A design method of a wide-band transmission relay optical system

Abstract

The application provides a design method of a wide-band transmission relay optical system, and aims at solving the technical problems of low efficiency and unstable imaging quality of the finally generated relay optical system caused by the existing method of selecting and building an initial structure of the relay optical system. The design method of the wide-band transmission relay optical system provided by the application comprises the following steps: according to the construction of the object side telecentric initial structure in the middle of the diaphragm, and according to the lens material pair meeting the achromatic condition selected according to the working waveband, an equal-curvature double-convex lens is taken as an optimization starting point to calculate the initial curvature radius of each lens; after the initial central thickness and air spacing of each lens are given, the modeling of the initial structure of the relay optical system is realized, and the optimization efficiency is greatly improved; finally, the field of view is gradually increased from zero field of view, and the final wide-band transmission relay optical system is obtained after iterative optimization, and this method can realize any relay magnification and high-quality imaging in a wide waveband range.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical imaging, in particular to a design method of a wide-band transmission relay optical system. BACKGROUND

[0002] A relay optical system is a kind of rear optical system with the function of transferring the image plane over a long distance, such as transferring the image plane of a front optical system to a detector or transferring the object plane to the next optical system to meet the needs of structure or optical design. The relay optical system is widely used in various front optical systems, such as sighting scopes, high-temperature endoscopes, copying optical systems, etc., which not only can be used to lengthen the optical system, but also can play a role in image conversion. With the development of industrial technology, the working waveband of optical instruments is required to be wider and wider, and the imaging quality of the system is required to be higher and higher. For example, in the objective system of ultra-wideband spectral imaging, it is necessary to increase the relay optical system to realize higher magnification and more target monitoring requirements. In the extreme environment (such as ultra-high temperature, ultra-low temperature, ultra-high pressure, ultra-low pressure, strong electromagnetic radiation, etc.) monitoring system, it is necessary to isolate the camera's electronic system from the environment to be measured through the relay optical system to ensure its stable work. Therefore, it is of great significance to design a wide-band transmission relay optical system.

[0003] At present, the relay optical system has more design degrees of freedom, which leads to the difficulty in selecting and building the initial structure. If the initial structure is not built properly, it is difficult to map the input parameters of the relay optical system such as numerical aperture, field of view, working waveband, object distance, and vertical axis magnification to the initial structure. In addition, due to the limitations of the size and the relay distance, the wide-band transmission relay optical system can usually only be designed as a small F number system, but such a system usually needs a complex lens group to correct its off-axis aberration and chromatic aberration, which further increases the difficulty in selecting and building the initial structure, so it is necessary to find an efficient initial structure to provide support for the efficient optimization of the relay optical system. Therefore, when selecting and building the initial structure of the relay optical system, the industry usually finds a roughly matched system from the historical design results as the initial structure of the relay optical system according to the design requirements of the system, or estimates a system as the initial structure of the relay optical system according to the design experience, but this method is usually inefficient and the imaging quality of the relay optical system generated finally is unstable. SUMMARY

[0004] The purpose of the present application is to solve the technical problems of the existing method for selecting and building the initial structure of the relay optical system, which is inefficient and unstable in the imaging quality of the relay optical system generated finally, and to provide a design method of a wide-band transmission relay optical system.

[0005] The technical concept of the present application is:

[0006] From the aberration theory, for the optical system whose structure parameters are completely symmetrical to the stop, the axial aberration (spherical aberration, axial chromatic aberration) is twice the value of any side, and the off-axis aberration (coma, distortion, off-axis chromatic aberration) can be offset each other, so it is necessary to select reasonable number of lenses and reasonable material combination to correct spherical aberration and axial chromatic aberration.

