Partitioned quarter-wave plate and design method thereof

Abstract

The invention relates to a partitioned quarter-wave plate and a design method thereof. The partitioned quarter-wave plate comprises a central through hole and a plurality of polarized light conversion groups surrounding the central through hole, and the design method comprises the following steps: determining a Jones matrix corresponding to a fast axis angle of a conversion region and a Jones vector of an illumination beam according to the fast axis angle of the conversion region, and calculating to obtain a vector of the illumination beam after passing through the conversion region; and making the component of the vector of the illumination beam passing through the conversion area not equal to 0 in the direction perpendicular to the normal and the component equal to 0 in the normal direction, and calculating to obtain the rotating angle of the fast axis relative to the polarization direction. Compared with the prior art, due to the central through hole, a 0-level light beam of circularly polarized light can be still circularly polarized light; + / -1-level light beams of the circularly polarized light penetrate through two conversion areas of the polarized light conversion group to be modulated into s-line polarized light, and the polarization direction of the illumination light beam group is regulated and controlled.

Description

Technical Field

[0001] This invention relates to structured light illumination imaging technology, and more particularly to partitioned quarter-wave plates and their design methods. Background Technology

[0002] Structured light illumination super-resolution microscopy has been widely used in biomedical imaging due to its low photobleaching, high compatibility, and fast imaging speed. To achieve high-modulation structured light illumination fringes, s-polarized light interferometry is typically used, which requires simultaneous modulation of the beam polarization direction while rotating the fringe direction. Polarization modulation can be achieved using electro-optic modulators, but this is costly and involves complex synchronization control. Alternatively, it can be achieved using partitioned half-wave plates, which require no synchronization control and are inexpensive. However, existing partitioned half-wave plate schemes are only suitable for two-dimensional structured light illumination imaging. In three-dimensional structured light illumination, fringes in different directions all pass through the same area of ​​the waveplate, making it impossible to modulate their polarization direction.

[0003] A search revealed that application publication number CN118483164A discloses a Mueller matrix ellipsometer and its detection method, specifically disclosing a symmetrically structured polarizing assembly and a polarizing analyzer assembly. Each assembly includes a regional waveplate and a linear polarizer. Each regional waveplate has eight regions with fan-ring cross-sections. The inner and outer diameters of these eight regions are identical, and every two regions form a pair with the same fast axis direction. The fast axis direction is divided into four directions, and the phase delay of each fan-ring is consistent. The emitted beam from any fan-ring in the first regional waveplate covers a portion of two adjacent fan-rings in the second regional waveplate. Furthermore, the arrangement order of the fan-rings corresponding to the fast axis directions in the first regional waveplate differs from that in the second regional waveplate, forming 16 different combinations of fan-ring fast axis directions corresponding to 16 detection units. However, this prior art cannot achieve control over the polarization direction.

[0004] In summary, the technical problem that needs to be solved is how to design a quarter-wave plate that can control the polarization direction and its design method. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art in that it cannot control the polarization direction by providing a partitioned quarter-wave plate and its design method.

[0006] The objective of this invention can be achieved through the following technical solutions.

[0007] According to one aspect of the present invention, a partitioned quarter-wave plate is provided, comprising a central through-hole and a plurality of polarization conversion groups surrounding the central through-hole, each polarization conversion group comprising two conversion regions spaced 180° apart and the fast axis directions of the two conversion regions being symmetrically arranged with the fast axis directions differing from each other by 180°. Each illumination beam group includes a 0th-order illumination beam modulated as circularly polarized light and ±1st-order illumination beams. The 0th-order illumination beam passes through a central aperture, and the ±1st-order illumination beams pass through two conversion regions of a polarization conversion group and are converted into linearly polarized light with a unified output direction.

[0008] As a preferred technical solution, the polarization conversion group consists of three groups.

[0009] As a preferred technical solution, the fast axis angle of the two conversion regions of the three sets of polarization conversion groups is 45° with the normal.

