Measurement Method for Gradient Refractive Index Material Wedge Mirror Compensation Based on Mach-Zehnder Interferometer

Abstract

This invention discloses a method for measuring the compensation of gradient refractive index materials with wedge mirrors based on a Mach-Zehnder interferometer. The method involves: constructing a Mach-Zehnder interferometer; placing the gradient refractive index material and a wedge mirror into the interferometer's interference cavity; measuring the first wavefront of the superimposed gradient refractive index material and wedge mirror using the interferometer; removing the gradient refractive index material from the interference cavity to obtain a second wavefront containing only the wedge mirror; calculating the transmission wavefront of the gradient refractive index material based on the first and second wavefronts; and calculating the refractive index change of the gradient refractive index material using the obtained transmission wavefront. This invention can compensate for gradient refractive index materials exceeding the measurement range of the interferometer, thereby obtaining their refractive index change.

Description

Technical Field

[0001] This invention belongs to the field of optical interferometry technology, and in particular, it is a method for measuring gradient refractive index material wedge mirrors based on Mach-Zehnder interferometers. Background Technology

[0002] Gradient refractive index (GRIN) materials are heterogeneous materials whose composition and structure change continuously within the material according to certain rules, resulting in a corresponding continuous change in refractive index. Based on the refractive gradient, GRIN materials can be broadly classified into three types: radially gradient refractive materials, axially gradient refractive materials, and spherically gradient refractive materials. GRIN optics can improve image quality, reduce the size and weight of optical systems, simplify manufacturing processes, and enable miniaturization, lightweighting, and high-quality optical systems, as well as easier assembly. They play an increasingly important role in optical communication, imaging, industrial, and biomedical sensing. Currently, GRIN optics has been widely used in various fields, but its application scope is still limited by its testing methods.

[0003] The refractive index distribution of gradient-index materials has a significant impact on their optical properties; therefore, accurate measurement of this distribution is crucial. Methods for measuring the refractive index distribution of gradient-index materials include prism techniques, schlieren analysis, interferometry, beam deflection, and optical coherence tomography. Among these, the use of a Mach-Zehnder interferometer has proven to be a more versatile and reliable method, applicable not only to visible light measurements but also to infrared measurements.

[0004] As research into gradient refractive index materials deepens, the gradient steepness of some materials becomes increasingly pronounced. This means that over the same lateral distance, the refractive index changes significantly, eventually exceeding the measurement range of conventional interferometers and rendering them unmeasurable. Expanding the interferometer's measurement range requires redesigning the imaging system, replacing lenses with lower F-number lenses, and replacing detectors with higher-resolution ones—a complex and costly approach.

[0005] In summary, the steepness of the refractive index gradient in some materials is too great for direct measurement by interferometers. Given that the interferometer is already encapsulated, expanding its measurement range is costly and complex. A simpler and more convenient method is needed to measure refractive index materials that are outside the measurement range. Summary of the Invention

[0006] The purpose of this invention is to provide a simple, low-cost, and convenient method for measuring gradient refractive index material wedge mirror compensation based on a Mach-Zehnder interferometer.

[0007] The technical solution to achieve the purpose of this invention is: a method for measuring gradient refractive index material wedge mirror compensation based on Mach-Zehnder interferometer, comprising the following steps:

[0008] Step 1: Construct the Mach-Zehnder interferometer;

[0009] Step 2: Place the gradient refractive index material and the wedge mirror into the interference cavity of the interferometer;

[0010] Step 3: Use an interferometer to measure the first wavefront of the gradient refractive index material and the wedge mirror superimposed at this time;

[0011] Step 4: Remove the gradient refractive index material from the interference cavity to obtain the second wavefront containing only the wedge mirror inside the interference cavity;

[0012] Step 5: Calculate the transmission wavefront of the gradient refractive index material based on the first and second wavefronts;

[0013] Step 6: Using the transmitted wavefront obtained in Step 5, calculate the refractive index change of the gradient refractive index material.

[0014] Furthermore, the compensation measurement is characterized by including two methods: single-mirror compensation measurement and dual-mirror compensation measurement.

[0015] Furthermore, when using single-mirror compensation measurement, the specific placement of the wedge mirror in step 2 is as follows:

[0016] After placing the gradient refractive index material in the test optical path, place the wedge mirror in the Mach-Zehnder interferometer test optical path and bring the wedge mirror as close as possible to the gradient refractive index material.

