner position thereof, sampling is carried out to obtain a series of light spot imaging, the connecting line of two corners is called an image surface translation coordinate axis, if the spatial attitude of the point spread function calibration device is changed in the translation process, namely the pitch angle α and the yaw angle β are changed, the unit direction vector (0,0, -1) of the linearly polarized light beam measured in the original dual-spot light beam vector measurement device is changed, and the unit direction vector of the linearly polarized light beam measured in the changed dual-spot light beam vector measurement device is assumed to be (m, n, q), and the equation relationship between the linearly polarized light beam and (0,0, -1) can be known from the change of the
Figure BDA0002400175740000121
The pitch angle α and the yaw angle β are obtained by solving the above formula, so that attitude return compensation is performed on attitude change generated by movement through the displacement table, if the spatial longitudinal height position of the point spread function calibration device is changed in the translation process, namely the position coordinates of light spots of the first detector are changed, longitudinal height return compensation is performed on the longitudinal height position generated by movement through the displacement table, and the light spot position of the first detector corresponding to the point spread function calibration device after translation is returned to the position of the light spot of the first detector recorded in the first step.
Fourthly, after the point spread function calibration device is translated in the minimum step length each time, Gaussian surface function fitting is carried out on the spot gray level image obtained on the image surface to obtain the central position coordinate of the spot gray level image, the spot gray level image is longitudinally divided into two parts by passing through the central position coordinate and a plane parallel to the Y-axis direction of the image surface, Gaussian surface function fitting and fitting value normalization are respectively carried out on the spot gray levels of the two parts, if the spot image is positioned in the paraxial region of the image surface image, the full widths at half maximum of the two Gaussian surface functions are equal, if the spot image is positioned in the non-paraxial region of the image surface image, the full widths at half maximum of the two Gaussian surface functions are not equal, the absolute difference value of the full widths at half maximum of the two Gaussian surface functions is stored, after the point spread function calibration device is linearly shifted, the corresponding full width at half maximum absolute value after all step length shifts is obtained, and the central position of all the obtained spot gray level, performing quadratic polynomial fitting by using all full width at half maximum absolute difference values as vertical coordinates, and performing S-shaped curve fitting on the full width at half maximum absolute difference value data on the left and right sides of the fitting polynomial by using the middle vertex position of the fitting polynomial as a division point (zero point), wherein the S-shaped curve fitting formula is as follows
Figure BDA0002400175740000131
In the formula I0、l1And l2Are fitting coefficients, L and s represent dependent and independent variables, respectively. The horizontal axis coordinates of the bottom inflection point of the S-shaped fitting curve of the divided left and right full width at half maximum absolute difference value data are (ln (l)1 left side)-1.317)/l2 left sideAnd (ln (l)1 right side)-1.317)/l2 right sideWherein l is1 left sideAnd l2 left sideRespectively, of the S-shaped fitting curve of the left full width at half maximum absolute difference value1And l2Coefficient of fit,/1 right sideAnd l2 right sideRespectively is l of S-shaped fitting curve of right full width at half maximum absolute difference value1And l2Fitting coefficient, coordinate on image plane translation coordinate axis (ln (l)1 left side)-1.317)/l2 left sideAnd (ln (l)1 right side)-1.317)/l2 right sideThe coordinate distance between the two is the diameter of the image surface paraxial imaging circular region, and the center of the image surface paraxial imaging circular region is ((ln (l)1 left side)-1.317)/l2 left side+(ln(l1 right side)-1.317)/l2 right side) And/2, determining the image plane paraxial imaging circular area, and the coordinate (ln (l) on the image plane translation coordinate axis1 left side)-1.317)/l2 left sideAnd (ln (l)1 right side)-1.317)/l2 right sideThe full width at half maximum of the Gaussian curved surface function of the light spot gray level image corresponding to the horizontal axis coordinate is taken, and then the horizontal axis coordinate ((ln (l)1 left side)-1.317)/l2 left side+(ln(l1 right side)-1.317)/l2 right side) And/2, carrying out difference operation on the full width at half maximum of the Gaussian curved surface function of the nearest light spot gray level image and the full width at half maximum of the Gaussian curved surface function of the light spot gray level image corresponding to the rest horizontal axis coordinates, and taking the absolute value of the difference to finally obtain the average value of all the absolute values of the difference.
