CN112379516B - Multi-object-plane simultaneous imaging method based on digital multiplexing lens - Google Patents
Multi-object-plane simultaneous imaging method based on digital multiplexing lens Download PDFInfo
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Abstract
The invention provides a simultaneous imaging method for multiple object planes based on a digital multiplexing lens. The digital multiplexing lens modulated by the liquid crystal spatial light modulator in a programming mode is combined with an axial multi-object-plane simultaneous imaging system formed by an infinite cylinder-length microscope objective front group with a fixed focal length, so that any section can be imaged clearly or a plurality of sections can be imaged clearly simultaneously within a certain depth range of a sample, and an image plane which is offset simultaneously along the axial direction and the transverse direction and has diffraction limited image quality is formed on the same imaging plane. The number of imaging surfaces, the axial interval and the transverse offset distance between the imaging surfaces of the system can be controlled and adjusted in real time through programming. The invention can realize a flexible three-dimensional imaging system with time and space resolution without axial scanning, and has important practical application value in the fields of biomedical imaging, pharmacology, material science and the like.
Description
Technical Field
The invention belongs to the field of optical imaging, and particularly relates to a simultaneous imaging method for multiple object planes based on a digital multiplexing lens.
Background
Optical imaging technology has been a major challenge to achieve flexible time and space simultaneous resolution imaging as a direct visualization tool for studying living cell life phenomena. The existing imaging technologies, including confocal laser scanning microscope, two-photon laser scanning microscope, multi-focus multi-photon microscopic imaging technology, optical coherence tomography technology, etc., need to realize horizontal and axial scanning imaging on samples, so that the imaging speed is limited, and the time resolution characteristic is lost.
Although the multi-focal plane parallel imaging method based on the deformed grating can realize multi-section simultaneous imaging, the section imaging capability is mainly concentrated on the lower diffraction order 0 and +/-1, and the diffraction energy of each order is not uniform. Based on the distorted Dammann grating and the multi-object-plane simultaneous imaging system, the problem of non-uniformity of cross-section imaging energy distribution is solved, more cross-section imaging is realized, but complex processing technology and detection technical means are involved, the flexibility and the real-time performance are not enough, and when the number of cross sections and the cross-section interval are changed, the distorted Dammann grating needs to be processed again.
Disclosure of Invention
The invention inlays ideal imaging lenses with different focal lengths and blazed gratings with different diffraction angles together, and generates a digital multiplexing lens by programming of a liquid crystal spatial light modulator (PLUTO). A method for simultaneously imaging multiple object planes based on a digital multiplexing lens is provided. The imaging method can enable any section to be imaged clearly within a certain depth range of a sample, or a plurality of sections to be imaged clearly at the same time, the imaging quality is the same, and the number of the section images, the section imaging interval and the section transverse offset distance are programmable and controllable in real time through a liquid crystal spatial light modulator (PLUTO). The invention realizes the function of the digital multiplexing lens through the liquid crystal spatial light modulator, thereby respectively realizing the focal lengths of the plurality of ideal imaging lenses and the diffraction angles of the plurality of blazed gratings.
The technical scheme of the invention is a simultaneous imaging method of multiple object planes based on a digital multiplexing lens, which comprises the following steps:
step 1: and constructing a multi-object-plane simultaneous imaging system model of the digital multiplexing lens.
Step 2: according to the constructed multi-object-plane simultaneous imaging system model and the combination rule of an ideal optical system, the control of the number of cross-section imaging and the cross-section imaging distance is realized by combining the focal length, the magnification, the image side main plane position, the object side main plane position of the imaging system, the object distance variation of the combined imaging system and the change distance of the object side main plane of the combined imaging system with the focal length of an ideal imaging lens.
And step 3: establishing a phase model of an ideal imaging lens in the liquid crystal spatial light modulator, and establishing a phase model of a blazed grating in the liquid crystal spatial light modulator; a different diffraction angle for each imaging section is achieved.
