Method for measuring atmospheric optical turbulence profile based on telescope focal plane annular image

Abstract

The application discloses a method for measuring atmospheric optical turbulence profile based on a telescope focal plane annular image, a telescope with a cone lens is used to obtain an achromatic annular image on a focal plane, then software algorithm is combined to process collected data, finally, according to the relationship between an angular power spectrum value, turbulence intensity and a weight function, the relationship between the angular power spectrum value of a wavefront flicker signal and the turbulence intensity and the weight function at a certain height is used to inversely obtain the turbulence profile, wherein the cone lens can be placed in front of the telescope or at a position before the focal point of the telescope. In the optical system of the application, there is no chromatic aberration, the image quality of the annular image is not affected in a use environment with a large temperature variation range, and any focusing device does not need to be added; the application has low cost, is easy to realize, has a simple hardware structure and is easy to assemble and adjust.

Description

Technical Field

[0001] This invention relates to the field of atmospheric optics, specifically a method for measuring atmospheric optical turbulence profiles using a telescope focal plane ring image. Background Technology

[0002] Astronomy is an observation-based discipline, but the correlation characteristics of light waves are affected by the randomly varying atmospheric refractive index, exhibiting irregular changes. This is one of the main reasons for the decline in imaging quality of ground-based astronomical telescopes. Therefore, atmospheric turbulence must be a crucial factor to consider when selecting an excellent astronomical observatory site.

[0003] Temperature fluctuations generate atmospheric optical turbulence, which in turn causes changes in light wave propagation, resulting in fluctuations in the angle of arrival and intensity of light waves. Currently, atmospheric optical turbulence is mainly measured directly using these fluctuations. Instruments based on the angle of arrival fluctuation include: Differential Image Motion Measurement Instrument (DIMM), Generalized Seeing Meter (GSM), and Interferometric Seeing Meter (ISM). Instruments based on the intensity fluctuation include: Multi-Aperture Scintillation Sensor (MASS), Single-Star Scintillation Analyzer (SCIDAR), Lunar Edge Profiler (PML), and Full-Aperture Scintillation Sensor (FASS).

[0004] Based on DIMM, MASS, and FASS, the Ring-Shaped Defocus Image Scintillation Sensor (RINGSS) was developed. RINGSS integrates the functions of DIMM, MASS, and FASS, making it the preferred instrument to replace DIMM, MASS, and MASS-DIMM in the future. RINGSS measures atmospheric optical turbulence parameters by observing the intensity distribution changes (wavefront scintillation) of the ring-shaped defocused image within the telescope's focal length. RINGSS first generates a ring-shaped defocused image of the target star, then processes the image, establishes a weighting function, and finally inverts the turbulence profile.

[0005] RINGSS combines the advantages of MASS and DIMM, and also boasts the benefits of low hardware cost, simple setup and adjustment, and easy portability. RINGSS uses two methods to measure total atmospheric seeing based on the same optical path.

[0006] Currently, there are two implementation schemes for the RINGSS optical system: cemented doublet positive lens and a combination of negative lens and cemented doublet positive lens. Both utilize the spherical aberration of the lens to achieve the function of a conical lens. A cemented doublet positive lens (or a combination of negative lens and cemented doublet positive lens) is added in front of the focal plane of the telescope, thereby forming a conical wavefront on the defocus surface inside the telescope to converge into a ring-shaped defocused image, and a filter (500-750nm) is used to reduce chromatic aberration.

[0007] However, this solution has problems: it produces significant chromatic aberration in environments with large temperature variations, affecting the image quality of the annular image and increasing the measurement error of the atmospheric optical turbulence profile. In other words, the impact of aberrations is significant, usually requiring the addition of a focusing device to adjust to the optimal image quality position. Additionally, the half-field of view is approximately 1 arcminute. Summary of the Invention

[0008] To address the aforementioned problems in existing technical solutions, the purpose of this invention is to provide a method for measuring atmospheric optical turbulence profiles based on a telescope focal plane annular image. Both proposed optimized designs can achieve chromatic aberration-free image quality and improve the signal-to-noise ratio of the annular image.

