CN111061063A - Pupil filtering far-field super-resolution imaging system and pupil filter design method - Google Patents

Pupil filtering far-field super-resolution imaging system and pupil filter design method Download PDF

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CN111061063A
CN111061063A CN201910726353.2A CN201910726353A CN111061063A CN 111061063 A CN111061063 A CN 111061063A CN 201910726353 A CN201910726353 A CN 201910726353A CN 111061063 A CN111061063 A CN 111061063A
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pupil
field
pupil filter
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CN111061063B (en
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王超
刘壮
史浩东
付强
李英超
魏明
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Changchun University of Science and Technology
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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/58—Optics for apodization or superresolution; Optical synthetic aperture systems
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/42—Diffraction optics, i.e. systems including a diffractive element being designed for providing a diffractive effect
    • G02B27/46—Systems using spatial filters

Abstract

A pupil filtering far-field super-resolution imaging system and a pupil filter design method belong to the technical field of super-resolution imaging, and are used for solving the problem that the final super-resolution imaging quality is seriously influenced in the existing far-field super-resolution imaging system with field diaphragm scanning, and the system is sequentially arranged along the light incidence direction: the system comprises a front-end optical objective, a field diaphragm, a collimating lens group, a pupil filter, an imaging lens and a CCD detector, wherein the front-end optical objective is used for imaging a distant scene at a system middle image plane, the field diaphragm is arranged at a rear focal plane of the front-end optical objective, namely the whole system middle image plane, a front focus of the collimating lens group is arranged at the system middle image plane, the pupil filter is arranged at a rear-end exit pupil position of a system formed by combining the front-end optical objective and the collimating lens group, the effective aperture position and size of the pupil filter are coincident with the exit pupil plane, the imaging lens performs secondary imaging on light passing through the pupil filter, and the target plane of the CCD detector is coincident with the secondary imaging plane.

Description

Pupil filtering far-field super-resolution imaging system and pupil filter design method
Technical Field
The invention belongs to the technical field of super-resolution imaging, and particularly relates to a pupil filtering far-field super-resolution imaging system and a pupil filter design method.
Background
Diffraction effects are a fundamental property of light waves, and thus the resolution of conventional optical systems is limited by the system numerical aperture NA and the operating wavelength λ. How to break through the optical diffraction limit and obtain super-resolution is one of the pursuits of unchanging the optical boundary to obtain more tiny details of an object scene. The placement of a wavefront modulation module, i.e., pupil filtering, at the system pupil is currently considered a promising technique for achieving far-field super-resolution.
The Chinese patent application numbers are: "201610517791.4" in patent name "a wide-band far-field super-resolution imaging device". The technical scheme is as follows: a broadband far-field super-resolution imaging device is characterized in that: this image device includes in proper order along light incident direction from left to right: the wavefront modulation module is used for modulating the phase amplitude of a light field, the wavefront modulation module is placed at the exit pupil surface position at the rear end of the combination system of the objective lens module and the relay imaging module, and the effective aperture position and the size of the wavefront modulation module are coincided with the exit pupil surface; wherein: the wavefront modulation module comprises one of the following components: the device comprises a 0/pi binary phase wavefront modulation module, a 0-2 pi continuous phase wavefront modulation module, an 0/1 amplitude wavefront modulation module, a 0-1 continuous amplitude wavefront modulation module or a combination of any phase modulation module and any amplitude modulation module.
In the technology, the field diaphragm is placed at the central position, the size of the diaphragm is reduced to the size of a diffraction limit focal spot, a light-transmitting small hole conjugated with the field diaphragm is added at the position of the CCD detector, the size of the small hole is the size of a super-resolution central focal spot, and super-resolution imaging in a confocal scanning mode can be realized by moving a sample or moving the whole optical imaging system.
