A system and method for measuring color difference of fog

Abstract

The present invention belongs to the technical field of atmospheric dispersion, and in particular to a system and method for measuring atmospheric chromatic aberration. The system includes a porous mirror installed on the telescope barrel cover, and the porous mirror is arranged in a circular array with the center of the barrel cover as the center of the circle. The porous mirrors are all wedge mirrors, and the thickness of the wedge mirror gradually increases from the center position of the barrel cover to the outside. The advantage of this invention is that the calibration operation can not only make the subsequent solution of atmospheric chromatic aberration not be affected by defocused imaging, but also ignore the processing error of the wedge angle to a certain extent. The imaging measurement method of regular polygons is realized by the non-regular polygon array, which relaxes the position requirements of the imaging spot, makes the actual experimental operation more convenient, and can also achieve the purpose of overcoming the defocused imaging effect caused by changes in ambient temperature.

Description

Technical Field

[0001] The present invention belongs to the technical field of atmospheric dispersion, and in particular relates to a system and method for measuring atmospheric chromatic aberration. Background Art

[0002] In the study of atmospheric light propagation, atmospheric refraction, as a key factor, has attracted increasing attention. This is especially true for horizontal or low-elevation transmission, where the influence of atmospheric dispersion is exacerbated by varying wavelengths. Therefore, quantitative measurement of dispersion can enhance the accuracy of relevant research results.

[0003] Dispersion can generally be divided into two parts. First, during the transmission of composite light, the refractive index of the transmission medium varies with wavelength, resulting in differences in optical path length, which in turn produces dispersion. This effect is particularly pronounced over long distances. What we often call atmospheric chromatic aberration is the dispersion effect of composite light sources during atmospheric transmission. Second, dispersion is generated by the receiving imaging system, which typically occurs in simpler refractive imaging systems. While there are many methods for eliminating dispersion in imaging systems, reflective imaging systems do not produce chromatic aberration. Telescopes like the Hubble Space Telescope and the recently launched Webb Space Telescope both use refracting telescope structures, enabling them to capture images from outer space without chromatic aberration. Therefore, Cassegrain telescopes can be used to observe atmospheric chromatic aberration throughout the entire atmosphere.

[0004] During actual observations, changes in ambient temperature can cause thermal deformation of optical components and supporting structures, leading to defocusing of the optical system's imaging plane. This defocusing can shift the center of mass of the light spot imaged off-axis, introducing errors in the subsequent calculation of the chromatic aberration. For micro-radian chromatic aberration, a shift of the imaging center of mass by approximately one pixel can produce a deviation of approximately 2 μrad, reaching the same magnitude as the measured chromatic aberration. This significantly affects the observed chromatic aberration and can even obscure the desired measurement results. Summary of the Invention

[0005] In order to solve the technical problem that the defocused imaging caused by temperature change causes the centroid shift to affect the measurement of the chromatic aberration of the entire layer of veil, the present invention proposes a system and method for measuring the chromatic aberration of veil. The specific technical solution is as follows:

[0006] A system for measuring chromatic aberration of haze includes a porous mirror mounted on a telescope tube cover. The porous mirrors are arranged in a circular array with the center of the tube cover as the center. The porous mirrors are all wedge mirrors, and the thickness of the wedge mirrors gradually increases from the center position of the tube cover to the outside.

[0007] Specifically, the light beam from the porous mirror is incident on the primary mirror, the primary mirror reflects the light beam onto the secondary mirror, and the secondary mirror reflects the light beam onto the imaging plane.

[0008] Specifically, the formula for calculating the haze color difference is:

[0009]

[0010] Among them, |OP1|, |OP2|...|OP k-1 |、|OP k | is the distance from the center of mass of the light spot formed by each wedge mirror to the center of the imaging plane, f is the focal length of the imaging system, and Δ1 represents the position offset of the kth light spot without considering atmospheric scattering. The formula is:

[0011]

[0012] Where δ1 and δ2 are the deflection angles of light with wavelengths λ1 and λ2 respectively, and α is the wedge angle of the wedge mirror. and are the refractive indices of light with wavelengths λ1 and λ2 in the wedge mirror, and the formula corresponding to the deflection angle is

[0013] δ=α(n-1).

[0014] Specifically, there are three wedge mirrors.

[0015] The method of using the above-mentioned system for measuring the color difference of the fog includes the following steps:

[0016] S1. A plurality of circular holes are formed in a circle-centered array on the lens barrel cover of the telescope, and fixed wedge mirrors are mounted on the circular holes. The thickness of the wedge mirror gradually increases from the center to the edge.