[0009] This invention was supported by the National Natural Science Foundation of China (NSFC) Youth Project "Study on Multi-Aperture Blaze of Single Stars in Telescope Entrance Pupil" (Project No. 11103050, from January 2012 to December 2014, completed), the NSFC General Project "Study on the Intensity and Vertical Distribution of Optical Turbulence in the Surface Layer of Astronomical Observatory Sites Based on Non-Contact Optical Measurement Method of Lunar Blaze" (Project No. 11473051, from January 2015 to December 2018, completed), and the NSFC General Project "Study on Near-Surface Atmospheric Optical Turbulence Profiles of Astronomical Observatory Sites Based on Triangulation Method of Binary Star Wavefront Blaze" (Project No. 11873012, from January 2019 to December 2022, completed).

[0010] This invention was also supported by the key research and development and transformation plan project of the Science and Technology Bureau of Haixi Mongolian and Tibetan Autonomous Prefecture, Qinghai Province, "Development and operation of a site MASS based on a high-performance camera in the Lenghu Saishiteng area" (project number 2020-YZ-101, from August 1, 2020 to July 31, 2023) and the National Natural Science Foundation of China project "Research on the optomechanical system of a large-aperture low-threshold imaging atmospheric Cherenkov telescope" (project number 12173063, from January 1, 2022 to December 31, 2025).

[0011] This invention proposes to use a conical lens to compress the light beam in the radial direction in the optical system design, compressing the diffraction image on the analysis plane into a ring-shaped image, thereby producing a clearer and sharper ring-shaped image on the focal plane, with no chromatic aberration in the entire wavelength range (400-1100nm), making the entire optical system more stable and simple, and helping to improve the signal-to-noise ratio.

[0012] The technical solution of the present invention is as follows:

[0013] A method for measuring atmospheric optical turbulence profiles based on telescope focal plane ring images involves using a telescope with a conical lens to obtain a chromatic aberration-free ring image on the focal plane. The acquired data is then processed using software algorithms. Finally, the turbulence profile is obtained by inversion based on the relationship between angular power spectral density, turbulence intensity, and a weighting function. The method includes the following steps:

[0014] (1) Set up an optical system for measuring atmospheric optical turbulence; the optical system consists of three parts: a telescope, a conical lens, and a camera. The conical lens is placed at the focal front of the telescope or in front of the telescope tube. When the conical lens is placed at the focal front of the telescope, the field of view is ±1 arcminute; when the conical lens is placed in front of the telescope tube, the field of view is ±10 arcminute.

[0015] (2) The camera is connected to the host computer, and its target surface is located at the focal plane of the telescope to receive a ring image without chromatic aberration;

[0016] (3) Process the data using software algorithms; process a series of ring-shaped images on the telescope focal plane, establish a weighting function, and finally base the data on the angular power spectrum value S. m With height h j Turbulence intensity J at the location j and weight function W m (h j The relationship between ) The turbulence profile is obtained through inversion.

[0017] Furthermore, the telescope is a GSO RC8 telescope (carbon fiber tube), and the camera is a Basler camera.

[0018] Furthermore, there is no chromatic aberration in the entire optical system; the image quality of the ring image is not affected in operating environments with a wide range of temperature variations, and no focusing device is required.

[0019] Furthermore, the specific steps include the following:

[0020] 1) Image centering: Utilizing the property that Fourier translation does not change the power spectrum, the ring-shaped image of each frame is centered by Fourier transform, and the background is subtracted;

[0021] 2) Processing annular images without chromatic aberration: Calculate the angular frequency signal to represent wavefront scintillation, statistically analyze the wavefront scintillation signal values ​​of a series of annular images, i.e., the square of the angular frequency signal modulus; divide the ring into several sector regions to measure the radius of the ring; and return parameters including flux, flux variance, ring width, average radius, and center position.