In the technical scheme of the patent, the field diaphragm is used for field selection, and large field imaging can be realized by a method of scanning the field diaphragm. However, the field diaphragm itself belongs to a micron-sized aperture, imaging light can also be diffracted when passing through the aperture, and the smaller the diameter of the diaphragm is, the more obvious the diffraction effect is, which causes broadening of a central focal spot main lobe of a point spread function and rising of side lobe energy, and seriously affects the super-resolution imaging quality at the final CCD detector.
Disclosure of Invention
The invention provides a pupil filtering far-field super-resolution imaging system and a pupil filter design method, aiming at solving the problems that in the existing far-field super-resolution imaging system scanned by a field diaphragm, the field diaphragm generates a diffraction effect, so that the central focal spot main lobe of a point spread function is widened, the energy of a side lobe is increased, and the final super-resolution imaging quality is seriously influenced.
The technical scheme adopted by the invention is as follows:
the pupil filtering far-field super-resolution imaging system is sequentially arranged along the incident direction of light rays as follows: the front-end optical objective lens is used for imaging a distant scene at the middle image surface of the system, the field diaphragm is arranged at the rear focal surface of the front-end optical objective lens, namely the middle image surface of the whole system, the front focus of the collimating lens group is arranged at the middle image surface of the system, the pupil filter is arranged at the rear-end exit pupil position of the system formed by combining the front-end optical objective lens and the collimating lens group, the effective aperture position and size of the pupil filter coincide with the exit pupil surface, the imaging lens performs secondary imaging on light passing through the pupil filter, and the target surface of the CCD detector coincides with the secondary imaging plane.
A method for designing a pupil filter, the method comprising the steps of:
step 1, designing a pupil filter initial structure by using a common global optimization algorithm, wherein the pupil filter is of a pure amplitude type, a pure phase type or a complex amplitude type, a modulation function of the pupil filter satisfies that after parallel light beams with working wavelengths pass through the pupil filter, the width of a main lobe of a point spread function formed at a focal plane is smaller than the width of a main lobe of a diffraction limit Airy spot of a system, and a wavefront modulation function of the pupil filter initial structure is expressed as:
P'(ρ,θ)＝W(ρ,θ)ei·t(ρ,θ)(A)
Wherein rho and theta are respectively radial and angular coordinates at the pupil, W (rho and theta) is an amplitude modulation function, and t (rho and theta) is a phase modulation function;
step 2, performing integral calculation according to Fresnel and Fraunhofer diffraction formulas to obtain the complex amplitude distribution of the wave front reaching the front surface of the pupil filter; the calculation process is as follows:
incident light field complex amplitude denoted as U1(ρ1,θ1) Complex amplitude U reaching the field diaphragm through the front end optical objective2(ρ2,θ2) The propagation of (a) is fraunhofer diffraction and can be expressed as:
Figure RE-GDA0002260844670000021
where ρ is1,ρ2，θ1，θ2Radial and angular coordinates of the light field at the front-end optical objective and the field stop, respectively, D1Is the clear aperture of the front-end optical objective lens, f1The focal length of the front-end optical objective lens is defined, lambda is the wavelength of incident light, and k is 2 pi/lambda;
the field stop in the system may be effected by a transmittance function U2(ρ2,θ2) To represent;
Figure RE-GDA0002260844670000022
U2'(ρ2,θ2)＝U2(ρ2,θ2)·P2(ρ2,θ2) (IV)
Wherein d is0Is the aperture of the field diaphragm, U2'(ρ2,θ2) For passing through field stopThe latter light field distribution;
the light is transmitted to the collimator objective from the field diaphragm, and then the light field complex amplitude after passing through the collimator objective can be obtained through the phase transformation of the collimator objective:
Figure RE-GDA0002260844670000031
Figure RE-GDA0002260844670000032
Figure RE-GDA0002260844670000033
wherein D2To collimate the aperture of the objective lens, d2For the distance of the intermediate image plane from the collimator objective, p3，θ3Radial and angular coordinates, U, at the collimator objective, respectively3(ρ3,θ3) For the front surface optical field distribution of the collimator objective, U3'(ρ3,θ3) For collimating the optical field distribution at the rear surface of the objective lens, P3(ρ3,θ3) Is a complex amplitude transmittance function of the collimating objective;
the plane where the collimating objective lens and the pupil filter are located is represented by a diffraction formula, and the complex amplitude of a light field reaching the pupil filter is as follows:
Figure RE-GDA0002260844670000034
wherein d is the distance from the collimating objective to the pupil filter, ρ and θ are the radial coordinate and the angular coordinate of the plane where the pupil filter is located, and U4(ρ, θ) is the complex amplitude reaching the front surface of the filter;
is provided with a U4The amplitude distribution of (ρ, θ) is V (ρ, θ), the phase distribution is Φ (ρ, θ), and the optical field distribution can be expressed as:
U4(ρ,θ)＝V(ρ,θ)ei·φ(ρ,θ)(nine);
step 3, designing a pupil filter complex amplitude compensation factor for compensating the field stop diffraction effect, and correcting the initial structure of the pupil filter obtained in the first step:
Figure RE-GDA0002260844670000035
the final pupil filter complex amplitude function should be multiplied by both:
Figure RE-GDA0002260844670000036
the design of the pupil filter is thus completed.