[0007] In order to achieve the above object, the technical solution of the present application is as follows:

[0008] A design method of a wide-band transmission relay optical system, which is characterized by comprising the following steps:

[0009] Step 1, according to the system parameters of the pre-optical system, the maximum outer diameter and the numerical aperture of the relay optical system are preliminarily determined, and then the object distance of the relay optical system is calculated; and then according to the object distance of the relay optical system and the required magnification, the focal length of the relay optical system is calculated;

[0010] Step 2, according to the numerical aperture of the relay optical system, the number of lenses of the relay optical system is calculated; based on the number of lenses, an object far initial structure with the stop in the middle is constructed; and then according to the focal length of the relay optical system, the optical power of each lens in the object far initial structure is distributed;

[0011] Step 3, according to the working waveband, a lens material pair satisfying the achromatic condition is selected;

[0012] Step 4, according to the selected lens material pair, an equal curvature biconvex lens is taken as the optimization starting point, the initial curvature radius of each lens is calculated; and given the initial central thickness and air gap of each lens, the modeling of the initial structure of the relay optical system is completed;

[0013] Step 5, by controlling the magnification, total length, rear intercept, image far, air gap of lens center and edge, lens center and edge thickness and diameter-thickness ratio of the initial structure of the relay optical system, the field of view is gradually increased from zero field of view, and the final wide-band transmission relay optical system is obtained after iterative optimization.

[0014] Further, step 3 is specifically:

[0015] According to the requirements of the working waveband, a plurality of lens material pairs with large difference in Abbe number are determined in the Abbe diagram, and a plurality of lens material pairs with small difference in partial dispersion are determined in the partial dispersion diagram;

[0016] Combined with the transmittance of different materials in the working waveband and the use scene, a lens material pair with the smallest ratio of partial dispersion difference to Abbe number difference is selected from the plurality of lens material pairs as the lens material pair satisfying the achromatic condition.

[0017] Further, in step 3, the working waveband is a far-infrared waveband, and the lens material pair is Ge and ZnSe.

[0018] Further, in step 1, the object distance l of the relay optical system is calculated by the following formula:

[0019]

[0020] wherein D0 is the maximum outer diameter of the relay optical system, and NA is the numerical aperture of the relay optical system;

[0021] In step 1, the focal length f' of the optical system is calculated by the following formula:

[0022]

[0023] wherein β is the sagittal magnification, l' is the image distance of the relay optical system.

[0024] Further, in step 2, the number of lenses N is calculated by the following formula:

[0025]

[0026] Further, in step 2, when assigning the optical power of each lens in the object-side telecentric initial structure according to the focal length of the relay optical system, an average assignment method is adopted.

[0027] Further, in step 4, the initial curvature radius of each lens is calculated by the following formula:

[0028]

[0029] wherein R k-1 is the initial curvature radius of the front surface of the lens, R k-2 is the initial curvature radius of the back surface of the lens, k represents the material type, n k represents the material refractive index of the k material corresponding to the center wavelength of the working waveband, φ i is the optical power of the lens, and i=1, 2, …, N.

[0030] Further, in step 4, according to the selected lens material, an equal-curvature lenticule is taken as the optimization starting point to calculate the initial curvature radius of each lens, which is specifically:

[0031] The N lenses are divided into two groups with the stop as the center, and the N / 2 lenses located in front of the stop are alternately used with two materials in the lens material pair selected in step 3, and an equal-curvature lenticule is taken as the optimization starting point to calculate the initial curvature radius of the N / 2 lenses in front of the stop;

[0032] The N / 2 lenses behind the diaphragm are arranged in mirror symmetry with the N / 2 lenses in front of the diaphragm, and the materials and initial curvature radii at the symmetric positions are the same.

[0033] Further, in step 4, the initial central thickness of each lens is determined according to the ratio of the thickness, and the air gap is 1 / 3-2 times the initial central thickness of the previous lens.

[0034] Further, in step 4, the initial central thickness of each lens is

[0035] The beneficial effects of the present application compared with the prior art are as follows:

[0036] 1. The design method of the wide-band transmissive relay optical system provided by the present application can efficiently construct the object-side telecentric initial structure in the middle of the diaphragm according to the basic formula and empirical formula of paraxial optics, and then select a lens material pair that meets the achromatic condition according to the working waveband, take an equal-curvature double-convex lens as the optimization starting point, and calculate the initial curvature radius of each lens; after the initial central thickness and air gap of each lens are given, the modeling of the initial structure of the relay optical system is realized, which is taken as the starting point of the optimization design, greatly improving the optimization efficiency, facilitating subsequent optimization and processing, and having the application potential of wide waveband, light weight, and long relay distance; the relay optical system constructed by the method can realize any relay magnification and high-quality imaging in a wide waveband range, and can be applied to various scenes and different application requirements.

