Digital micromirror device imaging system compensating for polarization aberration and design method thereof

Abstract

The application discloses a digital micromirror device (DMD) imaging system for compensating for polarization aberration and a design method thereof, and belongs to the technical field of polarization detection imaging. In order to solve the problems that polarization aberration can reduce the polarization imaging quality of an optical system and the existing polarization compensation methods have the problems of narrow applicable waveband range, complex compensation device, poor compensation real-time performance, compensation error accumulation and the like, the system comprises a telescope objective, an LD, an LR, a DMD, a relay projection objective and a polarization detector. After light enters the optical system, the light is firstly reflected by the telescope objective, then transmitted through the LD and the LR, and forms an image on the DMD. The formed image is reflected by the relay projection objective, and finally, a polarization image is generated on the polarization detector. The method can guide the design of a polarization imaging system containing the DMD, such as a coded spectrum polarization imaging system and a coded super-resolution polarization imaging system. The polarization compensation system has the advantages of simplicity, low cost, no motion and change of the device, and no influence on the reliability of the system.

Description

Technical Field

[0001] This invention relates to a digital micromirror imaging system and its design method for compensating polarization aberration, belonging to the field of polarization detection imaging technology. Background Technology

[0002] Polarization aberration characterizes the changes in amplitude, phase, and polarization state of light after it passes through an optical system. When a beam of light is incident non-orthogonally onto an optical interface, due to polarization aberration, the horizontal and vertical polarization components of the incident light have different reflectivities, resulting in differences in their amplitudes and phases, thus altering the polarization state of the light. Polarization aberration in an optical system is closely related to its structure and composition.

[0003] Digital micromirror devices (DMVs) are reflective spatial light modulators characterized by high resolution and fast response, making them widely used in computational imaging, such as snapshot spectral imaging and coded super-resolution imaging. When a DMV is inserted into the optical path, each micromirror rotates 12° or -12° along its central axis when in the on / off state, causing the incident light to tilt and producing significant polarization aberrations. This affects the polarization measurement accuracy and polarization imaging effect of the optical system, thus requiring analysis and compensation.

[0004] Chinese patent number "201610948257.9" is titled "A Reflective Polarization Aberration Compensation Device Based on Beam-Splitting Polarization Modulation." The device described in this patent is inserted into the parallel optical path of an optical system. A parallel beam of arbitrary polarization is incident on a polarization beam splitter and decomposed into two linearly polarized beams with mutually orthogonal polarization states and perpendicular propagation directions. The two beams pass through a first depolarization beam splitter and a second depolarization beam splitter, respectively. One beam is incident on a reflective pure-phase liquid crystal spatial light modulator for phase modulation, and the other beam is incident on a reflective pure-amplitude liquid crystal spatial light modulator for amplitude modulation. After being reflected by the first and second depolarization beam splitters, the two beams are then incident perpendicularly on a third depolarization beam splitter for beam combining before exiting. However, the device in this patent cannot be used in non-parallel optical paths. Furthermore, the polarization beam splitter described in the patent is a prism coated with a polarization splitting film. The prism has a relatively large optical thickness, resulting in significant absorption of infrared light, thus making it unsuitable for polarization compensation in the infrared band.

[0005] The Chinese patent number is "201210528727.8", and the patent title is "Ultra-high numerical aperture lithography imaging polarization compensation device and method". This patent uses the method of changing the polarization angle by changing the applied voltage of an electro-optic crystal to achieve polarization compensation of the system. In order to form a closed-loop feedback compensation, a polarization detection device must be placed at the focal plane of the system. In actual compensation, this polarization compensation method requires repeated detection, feedback, and compensation to achieve a relatively ideal compensation effect, which has problems such as complex compensation devices, poor real-time performance, and accumulation of compensation errors. Summary of the Invention

[0006] To address the problems of polarization aberration reducing the polarization imaging quality of optical systems, as well as the narrow applicable wavelength range, complex compensation devices, poor real-time performance, and accumulation of compensation errors in existing polarization compensation methods, this invention proposes a digital micromirror device imaging system for compensating polarization aberration and its design method.