And fifthly, taking the spatial attitude of the point spread function calibration device in the first step as an initial state, keeping the pitch angle and the spatial height of the spatial attitude of the point spread function calibration device unchanged, changing the deflection angle of the point spread function calibration device by a displacement table in a micro angle step length between-5 degrees and +5 degrees, repeating the second step and the third step after each micro deflection angle is changed to obtain an average value of corresponding difference absolute values after each micro deflection angle is changed, and adjusting the point spread function calibration device to the deflection spatial attitude corresponding to the minimum value of the average values through the displacement table.
And sixthly, keeping the space attitude and the space height of the point spread function calibration device in the fourth step unchanged, changing the pitch angle of the point spread function calibration device by a tiny angle step length between minus 5 degrees and plus 5 degrees through a displacement platform, repeating the second step and the third step after each tiny pitch angle change to obtain an average value of the corresponding difference absolute values after each tiny pitch angle change, and adjusting the point spread function calibration device to the pitch space attitude corresponding to the minimum value in the average values through the displacement platform.
Seventhly, recording the position coordinates of imaging light spots on any CCD detector in the double-light-spot light beam vector measuring device after linearly polarized light output by the optical fiber laser head is reflected by a refractor with a fixed position under the condition that the point spread function calibrating device is in the spatial attitude obtained by the steps, wherein the plane (object surface) on the glass slide is vertical to the optical axis of the microscope, and then adjusting an optical fiber laser head adjusting frame to enable the unit direction vector of the laser beam reflected by the plane beam splitter at the front end of the first detector to be (0,0, -1), namely the light sensing surface of the first detector is parallel to the optical axis of the microscope.
And eighthly, enabling the point spread function calibration device to generate a series of longitudinal displacements through the displacement table, keeping the obtained space attitude unchanged in the process, enabling the position coordinates of imaging light spots on the CCD detector in the double-light spot light beam vector measurement device recorded in the sixth step to be unchanged, if the position coordinates of the imaging light spots on the CCD detector are changed, carrying out return compensation through the displacement table, enabling the point spread function calibration device to correspond to the position coordinates of the light spots on the first detector after each longitudinal displacement, enabling all light spot position coordinate points to be on a straight line, enabling the straight line to be parallel to the optical axis of the microscope, and enabling all object planes perpendicular to the optical axis of the microscope and different in height to be calibrated through the position coordinates of the light spots on the first detector.
Ninthly, repeating the first step on each object plane perpendicular to the optical axis of the microscope to determine a paraxial imaging circular area of the microscope image plane, generating a micro distance by a translation point spread function calibration device (spherical nano fluorescent particles with known particle size), and ensuring that spot imaging of the nano fluorescent particles with known particle size on the microscope image plane is always in the paraxial imaging circular area, wherein the translated micro distance is the same translation distance of a linear polarized light source beam incident into a double-spot light beam vector measuring device, so that the translation distance value can be measured by a CCD (charge coupled device) detector in the double-spot light beam vector measuring device, and the absolute value of the translation distance of an imaging spot on the microscope image plane is divided by the translation micro distance measured by the double-spot light beam vector measuring device to obtain the microscopic magnification M corresponding to the object planeHeight。
In this embodiment of the present invention, step S108 further includes the following steps:
step S21, the microscopic magnification and the position coordinates of the light spots after the displacement table moves n minimum step lengths in the preset direction are substituted into the normalization function to obtain the target function, wherein the target function is
Figure BDA0002400175740000152
D is the particle diameter of the spherical nano fluorescent particles with known particle diameter, FHeight(xi,yi) Is the normalized Gaussian surface fitting distribution of the light spot image at the object plane height i, MHeightIs the microscopic magnification, IHeight(xi,yi) Is the point spread function of the microscope at object plane height i.
And step S22, carrying out minimum solving on the objective function to obtain a point spread function of the microscope when the height of the object plane is i.