And 4, step 4: the method comprises the steps of setting the number of ideal imaging lenses and the changed distance of an object side main plane of a combined system according to the requirements of the number of imaging sections and the imaging interval, calculating the focal length of the ideal imaging lenses by combining the set number of the ideal imaging lenses and the changed distance of the object side main plane of the combined system with the step 2, calculating the diffraction angle of a blazed grating by the step 3, constructing a phase model of the digital multiplexing lens on a liquid crystal spatial light modulator, and realizing the design functions of the ideal imaging lenses and the blazed grating in the digital multiplexing lens by the programmed modulation of the liquid crystal spatial light modulator.
Preferably, the multiple object plane simultaneous imaging system model of the digital multiplexing lens in step 1 includes:
the digital multiplexing lens is positioned on the back focal plane of the front group of the infinite cylinder length microobjective;
the digital multiplexing lens is composed of a plurality of ideal imaging lenses and a plurality of blazed gratings; the plurality of ideal imaging lenses are ideal imaging lenses with different focal lengths, and the plurality of blazed gratings are blazed gratings with different diffraction angles; the number of the ideal imaging lens is equal to that of the blazed grating, the ideal imaging lens and the blazed grating are both n, n is more than or equal to 1, and n is an integer;
the ideal imaging lens and the blazed grating are embedded together and are generated by programming modulation of a liquid crystal spatial light modulator;
preferably, the focal length of the combined imaging system in step 2 is:
f′zi＝f'obj
wherein, f'objIs set as the focal length of the front group of the microscope objective lens with infinite tube length, f'ziOf combined imaging system, i.e. at focal length f'objF 'is superposed on the image focal plane of the front group of the infinite tube length microscope objective lens'i i∈[1,n]Irrespective of the focal length f 'of the i-th ideal imaging lens'iHow to vary, the focal length f 'of the imaging system is combined'ziKeeping the same, wherein n is the number of ideal imaging lenses;
and 2, the magnification of the combined imaging system is as follows:
βzi＝β
wherein beta is the magnification of the front group of the microscope objective with infinite cylinder length, betaziMagnification for combined imaging system, i.e. at focal length f'objF 'is superposed on the image focal plane of the front group of the infinite tube length microscope objective lens'i i∈[1,n]Irrespective of the ith ideal imaging lensFocal length f of mirrori'how to vary, magnification of combined imaging system does not follow f'iN is the number of ideal imaging lenses;
the image space main plane position of the combined imaging system in the step 2 is as follows:
H'H′zi＝0
wherein H ' is the image side main plane, H ' of the front group of the infinite tube length microscope objective lens 'ziIs the image-side principal plane of the combined imaging system, i.e. at focal length f'objF 'is superposed on the image focal plane of the front group of the infinite tube length microscope objective lens'i i∈[1,n]Irrespective of the focal length f 'of the i-th ideal imaging lens'iHow to vary, H'ziAlways coincides with the image-side principal plane H 'of the objective lens front group, i.e. the image plane of the combined imaging system remains unchanged and does not follow f'iN is the number of ideal imaging lenses;
the main plane position of the object space of the combined imaging system in the step 2 is as follows:
h is the principal plane of object space of the front group of the microscope objective with infinite tube length, HziIs the object-side principal plane of the combined imaging system, i.e. at focal length f'objF 'is superposed on the image focal plane of the front group of the infinite tube length microscope objective lens'i i∈[1,n]Of the combined imaging system, object-side principal plane with f'iN is the number of ideal imaging lenses;
wherein lziFor combining the object distances of the imaging system, l' is the image distance of the front group of the microscope objective with infinite tube length, and the formula shows that the combination is combinedThe distance of the change of the object space of the image system is equal to the distance of the change of the main plane of the object space of the combined system, and n is the number of ideal imaging lenses;
the changed distance of the object space main plane of the combined system in the step 2 is as follows:
wherein, Δ ziThe distance changed by the main plane of the object space of the combined system after the ith imaging lens is loaded is n, and the n is the number of ideal imaging lenses;
calculating the focal length of the ideal imaging lens in the step 2 according to the changed distance of the object main plane of the combined system in the step 2;
by varying the number of ideal imaging lenses, i.e. n and fi' can be used for controlling the number of section imaging and the section imaging interval, i belongs to [1, n ]]