[0007] The technical solution of this invention is as follows:

[0008] A digital micromirror imaging system for compensating polarization aberration is characterized in that the system includes a telescope objective, an LD, a LR, a DMD, a relay projection objective, and a polarization detector; after light enters the optical system, it is first reflected by the telescope objective, then transmitted through a linear retarder (LD) and a linear attenuator (LR) to form a primary image on the DMD; the primary image is then reflected by the relay projection objective and finally generates a polarization image on the polarization detector.

[0009] A design method for a digital micromirror imaging system that compensates for polarization aberration includes the following steps:

[0010] The first step is to design the optical system. The magnification of the relay projection lens is calculated based on the mirror size of the DMD and the photosensitive surface size of the polarization detector. The telescope lens and the relay projection lens are designed separately, connected together, and their structure is adjusted to obtain a secondary imaging optical system with an intermediate image plane. Finally, the DMD is inserted at the intermediate image plane, and the system is optimized overall until the imaging quality is satisfactory.

[0011] The second step involves using a three-dimensional polarization tracing method to calculate and obtain the polarization aberration distribution of the DMD surface in both full-field-of-view and full-pupil coordinates, including biaxial attenuation and phase retardation. Biaxial attenuation represents the difference in transmittance between S-rays and P-rays, while phase retardation represents the phase difference between them. Specifically, S-rays and P-rays represent the two components of vibration perpendicular to and parallel to the incident surface when light rays are incident on the optical interface, respectively.

[0012] The third step is to select the position and orientation of the LD and LR. The surfaces of the LD and LR are perpendicular to the center ray of the incident beam, and they are placed sequentially in front of the DMD, close to the DMD.

[0013] Fourth, based on the tracing results from the second step, the field point on the DMD surface with the largest polarization aberration amplitude is obtained. Under this field of view condition, the ray corresponding to the pupil coordinates of the maximum polarization aberration is introduced as the reference ray for compensation. Based on the polarization aberration generated when the compensation reference ray is incident on the DMD surface, the specific parameters of LD and LR are designed.

[0014] The specific parameter design method for the LD is as follows:

[0015] For the compensation reference ray, the Jones matrix of the DMD surface can be expressed as:

[0016]

[0017] In the formula, A xx With A yy These represent the amplitude reflection coefficients of the S-beam and P-beam on the DMD, respectively. and Let A and P represent the phase reflection coefficients of the S-ray and P-ray on the DMD, respectively. xx With A yy , and It is derived from the following formula:

[0018]

[0019] r in formula (2) s DMD, r p,DMD The reflection coefficients of the S-ray and P-ray, respectively, when the compensation reference ray is reflected on the DMD, can be calculated by the following formula:

[0020]

[0021] In the above formula, θ DMD The angle of incidence of the light ray on the DMD can be obtained by ray tracing. The complex refractive index of the DMD is determined by the material of the DMD.

[0022] The Jones matrix of the aforementioned LD can be represented as:

[0023]

[0024] Intrinsic polarization state transmission coefficient t s With t p It can be calculated using the following formula:

[0025]

[0026] In the formula, n LD The refractive index of the LD is a quantity to be determined, θ. i This represents the incident angle of the compensation reference ray on the LD surface, which can be obtained from the second step of ray tracing.

[0027] The cumulative Jones matrix of DMD and LD can then be expressed as:

[0028]

[0029] The cumulative bidirectional attenuation of DMD and LD is readily obtained, expressed as:

[0030]

[0031] Substituting equation (5) into equation (7), we can obtain the cumulative bidirectional attenuation of DMD and LD based on the incident angle θ. i The refractive index n of LD2 LD A function with respect to the independent variable can be expressed as:

[0032]

[0033] To achieve the effect that the bidirectional attenuation introduced by the DMD is completely compensated by the LD, the Dia value should be 0. Where A... xx A yy With θ i Both can be obtained by ray tracing. Therefore, according to formula (8), by setting Dia = 0, the refractive index n of LD can be determined. LD This completed the design of the LD. When A xx >A yy At this time, the bidirectional attenuation direction generated by the DMD is the same as the vibration direction of the S-beam, and t is... s <t p That is, the binomial attenuation direction produced by the LD is the vibration direction of the P light; when A xx <A yy At this time, the bidirectional attenuation direction generated by the DMD is the P-light vibration direction, and t s >t p That is, the biaxial attenuation direction generated by the LD is the vibration direction of the S light, which can ensure that the biaxial attenuation direction generated by the LD is orthogonal to the biaxial attenuation direction generated by the DMD.