On each object plane which is vertical to the optical axis of the microscope and has different heights, the object plane light intensity normalization function of the known particle size nanometer fluorescent particles is f (x)o,yo)，
Figure BDA0002400175740000151
Wherein D is the particle diameter of the nano fluorescent particles, (x)o,yo) Is a coordinate value of a plane on the object plane, since the object plane is parallel to the image plane, (x)o,yo) Usable planar coordinate value (x) on image planei,yi) Instead, each object plane perpendicular to the optical axis of the microscope and having a different height corresponds to an imaging relationship of
Figure BDA0002400175740000153
Wherein, FHeight(xi,yi) Fitting distribution of normalized Gaussian surface of imaging light spot gray scale obtained on image surface under different height object surface conditions, IHeight(xi,yi) For point spread functions corresponding to object planes of different heights, by solving a minimization problem
Figure BDA0002400175740000161
Different heights can be obtained, each perpendicular to the optical axis of the microscopePoint spread function I corresponding to object planeHeight(xi,yi)。
Example two:
the embodiment of the present invention further provides a device for measuring a point spread function of a microscope, where the device for measuring a point spread function of a microscope is used to execute the method for measuring a point spread function of a microscope provided in the foregoing description of the embodiment of the present invention, and the following is a detailed description of the device for measuring a point spread function of a microscope provided in the embodiment of the present invention.
As shown in fig. 5, fig. 5 is a schematic diagram of the measuring device of the microscope point spread function, which includes: a first determining unit 10, an obtaining unit 20, a second determining unit 30 and a third determining unit 40.
The first determining unit 10 is configured to determine a first position coordinate of the optical fiber laser head, so that a first linearly polarized light is incident into a first detector, and a unit direction vector of the first linearly polarized light detected by the first detector is a preset unit direction vector, where the first linearly polarized light is a linearly polarized light which is emitted by the optical fiber laser head at the first position coordinate and is refracted by a refractor;
the acquiring unit 20 is configured to acquire a second position coordinate set sent by a second detector, and acquire a light spot image on an image plane of a microscope, where the second position coordinate set includes a plurality of second position coordinates, the second position coordinates are light spot position coordinates formed by nano fluorescent particles on the image plane of the microscope, the second position coordinates are used to represent an object plane height of the microscope, and the light spot image is used to represent a moving track of the nano fluorescent particles on the image plane of the microscope in a process that the displacement stage moves in a preset direction with a minimum step length;
the second determining unit 30 is configured to determine a microscopic magnification array of the microscope based on the spot image, the preset unit direction vector, and the second position coordinate set, where the microscopic magnification array includes a plurality of microscopic magnifications, and an object plane height value of one microscope corresponds to one microscopic magnification;
the third determining unit 40 is configured to determine a point spread function set by combining the normalization function and the microscopic magnification power set, where the point spread function set includes a plurality of point spread functions, and an object plane height value of a microscope corresponds to one point spread function.
In the embodiment of the invention, firstly, a first position coordinate of the optical fiber laser head is determined so as to enable first linearly polarized light to be emitted into a first detector, and a unit direction vector of the first linearly polarized light detected by the first detector is a preset unit direction vector; then, acquiring a second position coordinate set sent by a second detector and acquiring a light spot image on an image surface of the microscope; then, based on the light spot image, presetting a unit direction vector and a second position coordinate set, and determining a microscopic magnification array of the microscope; and finally, determining a point diffusion function group by combining the normalization function and the microscopic magnification power group, wherein the point diffusion function group comprises a plurality of point diffusion functions, the height value of the object plane of a microscope corresponds to one point diffusion function, the purpose of determining the point diffusion function corresponding to the longitudinal object plane perpendicular to the optical axis of the microscope is achieved, the technical problem that the longitudinal object plane perpendicular to the optical axis of the microscope cannot be determined in the prior art is solved, the longitudinal object plane perpendicular to the optical axis of the microscope is determined, and the technical effect of measuring the three-dimensional point diffusion function on the longitudinal object plane perpendicular to the optical axis of the microscope is achieved. Therefore, the technical effect of accurately determining the point spread function corresponding to the object plane at each height vertical to the optical axis of the microscope is achieved.
Preferably, the second determination unit is configured to: determining the target light spot image as a space attitude compensation quantity of the displacement platform after the displacement platform moves n minimum step lengths in a preset direction based on the light spot image, the preset unit direction vector and the second position coordinate; determining the target light spot image as a space attitude compensation quantity of a point spread function calibration device after the displacement platform moves n minimum step lengths in a preset direction based on the light spot image, the preset unit direction vector and the second position coordinate; and after the spatial attitude compensation of the point spread function calibration equipment is completed, determining the target light spot image as the microscopic magnification of the microscope after the displacement platform moves n minimum step lengths in the preset direction.
