Transparency smooth design and working method of annulus pupil modulation high-contrast coronagraph

Abstract

The invention discloses an annular pupil modulation high-contrast coronagraph transmittance smooth design and a working method. According to the method, circular radial transmittance gradient modulation is carried out on the pupil of the telescope, and suppression of strong diffraction light of a fixed star is realized. According to the pupil modulation design concept with the gradually-changed circular ring band transmittance, limited circular rings are adopted, the transmittance of each circular ring is the same, energy distribution of a fixed star at the pupil position of an optical system is changed by further restraining the transmittance difference between the adjacent circular rings, and the optimal high-contrast imaging performance is achieved. According to the modulation band, the transmittance design curve of the modulation band is integrally smooth by restraining the transmittance difference of adjacent bands, the manufacturing process problem caused by violent transmittance jump of a traditional optical filter can be solved, the machining precision is further guaranteed, and the problems of wavefront phase jump and the like caused by sudden change of the thickness of a film layer can be solved; and the high-contrast imaging performance of the whole system is finally improved.

Description

Technical Field

[0001] This invention belongs to the field of high-contrast imaging technology in astronomical optics, specifically relating to a coronagraph pupil transmittance gradient modulation filter for direct imaging of exoplanets and its optimal design method. Background Technology

[0002] Direct imaging of outer planets is a major challenge in astronomical research. Due to the significant differences in light intensity between stars and planets, a contrast ratio of better than 10 in the visible light band is required. -9 Therefore, a coronagraph system must be used to suppress the intense diffraction of light from stars. Transmittance-gradient pupil modulation is one of the core technologies of a high-contrast coronagraph.

[0003] Conventional optimization algorithms often produce solutions with excessively large variations in transmittance between adjacent regions. This means that in actual manufacturing, the thickness of the metal film in adjacent regions will differ significantly. Such abrupt changes in structure not only greatly increase the difficulty of controlling the coating process and the manufacturing cost, but also lead to problems such as wavefront phase jumps, affecting the system's contrast performance. Summary of the Invention

[0004] The present invention aims to solve the manufacturing difficulties caused by the large difference in transmittance between adjacent rings due to the existing ring transmittance gradient modulation, and the degradation of the final high contrast imaging performance caused by the influence of processing errors.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for smoothing the transmittance of a high-contrast coronagraph with annular pupil modulation is disclosed. This method employs annular transmittance gradient pupil modulation technology, where each annular band has the same transmittance, and radial transmittance gradient modulation is performed in a circular pattern. The modulation scheme improves contrast performance by optimizing the transmittance distribution of the annular bands, while simultaneously optimizing the smoothness performance between adjacent rings. When the contrast performance reaches 10... -7 Furthermore, the pupil amplitude modulation is considered complete when the smoothness performance index reaches the expected level.

[0007] Furthermore, the smoothness performance is referenced to the smoothness constraint factor, which is the root mean square slope value of the ring. A decrease in the root mean square slope value indicates that the smoothness performance is improving, while an increase in the root mean square slope value indicates that the smoothness performance is decreasing.

[0008] Furthermore, the smoothness constraint factor is expressed as:

[0009]

[0010] Where T represents the transmittance value of each band, and N represents the number of annular bands.

[0011] The electric field intensity of starlight on the pupil plane can be expressed as:

[0012]

[0013] in It is the pupil function.

[0014] On the back focal plane of the imaging system, the point spread function can be expressed as the square of the modulus of the pupil function:

[0015]

[0016] in This represents the Fourier transform.

[0017] The point spread function I can be seen from the formula. PSF Related to the amplitude A, and the square of the amplitude is the transmittance, the circular band pupil modulation scheme changes the amplitude of the light to change the energy distribution of the light.