[0034] Similarly, the specific parameter design method for the LR is as follows:

[0035] The aforementioned LR is a birefringent crystal, and its Jones matrix can be represented as:

[0036]

[0037] intrinsic polarization state phase transmission coefficient of LR and It can be calculated using the following formula:

[0038]

[0039] In the formula n o Let n be the refractive index of the o-ray in LR. e '(θ) represents the refractive index of the e-ray when the normal to the e-ray in the LR makes an angle θ with the optical axis of the crystal. It is the value that needs to be designed. d is the thickness of the LR, and λ represents the working wavelength.

[0040] n o and n e '(θ) can be obtained from the following formula:

[0041]

[0042] Where n LR Indicates the refractive index of LR; n o With n e Let n denote the refractive indices of the o-ray and the e-ray when the ray is incident perpendicularly to the interface in LR, respectively. Given a specific material, n... o With n e Given that θ represents the angle between the e-ray normal in LR and the crystal optical axis, it can be obtained using the following formula:

[0043]

[0044] In the above formula, θ j θ represents the angle of incidence of the light ray on the linear retarder LR, which can be obtained by the second step of ray tracing; n1 represents the refractive index of air; θ a The angle between the optical axis of the crystal and the normal to the crystal surface is represented, and the direction of the optical axis is determined by the crystal material. Substituting equation (11) into equation (10), the phase transmission coefficients of the intrinsically polarized S-rays and P-rays on LR can be expressed as:

[0045]

[0046] The cumulative Jones matrix of DMD and LR can be expressed as:

[0047]

[0048] The cumulative phase delay of DMD and LR can be expressed as:

[0049]

[0050] To achieve the effect that the phase delay introduced by DMD is completely compensated by LR, the following two conditions must be met: ① ②When hour, when hour, Greater than That is, the direction of the phase delay introduced by LR3 must be orthogonal to the direction of the phase delay on the DMD. According to formula (13), in the process of designing LR, the refractive index parameter n of the crystal material can be determined first. o n e Material thickness d, when n o Given d, under a specific wavelength λ, the phase reflection coefficient of the S-ray can be calculated. Then select a suitable P-light phase reflectance coefficient To satisfy the two compensation conditions mentioned above. Further determine the angle θ between the e-wave normal and the crystal optical axis, and then determine the angle θ between the crystal optical axis and the crystal surface normal according to formula (12). a Finally, the design of LR was completed.

[0051] The beneficial effects of this invention are as follows:

[0052] 1. This invention proposes a design method for a digital micromirror device (DMD) imaging system that compensates for polarization aberrations. This method can guide the design of polarization imaging systems containing DMDs, such as coded spectral polarization imaging systems and coded super-resolution polarization imaging systems.

[0053] 2. This invention utilizes weakly polarized devices, including LD and LR, to compensate for polarization aberrations in digital micromirror imaging systems. In practice, the LD is a flat glass plate, and the LR is a thin crystal sheet. This polarization compensation system has significant advantages such as simplicity, low cost, absence of moving or changing components, and no impact on system reliability. Attached Figure Description

[0054] Figure 1 Schematic diagram of a digital micromirror imaging system for compensating polarization aberrations;

[0055] Figure 2 This is the modulation transfer function (MTF) curve of the optical system.

[0056] Figure 3 This diagram shows the placement of the LD and LR and the direction of polarization aberrations introduced by the device.

[0057] Figure 4 A schematic diagram of the direction of light propagation in the crystal to compensate for the incident reference light beam on LR.

[0058] Figure 5 (a) is a schematic diagram of the magnitude and direction of the bidirectional attenuation of the system before compensation, and (b) is a schematic diagram of the magnitude and direction of the bidirectional attenuation of the system after compensation.

[0059] Figure 6 (a) is a schematic diagram of the magnitude and direction of the system phase delay before compensation, and (b) is a schematic diagram of the magnitude and direction of the system phase delay after compensation.

[0060] Figure 7 The simulation shows the polarization imaging acquisition of the system. (a) is the incident light information, (b) is the polarization imaging effect before compensation, and (c) is the polarization imaging effect after compensation. Detailed Implementation

[0061] The following description, in conjunction with the accompanying drawings and specific embodiments, provides further details.