Preferably, the second determination unit is configured to: determining a target light spot image and a target second position coordinate, wherein the target light spot image is the light spot image on the image surface of the microscope after the displacement platform moves for n minimum step lengths in the preset direction, and the target second position coordinate is the second position coordinate sent by the second detector after the displacement platform moves for n minimum step lengths in the preset direction; determining a target unit direction vector corresponding to the target second position coordinate, wherein the target unit direction vector is a unit direction vector of the first linearly polarized light detected by the first detector after the displacement table moves n minimum step lengths in a preset direction; determining a space attitude compensation quantity of the displacement table by using the target unit direction vector and a preset position direction vector, wherein the space attitude compensation quantity comprises at least one of the following components: a pitch angle compensation amount and a yaw angle compensation amount; and compensating the spatial attitude of the displacement table based on the spatial attitude compensation amount so that the target second position coordinate is changed into an initial second position coordinate after the displacement table completes the spatial attitude compensation, wherein the initial second position coordinate is a second position coordinate sent by the second detector before the displacement table moves in a preset direction.
Preferably, the second determination unit is configured to: performing Gaussian surface fitting on the target light spot image to obtain a Gaussian surface fitting image; performing full-width half-maximum difference calculation on the Gaussian surface fitting image to obtain a difference value of the Gaussian surface fitting image, and performing absolute value calculation on the difference value to obtain an absolute value of the difference value of the Gaussian surface fitting image; determining the space attitude compensation quantity of the point spread function calibration equipment based on the absolute value; and performing spatial attitude compensation on the point spread function calibration equipment based on the spatial attitude compensation amount of the point spread function calibration equipment, so that the target second position coordinate is changed into the initial second position coordinate after the point spread function calibration equipment completes the spatial attitude compensation.
Preferably, the second determination unit is configured to: after the compensation of the spatial attitude of the point spread function calibration equipment is completed, acquiring a translation distance sent by the first detector, wherein the translation distance is the translation distance of the first polarized light on the first detector; and determining the ratio of the moving distance to the translation distance as the microscopic magnification, wherein the moving distance is the distance between the light spot after the displacement table moves n minimum steps in the preset direction and the light spot after the displacement table moves n-1 minimum steps in the preset direction.
Preferably, the third determination unit is configured to: substituting the microscopic magnification factor and the position coordinates of the light spots after the displacement table moves n minimum step lengths in the preset direction into the normalization function to obtain an objective function, wherein the objective function is
Figure BDA0002400175740000191
D is the particle diameter of the nano fluorescent particles, FHeight(xi,yi) Is the normalized Gaussian surface fitting distribution of the light spot image at the object plane height i, MHeightIs the microscopic magnification, IHeight(xi,yi) Is the point spread function of the microscope when the height of the object plane is i; and carrying out minimum solving on the target function to obtain a point spread function of the microscope when the height of the object plane is i.
In a third aspect, an embodiment of the present invention further provides a computer-readable medium having non-volatile program codes executable by a processor, where the program codes cause the processor to execute the method for measuring a point spread function of a microscope described in the first embodiment.
In addition, in the description of the embodiments of the present invention, unless otherwise explicitly specified or limited, the terms "mounted," "connected," and "connected" are to be construed broadly, e.g., as meaning either a fixed connection, a removable connection, or an integral connection; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
In the description of the present invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of description and simplicity of description, but do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus, should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the several embodiments provided in the present application, it should be understood that the disclosed system, apparatus and method may be implemented in other ways. The above-described embodiments of the apparatus are merely illustrative, and for example, the division of the units is only one logical division, and there may be other divisions when actually implemented, and for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection of devices or units through some communication interfaces, and may be in an electrical, mechanical or other form.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of the embodiment.