[0010] As a preferred technical solution, each of the aforementioned conversion regions is a fan-shaped ring with a central angle of 60°; all polarization conversion groups form a circular ring.

[0011] As a preferred technical solution, the linearly polarized light is s-polarized light.

[0012] According to another aspect of the present invention, a design method for partitioned quarter-wave plates is provided, the specific process of which is as follows: Let the Jones vector of the incident ±1st order illumination beam be... The angle β through which the fast axis of the conversion region through which the illumination beam passes relative to the normal direction is; the Jones matrix corresponding to the conversion region through which the illumination beam passes is... The normal direction is the radial direction of the circular quarter-wave plate. The vector of the illumination beam after passing through the conversion region is ; , make The value of the angle β through which the fast axis rotates relative to the normal direction is obtained when the component perpendicular to the normal direction is not equal to 0 and the component in the normal direction is equal to 0. The angle β through which the fast axis of all converted regions of the quarter-wave plate rotates relative to the normal direction is calculated.

[0013] As a preferred technical solution, the angle β through which the fast axis rotates relative to the normal direction is 45° and is all left-handed 45°.

[0014] As a preferred technical solution, the Jones matrix corresponding to the conversion region through which the illumination beam passes is... ,in and Let be a rotation matrix. The value is an imaginary unit, and the angle is negative when β is left-handed.

[0015] As a preferred technical solution, the rotation matrix ; .

[0016] As a preferred technical solution, the Jones vector of the incident ±1 order illumination beam ,in, The electric field amplitude of the incident ±1st order illumination beam. It is the imaginary unit.

[0017] Compared with the prior art, the present invention has the following beneficial effects.

[0018] 1) The central through-hole of the partitioned quarter-wave plate provided by this invention can keep the 0th order circularly polarized light beam circularly polarized; the ±1st order circularly polarized light beams are modulated into s-linearly polarized light by passing through the two conversion regions of the polarization conversion group, thereby realizing the control of the normal direction of the illumination beam group; high-modulation interference fringes can still be achieved after the 0th order circularly polarized light and the ±1st order linearly polarized light interfere; and it is compatible with both three-dimensional structured light illumination imaging systems and two-dimensional structured light illumination imaging systems.

[0019] 2) The polarization conversion group of this invention consists of three groups, which are applicable to three-dimensional structured light illumination imaging systems (3D-SIM) using three sets of interference directions to achieve omnidirectional uniform expansion of the spectrum and high-modulation interference fringes; this invention can achieve interference fringe modulation in three interference directions of 0°, 60° and 120°, and is applicable to general three-dimensional structured light illumination imaging systems.

[0020] 3) The polarization conversion assembly of this invention is circular, which is the same shape as the existing quarter-wave plate, making it easy to install.

[0021] 4) This invention calculates the fast axis angle required to convert the ±1 order beam into linearly polarized light by using the vector after the beam passes through the partitioned quarter-wave plate, thus achieving a unified output of light polarized in different directions by the partitioned quarter-wave plate. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the structure of the quarter-wave plate of the present invention; Figure 2 This is a flowchart of the design method for the partitioned quarter-wave plate of the present invention; The numbers in the diagram are as follows: 1. Central through-hole; 2. Polarization conversion group; 20. Conversion area. Detailed Implementation

[0023] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0024] Example 1 like Figure 1 As shown, this embodiment provides a partitioned quarter-wave plate, including a central through-hole 1 and multiple sets of polarization conversion groups 2 surrounding the central through-hole 1. Figure 1 The direction indicated by the red arrow is the fast axis direction, and the direction indicated by the blue arrow is the normal direction.

[0025] Each polarization conversion group 2 includes two conversion regions 20 spaced 180° apart, and the fast axis directions of the two conversion regions 20 differ by 180°; each conversion region 20 is a fan-shaped ring, and all polarization conversion groups 2 form a circular ring.

