A method for obtaining a refractive index profile for a graded index lens

Abstract

This invention discloses a method for obtaining the refractive index distribution of a graded-index lens, relating to the field of graded-index lens technology. The method includes: sample preparation of the graded-index rod lens before electron probe microanalysis; and performing a full elemental scan at the center of the graded-index lens sample and an electron probe microanalysis of exchanged ions A along the lens diameter direction using an electron probe microanalysis instrument. + Line scan; based on electron probe point scan data, the refractive index at the center of the graded refractive index lens sample and the refractive index difference between the center and the edge are calculated using the HSD model; the relative intensity distribution of exchange ions in the graded refractive index lens sample is obtained based on electron probe line scan data; thus, the refractive index distribution of the graded refractive index lens sample is obtained; by analyzing the difference between the refractive index distribution of the same graded refractive index lens sample obtained by the present invention and the thin-film interferometry method, the present invention can easily and conveniently obtain the refractive index distribution of the graded refractive index lens.

Description

Technical Field

[0001] This invention relates to the field of graded refractive index lens technology, and more specifically to a method for obtaining the refractive index distribution of a graded refractive index lens. Background Technology

[0002] The production of graded-index lenses often utilizes specially made optical glass and employs an ion exchange process, where the base glass undergoes ion exchange with molten salt at a specific temperature and time. During ion exchange, monovalent ions in the base glass and molten salt diffuse into each other due to the concentration difference. The base glass is composed of various oxides; the bonds between these monovalent cations and oxygen are relatively weak and can break free at high temperatures, while the single bonds of other oxides in the glass are stronger and firmly bound in their positions, preventing movement. Two types of exchange ions are involved in the ion exchange process: A... + and B + The result of its ion exchange is that the A in the base glass... + The ion concentration changes from a fixed value to the highest concentration at the center of the gradient refractive index lens, with a gradual distribution from the center to the edge. Different cations have different volumes and polarizabilities, and their contributions to the refractive index of the base glass are also different. Therefore, the refractive index of the base glass changes after ion exchange, thus creating a gradient refractive index lens.

[0003] The refractive index distribution of a graded-index lens is an important indicator for understanding its performance. When the refractive index distribution curve of a graded-index lens deviates significantly from the ideal curve, it manifests as severe aberrations and distortion in the imaging field, and as unacceptable lens insertion loss in the optical communication field. Therefore, mastering the refractive index distribution of a graded-index lens is extremely important.

[0004] Currently, the main testing method for graded-index lenses is thin-film interferometry. Thin-film interferometry requires grinding and polishing both ends of the lens to achieve a sample thickness of less than 200 micrometers. The prepared sample is then placed into the interference optical path, and the refractive index distribution of the lens is obtained by analyzing the interference fringes. However, thin-film interferometry suffers from stringent sample preparation requirements and a long preparation cycle. For example, the sample thickness must be less than 200 micrometers, and the roughness and parallelism of the two end faces must be high, making processing difficult. Furthermore, thin-film interferometry requires constructing an interference optical path, and the two optical flats in the path must be strictly parallel, making the testing process complex and difficult to debug. Therefore, a method for obtaining the refractive index distribution of graded-index lenses is proposed to solve these problems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a method for obtaining the refractive index distribution of a graded refractive index lens, thus solving the problems existing in the prior art.

[0006] A method for obtaining the refractive index distribution of a graded-index lens includes the following steps:

[0007] An electron probe was used to perform a point scan of all elements at the center of the graded refractive index lens sample to obtain the mass fraction of each oxide at the center of the sample.

[0008] Based on the mass fraction of each oxide, the HSD model is used to calculate the refractive index at the center of the graded refractive index lens sample and the difference in refractive index between the center and the edge.

[0009] An electron probe was used to perform a line scan of the exchanged ions along the diameter of the sample of the graded refractive index lens, and the relative intensity of the element corresponding to the exchanged ion on the sample was obtained by comparing the intensity value from the center to the edge along the diameter with the intensity value at the center.

[0010] The refractive index distribution of the graded-index lens sample is obtained by adding the product of the refractive index at the center and the difference between the refractive index at the center and the edge, multiplied by the relative intensity distribution of exchanged ions and the refractive index difference. The formula for calculating the refractive index distribution of the graded-index lens sample is as follows:

[0011]

[0012] Where n(0) and Δn are the refractive index and refractive index difference at the center of the graded refractive index lens sample, This represents the relative intensity of the element used for ion exchange in the sample from the center to the edge.