[0062] like Figure 1 As shown, a digital micromirror device imaging system for compensating polarization aberration includes a telescope objective 1, an LD2, an LR3, a DMD4, a relay projection objective 5, and a polarization detector 6. After light enters the optical system, it is first reflected by the telescope objective 1, then transmitted through the LD2 and LR3 before being imaged once on the DMD4. This single image is then reflected by the relay projection objective 5 and finally generated as a polarization image on the polarization detector 6.

[0063] The optical system consists of telescope objective 1, DMD4, and relay projection objective 5; LD2 and LR3 are responsible for compensating for polarization aberrations in the entire digital micromirror device imaging system; DMD4 coincides with the intermediate image plane of the optical system and is responsible for encoding information; polarization detector 6 is a detector with a micro polarizer attached.

[0064] This invention relates to a digital micromirror imaging system and its design method for compensating for polarization aberrations. The specific steps are as follows:

[0065] The first step is to design the optical system. This optical system is a secondary imaging off-axis three-mirror system, and its parameters are set as follows:

[0066] Table 1 Optical System Parameters

[0067]

[0068] The system consists of a telescope objective 1, a DMD4, and a relay projection objective 5. The mirror surface width of DMD4 is calculated to be a1 = 13.824 mm, and the height is b1 = 11.0529 mm. The photosensitive surface width of polarization detector 6 is a2 = 10.88 mm, and the height is b2 = 8.704 mm. Therefore, the magnification of the relay projection objective 5 is the ratio of the target surface size of polarization detector 6 to the mirror surface size of DMD4. In this embodiment, the telescope objective 1 is designed using a single freeform surface mirror, and the relay projection objective 5 is designed using two freeform surface mirrors. The telescope objective 1 and the relay projection objective 5 are connected together and their structure adjusted to obtain an off-axis three-mirror secondary imaging optical system with an intermediate image plane. Finally, a DMD4 is inserted at the intermediate image plane to optimize the optical system as a whole until the imaging quality is satisfactory. The final system MTF curve is shown below. Figure 2 .

[0069] The second step involves using a three-dimensional polarization tracing method to calculate and obtain the polarization aberration distribution of the DMD4 surface in both full field-of-view and full pupil coordinates, including biaxial attenuation and phase retardation. Biaxial attenuation represents the difference in transmittance between S-rays and P-rays, while phase retardation represents the phase difference between them. Specifically, S-rays and P-rays represent the two components of vibration perpendicular to and parallel to the incident surface when light rays are incident on the optical interface, respectively.

[0070] The third step is to select the position and orientation of LD2 and LR3. The surfaces of LD2 and LR3 should be perpendicular to the center ray of the incident beam, and they should be placed sequentially 20mm in front of DMD4, close to DMD4. Figure 3 As shown.

[0071] Fourth, based on the tracing results from the second step, the field point on the DMD4 surface with the largest polarization aberration amplitude is obtained. Under this field of view condition, the ray corresponding to the pupil coordinates of the maximum polarization aberration is introduced as the reference ray for compensation. Based on the polarization aberration generated when the compensation reference ray is incident on the DMD4 surface, the specific parameters of LD2 and LR3 are designed.

[0072] The specific parameter design method for LD2 will be described in detail below:

[0073] For the compensation reference ray, the Jones matrix of the DMD4 plane can be expressed as:

[0074]

[0075] In the formula, A xx With A yy These represent the amplitude reflection coefficients of the S-beam and P-beam on DMD4, respectively. and Let A and P represent the phase reflection coefficients of the S-beam and P-beam, respectively, on DMD4. xx With A yy , and It is derived from the following formula:

[0076]

[0077] r in formula (17)s,DMD r p,DMD The reflection coefficients of the S-ray and P-ray, respectively, when the compensation reference ray is reflected on the DMD, can be calculated by the following formula:

[0078]

[0079] In the above formula, θ DMD The angle of incidence of the light ray on the DMD can be obtained by ray tracing. The complex refractive index of the DMD is determined by the material of the DMD.