By changing the corresponding diffraction angle theta of each imaging section in the x and y directionsx-i，θy-iThe transverse offset distance of the cross section and the corresponding diffraction angle theta in the x and y directions can be controlledx-i，θy-iThe method is realized by blazed gratings;
preferably, the step 3 of establishing a phase model of the ideal imaging lens in the liquid crystal spatial light modulator is as follows:
the digital multiplexing lens is a phase diagram generated by a liquid crystal spatial light modulator, and according to the Fourier optics theory, the phase modulation amount of the ith ideal imaging lens on the imaging wavefront is as follows:
where λ is the incident wavelength, x, y are coordinates with the center of the lens as the origin, and fi' is the focal length of the ith ideal imaging lens, and n is the number of the ideal imaging lenses;
setting the pixel resolution of the liquid crystal spatial light modulator as M x N, the pixel center distance as a, M being the number of rows of the liquid crystal spatial light modulator pixels, and N being the number of columns of the liquid crystal spatial light modulator pixels;
the center of the liquid crystal spatial light modulator is taken as the origin of coordinates, and the focal length is fiThe phase model of the ideal imaging lens of' in the liquid crystal spatial light modulator can be expressed as:
in the formula (mod)2πRepresenting a 2 pi operation, k being a first coefficient, l being a second coefficient, a being a pixel center-to-center distance, fi' is the focal length of the ith ideal imaging lens, M is the number of rows of the liquid crystal spatial light modulator pixels, N is the number of columns of the liquid crystal spatial light modulator pixels, and N is the number of the ideal imaging lenses;
and 3, establishing a phase model of the blazed grating in the liquid crystal spatial light modulator:
in order to realize that different axial section images are not overlapped in different areas of an image plane, emergent light beams of ideal imaging lenses with different focal lengths have different diffraction angles;
is realized by using a liquid crystal spatial light modulator to generate a blazed grating with a focal length fi' the outgoing beam of the i-th ideal imaging lens, which is loaded with the phase model distribution of the corresponding i-th blazed grating, is represented as:
in the formula, Tx-iIs the grating period, T, corresponding to the ith ideal imaging lens in the x direction by taking the pixel as a unity-iThe method comprises the steps that a grating period corresponding to the ith ideal imaging lens in the y direction by taking a pixel as a unit is defined, k is a first coefficient, l is a second coefficient, M is the number of rows of pixels of the liquid crystal spatial light modulator, N is the number of columns of the pixels of the liquid crystal spatial light modulator, and N is the number of the ideal imaging lenses;
after loading the ith blazed grating, corresponding to fiThe diffraction angles of the imaging cross-section light beam in the x and y directions are respectively as follows:
wherein a is the pixel center-to-center distance, Tx-iIs the grating period, T, corresponding to the ith ideal imaging lens in the x direction by taking the pixel as a unity-iThe grating period corresponding to the ith ideal imaging lens in the y direction by taking the pixel as a unit, and n is the number of the ideal imaging lenses;
the magnitude of the diffraction angle is respectively equal to Tx-iAnd Ty-iIn relation, the direction of the diffraction angle depends on the sign of k, l;
preferably, the phase model of the digital multiplexing lens in the liquid crystal spatial light modulator in step 4 is:
where a is the pixel center-to-center distance, fi' is the focal length of the ith ideal imaging lens, M is the number of rows of liquid crystal spatial light modulator pixels, N is the number of columns of liquid crystal spatial light modulator pixels, Tx-iIs the grating period, T, corresponding to the ith ideal imaging lens in the x direction by taking the pixel as a unity-iThe grating period corresponding to the ith ideal imaging lens in the unit of pixel in the y directionK is the first coefficient and l is the second coefficient.
The invention inlays ideal imaging lenses with different focal lengths and blazed gratings with different diffraction angles together, and generates a digital multiplexing lens by programming of a liquid crystal spatial light modulator (PLUTO). A method for simultaneously imaging multiple object planes based on a digital multiplexing lens is provided. The imaging method can enable any section to be imaged clearly within a certain depth range of a sample, or a plurality of sections to be imaged clearly at the same time, the imaging quality is the same, and the number of the section images, the section imaging interval and the section transverse offset distance are programmable and controllable in real time through a liquid crystal spatial light modulator (PLUTO). The invention realizes the function of the digital multiplexing lens through the liquid crystal spatial light modulator, thereby respectively realizing the focal lengths of the plurality of ideal imaging lenses and the diffraction angles of the plurality of blazed gratings.