[0017] S2. Using a monochromatic parallel cursor to determine the installation angle of the wedge mirror, so that the final imaging annular array is on the imaging plane;

[0018] S3. Obtain the chromatic aberration of the observed results under actual atmospheric dispersion. The formula is:

[0019]

[0020] Among them OP1, OP2...|OP k-1 |、|OP k | is the distance from the center of mass of the light spot formed by each wedge mirror to the center of the imaging plane, f is the focal length of the imaging system, and Δ1 represents the position offset of the kth light spot without considering atmospheric scattering. The formula is:

[0021]

[0022] The formula corresponding to the deflection angle is

[0023] δ=α(n-1).

[0024] Specifically, in step S1, three wedge mirrors are installed;

[0025] The coordinates of the center of mass of the three light spots are P1(x1,y1), P2(x2,y2) and P3(x3,y3), and the coordinates of point P are Therefore, we obtain:

[0026]

[0027]

[0028] so:

[0029] Δ2=(|PP′|-|P3P|)a

[0030] Where a is the pixel size;

[0031] The position shift Δ caused by atmospheric dispersion can be expressed as:

[0032] Δ=Δ2-Δ1

[0033] The final observed chromatic aberration of the entire target star's atmosphere It can be expressed as:

[0034]

[0035] The advantages of the present invention are that it utilizes the defocus imaging characteristics of the light spot to eliminate the effects of defocus imaging caused by ambient temperature changes. For micro-arc-level chromatic aberration caused by atmospheric chromatic aberration, the effects of defocus are very significant. The calibration operation not only ensures that the subsequent solution of atmospheric chromatic aberration is not affected by defocus imaging, but also, to a certain extent, ignores the machining errors of the wedge angle. The use of a regular polygon array to implement the imaging measurement method relaxes the requirements for the position of the imaging light spot, making actual experimental operations more convenient and also achieving the goal of overcoming the effects of defocus imaging caused by ambient temperature changes. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 The center of mass positions of K light spots with the same wavelength are arranged in a ring.

[0037] Figure 2(a) shows the spot distribution of four wedge mirrors.

[0038] Figure 2(b) shows the light spot distribution when five wedge mirrors are set up.

[0039] Figure 3 Schematic diagram of the installation of three wedge mirrors.

[0040] Figure 3 (a) is a diagram showing the positions of the monochromatic parallel cursor imaging spots under three wedge mirror states.

[0041] Figure 3 (b) is the defocused imaging diagram under the three wedge mirror states due to changes in ambient temperature.

[0042] Figure 3 (c) is the imaging diagram when the atmospheric dispersion is not considered in the three wedge mirror states.

[0043] Figure 3 (d) is the imaging diagram of actual atmospheric scattering in the three wedge mirror states.

[0044] Figure 4 This is a structural diagram of three wedge mirrors installed on the telescope's tube cover.

[0045] FIG5( a ) shows the position diagram of the monochromatic parallel cursor fixed imaging spot.

[0046] FIG5( b ) shows the position diagram of the defocused imaging spot.

[0047] Figure 5(c) shows the spot position diagram when atmospheric dispersion is not considered.

[0048] Figure 5(d) shows the spot position diagram when the atmosphere is actually dispersed.

[0049] In the picture:

[0050] 1. Telescope; 11. Primary mirror; 12. Wedge mirror; 13. Secondary mirror; 2. Imaging plane. DETAILED DESCRIPTION

[0051] like Figure 1 A system for measuring chromatic aberration of haze includes a multi-aperture mirror mounted on a telescope tube cover (1). The multi-aperture mirrors are arranged in a circular array centered around the center of the tube cover. Each multi-aperture mirror comprises a wedge-shaped mirror (12), with the thickness of the wedge-shaped mirror (12) gradually increasing from the center of the tube cover toward the outside. A light beam from the multi-aperture mirror is incident on a primary mirror (11), which reflects the light beam onto a secondary mirror (13). The secondary mirror (13) then reflects the light beam onto an imaging plane (2).