The invention has the beneficial effects that:
1. aiming at a pupil filtering far-field super-resolution imaging optical system for realizing large-field imaging in a mode of scanning a field diaphragm, the invention solves the problems that a main lobe of a central focal spot of a point spread function is widened and the energy of a side lobe is increased to seriously influence the final super-resolution imaging quality due to a diffraction effect generated by a small-hole field diaphragm by a design method of superposing a certain complex amplitude factor in a pupil filter; the super-resolution high-quality imaging can be realized in a large field range.
2. The invention only changes the pupil filter, does not increase the complexity of the optical path, and has simple structure and easy realization.
Drawings
FIG. 1 is a schematic diagram of a pupil filtering far field super-resolution imaging system according to the present invention;
FIG. 2 is a wavefront modulation complex amplitude distribution of a pupil filter initial structure;
FIG. 3 is a comparison of super-resolution spots with diffraction-limited Airy spots for a super-resolution system without a field stop and with a pupil filter as in FIG. 2;
FIG. 4 is a dashed line of a super-resolution system with field stops of different apertures added and pupil filters as shown in FIG. 2; the solid line is the super-resolution light spot of the system after the pupil filter adds corresponding compensation factors respectively.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings.
The technical scheme adopted by the invention is as follows:
as shown in fig. 1, the pupil-filtered far-field super-resolution imaging system is sequentially arranged along the incident direction of light rays as follows: front end optical objective 1, field diaphragm 2, the collimator group 3, pupil filter 4, imaging lens 5 and CCD detector 6, front end optical objective 1 is used for forming images far away the scene in the middle image plane department of system, field diaphragm 2 places the back focal plane of front end optical objective 1 promptly whole system middle image plane department, the preceding focus of collimator group 3 is in system middle image plane department, pupil filter 4 places the rear end exit pupil position of the system of front end optical objective 1 and the collimator group 3 combination, and pupil filter 4 effective aperture position and size and exit pupil plane coincidence, imaging lens 5 will carry out secondary imaging through the light of pupil filter 4, CCD detector 6 target surface with secondary imaging plane coincidence.
In this embodiment, the front-end optical objective lens 1, the collimator group 3, and the imaging lens 5 are all aberration-free ideal lenses, and the focal length and the aperture of the three lenses are 500mm and 10mm, respectively. The field diaphragm 2 is an iris diaphragm, and the diameter of the hole is 65-140 mu m.
The illumination wavelength of the system is incoherent light with the wavelength of lambda being 532 nm.