[0080] The Jones matrix of the aforementioned LD2 can be expressed as:

[0081]

[0082] Intrinsic polarization state transmission coefficient t s With t p It can be calculated using the following formula:

[0083]

[0084] In the formula, n LD The refractive index of LD2 is a quantity to be determined, θ. i The angle of incidence of the compensation reference ray on the LD2 surface is indicated by the angle of incidence, which can be obtained by the second step of ray tracing.

[0085] The cumulative Jones matrix of DMD4 and LD2 can then be expressed as:

[0086]

[0087] The cumulative bidirectional attenuation of DMD4 and LD2 is readily obtained, expressed as:

[0088]

[0089] Substituting equation (20) into equation (22), we can obtain that the cumulative bidirectional attenuation of DMD4 and LD2 is based on the incident angle θ. i The refractive index n of LD2 LD A function with respect to the independent variable can be expressed as:

[0090]

[0091] To achieve the effect that the bidirectional attenuation introduced by DMD4 is completely compensated by LD2, the Dia value should be 0. Where A... xx A yy With θ i Both can be obtained by ray tracing. Therefore, according to formula (23), by setting Dia = 0, the refractive index n of LD2 can be determined. LD Thus, the design of LD2 was completed. When Axx >A yy At this time, the bidirectional attenuation direction generated by DMD4 is the direction of S-beam vibration, and t s <t p That is, the binomial attenuation direction generated by LD2 is the vibration direction of P light; when A xx <A yy At this time, the bidirectional attenuation direction generated by DMD4 is the direction of P-light vibration, and t s >t p That is, the biaxial attenuation direction generated by LD2 is the vibration direction of S light, which can ensure that the biaxial attenuation direction generated by LD2 is orthogonal to the biaxial attenuation direction generated by DMD4.

[0092] In this embodiment, the ray with normalized field-of-view coordinates (1, -1) and pupil coordinates (0, -0.3) is used as the reference ray for compensation, compensating for the bidirectional attenuation of the system. When this ray is incident on the DMD4 surface, the amplitude reflection coefficient A of the S-ray is... xx =0.9908, the amplitude reflection coefficient A of P light yy =0.9894, θ i =10.24°. The refractive index n of LD2 is calculated using formula (20). LD =1.4328, thus obtaining the amplitude transmission coefficient t of the S-beam on LD2. s =0.8183,t p =0.8194. The magnitude of the bidirectional attenuation introduced by LD2 is Dia. LD =(|t s | 2 -|t p | 2 ) / (|t s | 2 +|t p | 2 ) = 1.41 × 10 -3 As shown in Figure (3), the biaxial attenuation direction of the compensation reference ray on DMD4 is the S-ray vibration direction, which is parallel to the X-axis of the global coordinate system, while the biaxial attenuation direction on LD2 is the P-ray vibration direction, which is parallel to the Y-axis. Compare the biaxial attenuation distribution diagram of the system before compensation (e.g., ...). Figure 5 (a) and the bidirectional attenuation distribution diagram of the compensated system (e.g.) Figure 5 (b) shows that the maximum bidirectional attenuation value of the system before compensation is 1.16 × 10⁻⁶. -3 The maximum bidirectional attenuation value of the compensated system is 4.55 × 10⁻⁶. -4 The cumulative bidirectional attenuation value corresponding to the compensation reference ray is 0. The bidirectional attenuation generated by the system is effectively compensated.

[0093] Similarly, the specific parameter design method for LR3 is as follows:

[0094] The LR3 mentioned above is a birefringent crystal, and its Jones matrix can be represented as:

[0095]

[0096] intrinsic polarization state phase transmission coefficient of LR3 and It can be calculated using the following formula:

[0097]

[0098] In the formula n o Let n be the refractive index of the o-ray in LR3. e '(θ) is the refractive index of the wave normal in LR3 at an angle θ to the optical axis, which is the value that needs to be designed. d is the thickness of LR3, and λ represents the working wavelength.

[0099] n o and n e '(θ) can be obtained from the following formula:

[0100]

[0101] Where n LR Indicates the refractive index of LR3; n o With n e Let n denote the refractive indices of the o-ray and e-ray (perpendicular incidence) in LR3, respectively. When the material is determined, n o With n e Given that θ represents the angle between the e-ray normal in LR3 and the optical axis of the crystal, it can be obtained using the following formula:

[0102]

[0103] In the above formula, θ j θ represents the angle of incidence of the ray on LR3, which can be obtained by ray tracing in the second step; n1 represents the refractive index of the medium before incident on the crystal; θ a It represents the angle between the optical axis of the crystal and the normal to the crystal surface. The direction of the optical axis is determined by the crystal material.