[0017] Furthermore, when using dual-mirror compensation measurement, the specific placement of the wedge mirror in step 2 is as follows:

[0018] After placing the gradient refractive index material in the test optical path, place the first wedge mirror in the test optical path of the Mach-Zehnder interferometer, making the first wedge mirror as close as possible to the gradient refractive index material; then place the second wedge mirror in the reference optical path of the Mach-Zehnder interferometer, making the second wedge mirror as close as possible to the beam combiner and beam splitter.

[0019] Furthermore, the first and second wedge mirrors have the same angle, material, and size, and the wavefront tilt direction caused by the first and second wedge mirrors is consistent.

[0020] Furthermore, in step 2, the direction of the wavefront tilt caused by the wedge mirror should be opposite to the direction of the gradient refractive index steepness, and the angle of the wedge mirror increases as the gradient slope of the sample to be tested increases.

[0021] Furthermore, step 3 involves measuring the first wavefront of the gradient refractive index material and the wedge mirror superimposed at this point using an interferometer, as detailed below:

[0022] Turn on the interferometer, place the region with the large gradient slope in the gradient refractive index material in the middle of the measurement area, and use the interferometer to measure the first wavefront W1(x,y) of the gradient refractive index material and the wedge mirror superimposed.

[0023] Furthermore, step 4 involves removing the gradient refractive index material from the interference cavity to obtain a second wavefront containing only the wedge mirror within the interference cavity, as detailed below:

[0024] Keeping the wedge mirror position unchanged, only the gradient refractive index material is removed, and the second wavefront W2(x,y) inside the interference cavity containing only the wedge mirror is measured using an interferometer.

[0025] Furthermore, in step 5, the transmission wavefront of the gradient refractive index material is W(x,y), calculated using the following formula:

[0026] W(x,y)=W1(x,y)-W2(x,y)

[0027] Where W1(x,y) is the first wavefront obtained in step 2, and W2(x,y) is the second wavefront obtained in step 3.

[0028] Furthermore, in step 6, the refractive index change of the gradient refractive index material is calculated using the transmitted wavefront obtained in step 5, as detailed below:

[0029] The peak-to-valley value of optical path difference (PV) is represented as OPD. PV :

[0030] OPD PV =W max (x,y)-W min (x,y)

[0031] Among them, W max (x,y), W min (x, y) represent the maximum and minimum values ​​of the transmission wavefront of the gradient refractive index material, respectively;

[0032] The refractive index change Δn of a gradient refractive index material is:

[0033] Δn=OPD PV / t

[0034] Where t is the thickness of the gradient refractive index material.

[0035] Compared with the prior art, the significant advantages of this invention are: (1) the range of measurable gradient refractive index materials can be expanded simply by adding a wedge mirror without destroying the existing structure of the interferometer; (2) the gradient refractive index samples that cannot be directly measured by the Mach-Zehnder interferometer can be measured with the help of a wedge mirror, and the accuracy is high, the operation is simple and the cost is low, which can meet the needs of expanding the measurement range of the interferometer. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the measurement method for gradient refractive index material wedge mirror compensation based on Mach-Zehnder interferometer according to the present invention.

[0037] Figure 2 The interferogram and measurement results of the GASS sample were obtained by directly measuring it using an interferometer. (a) shows the interferogram and (b) shows the measurement results.

[0038] Figure 3 This is the result of single-mirror compensation measurement, where Figure 3 (a) is the wavefront of the gradient refractive index sample and the wedge mirror superimposed. Figure 3 (b) shows wavefront data with only wedge mirrors. Figure 3 (c) is the wavefront data obtained by subtracting the wavefront data of only the wedge from the wavefront data of the gradient refractive index sample and the wedge mirror superimposed.

[0039] Figure 4 The results are from dual-mirror compensation measurements, where Figure 4 (a) is the wavefront of the gradient refractive index sample and the wedge mirror superimposed. Figure 4 (b) shows wavefront data with only wedge mirrors. Figure 4 (c) is the wavefront data obtained by subtracting the wavefront data of only the wedge from the wavefront data of the gradient refractive index sample and the wedge mirror superimposed. Detailed Implementation

[0040] It is readily understood that, based on the technical solution of this invention, those skilled in the art can conceive of various embodiments of this invention without altering its essential spirit. Therefore, the following specific embodiments and accompanying drawings are merely illustrative examples of the technical solution of this invention and should not be considered as the entirety of this invention or as limitations or restrictions on its technical solution.