The design method of the pupil filter 4 comprises the following steps:
1. designing the initial structure of the pupil filter by common global optimization algorithm (genetic algorithm, annealing algorithm, etc.), wherein the pupil filter can be pure amplitude type, pure phase type or complex amplitude type, the modulation function of the filter is such that after the parallel light beam with working wavelength passes through the filter, the main lobe width of the point spread function formed at the focal plane is less than the main lobe width of the diffraction limit Airy spots of the system, and the wavefront modulation function of the initial structure of the pupil filter is expressed as
P'(ρ,θ)＝W(ρ,θ)ei·t(ρ,θ)(A)
Where ρ, θ are radial and angular coordinates at the pupil, W (ρ, θ) is the amplitude modulation function, and t (ρ, θ) is the phase modulation function.
In the present embodiment, a four-ring stepped phase type pupil filter is selected as an initial structure, and the phase distribution is shown in fig. 2. When no field diaphragm is added, the width of the main lobe of the super-resolution light spot obtained by the modulation of the pupil filter is 48.5 μ M, that is, the super-resolution magnification G is 1.34, and M is 0.49; a comparison of the super-resolution spot with the diffraction limited airy disk is shown in figure 3.
As can be seen from fig. 3, the size d of the field stop is set so as to block high-intensity side lobes that affect imaging while not blocking main lobe information0Should satisfy 48.5 μm<d0<152 μm, the field stop aperture range of the present embodiment meets this requirement.
2. And (3) performing integral calculation according to Fresnel and Fraunhofer diffraction formulas to obtain the complex amplitude distribution of the wave front reaching the front surface of the pupil filter, wherein the calculation process is as follows:
incident light field complex amplitude denoted as U1(ρ1,θ1) Complex amplitude U reaching the field diaphragm through the front end optical objective2(ρ2,θ2) The propagation of (a) is fraunhofer diffraction and can be expressed as:
Figure RE-GDA0002260844670000051
where ρ is1,ρ2，θ1，θ2Radial and angular coordinates of the light field at the front-end optical objective and the field stop, respectively, D1Is the clear aperture of the front-end optical objective lens, f1And the focal length of the front-end optical objective lens is shown, wherein lambda is the wavelength of incident light, and k is 2 pi/lambda.
The field stop in the system may be effected by a transmittance function U2(ρ2,θ2) To indicate.
Figure RE-GDA0002260844670000052
U2'(ρ2,θ2)＝U2(ρ2,θ2)·P2(ρ2,θ2) (IV) wherein d0Is the aperture of the field diaphragm, U2'(ρ2,θ2) The light field distribution after passing through the field diaphragm is obtained;
the light field is transmitted to the collimator objective from the field diaphragm, and then the complex amplitude of the light field passing through the collimator objective can be obtained through the phase transformation of the collimator objective:
Figure RE-GDA0002260844670000053
Figure RE-GDA0002260844670000061
Figure RE-GDA0002260844670000062
wherein D2To collimate the aperture of the objective lens, d2The distance from the middle image surface to the collimator objective is 500mm in the example, rho3，θ3Radial and angular coordinates, U, at the collimator objective, respectively3(ρ3,θ3) For the front surface optical field distribution of the collimator objective, U3'(ρ3,θ3) For collimating the optical field distribution at the rear surface of the objective lens, P3(ρ3,θ3) As a function of the complex amplitude transmittance of the collimator objective.
The plane where the collimating objective lens and the pupil filter are located is represented by a diffraction formula, and the complex amplitude of a light field reaching the pupil filter is as follows:
Figure RE-GDA0002260844670000063
wherein d is the distance from the collimating objective to the pupil filter, in this case 1000mm, ρ, θ are the radial coordinate and the angular coordinate of the plane in which the pupil filter is located, U4(ρ, θ) is the complex amplitude that reaches the front surface of the filter. Since the incident light and the optical system are rotationally symmetric in this example, U4(ρ, θ) can be reduced to U with radial coordinates only4(ρ)。
Is provided with a U4The amplitude distribution of (ρ) is V (ρ), the phase distribution is φ (ρ), and the optical field distribution can be expressed as:
U4(ρ)＝V(ρ)ei·φ(ρ)(nine)
3. Designing a complex amplitude compensation factor of the pupil filter for compensating the diffraction effect of the field stop, and correcting the initial structure of the pupil filter obtained in the first step:
Figure RE-GDA0002260844670000064
this is because the compensation factor should have the following characteristics:
Figure RE-GDA0002260844670000065
then U is4(ρ)·Pt"(ρ) ═ 1. However, if there is a field stop, the amplitude of the light field portion reaching the exit pupil is less than 1, and in the above formula, the reciprocal of V (ρ) must be greater than 1, and the amplitude is the transmittance, and cannot be greater than 1. Therefore, further processing is required to divide the reciprocal data by V-1Peak value of (p), i.e.