[0018] Furthermore, the contrast objective function is the ratio of the sum of the point spread functions within the optimization region to the sum of the point spread functions within the reference region. A decrease in the objective function indicates improved contrast performance, while an increase indicates decreased contrast performance. The contrast objective function is expressed as:

[0019]

[0020] Furthermore, the composite evaluation function is formed by multiplying the contrast performance objective function and the smoothness constraint factor, and is used to simultaneously constrain contrast improvement and curve smoothness during the iteration process. The composite evaluation function is expressed as follows:

[0021]

[0022] Where n and m are exponents.

[0023] Furthermore, the parameters of the composite evaluation function are optimized, and the amplitude values ​​of all rings are controlled using an iterative optimization algorithm. The composite evaluation function value is calculated, and the trend of the composite evaluation function is used to determine whether the overall performance is improving. If the trend of the composite evaluation function is rising, it indicates that the overall performance is declining. In this case, the algorithm parameters and the composite evaluation function parameters are changed and the experiment is repeated until the trend of the objective function represents an improvement in contrast performance. If the trend of the composite evaluation function is falling, it indicates that the overall performance is improving. In this case, the algorithm is used for continuous iterative optimization.

[0024] Furthermore, the algorithm is used to initially optimize the amplitude values ​​of all rings until the system's contrast performance or smoothness constraint factor reaches the minimum requirement; it is then determined whether both parameters have decreased, and if not, the composite evaluation function parameters are adjusted and iterated again for optimization.

[0025] Furthermore, the amplitude modulation is completed when the value of the composite evaluation function no longer decreases, and the amplitude modulation iteration is exited. If the contrast performance and smoothness constraint factor terms do not meet the target, the parameters of the composite evaluation function are adjusted and the iteration is restarted.

[0026] Furthermore, a point spread function image of the high-contrast dark area is obtained on the post-imaging focal plane, and the imaging contrast after amplitude modulation is tested along the diagonal direction.

[0027] Compared with the prior art, the beneficial effects of the present invention are:

[0028] 1. The present invention proposes a smooth transmittance design and working method for a high-contrast coronagraph with annular pupil modulation. It adopts annular transmittance gradient modulation technology to perform annular transmittance gradient modulation. The structure is simple, the performance is stable, and it has high contrast over a wide working range, which can effectively suppress the diffraction of starlight.

[0029] 2. The present invention proposes a smooth transmittance design and working method for a high-contrast corona filter with annular pupil modulation, which can limit the transmittance variation of adjacent annular zones, achieve a smooth transition of the transmittance curve, solve the manufacturing problem caused by the sudden change in the transmittance of the filter, thus ensuring the processing progress, and can alleviate the problems of wavefront phase jump caused by the sudden change in film thickness.

[0030] 3. The present invention proposes a smooth transmittance design and working method for a high-contrast coronagraph with annular pupil modulation. By adopting a transmittance gradient modulation method, the light flux of the system is maximized, and high-contrast imaging performance in a large working area is achieved while ensuring the overall transmittance of the system. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the overall structure of the present invention;

[0032] Figure 2 This is a flowchart of pupil modulation;

[0033] Figure 3 It is the PSF image before modulation;

[0034] Figure 4 It is a modulated PSF image;

[0035] Figure 5 This is a schematic diagram of a ring-shaped filter with gradually increasing transmittance.

[0036] Figure 6 It is the modulated contrast curve;

[0037] Figure 7 It is the transmittance curve after modulation;

[0038] In the diagram: 1. Telescope entrance; 2. Simulated star light source; 3. Collimating lens; 4. Aperture stop; 5. Circular gradient transmittance filter; 6. Imaging mirror; 7. Imaging detector. Detailed Implementation

[0039] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention. Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0040] The present invention provides a transmittance smoothing design and operating method for a ring-banded pupil modulated high-contrast coronagraph based on, as follows Figure 1 The apparatus shown includes a telescope entrance 1, a stellar simulation light source 2, a collimating lens 3, an aperture stop 4, a ring-shaped transmittance gradient filter 5, an imaging mirror 6, and an imaging detector 7.