[0037] 2. The relay optical system constructed by the design method of the present application has the characteristics of object-side and image-side double-telecentricity and mirror symmetry of the front and rear parts about the diaphragm, and has important application value in the optical measurement system.

[0038] 3. The design method of the wide-band transmissive relay optical system provided by the present application takes the minimum value of the ratio of the middle partial dispersion difference to the Abbe number difference of the lens material pair as the criterion to construct a complex-achromatic relay optical system, and further realizes high-quality imaging in a wide waveband range. BRIEF DESCRIPTION OF DRAWINGS

[0039] Figure 1 The ΔP / Δν diagram of the plurality of lens material pairs obtained in step 3 of the design method of the wide-band transmissive relay optical system of the present application in the far-infrared waveband;

[0040] Figure 2 The modeling diagram of the initial structure of the relay optical system completed in step 4 of the embodiment of the present application;

[0041] Figure 3A schematic diagram of a wide-band transmissive relay optical system finally obtained after iterative optimization in step 5 of the embodiment of the present application;

[0042] Figure 4 A design point list diagram of the embodiment of the present application;

[0043] Figure 5 A design modulation transfer function curve diagram of the embodiment of the present application;

[0044] Figure 6 A design grid distortion diagram of the embodiment of the present application. DETAILED DESCRIPTION

[0045] In order to make the advantages and features of the present application clearer, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0046] A design method of a wide-band transmissive relay optical system, specifically comprising the following steps:

[0047] Step 1, calculating the focal length of the relay optical system.

[0048] Step 1.1, when designing the initial structure of the relay optical system, the parameters that need to be determined in advance include the numerical aperture of the relay optical system, the object height field of view, the working waveband, the maximum outer diameter and the magnification, and the above determined parameters are taken as input parameters to realize the design of the initial structure of the relay optical system. The numerical aperture of the relay optical system, the field of view, and the working waveband need to be determined according to the pre-optical system, wherein the numerical aperture of the relay optical system needs to be greater than or equal to the numerical aperture of the pre-optical system, the object height field of view of the relay optical system needs to be greater than or equal to the image height of the pre-optical system (i.e. the image height of the pre-optical system), and the working waveband of the relay optical system needs to completely cover the working waveband of the pre-optical system. In addition, the maximum outer diameter of the relay optical system is determined according to the actual operation space, and the magnification is determined according to the design requirement, which is usually-1.

[0049] This embodiment takes the design of a far-infrared transmissive relay optical system as an example for illustration.

[0050] The F number of the far-infrared transmissive relay optical system is the most commonly used F number of the pre-optical system in the far-infrared waveband, and the object height field of view is The working waveband is 8-12 μm (far-infrared waveband), the maximum outer diameter is 40 mm, the magnification is-1 (i.e. 1:1 imaging), and the total length of the relay optical system is not more than 150 mm.

[0051] Step 1.2, after determining the F number of the pre-optical system, the numerical aperture NA of the relay optical system is calculated by the following formula:

[0052]

[0053] Wherein, F / # is the F number of the front optical system, F / # = 1.

[0054] Considering leaving a certain margin, NA = 0.45 is selected.

[0055] Step 1.3, since the object distance of the relay optical system is limited by its radial optical size, the object distance l of the relay optical system is calculated according to the numerical aperture NA of the relay optical system and the maximum outer diameter D0 of the relay optical system, and the specific calculation formula is as follows:

[0056]

[0057] Step 1.4, since the object-image relationship of the near-axis optical system is: The magnification relationship is: Wherein, l' is the image distance of the relay optical system, f' is the focal length of the relay optical system, and β is the vertical axial magnification, then the following formula can be obtained:

[0058]

[0059] The focal length f' of the relay optical system in this embodiment can be calculated by the above formula, f' = 10mm.