[0022] 3) Noise estimation: Estimate the angular power spectrum and variance of motion in the differential sector region of the ring image, as well as the noise variance, including photon noise and readout noise;

[0023] 4) Calculate the weighting function: Use small-signal theory to establish a theoretical expression for the weighting function and explain the relationship between the signal and turbulence; since the propagation filter and the instrument filter are coupled to each other, they are combined to obtain the total filter; use the relationship between the total filter and the weighting function to solve for the weighting function.

[0024] 5) Inversion to obtain atmospheric optical turbulence profile: Using the relationship between the angular power spectrum of the wavefront scintillation signal of a series of ring images and the turbulence intensity and weighting function at a set height, the turbulence profile is obtained by inversion;

[0025] 6) The total seeing, free atmospheric seeing, atmospheric time constant, and isohalo angle are further calculated from the turbulence profile.

[0026] Furthermore, the imaging plane of the annular image is located at the focal plane of the telescope.

[0027] The beneficial effects of this invention are: there is no color difference. The image quality of the ring-shaped image is not affected in operating environments with large temperature variations, so no focusing device is required. Attached Figure Description

[0028] Figure 1 This is a ZEMAX 3D layout diagram that uses an RC system to simulate the GSO RC8 telescope barrel (RC system), i.e., placing the conical lens in front of the telescope focal length in this invention (optimization scheme one).

[0029] Figure 2 This is a ZEMAX dot plot showing the placement of the conical lens in front of the telescope (optimized scheme one) in this invention.

[0030] Figure 3 This is a ZEMAX 3D layout diagram that uses an RC system to simulate the GSO RC8 lens barrel (RC system), i.e., the ZEMAX 3D layout diagram in which the conical lens is placed in front of the lens barrel (optimized scheme 2) in this invention.

[0031] Figure 4 This is a ZEMAX dot plot showing the placement of the conical lens in front of the lens barrel (optimized scheme two) in this invention.

[0032] Figure 5 These are the weighting function curves for angular frequencies from m=1 to m=20 (corresponding sequentially from top to bottom) in this invention; where (a) is a logarithmic coordinate curve and (b) is a logarithmic coordinate curve.

[0033] Figure 6 These are the weight function curves at different turbulence heights; where (a)-(h) are the weight function curves at turbulence heights z of 0, 0.25km, 0.5km, 1km, 2km, 4km, 8km, and 16km, respectively.

[0034] Figure 7 These are ring images and light intensity curves; where (a) is a ring image taken by a ZWO ASI290MM camera, and (b) is the light intensity curve of the ring image taken by a ZWO ASI290MM camera.

[0035] (c) is a ring image taken by a BASLER acA720-520um camera, and (d) is the light intensity curve of the ring image taken by a BASLER acA720-520um camera.

[0036] (e) is the ring image under ideal conditions without turbulence, and (f) is the light intensity curve of the ring image under ideal conditions without turbulence.

[0037] Figure 8 This is a flowchart of a method for measuring atmospheric optical turbulence profiles based on telescope focal plane ring images.

[0038] Figure 9 This is a ZEMAX 3D layout diagram that uses the RC system to simulate the Celestron C5A lens barrel (Schmidt-Cassegrain system), which is the existing RINGSS scheme that uses the spherical aberration of a combination of negative lenses and cemented doublet positive lenses to achieve the function of a conical lens.

[0039] Figure 10 This is a ZEMAX dot plot that simulates the Celestron C5A lens barrel (Schmidt-Cassegrain system) using the RC system, which is the existing RINGSS scheme that uses the spherical aberration of a combination of negative lenses and cemented doublet positive lenses to achieve the function of a conical lens.