The invention can realize a flexible three-dimensional imaging system with time and space resolution without axial scanning, and has important practical application value in the fields of biomedical imaging, pharmacology, material science and the like.
Drawings
FIG. 1: a multi-object plane simultaneous imaging system of an digital multiplexing lens.
FIG. 2: focal length schematic of the combined imaging system.
FIG. 3: schematic diagram of two-dimensional matrix.
FIG. 4: and (5) calibrating a phase gray scale image.
FIG. 5: the method of the invention is a flow chart.
Detailed Description
In order to facilitate the understanding and implementation of the present invention for those of ordinary skill in the art, the present invention is further described in detail with reference to the accompanying drawings and examples, it is to be understood that the embodiments described herein are merely illustrative and explanatory of the present invention and are not restrictive thereof.
The liquid crystal spatial light modulator adopts a PLUTO-VIS type liquid crystal spatial light modulator produced by HOLOEYE company in Germany, the image plane size is 15.36mm multiplied by 8.64mm, the resolution MXN is 1920 multiplied by 1080, the pixel size is 8 mu M, the interval between pixels is 1 mu M, and the size a of a single pixel is 9 mu M
The following describes an embodiment of the present invention with reference to fig. 1 to 5 as follows:
a method for simultaneously imaging multiple object planes based on a digital multiplexing lens comprises the following specific steps:
step 1: a model of a multi-object plane simultaneous imaging system of an digitally multiplexed lens is constructed as shown in fig. 1.
The multiple object plane simultaneous imaging system model of the digital multiplexing lens in the step 1 comprises:
the digital multiplexing lens is positioned on the back focal plane of the front group of the infinite cylinder length microobjective;
the multi-object-plane simultaneous imaging system of the digital multiplexing lens adopts helium neon laser as an illumination light source, the wavelength lambda is 0.6328 mu, and the focal length f 'of a front group of an infinite cylinder length objective lens is selected'obj25mm, numerical aperture NA 0.25, multiplying factor beta 10×；
The digital multiplexing lens is composed of a plurality of ideal imaging lenses and a plurality of blazed gratings; the plurality of ideal imaging lenses are ideal imaging lenses with different focal lengths, and the plurality of blazed gratings are blazed gratings with different diffraction angles; the number of the ideal imaging lenses is equal to that of the blazed grating, n is 9, n is larger than or equal to 1, and n is an integer;
the ideal imaging lens and the blazed grating are embedded together and are generated by programming modulation of a liquid crystal spatial light modulator;
step 2: according to the constructed multi-object-plane simultaneous imaging system model and the combination rule of an ideal optical system, the control of the number of cross-section imaging and the cross-section imaging distance is realized by combining the focal length, the magnification, the image side main plane position, the object side main plane position of the imaging system, the object distance variation of the combined imaging system and the change distance of the object side main plane of the combined imaging system with the focal length of an ideal imaging lens.
As schematically shown in fig. 2;
f′zi＝f'obj
wherein, f'objIs set as the focal length of the front group of the microscope objective lens with infinite tube length, f'ziOf combined imaging system, i.e. at focal length f'objF 'is superposed on the image focal plane of the front group of the infinite tube length microscope objective lens'i i∈[1,n]Irrespective of the focal length f 'of the i-th ideal imaging lens'iHow to vary, the focal length f 'of the imaging system is combined'ziKeeping the same, wherein n is the number of ideal imaging lenses;
focal length f 'of the ith ideal imaging lens'iAccording to the requirements of the cross-section imaging distance and the changed distance of the main plane of the object space of the combined system in the step 2 in the invention content;
wherein, for P0Cross section,. DELTA.z0＝0,f0' -0, and P1To P8Cross section, set requirement Δ z1＝Δz2＝…＝Δz80.1mm as shown in figure 1;
f′1＝6250mm，f′2＝3125mm，f′3＝2083.33mm，f′4＝1562.5mm
f′5＝1250mm，f′6＝1041.67mm，f′7＝892.85mm，f′8＝781.25mm
and 2, the magnification of the combined imaging system is as follows:
βzi＝β