[0104] Substituting equation (26) into equation (25), the phase transmission coefficients of the intrinsic polarization states of S and P light on LR3 can be expressed as:

[0105]

[0106] The cumulative Jones matrix of DMD4 and LR3 can be expressed as:

[0107]

[0108] The cumulative phase delay between DMD4 and LR3 can be expressed as:

[0109]

[0110] To achieve the effect that the phase delay introduced by DMD4 is completely compensated by LR3, the following two conditions must be met: ① ②When hour, when hour, Greater than That is, the direction of the phase delay introduced by LR3 is orthogonal to the direction of the phase delay on DMD4. According to formula (28), in the process of designing LR3, the refractive index parameter n of the crystal material can be determined first. o n e Material thickness d, when n o Given d, under a specific wavelength λ, the phase reflection coefficient of the S-ray can be calculated. Then select a suitable P-light phase reflectance coefficient To satisfy the two compensation conditions mentioned above. Further determine the angle θ between the e-wave normal and the crystal optical axis, and then determine the angle θ between the crystal optical axis and the crystal surface normal according to formula (27). a Finally, the design of LR3 was completed.

[0111] In this embodiment, the ray with field-of-view coordinates (1, -1) and pupil coordinates (0, -0.3) serves as the compensation reference ray to compensate for the phase delay of the system. When this ray is incident on the DMD4 surface, the phase reflection coefficient of the S-ray is... Phase reflectance of P-light Introduced phase delay In this embodiment, to satisfy the two conditions required for phase delay compensation, we use a 0.1 mm thick MgF2 crystal as LR3, whose o-ray and e-ray refractive indices n e =1.378, n o =1.390. This can be obtained using formula (25). Then determine The angle θ between the e-ray normal and the optical axis is found to be 4.25°. The incident angle θ of the compensated reference ray on the linear retarder LR is also known. j =10.24°, θ j Substituting θ into formula (27), the angle θ between the optical axis of the crystal and the normal to the crystal surface is obtained. a=8.10°, thus completing the design of LR3. As shown in Figure (3), the phase delay direction generated by the compensating reference ray on DMD4 is the P-ray vibration direction, parallel to the Y-axis of the global coordinate system, and the magnitude of the phase delay generated on LR3 is The direction is the S-axis vibration direction, parallel to the X-axis. In this embodiment, the simulated LR3 is a uniaxial crystal material. Its optical axis direction, incident light direction, o-vector, e-vector propagation direction, and e-wave normal direction are shown in Figure 4. The phase delay distribution of the system before compensation is compared (e.g.,...). Figure 6 (a) and the phase delay distribution diagram of the compensated system (e.g.) Figure 6 (b) It can be seen that the maximum phase delay value on DMD4 before compensation is 9.52 × 10⁻⁶. -3 The maximum cumulative phase delay between DMD4 and LR3 after compensation is 4.64 × 10 rad. -3 rad, where the cumulative phase delay corresponding to the compensating reference ray is 0. The phase delay generated by the system is effectively compensated.

[0112] Finally, a system polarization imaging simulation was performed, such as... Figure 7 As shown. (a) is the incident light information, (b) is the polarization imaging effect before compensation, and (c) is the polarization imaging effect after compensation. Comparing the system imaging simulation effects before and after compensation, before adding the polarization compensation device, S0 image1 S2 image1 and S3 image1 The ideal intensities are 1, 0, and 0, respectively. Due to polarization aberrations in the system, S0 image1 S2 image1 and S3 image1 The actual intensities became 0.978, 0.036, and 0.021, respectively. After adding the polarization compensation device, S0 image2 S2 image2 and S3 image2 The image intensities became 0.996, 0.014, and 0.001, respectively. It is readily apparent that after polarization compensation, the accuracy of acquiring polarization information for S0, S2, and S3 improved by 1.8%, 2.2%, and 2.0%, respectively, indicating that the proposed polarization compensation method achieved good results.