[0026] Each illumination beam group includes a 0th-order illumination beam modulated into circularly polarized light and ±1st-order illumination beams. The 0th-order illumination beam passes through the central aperture 1, and the ±1st-order illumination beams pass through the two conversion regions 20 of a polarization conversion group 2 and are converted into linearly polarized light with a unified output direction, such as s-polarized light.

[0027] In 3D structured light illumination imaging systems (3D-SIM), three sets of interference directions are typically used to achieve omnidirectional uniform spectral spread and high-modulus interference fringes. Each set of interference fringes is formed by a pair of ±1st order beams, thus involving a total of 6 ±1st order illumination beams (±0°, ±60°, ±120°) across the three sets of directions. Since each ±1st order beam propagates in a different direction, to ensure that each beam achieves a conversion from circularly polarized to linearly polarized light, a partitioned quarter-wave plate (Pizza QWP) with 6 different fast axis directions must be designed. Each beam passes through a dedicated conversion region 20, ensuring that all directions output a uniform linear normal direction, ultimately constructing 3 interference directions (0°, 60°, 120°).

[0028] Example 2 like Figure 2 As shown, the present invention provides a design method for Embodiment 1. The ultimate goal of this embodiment is to convert circularly polarized light into s-polarized light by passing it through a waveplate region along a specific fast axis.

[0029] Assuming the input is left-handed circularly polarized light, its Jones vector is: ,in The electric field amplitude of the incident ±1st order illumination beam. The imaginary unit, The component of the vector parallel to the normal direction is a real number, and the y-direction component is 90° out of phase with the x-direction component.

[0030] The fast axis rotates by an angle β relative to the normal direction and is left-handed; the Jones matrix corresponding to the conversion region 20 through which the illumination beam passes is... , ,in and For rotation matrix, , .

[0031] The vector of the illumination beam after passing through the conversion region 20 is ; .

[0032] make With the component perpendicular to the normal direction not equal to 0 and the component in the normal direction equal to 0, the angle β through which the fast axis rotates relative to the normal direction is -45°.

[0033] at this time, , , , The final output electric field exists in only one direction, namely linearly polarized light; perpendicular to the normal direction, the linear polarization direction of the output from the quarter-wave plate is... .

[0034] Because a quarter-wave plate, when its fast axis is 45° to the normal direction, can make the fast axis component phase 90°, thus achieving complete conversion between circular and linear polarization, this invention designs the fast axis angle β of each beam of illumination light (positive and negative 1 orders) passing through the fan-shaped region, ensuring that its incident direction is always 45 degrees to the fast axis, thereby guaranteeing optimal polarization conversion effect and uniform direction.

[0035] In three-dimensional structured illumination microsystems (3D-SIM), three interference directions (0°, 60°, and 120°) are typically used to achieve uniform spectral spread and high-modulus interference fringes. The interference fringes in each direction are formed by a pair of ±1st order diffracted beams in opposite directions. The output normal directions of each pair of ±1st order beams must be aligned to ensure that the interference fringes have a high-modulus structure.

[0036] The specific interference direction and the corresponding ±1st order incident light angles are as follows: The output normal direction corresponding to each pair of ±1 order beams is the perpendicular direction of the interference fringe direction (i.e., the s-normal direction).

[0037] like Figure 2 As shown, the angle between the normal (black dashed line) and the fast axis is defined as 45°, and the final output polarization direction is perpendicular to the normal direction.

[0038] For each set of interference directions, suppose we want to achieve the target output normal direction. The corresponding fast axis angle β is calculated using the following formula: .

[0039] Simultaneously, the fast axes of two adjacent waveplates are rotated by 60 degrees in sequence, ultimately resulting in the modulation of three sets of six beams of light, and finally obtaining three sets of interference fringes. Assume the middle set of fringes is at 0 degrees, and the other two sets of fringes are interference fringes at 60 degrees and 120 degrees.

[0040] The polarization direction of each sector is perpendicular to the normal direction (the black dashed line in the diagram), and maintains a 45° angle with the fast axis direction. The polarization direction is rotated 45° counterclockwise relative to the fast axis direction. Therefore, the angle between the fast axis direction and the normal is 45°. The waveplate is divided into six sectors, each with an angle of 60°, and the output polarization direction is also rotated 60° from the adjacent sector.