wherein beta is the magnification of the front group of the microscope objective with infinite cylinder length, betaziMagnification for combined imaging system, i.e. at focal length f'objF 'is superposed on the image focal plane of the front group of the infinite tube length microscope objective lens'i i∈[1,n]Irrespective of the focal length f 'of the i-th ideal imaging lens'iHow varied, the magnification of the combined imaging system is not f'iN is the number of ideal imaging lenses;
the image space main plane position of the combined imaging system in the step 2 is as follows:
H'H′zi＝0
wherein H' is an infinite cylinder length micro-objectImage-side principal plane, H 'of the front mirror group'ziIs the image-side principal plane of the combined imaging system, i.e. at focal length f'objF 'is superposed on the image focal plane of the front group of the infinite tube length microscope objective lens'i i∈[1,n]Irrespective of the focal length f 'of the i-th ideal imaging lens'iHow to vary, H'ziAlways coincides with the image-side principal plane H 'of the objective lens front group, i.e. the image plane of the combined imaging system remains unchanged and does not follow f'iN is the number of ideal imaging lenses;
the main plane position of the object space of the combined imaging system in the step 2 is as follows:
h is the principal plane of object space of the front group of the microscope objective with infinite tube length, HziIs the object-side principal plane of the combined imaging system, i.e. at focal length f'objF 'is superposed on the image focal plane of the front group of the infinite tube length microscope objective lens'i i∈[1,n]Of the combined imaging system, object-side principal plane with f'iN is the number of ideal imaging lenses;
wherein is 1ziThe object distance of the combined imaging system, l' is the image distance of the front group of the infinite tube-length microscope objective, the formula shows that the distance of the object space change of the combined imaging system is equal to the distance of the object space main plane change of the combined imaging system, and n is the number of ideal imaging lenses;
the changed distance of the object space main plane of the combined system in the step 2 is as follows:
wherein, Δ ziThe distance changed by the main plane of the object space of the combined system after the ith imaging lens is loaded is n, and the n is the number of ideal imaging lenses;
calculating the focal length of the ideal imaging lens in the step 2 according to the changed distance of the object main plane of the combined system in the step 2;
by varying the number of ideal imaging lenses, i.e. n and fi' can be used for controlling the number of section imaging and the section imaging interval, i belongs to [1, n ]]
By changing the corresponding diffraction angle theta of each imaging section in the x and y directionsx-i，θy-iThe transverse offset distance of the cross section and the corresponding diffraction angle theta in the x and y directions can be controlledx-i，θy-iThe method is realized by blazed gratings;
and step 3: establishing a phase model of an ideal imaging lens in the liquid crystal spatial light modulator, and establishing a phase model of a blazed grating in the liquid crystal spatial light modulator; a different diffraction angle for each imaging section is achieved.
the digital multiplexing lens is a phase diagram generated by a liquid crystal spatial light modulator, and according to the Fourier optics theory, the phase modulation amount of the ith ideal imaging lens on the imaging wavefront is as follows:
where λ is the incident wavelength, x, y are coordinates with the center of the lens as the origin, and fi' is the focal length of the ith ideal imaging lens, and n is the number of the ideal imaging lenses;
setting the pixel resolution of the liquid crystal spatial light modulator as M x N, the pixel center distance as a, M being the number of rows of the liquid crystal spatial light modulator pixels, and N being the number of columns of the liquid crystal spatial light modulator pixels;
the center of the liquid crystal spatial light modulator is taken as the origin of coordinates, and the focal length is fiThe phase model of the ideal imaging lens of' in the liquid crystal spatial light modulator can be expressed as:
in the formula (mod)2πRepresenting a 2 pi operation, k being a first coefficient, l being a second coefficient, a being a pixel center-to-center distance, fi' is the focal length of the ith ideal imaging lens, M is the number of rows of the liquid crystal spatial light modulator pixels, N is the number of columns of the liquid crystal spatial light modulator pixels, and N is the number of the ideal imaging lenses;