[0041] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention.

[0042] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the invention or its application or use.

[0043] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and equipment should be considered part of the specification.

[0044] In all the examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0045] Combination Figure 1 This invention discloses a method for measuring gradient refractive index materials using a wedge mirror based on a Mach-Zehnder interferometer, comprising the following steps:

[0046] Step 1: Construct the Mach-Zehnder interferometer;

[0047] Step 2: Place the gradient refractive index material and the wedge mirror into the interference cavity of the interferometer;

[0048] Step 3: Use an interferometer to measure the first wavefront of the gradient refractive index material and the wedge mirror superimposed at this time;

[0049] Step 4: Remove the gradient refractive index material from the interference cavity to obtain the second wavefront containing only the wedge mirror inside the interference cavity;

[0050] Step 5: Calculate the transmission wavefront of the gradient refractive index material based on the first and second wavefronts;

[0051] Step 6: Using the transmitted wavefront obtained in Step 5, calculate the refractive index change of the gradient refractive index material.

[0052] As a specific example, the compensation measurement includes two methods: single-mirror compensation measurement and dual-mirror compensation measurement.

[0053] As a specific example, when using single-mirror compensation measurement, the wedge mirror placement position in step 2 is as follows:

[0054] After placing the gradient refractive index material in the test optical path, place the wedge mirror in the Mach-Zehnder interferometer test optical path and bring the wedge mirror as close as possible to the gradient refractive index material.

[0055] As a specific example, when using dual-mirror compensation measurement, the wedge mirror placement position in step 2 is as follows:

[0056] After placing the gradient refractive index material in the test optical path, place the first wedge mirror in the test optical path of the Mach-Zehnder interferometer, making the first wedge mirror as close as possible to the gradient refractive index material; then place the second wedge mirror in the reference optical path of the Mach-Zehnder interferometer, making the second wedge mirror as close as possible to the beam combiner and beam splitter.

[0057] As a specific example, the first wedge mirror and the second wedge mirror have the same angle, material, and size, and the wavefront tilt direction caused by the first wedge mirror and the second wedge mirror is the same.

[0058] As a specific example, in step 2, the direction of the wavefront tilt caused by the wedge mirror should be opposite to the direction of the gradient refractive index steepness, and the angle of the wedge mirror increases as the gradient slope of the sample to be tested increases.

[0059] As a specific example, step 3 involves using an interferometer to measure the first wavefront of the gradient refractive index material and the wedge mirror superimposed at this point, as detailed below:

[0060] Turn on the interferometer, place the region with the large gradient slope in the gradient refractive index material in the middle of the measurement area, and use the interferometer to measure the first wavefront W1(x,y) of the gradient refractive index material and the wedge mirror superimposed.

[0061] As a specific example, step 4 involves removing the gradient refractive index material from the interference cavity to obtain a second wavefront containing only the wedge mirror within the interference cavity, as detailed below:

[0062] Keeping the wedge mirror position unchanged, only the gradient refractive index material is removed, and the second wavefront W2(x,y) inside the interference cavity containing only the wedge mirror is measured using an interferometer.

[0063] As a specific example, the transmission wavefront of the gradient refractive index material in step 5 is W(x,y), and the calculation formula is as follows:

[0064] W(x,y)=W1(x,y)-W2(x,y)

[0065] Where W1(x,y) is the first wavefront obtained in step 2, and W2(x,y) is the second wavefront obtained in step 3.

[0066] As a specific example, step 6 uses the transmitted wavefront obtained in step 5 to calculate the refractive index change of the gradient refractive index material, as detailed below:

[0067] The peak-to-valley value of optical path difference (PV) is represented as OPD. PV :

[0068] OPD PV =W max (x,y)-W min (x,y)

[0069] Among them, W max (x,y), W min (x, y) represent the maximum and minimum values ​​of the transmission wavefront of the gradient refractive index material, respectively;

[0070] The refractive index change Δn of a gradient refractive index material is:

[0071] Δn=OPD PV / t

[0072] Where t is the thickness of the gradient refractive index material.