Claims

1. A design method for a digital micromirror imaging system that compensates for polarization aberration, characterized in that, The method includes the following steps: The first step is to design the optical system; The magnification of the relay projection lens is calculated based on the mirror size of DMD (4) and the photosensitive surface size of polarization detector (6); the telescope objective (1) and the relay projection lens (5) are designed respectively, connected together and the structure is adjusted to obtain a secondary imaging optical system with an intermediate image plane; finally, DMD (4) is inserted at the intermediate image plane and the system is optimized as a whole until the system imaging quality is good. The second step is to use the three-dimensional polarization tracing method to calculate and obtain the polarization aberration distribution of the DMD (4) surface in the full field of view coordinates and the full pupil coordinates, including biaxial attenuation and phase delay; biaxial attenuation represents the difference in transmittance between S-ray and P-ray, and phase delay represents the phase difference between S-ray and P-ray; where S-ray and P-ray respectively represent the two components of vibration perpendicular to the incident surface and vibration parallel to the incident surface when the light is incident on the optical interface; The third step is to select the position and orientation of the linear delay unit LD (2) and the linear attenuator LR (3); The surfaces of the linear delayer LD (2) and the linear attenuator LR (3) are perpendicular to the center ray of the incident beam and are placed in front of DMD (4) and close to DMD (4) in sequence; Fourth step: Based on the tracing results of the second step, obtain the field point on the DMD (4) surface with the largest polarization aberration amplitude; Under this field of view, the ray corresponding to the pupil coordinate with the maximum polarization aberration is introduced as the reference ray for compensation; based on the polarization aberration generated when the compensation reference ray is incident on the surface of DMD (4), the specific parameters of the linear delay LD (2) and the linear attenuator LR (3) are designed.

2. The design method for a digital micromirror imaging system with polarization aberration compensation according to claim 1, characterized in that, The specific parameter design method for the linear delayer LD(2) in the fourth step is as follows: For the compensation reference ray, the Jones matrix of the DMD(4) plane can be expressed as: (one); In the formula, J DMD Let A be the Jones matrix of the DMD(4) surface. xx With A yy Let φ represent the amplitude reflection coefficients of the S-beam and P-beam on the DMD (4), respectively. xx With φ yy Let A and P represent the phase reflection coefficients of the S-ray and P-ray on the DMD (4), respectively; where A xx With A yy φ xx With φ yy It is derived from the following formula: (two); In formula (ii), r s,DMD r p,DMD The reflection coefficients of the S-ray and P-ray when the compensation reference ray is reflected on DMD (4) are respectively, and can be calculated by the following formula: (three); In the above formula, θ DMD The angle of incidence of the ray on DMD(4) can be obtained by ray tracing. The complex refractive index of DMD(4) is determined by the material of DMD(4); The Jones matrix of the linear delay LD(2) can be expressed as: (Four); Intrinsic polarization state transmission coefficient t s With t p It can be calculated using the following formula: (five); In the formula, n LD Let θ represent the refractive index of the linear retarder LD(2), which is a quantity to be determined. i The angle of incidence of the compensation reference ray on the surface of the linear delayer LD(2) can be obtained by the second step of ray tracing. The cumulative Jones matrix of DMD(4) and the linear delayer LD(2) can be expressed as: (six); The cumulative bidirectional attenuation of DMD(4) and linear delay LD(2) is readily obtained, expressed as: (seven); Substituting equation (v) into equation (vii), we can obtain that the cumulative bidirectional attenuation of DMD (4) and linear delayer LD (2) is based on the incident angle θ. i The refractive index n of the linear retarder LD(2) LD A function with respect to the independent variable can be expressed as: (eight); To achieve the effect that the bidirectional attenuation introduced by DMD (4) is completely compensated by the linear delayer LD (2), the value of Dia should be 0; where A xx A yy With θ i Both can be obtained by ray tracing. Therefore, according to formula (8), by setting Dia=0, the refractive index n of the linear retarder LD(2) can be determined. LD Thus, the design of the linear delay LD(2) was completed; when A xx >A yy At this time, the bidirectional attenuation direction generated by DMD(4) is the vibration direction of S-light, and t s <t p That is, the binomial attenuation direction generated by the linear retarder LD(2) is the vibration direction of the P light; when A xx <A yy When the bidirectional attenuation direction generated by DMD(4) is the direction of P-light vibration, then t s >t p That is, the biaxial attenuation direction generated by the linear delay LD (2) is the vibration direction of the S light, which can ensure that the biaxial attenuation direction generated by the linear delay LD (2) is orthogonal to the biaxial attenuation direction generated by the DMD (4).