[0052] The system uses a monochromatic parallel light source to calibrate the installation angle of the wedge mirror 12 so that the final imaging result is as follows: Figure 1 The center of mass of K light spots with the same wavelength are arranged in a ring. When measuring the target star, the ideal imaging result when no filter is installed and atmospheric dispersion is not considered is that all the light spots are in a ring array. On this basis, considering the defocus imaging result caused by the change of ambient temperature, the center of mass of the light spot is still arranged in a ring, but it will be scaled proportionally. When a specific filter is installed in front of the wedge mirror 12, the light of the required wavelength is obtained, where P1, P2...P k-1 The wavelength is λ1, P kThe wavelength of the target star is λ2. Without considering atmospheric dispersion, the positions of the light spots at wavelengths λ1 and λ2 are obtained through the filter. In this case, the position of the λ2 imaging spot deviates because the wedge mirror 12 deflects light of different wavelengths at different angles. If the wedge angle of the wedge mirror 12 is α, the deflection angle is:

[0053] δ=α(n-1)

[0054] therefore:

[0055]

[0056] Where δ1 and δ2 are the deflection angles of light with wavelengths λ1 and λ2, respectively. and are the refractive indices of light with wavelengths λ1 and λ2 in the wedge mirror 12, respectively. Δ1 represents the position offset of the kth light spot without considering atmospheric scattering.

[0057] Under the actual atmospheric dispersion, the spot positions of wavelengths λ1 and λ2 obtained by the filter are the actual final observation results. The atmospheric chromatic aberration of the entire layer has atmospheric dispersion only in the vertical direction, and no atmospheric dispersion in the horizontal direction. For the sake of simplicity in calculation, when the initial wedge mirror 12 is calibrated, the final imaging position of the spot with wavelength λ2 and the center of the regular polygon are connected in the vertical direction. Through P1, P2...P k-1 The position coordinates of point O can be obtained from the spot position, so the chromatic aberration can be expressed as:

[0058]

[0059] In the case of actual atmospheric dispersion, the spot distribution diagram when four wedge mirrors 12 are set is shown in FIG2( a ), and the spot distribution diagram when five wedge mirrors 12 are set is shown in FIG2( b ).

[0060] The following describes in detail the arrangement of the three wedge mirrors 12:

[0061] The installation diagram of the three wedge mirrors 12 is as follows: Figure 3 As shown, Figure 3 (a) The centroids of the three light spots with the same wavelength are arranged in an equilateral triangle. When measuring the target star, the ideal imaging result is the same as the one without installing the filter and without considering the atmospheric dispersion. Figure 3 (a). On this basis, considering the defocus imaging results caused by the change of ambient temperature, Figure 3 As shown in (b), the center of mass of the light spot is still arranged in an equilateral triangle. When a specific filter is installed in front of the wedge mirror 12, we can get the light of the required wavelength. Figure 3 (c) Considering the influence of actual atmospheric dispersion, the final imaging result is as follows Figure 3(d) As shown. The structure diagram of the three wedge mirrors 12 installed on the tube cover of the telescope 1 is shown in Figure 4 shown.

[0062] Defocused imaging caused by temperature changes can be seen as Figure 3(a) to Figure 3(b) During this process, as the focal plane position changes forward and backward, the offsets of the three spot centroids remain the same, and the final three centroids still form an equilateral triangle. The two triangles can be considered proportionally scaled. This is how this method overcomes the effect of defocus error on observation results. Using the geometric relationship of the equilateral triangle, the theoretical position of the spot centroid when theoretically free of dispersion can be determined, and finally, the desired chromatic aberration can be calculated using the observation results.

[0063] Figure 3 (c) shows the positions of the light spots at wavelengths λ1 and λ2 obtained through the filter, without considering atmospheric dispersion, for the target star. It can be seen that two wavelengths of light, λ1, and one wavelength of light, λ2, are required. Without considering atmospheric dispersion, the position of the λ2 imaging spot deviates because wedge mirror 12 deflects light of different wavelengths at different angles. If the wedge angle of wedge mirror 12 is α, the deflection angle is:

[0064] δ=α(n-1)

[0065] therefore:

[0066]

[0067] Where n λ1 and n λ2 are the refractive indices of light with wavelengths λ1 and λ2 in the wedge mirror 12 respectively.

[0068] Figure 3 (d) shows the position of the light spots with wavelengths of λ1 and λ2 obtained through the filter under actual atmospheric dispersion. It is the actual final observation result. The atmospheric dispersion of the entire layer of haze is only in the vertical direction, and is considered to be absent in the horizontal direction. As can be seen from the figure, the coordinates of the center of mass of the three light spots are P1(x1,y1), P2(x2,y2) and P3(x3,y3). The coordinates of point P are Therefore, we can obtain:

[0069]

[0070]

[0071] so:

[0072] Δ2=(|PP′|-|P3P|)a

[0073] Where a is the pixel size.