[0040] Figure 11 yes Figure 9 Structural matrix plot of the aluminum lens barrel for multiple structural thermal analysis of the optical system (using an RC system to simulate the Celestron C5A lens barrel (Schmidt-Cassegrain system)).

[0041] Figure 12 yes Figure 1 Structural matrix point plot of multiple structure thermal analysis of optical system (using RC system to simulate GSO RC8 lens barrel (RC system)).

[0042] Figure 13 It is regulation Figure 9 The structure matrix dot plot in the optical system where the distance between the telescope and the lens, and the ring width of the inner defocused ring image both achieve optimal image quality.

[0043] Figure 14 yes Figure 1 The optical system, when adjusting the distance between the telescope and the conical lens, still achieves a structure matrix dot plot where the ring width of the annular image reaches the diffraction limit.

[0044] Figure 15 yes Figure 9Structural matrix plot of the carbon fiber lens barrel for thermal analysis of the optical system (using an RC system to simulate the Celestron C5A lens barrel (Schmidt-Cassegrain system)). Detailed Implementation

[0045] The present invention will now be described in further detail with reference to the accompanying drawings.

[0046] This invention utilizes a telescope with an added conical lens to obtain a chromatic aberration-free annular image on the focal plane. Then, it processes the acquired data using software algorithms, and finally, based on the relationship between the angular power spectrum, turbulence intensity, and a weighting function, inverts and obtains the turbulence profile. Figure 8 As shown, it includes the following steps:

[0047] (1) Set up an optical system for measuring atmospheric optical turbulence; the optical system consists of three parts: a telescope, a conical lens, and a camera. The conical lens is placed at the focal front of the telescope or in front of the telescope tube. When the conical lens is placed at the focal front of the telescope, the field of view is ±1 arcminute; when the conical lens is placed in front of the telescope tube, the field of view is ±10 arcminute.

[0048] (2) The camera is connected to the host computer, and its target surface is located at the focal plane of the telescope to receive a ring image without chromatic aberration;

[0049] (3) Process the data using software algorithms; process a series of ring-shaped images on the telescope focal plane, establish a weighting function, and finally base the data on the angular power spectrum value S. m With height h j Turbulence intensity J at the location j and weight function W m (h j The relationship between ) The turbulence profile is obtained through inversion.

[0050] This embodiment presents two schemes for measuring atmospheric optical turbulence profiles based on telescope focal plane ring images. Both telescopes use GSO RC8 (carbon fiber tube) and employ a Ritchey-Chrétien optical design. The two schemes are described as follows: (1) Scheme 1: Add a cone lens in front of the telescope focal plane, resulting in a small field of view (±1 AMM) and no chromatic aberration. (2) Scheme 2: Add a cone lens in front of the telescope tube, resulting in a wide field of view (±10 AMM), no chromatic aberration, and the best imaging effect.

[0051] RINGSS has a simple hardware structure but a relatively complex software algorithm. The method for measuring atmospheric optical turbulence profiles using a ring image scintillation sensor involves obtaining achromatic ring images using the two RINGSS optical system designs described above. These ring images are then processed, and a weighting function is established. Finally, based on the relationship between the angular power spectrum, turbulence intensity, and the weighting function, the turbulence profile is retrieved. The specific steps include:

[0052] (1) Image centering: Taking advantage of the property that Fourier translation does not change the power spectrum, the ring image of each frame is centered by Fourier transform and the background is subtracted.

[0053] (2) Processing annular images without chromatic aberration. Calculate the angular frequency signal to represent wavefront scintillation, and statistically analyze the wavefront scintillation signal values ​​of a series of annular images, i.e., the square of the angular frequency signal modulus (angular power spectrum value). Divide the ring into 8 sector regions to measure the ring radius. Return parameters such as flux, flux variance, ring width, average radius, and center position.

[0054] (3) Noise estimation. In order to accurately estimate the atmospheric optical turbulence profile and atmospheric parameters, it is necessary to estimate the angular power spectrum of the ring image and the variance of the motion of the differential sector region, as well as the noise variance, including photon noise and readout noise.