[0060] Step 2, calculate the number of lenses of the relay optical system and construct the object side telecentric initial structure with the stop in the middle.

[0061] Step 2.1, according to the numerical aperture NA of the relay optical system and the corresponding empirical formula, the number of lenses N of the relay optical system is calculated. The specific calculation formula is:

[0062]

[0063] Wherein, Indicates rounding up.

[0064] Step 2.2, after obtaining the number of lenses N of the relay optical system, the object side telecentric initial structure with the stop in the middle is constructed in the ZEMAX software based on the number of lenses N. In this embodiment, the number of lenses N calculated is 10, so the object side telecentric initial structure with the stop in the middle needs to be constructed based on 10 lenses.

[0065] Step 2.3, according to the focal length distribution of the optical system, the optical power of each of the 10 lenses in the object side telecentric initial structure is determined, and specifically, the optical power of each lens is determined by the following formula:

[0066]

[0067] Wherein, φ iis the optical power of each lens, i = 1, 2,…, 10.

[0068] Preferably, in this embodiment, the optical power is distributed in an even distribution manner. Since the focal length f' of the relay optical system in this embodiment is 10 mm, the optical power of each lens is obtained to be 0.01 / mm.

[0069] Step 3: Select a lens material pair that meets the achromatic condition according to the working band.

[0070] To meet the needs of ultra-wideband applications, it is usually necessary to design the optical system with apochromatic aberration. This means that axial chromatic aberration and secondary spectra are eliminated by selecting lens material pairs. For transmissive optical systems, chromatic aberration comes from the difference in refractive index of the lens material for light of different wavelengths. To achieve apochromatic design for relay optical systems, the lens material selection method is as follows:

[0071] According to the requirements of the working band, select multiple groups of Abbe numbers (ν λ ) is used to eliminate the axial chromatic aberration of the relay optical system; then, according to the requirements of the working band, multiple groups of partial dispersion (P λ1,λ2 ) lens material pairs with a small difference in Abbe number are used to eliminate the secondary spectrum of the relay optical system. Specifically, each set of lens material pairs includes two lens materials, a lens material pair with a large difference in Abbe number, i.e., a lens material pair with a large difference in Abbe number between the two lens materials, and a lens material pair with a small difference in partial dispersion, i.e., a lens material pair with a small difference in partial dispersion between the two lens materials.

[0072] Then, taking into account the transmittance of different materials within the working band and the requirements of the lens material in the usage scenario (such as high temperature resistance, high humidity resistance, high transmittance, etc.), a suitable lens material pair is selected from the multiple groups of lens material pairs determined above as the lens material pair that meets the achromatic condition. The selection criterion is the lens material pair with the smallest ratio of the partial dispersion difference ΔP to the Abbe number difference Δν in the lens material pair, that is, the lens material pair with the smallest ΔP / Δν value is selected.

[0073] like Figure 1 Figure 2 is a schematic diagram of the ΔP / Δν of multiple lens material pairs obtained in the far-infrared band in this embodiment. It can be seen that, taking germanium (Ge), which has the most widely used material, as a benchmark, the ΔP / Δν value of germanium (Ge) and silicon (Si) is the lowest. However, since the maximum transmittance of Si is 10μm, and the transmittance of materials in the far-infrared band is 8μm-12μm, germanium (Ge) and zinc selenide (ZnSe) are selected as the lens material pair in this embodiment.

[0074] Step 4: Divide the 10 lenses into two groups with the aperture as the center, each group with 5 lenses. First, optimize the 5 lenses located in front of the aperture. During optimization, the 5 lenses use Ge and ZnSe as lens materials alternately, that is, the first lens is Ge, the second lens is ZnSe, the third lens is Ge, the fourth lens is ZnSe, and the fifth lens is Ge. Then, using the equal curvature biconvex lens as the optimization starting point, calculate the initial curvature radius of the 5 lenses using the following formula:

[0075]

[0076] Among them, R Ge-1 Indicates the initial curvature radius of the front surface of the lens made of Ge, R Ge-2 Indicates the initial curvature radius of the back surface of the lens made of Ge, n Ge is the material refractive index of Ge corresponding to the central wavelength of the working band; R ZnSe-1 The initial curvature radius of the front surface of the lens made of ZnSe is shown, R ZnSe-2 Indicates the initial curvature radius of the back surface of the lens made of ZnSe, n ZnSe is the material refractive index of ZnSe corresponding to the central wavelength of the working band.