[0041] At this point, we have obtained all the fast axis angles for the six regions.

[0042] Taking ±1st order diffraction light at ±120° as an example: 1. Jones vector of left-handed polarized light: ; 2. Assume the angle between the fast axis of the waveplate and the direction of the normal to the center of the circle is β. The Jones matrix of a quarter-wave plate at a fast axis angle of β is: ; The rotation matrix is: ; ; 3. By converting region 20.

[0043] 4. Polarization conversion occurs: The quarter-wave plate converts left-handed circularly polarized light into linearly polarized light in a direction that is 45° left-handed along the fast axis.

[0044] 255° - 45° = 210°; 75° - 45° = 30°; These two directions are equivalent linear normal directions (210° = 30° + 180°), meaning the output electric field directions are the same (difference only by π phase). This ensures that the two beams of light have the same normal direction (210°) when they converge on the sample plane, thus allowing interference to occur.

[0045] 5. Because their wave vectors are symmetrical in direction, have consistent polarization, and have good coherence, they form interference fringes along the 120° direction on the sample surface.

[0046] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A partitioned quarter-wave plate, characterized in that, It includes a central through hole (1) and multiple polarization conversion groups (2) surrounding the central through hole (1). Each polarization conversion group (2) includes two conversion regions (20) spaced 180° apart, and the two conversion regions (20) are symmetrically arranged with their fast axis directions differing by 180° from each other. Each illumination beam group includes a 0th-order illumination beam and ±1st-order illumination beams modulated into circularly polarized light. The 0th-order illumination beam passes through a central through-hole (1), and the ±1st-order illumination beams pass through two conversion regions (20) of a polarization conversion group (2) and are converted into linearly polarized light with a uniform output direction.

2. A partitioned quarter-wave plate according to claim 1, characterized in that, The polarization conversion group (2) consists of three groups.

3. A partitioned quarter-wave plate according to claim 2, characterized in that, The fast axis angle of the two conversion regions (20) of the three polarization conversion groups (2) is 45° with the normal.

4. A partitioned quarter-wave plate according to claim 1, characterized in that, Each of the aforementioned conversion regions (20) is a fan-shaped ring with a central angle of 60°; all polarization conversion groups (2) form a ring.

5. A partitioned quarter-wave plate according to claim 1, characterized in that, The linearly polarized light mentioned is s-polarized light.

6. A design method for a partitioned quarter-wave plate as described in any one of claims 1 to 5, characterized in that, The specific process is as follows: Let the Jones vector of the incident ±1st order illumination beam be... The fast axis of the conversion region (20) through which the illumination beam passes rotates by an angle β relative to the normal direction; the Jones matrix corresponding to the conversion region (20) through which the illumination beam passes is... The normal direction is the radial direction of the circular quarter-wave plate. The vector of the illumination beam after passing through the conversion region (20) is ; , make The value of the angle β through which the fast axis rotates relative to the normal direction is obtained when the component perpendicular to the normal direction is not equal to 0 and the component in the normal direction is equal to 0. The angle β through which the fast axis rotates relative to the normal direction is calculated for all conversion regions (20) of the quarter-wave plate.

7. The design method according to claim 6, characterized in that, The angle β through which the fast axis rotates relative to the normal direction is 45°, and all of them are left-handed 45°.

8. The design method according to claim 6, characterized in that, The Jones matrix corresponding to the conversion region (20) through which the illumination beam passes. ,in and For rotation matrix, The value is an imaginary unit, and the angle is negative when β is left-handed.

9. The design method according to claim 8, characterized in that, The rotation matrix ; .

10. The design method according to claim 6, characterized in that, Jones vector of the incident ±1st order illumination beam ,in, The electric field amplitude of the incident ±1st order illumination beam. It is the imaginary unit.

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