and 3, establishing a phase model of the blazed grating in the liquid crystal spatial light modulator:
in order to realize that different axial section images are not overlapped in different areas of an image plane, emergent light beams of ideal imaging lenses with different focal lengths have different diffraction angles;
is realized by using a liquid crystal spatial light modulator to generate a blazed grating with a focal length fi' the outgoing beam of the i-th ideal imaging lens, which is loaded with the phase model distribution of the corresponding i-th blazed grating, is represented as:
in the formula, Tx-iIs the grating period, T, corresponding to the ith ideal imaging lens in the x direction by taking the pixel as a unity-iIs the grating period corresponding to the ith ideal imaging lens in the y direction by taking the pixel as a unit, k is a first coefficient, l is a second coefficient, and M is the pixel of the liquid crystal spatial light modulatorThe number of rows, N the number of columns of liquid crystal spatial light modulator pixels, and N the number of ideal imaging lenses;
after loading the ith blazed grating, corresponding to fiThe diffraction angles of the imaging cross-section light beam in the x and y directions are respectively as follows:
wherein a is the pixel center-to-center distance, Tx-iIs the grating period, T, corresponding to the ith ideal imaging lens in the x direction by taking the pixel as a unity-iThe grating period corresponding to the ith ideal imaging lens in the y direction by taking the pixel as a unit, and n is the number of the ideal imaging lenses;
the magnitude of the diffraction angle is respectively equal to Tx-iAnd Ty-iIn relation, the direction of the diffraction angle depends on the sign of k, l;
and 4, step 4: the method comprises the steps of setting the number of ideal imaging lenses and the changed distance of an object side main plane of a combined system according to the requirements of the number of imaging sections and the imaging interval, calculating the focal length of the ideal imaging lenses by combining the set number of the ideal imaging lenses and the changed distance of the object side main plane of the combined system with the step 2, calculating the diffraction angle of a blazed grating by the step 3, constructing a phase model of the digital multiplexing lens on a liquid crystal spatial light modulator, and realizing the design functions of the ideal imaging lenses and the blazed grating in the digital multiplexing lens by the programmed modulation of the liquid crystal spatial light modulator.
where a is the pixel center-to-center distance, fiIs the focal length of the ith ideal imaging lens, M is the number of rows of liquid crystal spatial light modulator pixels, N is the number of columns of liquid crystal spatial light modulator pixels, Tx-iIs the grating period, T, corresponding to the ith ideal imaging lens in the x direction by taking the pixel as a unity-iThe grating period corresponding to the ith ideal imaging lens is in the y direction by taking a pixel as a unit, k is a first coefficient, and l is a second coefficient.
The phase distribution of the digital multiplex lens is shown in table 1:
TABLE 1 phase distribution of digitally multiplexed lenses
And 5: matlab is called to generate a two-dimensional matrix, and 9 phase distributions are randomly assigned with initial values to the two-dimensional matrix, as shown in FIG. 3.
Step 6: as shown in fig. 4, which is a scaled phase grayscale diagram, the phase modulation amount corresponding to each pixel point in the matrix is calculated according to the phase expression in table 1, and a grayscale matrix is generated.
The PLUTO works by changing the addressing voltage to control the phase modulation amount of each pixel, the manufacturer of PLUTO already maps the driving voltage to the gray value displayed by the computer when the PLUTO leaves the factory, the manufacturer gives a (gray-phase) customer lookup table, but specifically, each device needs to be recalibrated to obtain the gray-phase calibration curve shown in fig. 4, and the gray corresponding to the curve is loaded on the driving software of the PLUTO to realize the required phase modulation.
And 7: a gray scale map is generated using the Imwrite function and loaded onto the spatial light modulator.
It should be understood that parts of the specification not set forth in detail are well within the prior art.