[0077] The five lenses behind the aperture and the five lenses in front of the aperture are mirror-symmetrically arranged about the aperture. The materials and initial curvature radii at the symmetrical positions are the same. After obtaining the initial curvature radii of the ten lenses, the center thickness and air gap of each lens are given. Considering the processability, the center thickness range of the lens needs to be determined based on a reasonable diameter-to-thickness ratio, which is usually selected as The air gap can be set to 1 / 3 to 2 times the center thickness of the previous lens. Therefore, considering the limitation of the total length of the optimized system, in this embodiment, the center thickness of the given 10 lenses is 4mm, and the air gap between lenses and between lenses and apertures is 1.5mm.

[0078] According to the above calculation results, the initial structure of the relay optical system is modeled in ZEMAX software, as follows: Figure 2 The initial structure of the relay optical system has an aperture type of object space NA, an aperture value of 0.45, and a telecentric object space; the field of view type is object height, and the size is The working band is 8μm-12μm; the distance from the object to the front surface of the first lens (front intercept) is 20mm, and the distance from the rear surface of the last lens to the image plane (back intercept) is 20mm.

[0079] Step 5, after the modeling of the initial structure of the relay optical system, the field of view is gradually increased from zero field of view by controlling the magnification, total length (relay distance), back aperture, telecentricity of the image side, air gap of the lens center and edge, lens center and edge thickness, and the diameter-thickness ratio of the initial structure of the relay optical system, and the final wide-band transmission relay optical system is obtained after iterative optimization, as shown in Figure 3 The far-infrared transmission relay optical system is a coaxial optical system, and there are a total of 10 lenses. The materials of the 1st-3rd and 8th-10th lenses are Ge, and the materials of the 4th-7th lenses are ZnSe. All the lenses are spherical. The physical stop is located between the 5th and 6th lenses, and the lenses 1-5 and the lenses 6-10 are completely symmetrical about the stop. The parameters of the relay optical system in this embodiment are shown in the following table:

[0080]

[0081]

[0082] The first thickness corresponding to each lens in Table 1 is the center thickness of the current lens, and the second thickness is the air gap between the current lens and the next lens or between the current lens and the stop. It can be seen that the vertical magnification β of the far-infrared transmission relay optical system is -1, the stop size is Φ24.577, the back aperture is 20mm, the maximum image-side telecentricity is not more than 0.07°, and the overall spatial size of the optical part is less than Φ40mm (XY) × 150mm (Z).

[0083] Figure 4 The design point diagram of this embodiment is shown in the figure. It can be seen that the GEO radius of the design full-field point diagram is not more than the Airy spot radius of 13.56μm. Figure 5 The design modulation transfer function curve of this embodiment is shown in the figure. It can be seen that the design modulation transfer function is higher than 0.5 at 33.3 lines per mm, and the imaging quality is excellent. Figure 6 The grid distortion diagram of this embodiment is shown in the figure. It can be seen that the design grid distortion of the transmission path is not more than 0.008%.

[0084] The above description is only to illustrate the technical solutions of the present application, and is not a limitation. For ordinary skilled persons in the art, the specific technical solutions described in the above embodiments can be modified or some technical features can be replaced by equivalents, and these modifications or replacements do not change the essence of the corresponding technical solutions from the scope of the technical solutions protected by the present application.