[0013] Furthermore, the graded refractive index lens includes various oxides, and its fabrication process employs ion exchange technology.

[0014] Furthermore, it also includes sample preparation; the sample preparation includes cutting the rod lens and grinding and polishing one end face of the lens; the cutting of the rod lens ensures that the length of the rod lens does not exceed 25mm; after grinding and polishing one end face of the lens, the end face is subjected to gold spraying or carbon spraying treatment.

[0015] Furthermore, the formula for calculating the central refractive index is:

[0016]

[0017] Where M is a cation in the sample, N M N represents the number of moles of cation M corresponding to each mole of oxygen atoms in the glass. M It is related to the mass fraction of each oxide in the sample, α M Let M be a constant related to cation M, K be an empirical constant ranging from 0 to 0.05, and b be a constant related to N. Si The constant c is related to the range of values.M It is a constant related to the cation M.

[0018] Furthermore, the formula for calculating the refractive index difference is:

[0019]

[0020] Where V0 is the volume corresponding to one gram of oxygen, ΔV is the change in volume corresponding to one gram of oxygen, and ΔR is the change in refractive index corresponding to one gram of oxygen for the exchanged ions.

[0021] Furthermore, the intensity values ​​of the elements corresponding to the exchanged ions along the diameter direction from the center to the edge are obtained using a fitting function:

[0022] I(r)=a×(1-0.5×b×r 2 +c×r 4 +d×r 6 )

[0023] After normalizing the fitting results, the relative intensities of the elements corresponding to the exchanged ions from the center to the edge are:

[0024]

[0025] Where a, b, c and d are unknowns related to the performance of the graded refractive index lens, r is a variable representing all points along the radial direction, and I(0) is the intensity value of the element corresponding to the exchanged ion at the center of the lens sample.

[0026] This invention provides a method for obtaining the refractive index distribution of a graded-index lens, which has the following beneficial effects:

[0027] Compared with the commonly used thin-film interferometry, this invention only requires grinding and polishing one end face of the graded-index lens, and the sample thickness is less than 25 mm. Thin-film interferometry, on the other hand, has strict sample preparation requirements and a long preparation cycle, such as requiring a sample thickness of less than 200 micrometers, high roughness and parallelism requirements on both end faces, and significant processing difficulty. Furthermore, the electron probe microanalysis involved in this invention has relevant instruments, allowing for direct measurement after sample preparation. Thin-film interferometry, however, requires the construction of an interference optical path, where the two optical flats must be strictly parallel, making adjustment difficult. Through the difference analysis of the refractive index distribution of the same graded-index lens sample tested using this invention and the thin-film interferometry, the error between the two methods is less than 0.72% over the entire radius of the graded-index lens. This invention can easily and conveniently obtain the refractive index distribution of a graded-index lens. Attached Figure Description

[0028] Figure 1 This is a schematic diagram showing the intensity distribution of element A, which participates in ion exchange, at different locations in a graded refractive index lens.

[0029] Figure 2 This is a schematic diagram of the refractive index distribution of the same graded refractive index lens sample obtained using the present invention and the thin-film interferometry method. Detailed Implementation

[0030] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0031] A method for obtaining the refractive index distribution of a graded-index lens includes the following steps:

[0032] Step 1: Sample preparation for electron probe microanalysis of the graded-index bar lens. The sample preparation process includes cutting the bar lens, with a length not exceeding 25 mm; grinding and polishing one end face of the lens until the sample surface is free of scratches; and then performing gold or carbon spraying on this end face after grinding and polishing.

[0033] Step 2: Use an electron probe microanalysis instrument to perform a full elemental scan at the center of the graded refractive index lens sample and to scan for exchanged ions A along the lens diameter. + Line scan.

[0034] Step 3: Calculate the refractive index at the center and the difference in refractive index between the center and the edge of the gradient refractive index lens sample using the HSD model (Fantone S D. Refractive index and spectral models for gradient-index materials.[J]. Applied optics, 1983, 22(3)) based on the electron probe spot scan data.