[0055] (4) Calculate the weighting function. (Turbulent layer) Use small-signal theory to establish a theoretical expression for the weighting function to explain the relationship between the signal and turbulence. Since the propagation filter and the instrument filter are coupled, they are combined to obtain the total filter. The weighting function can be obtained by using the relationship between the total filter and the weighting function.

[0056] (5) The atmospheric optical turbulence profile is obtained by inversion. The turbulence profile is obtained by inverting the relationship between the angular power spectrum of the wavefront scintillation signal of a series of ring images and the turbulence intensity and weighting function at a certain height.

[0057] (6) The total seeing, free atmospheric seeing, atmospheric time constant, and isohalo angle can be further calculated from the turbulence profile.

[0058] This invention mainly comprises two parts: optimization of the optical system hardware structure and software algorithm recovery of atmospheric turbulence profiles. For example... Figure 1 and Figure 3 The diagram shows two optimized schemes for an optical system using a ring-shaped image scintillation sensor to recover the profile of atmospheric optical turbulence. The entire optical path includes a 203mm aperture GSO RC8 telescope (carbon fiber tube) and a conical lens. The conical lens is positioned in front of the telescope's entrance pupil, forming a ring image with a full field of view of 20 arcminutes and a radius of 15 arcseconds. The software version used for the optical design simulation is ZEMAX OpticStudio 21.3.1. Figure 1 The optical path diagram represents optimized scheme one, where the conical lens is placed at the focal front of the telescope, with a field of view of ±1 arcminute. The point diagram of this optical path is shown below. Figure 2 As shown, the telescope focal plane ring images of the two fields of view at 0° and 1 angular fraction are displayed. It can be seen that the ring images of different wavelengths overlap, and the optical system has no chromatic aberration. Figure 3 The optical path diagram is for optimized scheme two, where the conical lens is placed in front of the telescope, with a field of view of ±10 arcminutes; the point diagram of this optical path is as follows. Figure 4 As shown, the telescope focal plane ring images at three fields of view—0°, 5 AM, and 10 AM—are displayed. It can be seen that the ring images of different wavelengths overlap, and the optical system exhibits no chromatic aberration. The field of view in Scheme 2 is larger than that in Scheme 1, resulting in better imaging performance.

[0059] like Figure 9 The diagram shown is a 3D layout of ZEMAX, which utilizes the spherical aberration of a combination of a negative lens and a cemented doublet positive lens to achieve the function of a conical lens in the existing RINGSS scheme. It uses an RC system to simulate the Celestron C5A telescope barrel (Schmidt-Cassegrain system), with the simulated barrel material being aluminum. By combining a negative lens with a cemented doublet positive lens, the spherical aberration of the lenses is used to achieve the function of a conical lens, forming a conical wavefront on the defocusing surface within the telescope to converge into a ring-shaped defocused image. The dot plot on the image plane of this optical system is shown below. Figure 10 As shown, there is a relatively large chromatic difference, and the ring images of different wavelengths are distributed quite dispersedly.

[0060] Figure 9 The optical system shown is a simulation of the Celestron C5A telescope barrel (Schmidt-Cassegrain system) using an RC system. Multiple structural thermal analyses were conducted at different ambient temperatures. The optomechanical structures of the telescope barrel and the rear lens are all made of aluminum. Structure 1 corresponds to 20℃, structure 2 corresponds to -20℃, and structure 3 corresponds to 0℃. Figure 11 As shown, is Figure 9 The structural matrix plot of the optical system's multi-structure thermal analysis shows that the ring image is significantly affected by temperature. As the temperature decreases, both the diameter and width of the ring image increase significantly, and the width of the inner defocused ring image does not reach the diffraction limit. When the inner defocused ring image achieves optimal image quality, the distance between the telescope and the negative lens shifts inward by 2.5 mm and outward by 2.5 mm relative to the position at 0℃ at 20℃ and -20℃, respectively. This indicates that an optical system using an aluminum telescope barrel and utilizing the spherical aberration of a negative lens and a cemented doublet positive lens to achieve the function of a conical lens requires a focusing device to adjust the distance between the telescope and the negative lens under different ambient temperatures to achieve a position with good imaging effect. Figure 13To adjust the distance between the telescope and the lens so that the ring width of the inner defocused surface annular image reaches optimal image quality at 20℃, -20℃, and 0℃, a structural matrix dot plot is needed. In short, this optical system requires a focusing device to adjust the distance between the telescope and the negative lens to an optimal position to obtain a sharp annular image on the inner defocused surface.