Claims

1. A design method of a wide-band transmissive relay optical system, characterized by, The method comprises the following steps: Step 1, preliminarily determining the maximum outer diameter and numerical aperture of the relay optical system according to the system parameters of the pre-optical system, and then calculating the object distance of the relay optical system; Then, the focal length of the relay optical system is calculated according to the object distance of the relay optical system and the required magnification; Step 2, the number of lenses of the relay optical system is calculated according to the numerical aperture of the relay optical system; the lens number is used as the basis to construct an initial structure of the object far field; Then, the refractive power of each lens in the initial structure of the object far field is distributed according to the focal length of the relay optical system; Step 3, selecting a lens material pair that meets the achromatic condition according to the working waveband; Step 4, calculating the initial curvature radius of each lens by taking the equal curvature biconvex lens as the optimization starting point according to the selected lens material pair; Given the initial central thickness and air gap of each lens, the modeling of the initial structure of the relay optical system is completed; Step 5, by controlling the magnification, total length, rear intercept, image far field, air gap of the lens center and edge, lens center and edge thickness, and diameter-thickness ratio of the initial structure of the relay optical system, the field of view is gradually increased from zero field of view, and the final wide waveband transmission type relay optical system is obtained after iterative optimization.

2. The method of designing a broadband transmissive relay optical system according to claim 1, wherein Step 3 is specifically: According to the requirements of the working waveband, a plurality of lens material pairs with large Abbe number difference are determined in the Abbe diagram, and a plurality of lens material pairs with small partial dispersion difference are determined in the partial dispersion diagram; Combining the transmittance of different materials in the working waveband and the use scene, a lens material pair with the smallest ratio of partial dispersion difference to Abbe number difference is selected from the plurality of lens material pairs as the lens material pair that meets the achromatic condition.

3. The design method of the wide waveband transmission type relay optical system according to claim 2, wherein: In step 3, the working waveband is the far infrared waveband, and the lens material pair is Ge and ZnSe.

4. The design method of the wide waveband transmission type relay optical system according to any one of claims 1-3, wherein: In step 1, the object distance l of the relay optical system is calculated by the following formula: Wherein, D0 is the maximum outer diameter of the relay optical system, and NA is the numerical aperture of the relay optical system; In step 1, the focal length f' of the optical system is calculated by the following formula: where β is the magnification in the direction of the optical axis, l' is the image distance of the relay optical system.

5. The design method of the wide waveband transmission type relay optical system according to claim 4, wherein: In step 2, the number of lenses N is calculated by the following formula:

6. The design method of the wide waveband transmission type relay optical system according to claim 5, wherein: In step 2, when distributing the refractive power of each lens in the initial structure of the object far field according to the focal length of the relay optical system, an average distribution method is adopted.

7. The design method of the wide waveband transmission type relay optical system according to claim 6, wherein: In step 4, the initial curvature radius of each lens is calculated by the following formula: wherein R k-1 is the initial curvature radius of the front surface of the lens, R k-2 is the initial curvature radius of the back surface of the lens, k indicates the material type, n k indicates the material refractive index of the k material corresponding to the center wavelength of the working waveband, φ i is the optical power of the lens, and i = 1, 2, …, N.

8. The design method of the wide waveband transmission type relay optical system according to claim 7, wherein: In step 4, the initial curvature radius of each lens is calculated by taking the equal curvature biconvex lens as the optimization starting point according to the selected lens material, and the specific method is as follows: The N lenses are divided into two groups with the diaphragm as the center, the N / 2 lenses before the diaphragm are alternately used with two materials in the lens material pair selected in step 3, and an equal-curvature biconvex lens is used as an optimization starting point to calculate the initial curvature radius of the N / 2 lenses before the diaphragm; The N / 2 lenses behind the diaphragm are arranged in one-to-one mirror symmetry with the N / 2 lenses before the diaphragm about the diaphragm, and the materials and initial curvature radii on the symmetric positions are the same.

9. The design method of a wide-band transmissive relay optical system according to claim 8, characterized in that: In step 4, the initial central thickness of each lens is determined according to the diameter-thickness ratio, and the air gap is 1 / 3-2 times the initial central thickness of the previous lens.

10. The design method of a wide-band transmissive relay optical system according to claim 9, characterized in that: In Step 4, the initial center thickness of each lens piece is

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