[0035] The electron probe spot scan results show that the mass fraction of each oxide at the center of the graded refractive index lens sample is:

[0036] 0.4903SiO2-0.2869A2O-0.1622CO-0.0468D2O-0.0138E2O

[0037] Where A, D, and E are monovalent cations, A is the cation participating in ion exchange in the lens, D is the cation participating in ion exchange in the molten salt, and C is a divalent cation. The central refractive index is calculated using the following formula:

[0038]

[0039] Where M represents one of the cations in the sample (Si, A, C, D, E), and N... MN represents the number of moles of cation M corresponding to each mole of oxygen atoms in the glass. M It is related to the mass fraction of each oxide in the sample, α M Let M be a constant related to cation M, K be a constant taking the value 0, and b be a constant related to N. Si The constant c is related to the range of values. M The constant related to cation M is used to calculate the refractive index difference using the following formula:

[0040]

[0041] Where V0 is the volume corresponding to one gram of oxygen, ΔV is the change in volume corresponding to one gram of oxygen, and ΔR is the change in refractive index corresponding to one gram of oxygen for the exchange ions. The constant information corresponding to different cations in the formula can be obtained by looking up the table in the literature (Fantone SD. Refractive index and spectral models for gradient-index materials.[J]. Applied optics,1983,22(3)). After looking up the table, the refractive index at the center of the sample at a wavelength of 632.8nm is calculated to be 1.6050, and the refractive index difference between the center and the edge of the gradient refractive index lens sample is 0.0769.

[0042] Step 4: Obtain the refractive index distribution of the graded refractive index lens sample based on the electron probe line scan data.

[0043] The line scan result of swapping element A is as follows Figure 1 As shown, the fitting result obtained using the fitting function is:

[0044] I(r) = 489.3 × (1 - 0.5 × 1.76 × r) 2 +0.652×r 4 +1.258×r 6 ),

[0045] After normalization, the relative strength of the exchange element A is:

[0046]

[0047] The formula for calculating the refractive index distribution of a graded-index lens is:

[0048]

[0049] Therefore, in this embodiment, the refractive index distribution of the graded-index lens sample is n(r) = 1.605 - 0.5 × 0.135 × r 2 +0.050×r 4 -0.097×r 6 ,like Figure 2 As shown, the solid line represents the refractive index distribution obtained using the present invention, and the dashed line represents the refractive index distribution obtained using the thin-film interferometry method. The error in the refractive index distribution of the same graded refractive index lens sample obtained by the present invention and the thin-film interferometry method at a wavelength of 632.8 nm is less than 0.72% over the entire radius range of the graded refractive index lens.

[0050] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for obtaining the refractive index distribution of a graded-index lens, characterized in that, Includes the following steps: Sample preparation process to obtain graded refractive index lens samples includes: cutting the rod lens so that the length of the rod lens does not exceed 25mm; grinding and polishing one end face of the lens; and spraying gold or carbon onto the ground and polished end face. An electron probe was used to perform a point scan of all elements at the center of the graded refractive index lens sample to obtain the mass fraction of each oxide at the center of the sample. Based on the mass fraction of each oxide, the HSD model is used to calculate the refractive index at the center of the graded refractive index lens sample and the difference in refractive index between the center and the edge. An electron probe was used to perform a line scan of the exchanged ions along the diameter of the sample of the graded refractive index lens, and the relative intensity of the element corresponding to the exchanged ion on the sample was obtained by comparing the intensity value from the center to the edge along the diameter with the intensity value at the center. The refractive index distribution of a graded-index lens sample is determined using the following formula: in, and The refractive index and the refractive index difference at the center of the graded refractive index lens sample. The relative intensity of the element used for ion exchange in the sample from the center to the edge; the formula for calculating the refractive index at the center is: in, M It is a cation in the sample. The cation corresponding to each mole of oxygen atom in the sample M The number of moles, It is related to the mass fraction of each oxide in the sample. To be with cations M Relevant constants, It is an empirical constant that takes values ​​from 0 to 0.

05. To and Constants related to the range of values, To be with cations M The relevant constants; the formula for calculating the refractive index difference is: ;in, This represents the volume corresponding to each gram of oxygen. This represents the volume change corresponding to each gram of oxygen. The change in refractive index per gram of oxygen corresponding to the exchanged ions; the intensity value of the element corresponding to the exchanged ions along the diameter direction from the center to the edge is fitted using a fitting function: After normalizing the fitting results, the relative intensities of the elements corresponding to the exchanged ions from the center to the edge are: ;in, a , b , c and d It is an unknown quantity and is related to the performance of the graded refractive index lens. r Let be a variable representing all points along the radial direction. I (0) is the intensity value of the element corresponding to the exchange ion at the center of the lens sample.

2. The method for obtaining the refractive index distribution of a graded-index lens according to claim 1, characterized in that, The graded refractive index lens includes various oxides, and its fabrication process employs ion exchange technology.

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