[0061] Figure 1 The optical system shown is an RC system that simulates the GSO RC8 lens barrel (RC system). It also uses multiple structural thermal analyses at different ambient temperatures. The simulated lens barrel material is carbon fiber, and the optomechanical structure of the rear lens is set to aluminum. Structure 1 corresponds to 20℃, structure 2 corresponds to -20℃, and structure 3 corresponds to 0℃. Figure 12 As shown, is Figure 1 The structural matrix plot of the optical system's multi-structure thermal analysis shows that when the distance between the telescope and the conical lens remains constant at different temperatures, the ring pattern changes very little under different ambient temperatures, and the ring width still reaches the diffraction limit. For example... Figure 14 As shown, is Figure 1 Even with adjustments to the distance between the telescope and the conical lens, the ring width of the annular image still reaches the diffraction-limited structure matrix dot plot. Figure 12 In comparison, it can be seen that both the diameter and width of the annular image on the focal plane change, but the width of the annular image still reaches the diffraction limit. This indicates that the optical system with the added conical lens in this invention exhibits no chromatic aberration and maintains good imaging performance even under varying temperature conditions, eliminating the need for a focusing device.

[0062] like Figure 15 The diagram shown is a structural matrix plot of a simulated carbon fiber Celestron C5A lens barrel combined with a negative lens and a cemented doublet positive lens for multiple structural thermal analysis. It can be seen that the ring width of the inner defocus ring image still does not reach the diffraction limit, but compared with... Figure 11 The image quality has been greatly improved, indicating that the primary reason for the need for a focusing device in optical systems using the aluminum Celestron C5A lens barrel combined with negative and cemented doublet positive lenses is the significant temperature influence on the lens barrel material. In summary, only the carbon fiber GSO RC8 lens barrel optical system with added conical lenses exhibits good image quality under varying temperature conditions, achieving the diffraction limit in the ring image, eliminating the need for a focusing device, and exhibiting no chromatic aberration in the ring image.

[0063] The principle and process of reconstructing atmospheric turbulence profiles using software algorithms are as follows. The two key aspects of the RINGSS algorithm are the signal processing algorithm and the calculation of the weighting function.

[0064] The chromatic aberration-free annular image obtained by processing the optimized optical structure described above is used to calculate the angular frequency signal a. m, to represent wavefront scintillation, used to calculate the statistics required for measuring turbulence. Formula (1) represents the intensity change of the ring image, i.e., template M. m，i The weighted average, where m is the angular frequency, I i I is the pixel value, and I0 is the total light intensity, used for normalization. Template M m (r, θ) = f(r)e imθ , where f(r) is the annular aperture function. The wavefront scintillation signal values ​​S of a series of annular images are statistically analyzed. m That is, angular frequency signal a m The square of the modulus is called the angular power spectral density (APS).

[0065]

[0066] A theoretical expression for the weighting function is established to explain the relationship between the signal and turbulence. Under Fraunhofer diffraction conditions, an instrument filter is established using the relationship between the image plane intensity and the entrance pupil light field, thus introducing the influence of system aberrations and template on the weighting function. Furthermore, wavefront amplitude fluctuations and phase fluctuations are uniformly introduced into the propagation filter. Since the propagation filter and the instrument filter are coupled, they are finally combined to obtain the total filter PQ(f), as shown in equation (2). and The instrument response corresponds to the phase and amplitude. This is achieved using the total filter PQ(f) and the weighting function W. m The relationship, i.e., equation (3), can be used to solve for the weight function.