Figure RE-GDA0002260844670000066
The modified pupil filter complex amplitude function should be multiplied by both:
Figure RE-GDA0002260844670000071
in this embodiment, the complex amplitude compensation factor is represented analytically by polynomial fitting, so as to facilitate processing. Order to
Figure RE-GDA0002260844670000072
Phi' (ρ) — phi (ρ), then:
P'(ρ)＝V'(ρ)ei·φ'(ρ)(twelve)
A fourth order polynomial fit is made to V '(ρ) and Φ' (ρ), respectively:
V'(ρ)＝a10·ρ4+a11·ρ3+a12·ρ2+a13·ρ+a14(thirteen)
φ'(ρ)＝b10·ρ4+b11·ρ3+b12·ρ2+b13·ρ+b14(fourteen)
The coefficients of each term of the corresponding polynomial for different diaphragm sizes are shown in tables 1 and 2.
TABLE 1 Complex amplitude Compensation factor amplitude transmittance fitting polynomial parameters
Figure RE-GDA0002260844670000073
TABLE 2 Complex amplitude Compensation factor phase distribution fitting polynomial parameters
Figure RE-GDA0002260844670000074
The final modified pupil filter modulation function is expressed as:
Figure RE-GDA0002260844670000075
the modified pupil filter designed according to the principle is inserted into the system and simulated to obtain a final image surface light field light intensity normalized distribution curve, and the final image surface light field light intensity normalized distribution curve is compared with the light intensity normalized distribution curve before compensation, as shown in fig. 4. Therefore, after the modified pupil filter is added, the light intensity distribution of the CCD image plane is almost coincident with the initial structure only using the pupil filter without the visual field diaphragm, which shows that the complex amplitude type pupil filter designed according to the principle performs good modification on the diffraction effect of the visual field diaphragm, and can perform high-quality super-resolution imaging.

Claims (4)

1. The pupil filtering far-field super-resolution imaging system is characterized in that the system is sequentially arranged along the incident direction of light rays as follows: a front end optical objective (1), a field diaphragm (2), a collimating lens group (3), a pupil filter (4), an imaging lens (5) and a CCD detector (6),
the front-end optical objective (1) is used for imaging a far scene at a system intermediate image plane;
the field diaphragm (2) is placed on the back focal plane of the front-end optical objective (1), namely the middle image plane of the whole system;
the front focus of the collimating lens group (3) is at the middle image surface of the system; the pupil filter (4) is placed at the rear exit pupil position of a system formed by combining the front optical objective lens (1) and the collimating lens group (3), and the effective aperture position and the effective size of the pupil filter (4) are superposed with the exit pupil surface;
the imaging lens (5) carries out secondary imaging on the light rays passing through the pupil filter (4);
the target surface of the CCD detector (6) is superposed with the secondary imaging plane.
2. The pupil-filtered far-field super-resolution imaging system according to claim 1, wherein the front-end optical objective (1), the collimator set (3) and the imaging lens (5) are aberration-free ideal lenses, and have a focal length of 500mm and a caliber of 10 mm.
3. Pupil filtered far-field super-resolution imaging system according to claim 1, characterized in that the field stop (2) is an iris stop with a stop aperture diameter of 65-140 μm.