[0041] like Figure 1 As shown, the coronagraph system is arranged sequentially along the optical path: telescope entrance 1, stellar simulation light source 2, collimating lens 3, aperture stop 4, annular transmittance gradient filter 5, and imaging mirror 6, ultimately imaging onto detector 7. The telescope entrance 1 serves as the front focal plane of the entire imaging system; the stellar simulation light source 2 is placed at this focal point, and its emitted light is collimated by the collimating lens 3 to form a parallel beam, simulating incident starlight from an infinitely distant star; subsequently, the beam passes through the aperture stop 4, effectively suppressing stray light interference from outside the system; the collimated beam is incident on the annular transmittance gradient filter 5, which consists of multiple concentric annular bands, each with different and segmented constant transmittance, used to perform annular radial transmittance gradient modulation on the pupil; the modulated light field is Fourier transformed by the imaging mirror 6, forming a point spread function image on its back focal plane, i.e., the plane where detector 7 is located, thus achieving high-contrast imaging.

[0042] like Figure 2 As shown, the present invention provides a transmittance smoothing design and operating method for a ring-banded pupil modulated high-contrast coronagraph, comprising the following steps:

[0043] The first step is to determine the number of modulation ring bands, the working angle, and the optimization area based on performance requirements. In this embodiment, the central area (without optimization) is a circular area with a radius of 4λ / D. The optimization area is selected as a ring area with a width greater than 4λ / D and a width less than 16λ / D, that is, the inner working angle is 4λ / D and the outer working angle is 16λ / D. λ is the wavelength of light and D is the aperture. The optimization area is calculated and set based on λ and D.

[0044] The second step involves employing annular pupil transmittance modulation technology. The optimization area is divided into annular zones of equal width along the radial direction of the pupil, with consistent transmittance within the same zone. By altering the amplitude distribution of each annular zone, the transmittance of each zone is adjusted to improve imaging contrast and transmittance smoothness. Based on the system's initial transmittance values ​​for each annular zone, N annular zones will have N transmittance values. Specifically, a continuously varying transmittance function curve is set as the optimization starting point, extending radially from the pupil center.

[0045] The third step is to change the light transmittance of each ring band through an amplitude optimization algorithm;

[0046] The smoothness performance is referenced by the smoothness constraint factor, which is the root mean square slope value. A decrease in the root mean square slope value indicates that the smoothness performance is improving, while an increase in the root mean square slope value indicates that the smoothness performance is decreasing.

[0047] Furthermore, the smoothness constraint factor is expressed as:

[0048]

[0049] Where T represents the transmittance value of each band, and N represents the number of annular bands.

[0050] The electric field intensity of starlight on the pupil plane can be expressed as:

[0051]

[0052] in It is the pupil function.

[0053] On the back focal plane of the coronagraph system, the point spread function can be expressed as the square of the modulus of the pupil function:

[0054]

[0055] in This represents the Fourier transform.

[0056] The point spread function I can be seen from the formula. PSF Related to amplitude A, the circular band pupil modulation scheme changes the energy distribution of light by altering the amplitude of the light.

[0057] Furthermore, the contrast objective function is the ratio of the sum of the point spread functions within the optimization region to the sum of the point spread functions within the reference region. A decrease in the objective function indicates improved contrast performance, while an increase indicates decreased contrast performance. The contrast objective function is expressed as:

[0058]

[0059] Furthermore, the composite evaluation function, which combines the contrast performance objective function and the smoothness constraint factor through a power-weighted combination, is used to simultaneously constrain contrast improvement and curve smoothness during the iteration process. The composite evaluation function is expressed as follows:

[0060]

[0061] Where n and m are exponents.

[0062] As can be seen from the formula, the composite evaluation function determines the optimization priority by setting the exponential terms of the contrast performance objective function and the smoothness constraint factor. The ring-band pupil modulation scheme achieves the goal of simultaneously reducing the point spread function intensity and the smoothness constraint factor by changing the amplitude of each ring.