In addition, functional units in the embodiments of the present invention may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (10)

1. A method for measuring a point spread function of a microscope is applied to a microscope point spread function measuring device, and comprises the following steps:
determining a first position coordinate of the optical fiber laser head so that first linearly polarized light is emitted into a first detector, wherein a unit direction vector of the first linearly polarized light detected by the first detector is a preset unit direction vector, and the first linearly polarized light is linearly polarized light which is emitted by the optical fiber laser head at the first position coordinate and is refracted by a refractor;
acquiring a second position coordinate set sent by a second detector and acquiring a light spot image on an image surface of the microscope, wherein the second position coordinate set comprises a plurality of second position coordinates, the second position coordinates are light spot position coordinates formed by nano fluorescent particles on the image surface of the microscope, the second position coordinates are used for representing the height of an object plane vertical to the optical axis of the microscope, and the light spot image is used for representing the moving track of the nano fluorescent particles on the image surface of the microscope in the process that a displacement table moves in a preset direction with a minimum step length;
determining a microscopic magnification array of the microscope based on the spot image, the preset unit direction vector and the second position coordinate set, wherein the microscopic magnification array comprises a plurality of microscopic magnification factors, and the object plane height value of one microscope corresponds to one microscopic magnification factor;
and determining a point diffusion function group by combining the normalization function and the microscopic magnification power group, wherein the point diffusion function group comprises a plurality of point diffusion functions, and the object plane height value of one microscope corresponds to one point diffusion function.
2. The method of claim 1, wherein determining the set of microscopic magnification times of the microscope based on the set of predetermined unit direction vectors and the set of second position coordinates for the image of the spot comprises:
determining a target light spot image and a target second position coordinate, wherein the target light spot image is the light spot image on the image surface of the microscope after the displacement platform moves for n minimum step lengths in the preset direction, and the target second position coordinate is the second position coordinate sent by the second detector after the displacement platform moves for n minimum step lengths in the preset direction;
determining the space attitude compensation quantity of the displacement platform after the displacement platform moves n minimum step lengths in the preset direction based on the light spot image, the preset unit direction vector and the second position coordinate;
determining the target light spot image as a space attitude compensation quantity of a point spread function calibration device after the displacement platform moves n minimum step lengths in a preset direction based on the light spot image, the preset unit direction vector and the second position coordinate;
and after the spatial attitude compensation of the point spread function calibration equipment is completed, determining the microscopic magnification of the microscope after the displacement platform moves n minimum step lengths in the preset direction.
3. The method according to claim 2, wherein determining the target spot image as a spatial attitude compensation amount of the displacement stage after the displacement stage moves n minimum steps in a preset direction based on the spot image, the preset unit direction vector and the second position coordinate comprises:
determining a target unit direction vector corresponding to the target second position coordinate, wherein the target unit direction vector is a unit direction vector of the first linearly polarized light detected by the first detector after the displacement table moves n minimum step lengths in a preset direction;
determining a space attitude compensation quantity of the displacement table by using the target unit direction vector and a preset position direction vector, wherein the space attitude compensation quantity comprises at least one of the following components: a pitch angle compensation amount and a yaw angle compensation amount;
and compensating the spatial attitude of the displacement table based on the spatial attitude compensation amount so that the target second position coordinate is changed into an initial second position coordinate after the displacement table completes the spatial attitude compensation, wherein the initial second position coordinate is a second position coordinate sent by the second detector before the displacement table moves in a preset direction.
4. The method according to claim 3, wherein determining the target spot image as a spatial attitude compensation amount of the point spread function calibration device after the displacement stage moves n minimum steps in a preset direction based on the spot image, the preset unit direction vector and the second position coordinate comprises:
performing Gaussian surface fitting on the target light spot image to obtain a Gaussian surface fitting image;
performing full-width half-maximum difference calculation on the Gaussian surface fitting image to obtain a difference value of the Gaussian surface fitting image, and performing absolute value calculation on the difference value to obtain an absolute value of the difference value of the Gaussian surface fitting image;
determining the space attitude compensation quantity of the point spread function calibration equipment based on the absolute value;
and performing spatial attitude compensation on the point spread function calibration equipment based on the spatial attitude compensation amount of the point spread function calibration equipment, so that the target second position coordinate is changed into the initial second position coordinate after the point spread function calibration equipment completes the spatial attitude compensation.
5. The method of claim 4, wherein after completing the spatial pose compensation of the point spread function calibration device, determining the target spot image as n minimum steps of movement of the displacement stage in a preset direction, the microscopic magnification of the microscope comprises:
acquiring a translation distance sent by the first detector, wherein the translation distance is the translation distance of the first linearly polarized light on the first detector;
and determining the ratio of the moving distance to the translation distance as the microscopic magnification, wherein the moving distance is the distance between the light spot after the displacement table moves n minimum steps in the preset direction and the light spot after the displacement table moves n-1 minimum steps in the preset direction.