4. A method for designing a pupil filter, the method comprising the steps of:
step 1, designing a pupil filter initial structure by using a common global optimization algorithm, wherein the pupil filter is of a pure amplitude type, a pure phase type or a complex amplitude type, a modulation function of the pupil filter satisfies that after parallel light beams with working wavelengths pass through the pupil filter, the width of a main lobe of a point spread function formed at a focal plane is smaller than the width of a main lobe of a diffraction limit Airy spot of a system, and a wavefront modulation function of the pupil filter initial structure is expressed as:
P'(ρ,θ)＝W(ρ,θ)ei·t(ρ,θ)(A)
Wherein rho and theta are respectively radial and angular coordinates at the pupil, W (rho and theta) is an amplitude modulation function, and t (rho and theta) is a phase modulation function;
step 2, performing integral calculation according to Fresnel and Fraunhofer diffraction formulas to obtain the complex amplitude distribution of the wave front reaching the front surface of the pupil filter; the calculation process is as follows:
incident light field complex amplitude denoted as U1(ρ1,θ1) Complex amplitude U reaching the field diaphragm through the front end optical objective2(ρ2,θ2) The propagation of (a) is fraunhofer diffraction and can be expressed as:
Figure RE-FDA0002380058350000011
where ρ is1,ρ2，θ1，θ2Radial and angular coordinates of the light field at the front-end optical objective and the field stop, respectively, D1Is the clear aperture of the front-end optical objective lens, f1The focal length of the front-end optical objective lens is defined, lambda is the wavelength of incident light, and k is 2 pi/lambda;
the field stop in the system may be effected by a transmittance function U2(ρ2,θ2) To represent;
Figure RE-FDA0002380058350000021
U2'(ρ2,θ2)＝U2(ρ2,θ2)·P2(ρ2,θ2) (IV)
Wherein d is0Is the aperture of the field diaphragm, U2'(ρ2,θ2) The light field distribution after passing through the field diaphragm is obtained;
the light is transmitted to the collimator objective from the field diaphragm, and then the light field complex amplitude after passing through the collimator objective can be obtained through the phase transformation of the collimator objective:
Figure RE-FDA0002380058350000022
Figure RE-FDA0002380058350000023
Figure RE-FDA0002380058350000024
wherein D2To collimate the aperture of the objective lens, d2For the distance of the intermediate image plane from the collimator objective, p3，θ3Radial and angular coordinates, U, at the collimator objective, respectively3(ρ3,θ3) For the front surface optical field distribution of the collimator objective, U3'(ρ3,θ3) For collimating the optical field distribution at the rear surface of the objective lens, P3(ρ3,θ3) Is a complex amplitude transmittance function of the collimating objective;
the plane where the collimating objective lens and the pupil filter are located is represented by a diffraction formula, and the complex amplitude of a light field reaching the pupil filter is as follows:
Figure RE-FDA0002380058350000025
wherein d is the distance from the collimating objective to the pupil filter, ρ and θ are the radial coordinate and the angular coordinate of the plane where the pupil filter is located, and U4(ρ, θ) is the complex amplitude reaching the front surface of the filter;
is provided with a U4The amplitude distribution of (ρ, θ) is V (ρ, θ), the phase distribution is Φ (ρ, θ), and the optical field distribution can be expressed as:
U4(ρ,θ)＝V(ρ,θ)ei·φ(ρ,θ)(nine);
step 3, designing a pupil filter complex amplitude compensation factor for compensating the field stop diffraction effect, and correcting the initial structure of the pupil filter obtained in the first step:
Figure RE-FDA0002380058350000031
the final pupil filter complex amplitude function should be multiplied by both:
Figure RE-FDA0002380058350000032
the design of the pupil filter is thus completed.
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CN112882246B (en) * 2021-03-05 2022-11-29 辽宁大学 Super-resolution imaging system and method based on filtering incoherent light field intensity high-order autocorrelation
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CN115128809B (en) * 2022-05-17 2023-11-28 南京工业职业技术大学 Grating efficiency distribution characterization and optimization method for realizing uniform imaging of holographic waveguide display system

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