[0063] The fourth step is to optimize the parameters of the composite evaluation function and use an iterative optimization algorithm to control the amplitude values ​​of all rings. Calculate the composite evaluation function value and determine whether the overall performance is improving based on the trend of the composite evaluation function. If the trend of the composite evaluation function is rising, it indicates that the overall performance is declining. In this case, change the algorithm parameters and the composite evaluation function parameters and re-experiment until the trend of the composite function declines. If the trend of the composite evaluation function is declining, it indicates that the overall performance is improving. In this case, use the algorithm to continuously iterate and optimize.

[0064] The fifth step involves using an algorithm to continuously optimize the amplitude values ​​of all loops; in this example, this is set to achieve a system contrast performance of 10. -5 Or the smoothness constraint factor S is less than 0.1, where the contrast performance reaches 10. -5 This indicates that the brightness of points within the optimization region differs from that of the brightest point by more than 100,000 times; determine whether both parameters have decreased. If not, adjust the parameters of the composite evaluation function and continue to step five for iterative optimization.

[0065] Step 6: Continue optimization until the composite evaluation function value no longer decreases, at which point amplitude modulation is complete, and the amplitude modulation iteration ends; optimize contrast performance to achieve 10. -7 Furthermore, the smoothness constraint factor S is considered to be successful if it is less than 0.02 in this example; otherwise, continue to step 5 and iterate again.

[0066] Step 7, the result is as follows Figures 3-7 As shown: Figure 3 The PSF image before modulation. Figure 4 The image is a modulated PSF image, from which the significant optimization effect can be clearly seen. Figure 5 This is a schematic diagram of a ring-shaped filter with gradually increasing transmittance. Figure 6 For the amplitude-modulated pupil, the smoothness constraint factor is less than 0.02; Figure 7The image shows the modulated contrast curve, from which it can be seen that within the optimization range, the contrast is better than 10. -8 .

[0067] In summary, this invention provides a transmittance smoothing design method for a high-contrast imaging coronagraph with annular band modulation. This method modulates the radial transmittance of the telescope's pupil in a circular pattern, suppressing strong diffraction light from stars. This annular transmittance-gradient pupil modulation design utilizes a limited number of annular bands, each with the same transmittance. By further constraining the transmittance differences between adjacent bands, the energy distribution of the star at the pupil position in the optical system is altered, achieving optimal high-contrast imaging performance. This modulation band, by constraining the transmittance differences between adjacent bands, makes the overall transmittance design curve smooth, overcoming the manufacturing difficulties caused by drastic transmittance jumps in traditional filters, thus ensuring processing accuracy. Furthermore, it alleviates problems such as wavefront phase jumps caused by abrupt changes in film thickness. A smooth transmittance design and operating method for a high-contrast coronagraph with annular pupil modulation is proposed. By optimizing the transmittance value of the modulation band, strong diffraction light from stars is suppressed, thus meeting the requirements for optimal high-contrast imaging. By optimizing the transmittance difference between adjacent annular bands, the problems of wavefront sensitivity to transmittance abrupt changes and manufacturing difficulties of the pupil modulation filter are solved, ensuring its processing accuracy and ultimately improving the high-contrast imaging performance of the entire system.

[0068] The above embodiments are merely typical implementations of the present invention and are not intended to limit the present invention. Any equivalent substitutions or improvements made within the scope of the claims of the present invention are within the protection scope of the present invention.