[0067]

[0068]

[0069] Using formula (4), the angular power spectrum S m With height h j Turbulence intensity J at the location j and weight function W m (h j The relationship between the two conditions is used to invert the turbulence profile. The total seeing, free atmospheric seeing, and isomorphic angles can be further calculated from the turbulence profile.

[0070]

[0071] like Figure 5 The table shows twenty weighted function curves for angular frequencies m from 1 to 20 (corresponding to m=1 to m=20 from top to bottom), and the corresponding instrument parameters are shown in Table 1. Figure 5 In the figure, (a) is the logarithmic curve. Figure 5Figure (b) shows the logarithmic coordinate curves. The horizontal axis represents the turbulence height z, ranging from 0 to 32 km, and the vertical axis represents the weighting function value in meters (m). -1 / 3 It can be seen that the small m signal mainly comes from turbulence at high altitudes, while the large m signal mainly comes from low-altitude turbulence closer to the ground.

[0072] Table 1 Instrument Parameters

[0073] EPS (center occlusion) 89mm Pixel [arcsec] 0.7l ringradpix (ring radius) 20 pixels mmax (angular frequency) 20 ron (readout noise) 1.1

[0074] Figure 6 The figures show the weighting function curves at turbulent discrete layer heights z of 0, 0.25 km, 0.5 km, 1 km, 2 km, 4 km, 8 km, and 16 km. The solid line represents the weighting function curve of the optical system with the conical lens placed in front of the telescope in this scheme, while the dashed line represents the weighting function curve of the original optical system using a cemented doublet with spherical aberration. It can be seen that the weighting function curve of the scheme with the conical lens placed in front of the telescope is more stable and smoother, and the two weighting function curves differ significantly.

[0075] Figure 7 (a)-(d) show the actual captured ring-shaped images superimposed with turbulence (i.e., the average of multiple short exposure images) and their light intensity curves. Figure 7 Image (a) shows an inner defocus ring image captured by a ZWO ASI290MM camera, i.e., a ring image obtained using an existing optical system employing a cemented doublet achromatic lens with spherical aberration. A distinct secondary ring image can be clearly seen within the ring image itself. Figure 7 Correspondingly, a strong secondary peak can also be seen in (b) of the curve. The horizontal axis of the curve represents the pixel position, and the vertical axis represents the light intensity. Figure 7 Image (c) shows a focal plane ring image taken using a BASLER camera with a conical lens placed in front of the focal plane, representing the optical system optimization scheme proposed in this invention. The secondary rings within the ring image are even darker. Figure 7 The light intensity curve in (d) also becomes smoother, with the horizontal axis representing pixel position and the vertical axis representing light intensity. Figure 7 In the image (e), the simulated annular image under the ideal conditions of the present invention is an instantaneous CCD image without turbulence superposition. Figure 7 In the image (f), the light intensity curve of the non-turbulent ring image is shown. The horizontal axis represents the pixel position, and the vertical axis represents the normalized light intensity. The secondary peak of the diffraction dark ring can be seen.

[0076] Both ZEMAX optical design simulations and experiments demonstrate that the proposed solution is feasible and effectively optimizes the method for recovering atmospheric optical turbulence profiles using a ring-shaped image scintillation sensor. This provides more possibilities for future long-term monitoring of turbulence at astronomical and field sites, replacing MASS, DIMM, and MASS-DIMM.