It should be understood that the above description of the preferred embodiments is given for clarity and not for any purpose of limitation, and that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (3)
1. A multi-object-plane simultaneous imaging method based on a digital multiplexing lens is characterized by comprising the following steps:
step 1: constructing a multi-object-plane simultaneous imaging system model of the digital multiplexing lens;
step 2: according to the constructed multi-object-plane simultaneous imaging system model and the combination rule of an ideal optical system, the control of the number of cross-section imaging and the cross-section imaging distance is realized by combining the focal length, the magnification, the image side main plane position, the object side main plane position of the imaging system, the object distance variation of the combined imaging system and the change distance of the object side main plane of the combined imaging system with the focal length change of an ideal imaging lens;
and step 3: establishing a phase model of an ideal imaging lens in the liquid crystal spatial light modulator, and establishing a phase model of a blazed grating in the liquid crystal spatial light modulator; different diffraction angles of each imaging section are realized;
and 4, step 4: setting the number of ideal imaging lenses and the changed distance of the object side main plane of the combined system according to the requirements of the number of imaging sections and the imaging interval, calculating the focal length of the ideal imaging lenses by combining the set number of the ideal imaging lenses and the changed distance of the object side main plane of the combined system with the step 2, calculating the diffraction angle of the blazed grating by the step 3, constructing a phase model of the digital multiplexing lens on the liquid crystal spatial light modulator, and realizing the design functions of the ideal imaging lenses and the blazed grating in the digital multiplexing lens by the programmed modulation of the liquid crystal spatial light modulator;
the multiple object plane simultaneous imaging system model of the digital multiplexing lens in the step 1 comprises:
the digital multiplexing lens is positioned on the back focal plane of the front group of the infinite cylinder length microobjective;
the digital multiplexing lens is composed of a plurality of ideal imaging lenses and a plurality of blazed gratings; the plurality of ideal imaging lenses are ideal imaging lenses with different focal lengths, and the plurality of blazed gratings are blazed gratings with different diffraction angles; the number of the ideal imaging lens is equal to that of the blazed grating, the ideal imaging lens and the blazed grating are both n, n is more than or equal to 1, and n is an integer;
the ideal imaging lens and the blazed grating are embedded together and are generated by programming modulation of a liquid crystal spatial light modulator;
step 2, the focal length of the combined imaging system is as follows:
f′zi＝f′obj
wherein, f'objIs set as the focal length of the front group of the microscope objective lens with infinite tube length, f'ziOf combined imaging system, i.e. at focal length f'objF 'is superposed on the image focal plane of the front group of the infinite tube length microscope objective lens'ii∈[1,n]Irrespective of the focal length f 'of the i-th ideal imaging lens'iHow to vary, the focal length f 'of the imaging system is combined'ziKeeping the same, wherein n is the number of ideal imaging lenses;
and 2, the magnification of the combined imaging system is as follows:
βzi＝β
wherein beta is the magnification of the front group of the microscope objective with infinite cylinder length, betaziMagnification for combined imaging system, i.e. at focal length f'objF 'is superposed on the image focal plane of the front group of the infinite tube length microscope objective lens'ii∈[1,n]Irrespective of the focal length f 'of the i-th ideal imaging lens'iHow varied, the magnification of the combined imaging system is not f'iN is the number of ideal imaging lenses;
the image space main plane position of the combined imaging system in the step 2 is as follows:
H'H′zi＝0
wherein H ' is the image side main plane, H ' of the front group of the infinite tube length microscope objective lens 'ziIs the image-side principal plane of the combined imaging system, i.e. at focal length f'objImage space focal plane superposition focal of front group of infinite tube length microscope objectiveDistance is f'ii∈[1,n]Irrespective of the focal length f 'of the i-th ideal imaging lens'iHow to vary, H'ziAlways coincides with the image-side principal plane H 'of the objective lens front group, i.e. the image plane of the combined imaging system remains unchanged and does not follow f'iN is the number of ideal imaging lenses;
the main plane position of the object space of the combined imaging system in the step 2 is as follows:
i∈[1,n]
h is the principal plane of object space of the front group of the microscope objective with infinite tube length, HziIs the object-side principal plane of the combined imaging system, i.e. at focal length f'objF 'is superposed on the image focal plane of the front group of the infinite tube length microscope objective lens'ii∈[1,n]Of the combined imaging system, object-side principal plane with f'iN is the number of ideal imaging lenses;
step 2 object distance position with f 'of combined imaging system'iThe change is as follows:
i∈[1,n]
wherein lziThe distance of the object space of the combined imaging system is l' is the image distance of the front group of the infinite tube-length microscope objective, the formula shows that the distance of the object space change of the combined imaging system is equal to the distance of the change of the main plane of the object space of the combined system, and n is the number of ideal imaging lenses;
the changed distance of the object space main plane of the combined system in the step 2 is as follows:
i∈[1,n]
wherein, Δ ziThe distance changed by the main plane of the object space of the combined system after the ith imaging lens is loaded is n, and the n is the number of ideal imaging lenses;
calculating the focal length of the ideal imaging lens in the step 2 according to the changed distance of the object main plane of the combined system in the step 2;
by varying the number of ideal imaging lenses, i.e. n and f'iCan be used for controlling the number of cross-section imaging and the cross-section imaging interval, i belongs to [1, n ]]
By changing the corresponding diffraction angle theta of each imaging section in the x and y directionsx-i，θy-iThe transverse offset distance of the cross section and the corresponding diffraction angle theta in the x and y directions can be controlledx-i，θy-iBy means of blazed gratings.