[0073] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0074] Example

[0075] The Mach-Zehnder interferometer used in this embodiment is an Interfine CMIZ-I long-wave infrared interferometer with a working wavelength of λ = 10.6 μm and a test aperture of Φ30 mm.

[0076] This embodiment employs a wedge-mirror compensation measurement method based on a Mach-Zehnder interferometer, according to the present invention, to perform compensation measurements on gradient refractive index materials that are outside the measurement range of the Interfly CMIZ-I long-wave infrared interferometer.

[0077] The sample used in this embodiment to measure the gradient refractive index is a GASS sample from Ningbo University, with a thickness t = 1.21 mm and a refractive index change Δn = 0.22. Combined with... Figure 2 , Figure 2 (a) in the diagram is an interferogram. Figure 2 (b) in the figure shows the measurement results. When the interferometer is used to directly measure the gradient refractive index sample, the sample is placed in the test optical path. The middle fringes of the obtained interferogram are not clear and the information is missing. The measurement results differ greatly from the nominal value of the sample.

[0078] Combination Figure 3 ,in Figure 3 In the image (a), the wavefront of the gradient refractive index sample and the wedge mirror is superimposed. Figure 3 (b) in the figure represents wavefront data with only the wedge mirror. Figure 3 In the diagram, (c) represents the wavefront data obtained by subtracting the wavefront data of the wedge mirror alone from the wavefront data of the gradient refractive index sample and the wedge mirror superimposed. Using single-mirror compensation measurement, the sample to be tested is placed in the test optical path, and then the wedge mirror is placed in the test optical path of the Mach-Zehnder interferometer, with the wedge mirror as close to the material as possible. The interferometer measures the wavefront of the gradient refractive index sample and the wedge mirror superimposed at this point. The gradient refractive index sample is then removed from the interferometer cavity, obtaining the wavefront data of the wedge mirror alone within the interferometer cavity. The wavefront data of the gradient refractive index sample is obtained by subtracting the wavefront data of the wedge mirror alone from the wavefront of the gradient refractive index sample and the wedge mirror superimposed. The measurement result Δn = 0.211 is calculated according to the formula.

[0079] Combination Figure 4 ,in Figure 4 In the image (a), the wavefront of the gradient refractive index sample and the wedge mirror is superimposed. Figure 4 (b) in the figure represents wavefront data with only the wedge mirror. Figure 4 In Figure (c), the wavefront data is obtained by subtracting the wavefront data of the wedge mirror alone from the wavefront data of the superimposed gradient refractive index sample and the wedge mirror. Using dual-mirror compensation measurement, the sample to be tested is placed in the test optical path, and then wedge mirror ① is placed in the test optical path of the Mach-Zehnder interferometer, as close as possible to the sample. Wedge mirror ② is placed in the reference optical path of the Mach-Zehnder interferometer, as close as possible to the beam combiner and splitter. The wavefront of the superimposed gradient refractive index sample and the wedge mirror is measured using the interferometer. The gradient refractive index sample is then removed from the interferometer cavity, and the wavefront data of the wedge mirror alone is obtained within the interferometer cavity. The wavefront data of the gradient refractive index sample is obtained by subtracting the wavefront data of the wedge mirror alone from the wavefront of the superimposed gradient refractive index sample and the wedge mirror. The measurement result Δn = 0.217 is calculated according to the formula. The measurement error is 1.36%.

[0080] To verify the reliability of the experimental results of this invention, the results obtained using the wedge mirror compensation method were compared with the nominal values ​​of the gradient refractive index samples. When using single-mirror compensation, the gradient refractive index deviation was approximately 0.009, with a relative measurement error of 4.09%. When using dual-mirror compensation, the gradient refractive index deviation was approximately 0.003, with a relative measurement error of 1.36%. The experimental results show that the method proposed in this invention has high measurement accuracy and stable results, and the angle and number of wedge mirrors can be selected according to different samples.

[0081] In summary, the wedge-mirror compensation method for measuring gradient refractive index materials based on Mach-Zehnder interferometer proposed in this invention can expand the measurement range. It can measure gradient refractive index samples that cannot be directly measured using Mach-Zehnder interferometer with the help of a wedge mirror. It has high accuracy, simple operation, and low cost, and can meet the need to expand the measurement range of interferometer.