3. The design method for a digital micromirror imaging system with polarization aberration compensation according to claim 2, characterized in that, The specific parameter design method for the linear attenuator LR(3) in the fourth step is as follows: The linear attenuator LR(3) is a birefringent crystal, and its Jones matrix can be expressed as: (Nine); The intrinsic polarization state phase transmission coefficient φ of the linear attenuator LR(3) s With φ p It can be calculated using the following formula: (ten); In the formula n o Let n be the refractive index of the o-ray in the linear attenuator LR(3). e '(θ) represents the refractive index of the e-ray when the normal of the e-ray wave in the linear attenuator LR(3) makes an angle θ with the optical axis of the crystal. It is the value that needs to be designed. d is the thickness of the linear attenuator LR(3), and λ represents the working wavelength. n o and n e '(θ) can be obtained from the following formula: (eleven); Where n LR The refractive index of the linear attenuator LR(3) is represented by n. o With n e Let n denote the refractive indices of the o-ray and the e-ray when the ray is incident perpendicularly to the interface in the linear attenuator LR(3), respectively. When the material is determined, n o With n e Given that θ represents the angle between the e-wave normal and the crystal optical axis in the linear attenuator LR(3), it can be obtained by the following formula: (twelve); In the above formula, θ j θ represents the angle of incidence of the light ray on the linear attenuator LR(3), which can be obtained by the second step of ray tracing; n1 represents the refractive index of air; θ a The angle between the optical axis of the crystal and the normal to the crystal surface is represented. The direction of the optical axis is determined by the crystal material. Substituting formula (XI) into formula (X), the phase transmission coefficients of the intrinsic polarization states of S-rays and P-rays on the linear attenuator LR(3) can be expressed as: (Thirteen); The cumulative Jones matrix of DMD(4) and the linear attenuator LR(3) can be expressed as: (fourteen); J DMD Let A be the Jones matrix of the DMD(4) surface. xx With A yy Let φ represent the amplitude reflection coefficients of the S-beam and P-beam on the DMD (4), respectively. xx With φ yy Let S and P represent the phase reflection coefficients of the S-beam and P-beam on DMD (4), respectively. The cumulative phase delay between DMD(4) and linear attenuator LR(3) can be expressed as: (fifteen); To achieve the effect that the phase delay introduced by DMD (4) is completely compensated by the linear attenuator LR (3), the following two conditions must be met: ①φ s -φ p =-(φ xx -φ yy ); ② When φ xx >φ yy At that time, φ s <φ p When φ xx <φ yy At that time, φ s Greater than φ p That is, the direction of the phase delay introduced by the linear attenuator LR (3) must be orthogonal to the direction of the phase delay on DMD (4); according to formula (xiii), in the process of designing the linear attenuator LR (3), the refractive index parameter n of the crystal material is first determined. o n e Material thickness d, when n o Given d, under a specific wavelength λ, the phase reflection coefficient φ of the S-ray can be calculated. s Then select a suitable P-light phase reflection coefficient φ p To satisfy the above two compensation conditions; according to φ p Next, determine the angle θ between the e-wave normal and the crystal optical axis, and then determine the angle θ between the crystal optical axis and the crystal surface normal according to formula (xii). a Finally, the design of the linear attenuator LR(3) was completed.

4. The imaging system designed by the digital micromirror device imaging system design method for compensating polarization aberration according to claim 1 is characterized in that, The system includes a telescope objective (1), a linear retarder LD (2), a linear attenuator LR (3), a DMD (4), a relay projection objective (5), and a polarization detector (6). After light enters the optical system, it is first reflected by the telescope objective (1), and then transmitted through the linear retarder LD (2) and the linear attenuator LR (3) to form a primary image on the DMD (4). The primary image is then reflected by the relay projection objective (5) and finally generated as a polarization image on the polarization detector (6).

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