2. The method of claim 1, wherein the method comprises:
step 3, establishing a phase model of the ideal imaging lens in the liquid crystal spatial light modulator is as follows:
the digital multiplexing lens is a phase diagram generated by a liquid crystal spatial light modulator, and according to the Fourier optics theory, the phase modulation amount of the ith ideal imaging lens on the imaging wavefront is as follows:
i∈[1,n]
wherein λ is an incident wavelength, x, y are coordinates with the center of the lens as an origin, and f'iIs the focal length of the ith ideal imaging lens, and n is the number of the ideal imaging lenses;
setting the pixel resolution of the liquid crystal spatial light modulator as M x N, the pixel center distance as a, M being the number of rows of the liquid crystal spatial light modulator pixels, and N being the number of columns of the liquid crystal spatial light modulator pixels;
the focal length is f 'by taking the center of the liquid crystal spatial light modulator as the origin of coordinates'iThe phase model of the ideal imaging lens in the liquid crystal spatial light modulator can be expressed as:
i∈[1,n]
in the formula (mod)2πRepresenting 2 pi complementation operation, k being a first coefficient, l being a second coefficient, a being a pixel center distance, f'iThe focal length of the ith ideal imaging lens is, M is the number of rows of the pixels of the liquid crystal spatial light modulator, N is the number of columns of the pixels of the liquid crystal spatial light modulator, and N is the number of the ideal imaging lenses;
and 3, establishing a phase model of the blazed grating in the liquid crystal spatial light modulator:
in order to realize that different axial section images are not overlapped in different areas of an image plane, emergent light beams of ideal imaging lenses with different focal lengths have different diffraction angles;
realized by generating a blazed grating with a liquid crystal spatial light modulator, for a focal length of f'iThe loaded phase model distribution of the corresponding ith blazed grating of the outgoing beam of the ith ideal imaging lens is expressed as:
i∈[1,n]
in the formula, Tx-iIs the grating period, T, corresponding to the ith ideal imaging lens in the x direction by taking the pixel as a unity-iIs a y directionIn the grating period corresponding to the ith ideal imaging lens taking a pixel as a unit, k is a first coefficient, l is a second coefficient, M is the number of rows of pixels of the liquid crystal spatial light modulator, N is the number of columns of the pixels of the liquid crystal spatial light modulator, and N is the number of the ideal imaging lenses;
step 3, each imaging section has different diffraction angles:
f 'after loading the ith blazed grating'iThe diffraction angles of the imaging cross-section light beams in the x and y directions are respectively as follows:
i∈[1,n]
wherein a is the pixel center-to-center distance, Tx-iIs the grating period, T, corresponding to the ith ideal imaging lens in the x direction by taking the pixel as a unity-iThe grating period corresponding to the ith ideal imaging lens is in the y direction by taking a pixel as a unit, and n is the number of the ideal imaging lenses;
the magnitude of the diffraction angle is respectively equal to Tx-iAnd Ty-iIn this regard, the direction of the diffraction angle depends on the sign of k, l.
3. The method of claim 1, wherein the method comprises:
step 4, the phase model of the digital multiplexing lens in the liquid crystal spatial light modulator is as follows:
i∈[1,n]
wherein a is pixel center distance, f'iIs the focal length of the ith ideal imaging lens,m is the number of rows of liquid crystal spatial light modulator pixels, N is the number of columns of liquid crystal spatial light modulator pixels, Tx-iIs the grating period, T, corresponding to the ith ideal imaging lens in the x direction by taking the pixel as a unity-iThe grating period corresponding to the ith ideal imaging lens is in the y direction by taking a pixel as a unit, k is a first coefficient, and l is a second coefficient.
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