Claims

1. A method for measuring gradient refractive index material wedge mirror compensation based on Mach-Zehnder interferometer, characterized in that, Includes the following steps: Step 1: Construct the Mach-Zehnder interferometer; Step 2: Place the gradient refractive index material and the wedge mirror into the interference cavity of the interferometer, and bring the wedge mirror as close as possible to the gradient refractive index material; the wavefront tilt direction caused by the wedge mirror should be opposite to the direction of the gradient refractive index steepness, and the angle of the wedge mirror increases as the gradient slope of the gradient refractive index sample increases; Step 3: Use an interferometer to measure the first wavefront of the gradient refractive index material and the wedge mirror superimposed at this time; Step 4: Remove the gradient refractive index material from the interference cavity to obtain the second wavefront containing only the wedge mirror inside the interference cavity; Step 5: Calculate the transmission wavefront of the gradient refractive index material based on the first and second wavefronts; Step 6: Using the transmitted wavefront obtained in Step 5, calculate the refractive index change of the gradient refractive index material.

2. The method for measuring gradient refractive index material wedge mirror compensation based on Mach-Zehnder interferometer according to claim 1, characterized in that, The compensation measurement includes two methods: single-mirror compensation measurement and dual-mirror compensation measurement.

3. The method for measuring gradient refractive index material wedge mirror compensation based on Mach-Zehnder interferometer according to claim 2, characterized in that, When using single-mirror compensation measurement, the specific placement of the wedge mirror in step 2 is as follows: After placing the gradient refractive index material in the test optical path, place the wedge mirror in the Mach-Zehnder interferometer test optical path.

4. The method for measuring gradient refractive index material wedge mirror compensation based on Mach-Zehnder interferometer according to claim 2, characterized in that, When using dual-mirror compensation measurement, the specific placement of the wedge mirror in step 2 is as follows: After placing the gradient refractive index material in the test optical path, place the first wedge mirror in the test optical path of the Mach-Zehnder interferometer, making the first wedge mirror as close as possible to the gradient refractive index material; then place the second wedge mirror in the reference optical path of the Mach-Zehnder interferometer, making the second wedge mirror as close as possible to the beam combiner and beam splitter.

5. The method for measuring gradient refractive index material wedge mirror compensation based on Mach-Zehnder interferometer according to claim 4, characterized in that, The first and second wedge mirrors have the same angle, material, and size, and the wave surface tilt direction caused by the first and second wedge mirrors is the same.

6. The method for measuring gradient refractive index material wedge mirror compensation based on Mach-Zehnder interferometer according to claim 1, characterized in that, Step 3 involves using an interferometer to measure the first wavefront of the gradient refractive index material and the wedge mirror superimposed at this point, as detailed below: Turn on the interferometer, place the region with the large gradient slope in the gradient refractive index material in the middle of the measurement area, and use the interferometer to measure the first wavefront W1(x,y) of the gradient refractive index material and the wedge mirror superimposed.

7. The method for measuring gradient refractive index material wedge mirror compensation based on Mach-Zehnder interferometer according to claim 1, characterized in that, Step 4 involves removing the gradient refractive index material from the interference cavity to obtain the second wavefront containing only the wedge mirror within the interference cavity, as detailed below: Keeping the wedge mirror position unchanged, only the gradient refractive index material is removed, and the second wavefront W2(x,y) inside the interference cavity containing only the wedge mirror is measured using an interferometer.

8. The method for measuring gradient refractive index material wedge mirror compensation based on Mach-Zehnder interferometer according to claim 1, characterized in that, In step 5, the transmission wavefront of the gradient refractive index material is W(x,y), and the calculation formula is as follows: W(x,y)=W1(x,y)-W2(x,y) Where W1(x,y) is the first wavefront obtained in step 3, and W2(x,y) is the second wavefront obtained in step 4.

9. The method for measuring gradient refractive index material wedge mirror compensation based on Mach-Zehnder interferometer according to claim 1, characterized in that, Step 6 involves using the transmitted wavefront obtained in step 5 to calculate the refractive index change of the gradient refractive index material, as detailed below: The peak-to-valley value of optical path difference (PV) is represented as OPD. PV : OPD PV =W max (x,y)-W min (x,y) Among them, W max (x,y), W min (x, y) represent the maximum and minimum values ​​of the transmission wavefront of the gradient refractive index material, respectively; The refractive index change Δ of gradient refractive index materials n for: Δ n = OPD PV / t in, t The thickness of the gradient refractive index material.

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