6. The method of claim 2, wherein determining a set of point spread functions in combination with a normalization function and the set of microscopic magnification factors comprises:
substituting the microscopic magnification factor and the position coordinates of the light spots after the displacement table moves n minimum step lengths in the preset direction into the normalization function to obtain an objective function, wherein the objective function is
Figure FDA0002400175730000031
D is the particle diameter of the nano fluorescent particles, FHeight(xi,yi) Is the normalized Gaussian surface fitting distribution of the light spot image at the object plane height i, MHeightIs the microscopic magnification, IHeight(xi,yi) Is the point spread function of the microscope when the height of the object plane is i;
and carrying out minimum solving on the target function to obtain a point spread function of the microscope when the height of the object plane is i.
7. A measuring device of a microscope point spread function is characterized by being applied to a microscope point spread function measuring device and comprising: a first determining unit, an obtaining unit, a second determining unit and a third determining unit, wherein,
the first determining unit is used for determining a first position coordinate of the optical fiber laser head so as to enable first linearly polarized light to enter a first detector, and the unit direction vector of the first linearly polarized light detected by the first detector is a preset unit direction vector, wherein the first linearly polarized light is linearly polarized light which is emitted by the optical fiber laser head at the first position coordinate and is refracted by a refractor;
the acquiring unit is used for acquiring a second position coordinate set sent by a second detector and acquiring a light spot image on the image surface of the microscope, wherein the second position coordinate set comprises a plurality of second position coordinates, the second position coordinates are light spot position coordinates formed by the nano fluorescent particles on the image surface of the microscope, the second position coordinates are used for representing the height of the object surface of the microscope, and the light spot image is used for representing the moving track of the nano fluorescent particles on the image surface of the microscope in the process that the displacement table moves in the preset direction with the minimum step length;
the second determining unit is configured to determine a microscopic magnification array of the microscope based on the spot image, the preset unit direction vector, and the second position coordinate set, where the microscopic magnification array includes a plurality of microscopic magnifications, and an object plane height value of one microscope corresponds to one microscopic magnification;
and the third determining unit is used for determining a point spread function set by combining the normalization function and the microscopic magnification power set, wherein the point spread function set comprises a plurality of point spread functions, and the object plane height value of one microscope corresponds to one point spread function.
8. The apparatus of claim 7, wherein the second determining unit is configured to:
determining a target light spot image and a target second position coordinate, wherein the target light spot image is the light spot image on the image surface of the microscope after the displacement platform moves for n minimum step lengths in the preset direction, and the target second position coordinate is the second position coordinate sent by the second detector after the displacement platform moves for n minimum step lengths in the preset direction;
determining the target light spot image as a space attitude compensation quantity of the displacement platform after the displacement platform moves n minimum step lengths in a preset direction based on the light spot image, the preset unit direction vector and the second position coordinate;
determining the target light spot image as a space attitude compensation quantity of a point spread function calibration device after the displacement platform moves n minimum step lengths in a preset direction based on the light spot image, the preset unit direction vector and the second position coordinate;
and after the spatial attitude compensation of the point spread function calibration equipment is completed, determining the target light spot image as the microscopic magnification of the microscope after the displacement platform moves n minimum step lengths in the preset direction.
9. The apparatus of claim 8, wherein the second determining unit is configured to:
determining a target unit direction vector corresponding to the target second position coordinate, wherein the target unit direction vector is a unit direction vector of the first linearly polarized light detected by the first detector after the displacement table moves n minimum step lengths in a preset direction;
determining a space attitude compensation quantity of the displacement table by using the target unit direction vector and a preset position direction vector, wherein the space attitude compensation quantity comprises at least one of the following components: a pitch angle compensation amount and a yaw angle compensation amount;
and compensating the spatial attitude of the displacement table based on the spatial attitude compensation amount so that the target second position coordinate is changed into an initial second position coordinate after the displacement table completes the spatial attitude compensation, wherein the initial second position coordinate is a second position coordinate sent by the second detector before the displacement table moves in a preset direction.
10. A computer-readable medium having non-volatile program code executable by a processor, wherein the program code causes the processor to perform the method of measuring a point spread function of a microscope according to any one of claims 1 to 7.
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