[0074] The position shift Δ caused by atmospheric dispersion can be expressed as:

[0075] Δ=Δ2-Δ1

[0076] The final observed chromatic aberration of the entire target star's atmosphere It can be expressed as:

[0077]

[0078] For the arrangement of the imaging positions of the light spots, the requirements can be appropriately relaxed, that is, the shape and position of the arrangement of the centroids of the light spots do not necessarily have to strictly meet the requirements of an equilateral triangle, as shown in Figure 5. Figure 5(a) shows the calibration of the wedge mirror 12 by a monochromatic parallel light source, and the final arrangement of the centroids of the imaging light spots is a general triangle. Figure 5(b) shows the defocused imaging caused by changes in ambient temperature. The triangle of the arrangement of the centroids of the light spots at this time can be seen as the result of geometric scaling compared to that in Figure 5(a). Figure 5(c) shows the imaging positions of two light spots with a wavelength of λ1 and a light spot with a wavelength of λ2 when the light band we need is selected by a filter, without considering atmospheric dispersion. Figure 5(d) is the imaging result based on Figure 5(c) taking into account the actual atmospheric dispersion.

[0079] When solving the chromatic aberration of haze using a non-equilateral triangle imaging arrangement, the characteristics of the imaging triangle are calibrated in Figure 5(a), which serves as the basis for the entire solution process. The coordinate positions of the centroids of the three light spots are P 01 (x 01 ,y 01 ), P 02 (x 02 ,y 02 ) and P 03 (x 03 ,y 03 ), O0(x0,y0) is the center of the triangle circumcircle. Therefore, we can get:

[0080]

[0081]

[0082]

[0083] Substituting the coordinates of the three points into the above formula, we can find O0(x0,y0). 03 The angle with the vertical direction is β, and we can get:

[0084]

[0085] The wedge mirror 12 with a wedge angle of α deflects light of different wavelengths at different angles. The difference in deflection in FIG5(c) can be expressed as:

[0086]

[0087] Using the previously calibrated triangle characteristic angles θ1, θ2, θ3 and Solve the actual whole-layer chromatic aberration in Figure 5(d). First, we can get the position coordinates of the actual imaging spot P1(x1,y1), P2(x2,y2) and P3(x3,y3). Assume that O1(x 10 ,y 10 ) and P′(x′,y′).

[0088]

[0089] According to the cosine theorem above, we can get the point P'(x',y'), and then substitute P1(x1,y1), P2(x2,y2) and P'(x',y') into the following formula to get O1(x 10 ,y 10 ).

[0090]

[0091] Using the cosine theorem in triangle ΔO1P″P3, we can get

[0092] |O1P3| 2 =|O1P″| 2 +|P3P″| 2 -2|O1P″||P3P″|cosβ

[0093] Also because

[0094] O1P″=O1P′-Δ1

[0095] Therefore, Δ can be obtained, and then the color difference of the entire layer of fog can be obtained

[0096]

[0097] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for measuring chromatic aberration of air, characterized in that: The invention comprises using a porous mirror mounted on a lens barrel cover of a telescope (1), wherein the porous mirrors are arranged in a circular array with the center of the lens barrel cover as the center, and the porous mirrors are all wedge mirrors (12), and the thickness of the wedge mirrors (12) gradually increases from the center position of the lens barrel cover to the outside; The method comprises the following steps: S1. A plurality of circular holes are formed in a circle-centered array on a lens barrel cover of a telescope (1), and fixed wedge mirrors (12) are mounted on the circular holes, wherein the thickness of the wedge mirror (12) gradually increases from the circle center toward the edge; S2, using a monochromatic parallel cursor to determine the installation angle of the wedge mirror (12) so that the final imaging annular array is on the imaging plane (2); S3. Obtain the chromatic aberration of the observed results under actual atmospheric dispersion. The formula is: in 、 … 、 is the distance from the centroid of the light spot formed by each wedge mirror (12) to the center of the imaging plane (2), is the focal length of the imaging system, It represents the position offset of the kth spot without considering atmospheric scattering. The formula is: in and The wavelengths are and The deflection angle of light, is the wedge angle of the wedge mirror (12), and The wavelengths are and The refractive index of light in the wedge mirror (12); the formula corresponding to the deflection angle is ； In step S1, three wedge mirrors (12) are installed; The coordinates of the centroid positions of the three light spots are 、 and ,point The coordinates of the position are , therefore, we obtain: so: Where, is the pixel size; Position shift caused by atmospheric dispersion Expressed as: The final observed chromatic aberration of the entire target star's atmosphere Expressed as: 。 2. The method for measuring chromatic aberration of fog according to claim 1, wherein: The light beam from the porous mirror is incident on the primary mirror (11), the primary mirror (11) reflects the light beam onto the secondary mirror (13), and the secondary mirror (13) reflects the light beam onto the imaging plane (2).

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