[0077] In summary, this invention proposes a method for measuring atmospheric optical turbulence profiles based on a telescope focal plane annular image. The GSO RC8 telescope optical system, with the addition of a conical lens, obtains a chromatic aberration-free annular image on the focal plane. The conical lens can be placed in front of the telescope or at the focal front position, with the former providing better imaging. The software algorithm processes the chromatic aberration-free annular image obtained from the optical setup, calculates the angular frequency signal to represent wavefront scintillation, uses it to calculate the statistics required for turbulence measurement, and establishes a theoretical expression for the weighting function to explain the relationship between the signal and turbulence. Using the relationship between the angular power spectrum of the wavefront scintillation signal, the turbulence intensity at a certain altitude, and the weighting function, the turbulence profile is inverted to obtain the turbulence profile. The optical system of this invention is free of chromatic aberration, does not affect the image quality of the annular image under varying temperature conditions, and requires no additional focusing device. It is low-cost, easy to implement, has a simple hardware structure, and is easy to assemble and adjust.

[0078] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for measuring atmospheric optical turbulence profiles based on a telescope focal plane annular image, characterized in that: A chromatic aberration-free annular image on the focal plane is obtained using a telescope with an added conical lens. The acquired data is then processed using software algorithms. Finally, the turbulence profile is obtained by inversion based on the relationship between the angular power spectrum, turbulence intensity, and weighting function. The process includes the following steps: (1) Set up an optical system for measuring atmospheric optical turbulence; the optical system consists of three parts: a telescope, a conical lens, and a camera. The conical lens is placed at the focal front of the telescope or in front of the telescope tube; when the conical lens is placed at the focal front of the telescope, the field of view is... Angle numeral; when the conical lens is placed in front of the telescope tube, the field of view is Centimeters; (2) The camera is connected to the host computer, and its target surface is located at the focal plane of the telescope to receive a ring image without chromatic aberration; (3) Process data using software algorithms; process a series of ring-shaped images on the focal plane of the telescope and establish a weighting function, and finally base the data on the angular power spectrum. With height Turbulence intensity at and weight function Relationship The turbulence profile is obtained through inversion; Specifically, the steps include the following: 1) Image centering: Utilizing the property that Fourier translation does not change the power spectrum, the ring-shaped image of each frame is centered by Fourier transform, and the background is subtracted; 2) Processing annular images without color difference: Calculate the angular frequency signal to represent wavefront scintillation, statistically analyze the wavefront scintillation signal values ​​of a series of annular images, i.e., the square of the angular frequency signal modulus; divide the ring into several sector regions to measure the radius of the ring; and return parameters including flux, flux variance, ring width, average radius, and center position. 3) Noise estimation: Estimate the angular power spectrum and variance of motion in the differential sector region of the ring image, as well as the noise variance, including photon noise and readout noise; 4) Calculate the weighting function: Use small-signal theory to establish a theoretical expression for the weighting function and explain the relationship between the signal and turbulence; since the propagation filter and the instrument filter are coupled to each other, they are combined to obtain the total filter; use the relationship between the total filter and the weighting function to solve for the weighting function. 5) Inversion to obtain atmospheric optical turbulence profile: Using the relationship between the angular power spectrum of the wavefront scintillation signal of a series of ring images and the turbulence intensity and weighting function at a set height, the turbulence profile is obtained by inversion; 6) The total seeing, free atmospheric seeing, atmospheric time constant, and isohalo angle are further calculated from the turbulence profile.

2. The method for measuring atmospheric optical turbulence profiles based on a telescope focal plane ring image according to claim 1, characterized in that: The telescope is a GSO RC8 telescope, and the camera is a BASLER acA720-520um.

3. The method for measuring atmospheric optical turbulence profiles based on a telescope focal plane annular image according to claim 1, characterized in that: There is no chromatic aberration in the entire optical system; the image quality of the ring image is not affected in operating environments with a large temperature range, and no focusing device is required.

4. The method for measuring atmospheric optical turbulence profiles based on a telescope focal plane annular image according to claim 1, characterized in that: The imaging plane of the annular image is located at the focal plane of the telescope.

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