Claims

1. A smooth transmittance design and operating method for a ring-banded pupil modulated high-contrast coronagraph, characterized in that, A ring-shaped transmittance gradient pupil modulation technique is employed to modulate the radial transmittance of the telescope's pupil in a ring shape, thereby suppressing strong diffraction light from stars. This ring-shaped transmittance gradient pupil modulation uses rings of equal width and finite quantity, ensuring consistent transmittance within the same ring to alter the energy distribution of the star at the pupil position in the optical system, achieving optimal high-contrast imaging performance. The finite transmittance modulation bands constrain the transmittance differences between adjacent bands, resulting in a smooth overall transmittance design curve and guaranteeing the processing accuracy of the transmittance strips. The transmittance gradient modulation method includes the following steps: Step 1: Determine the system's imaging contrast requirements, and improve the final imaging contrast performance by increasing the number of ring bands; determine the number of modulation bands. Step 2: Set the initial transmittance distribution of the modulation ring and introduce a smoothness constraint factor to limit the transmittance difference between adjacent rings; Step 3: Establish a composite evaluation function that includes contrast performance and transmittance smoothness index. During the optimization process, the transmittance value of each band is adjusted synchronously. By setting the composite evaluation function, the smooth transition of high contrast imaging performance and transmittance curve is ensured. Step 4: Input the initial transmittance values ​​of the annular bands into the high-contrast imaging calculation simulation system, and update the transmittance values ​​of each band independently through an iterative optimization algorithm; Step 5: Calculate the imaging contrast within the target detection area in real time to determine whether it meets the preset ultra-high contrast performance; calculate the overall transmittance smoothness constraint factor of the ring to determine whether it meets the preset smoothness performance.

2. The transmittance smoothing design and working method of a ring-banded pupil modulated high-contrast coronagraph according to claim 1, characterized in that, The smoothness constraint factor uses the root mean square slope value. By minimizing the root mean square slope value, the transmittance difference between adjacent rings is constrained, thereby improving the stability of the manufacturing process. A decrease in the root mean square slope value indicates that the smoothness performance is improving, while an increase in the root mean square slope value indicates that the smoothness performance is decreasing.

3. The transmittance smoothing design and working method of a ring-banded pupil modulated high-contrast coronagraph according to claim 2, characterized in that, The smoothness constraint factor is expressed as follows: ； Where T represents the transmittance value of each band, and N represents the number of annular bands.

4. The transmittance smoothing design and working method of a ring-banded pupil modulated high-contrast coronagraph according to claim 1, characterized in that, The contrast performance is referenced to an objective function, which is the ratio of the sum of the point spread functions within the optimization region to the sum of the point spread functions within the central region. A decrease in the objective function value indicates an improvement in contrast performance, while an increase in the objective function value indicates a decrease in contrast performance.

5. The transmittance smoothing design and working method of a ring-banded pupil modulated high-contrast coronagraph according to claim 4, characterized in that, The electric field intensity of starlight on the pupil plane of the optical system is expressed as: ； in It is the pupil function; On the back focal plane of the imaging system, the point spread function (PSF) can be expressed as the square of the pupil function modulo: ； in Indicates Fourier transform; The contrast objective function is expressed as: ； Where I PSF(optimized) I represents the point spread function within the optimization region. PSF(core) This represents the point spread function within the central region.

6. The transmittance smoothing design and working method of a ring-banded pupil modulated high-contrast coronagraph according to claim 1, characterized in that, The composite evaluation function is formed by multiplying the contrast performance objective function and the smoothness constraint factor. It is used to simultaneously constrain contrast improvement and curve smoothness during the iteration process. The composite evaluation function is expressed as: ； Where n and m are exponents; The contrast objective function is expressed as: ； Where I PSF(optimized) I represents the point spread function within the optimization region. PSF(core) Represents the point spread function within the central region; The smoothness constraint factor is expressed as follows: ； Where T represents the transmittance value of each band, and N represents the number of annular bands.

7. The transmittance smoothing design and working method of a ring-banded pupil modulated high-contrast coronagraph according to claim 1, characterized in that, The point spread function image of the high-contrast dark area is obtained on the back focal plane of the coronagraph system, and the imaging contrast after amplitude modulation is tested along the diagonal direction.

Images