A method for calibrating the length of an interferometer cavity of a fizeau wavemeter

Abstract

This invention discloses a method for calibrating the cavity length of a Fizeau wavelength meter interferometer cavity, comprising: acquiring interference fringe patterns of two lasers of known wavelengths passing through two Fizeau interferometer cavities, and extracting interference signals I1 and I2; extracting the fractional initial phase of the two interference fringes and the ideal cavity length h0 and the two known wavelengths, and calculating the interference order of the fringes at the initial position and rounding it; calculating the cavity lengths h1 and h2 using the above parameters, and constructing a system of equations with the relationship between the actual cavity length and the actual cavity length, and solving for the initial calibration cavity lengths h′1 and h′2; replacing h0 with h′1 and h′2 and repeating the above process to solve for the cavity length to obtain the calibration cavity length h. cal1 and h cal2 The obtained h cal1 and h cal2 After subtracting from the arrays h′1 and h′2, perform least squares calculations to find the cavity length value corresponding to the minimum value in each group, and then calculate the average to obtain the final calibrated value h of the cavity length. cal This method is simple and fast, and the calibrated cavity length has high accuracy, ensuring the accuracy of wavelength measurement by the Fizeau wavelength meter.

Description

Technical Field

[0001] This invention belongs to the field of optical precision measurement technology, and in particular, it is a method for calibrating the cavity length of a Fizeau wavelength meter interferometer cavity. Background Technology

[0002] Laser wavelength serves as a benchmark for precision optical systems, determining the accuracy and performance of both the system and the measurement technology. High-precision measurement of laser wavelength is crucial for ensuring the accuracy of optical systems. Laser wavelength is also an important parameter in precision machining, precision mechanical manufacturing, and microelectronics. Accurate wavelength measurement not only guarantees measurement accuracy but is also a key technology for traceability. Therefore, precise calibration of the Fizeau interferometer cavity length in a high-precision Fizeau wavelengthmeter is essential. Inaccurate calibration of the interferometer cavity length can lead to skipping steps during wavelength measurement, ultimately resulting in low measurement accuracy.

[0003] Among existing cavity length calibration methods, the cavity length calibration process of the Fizeau wavelength meter studied by the Shanghai Institute of Optics and Fine Mechanics uses M lasers (M≥2) of known wavelengths as light sources to acquire M sets of interference fringe patterns. The period of the Fizeau fringes and the distance from the first maximum to the origin of the array are obtained from the fringe patterns, and the cavity length is determined using the phase recombination method. This method uses a large number of lasers, resulting in high cost and low cavity length calibration accuracy; the final relative accuracy of the wavelength measurement is 2×10⁻⁶. -6 . Summary of the Invention

[0004] The purpose of this invention is to address the problems existing in the prior art by providing a method for calibrating the cavity length of a Fizeau wavelength meter interferometer.

[0005] The technical solution to achieve the objective of this invention is: a method for calibrating the cavity length of a Fizeau wavelength meter interferometer, the method comprising the following steps:

[0006] Step 1: Using two frequency-stabilized lasers of known wavelengths as light sources, acquire two interference fringe patterns after they pass through two Fizeau interferometer cavities respectively;

[0007] Step 2: Extract interference signals I1 and I2 from the two interference fringe patterns, respectively;

[0008] Step 3: Based on the interference signals I1 and I2, extract the fractional initial phase of the interference fringes respectively. and

[0009] Step 4: Using the ideal cavity length h0 of the Fizeau interferometer cavity and two known wavelengths λ1 and λ2, calculate the interference orders m1 and m2 of the two interference fringes at the initial position and round them down;

[0010] Step 5, based on the fractional initial phase Given the interference orders m1 and m2 and the known λ1 and λ2, calculate the cavity lengths h1 and h2 of the two Fizeau interferometer cavities;

[0011] Step 6: Based on the relationship between h1 and h2 and the actual cavity length, construct a system of equations and solve for the initial calibration cavity lengths h1′ and h2′. h1′ and h2′ are both one-dimensional arrays composed of n data points.

[0012] Step 7: Replace h0 with h1′ and h2′ respectively, and repeat steps 4 and 5 above to calculate the final calibration cavity length h. cal1 and h cal2 The array will yield h. cal1 and h cal2 After subtracting the array from arrays h1′ and h2′, perform least squares calculation to obtain the position of the minimum difference between the two arrays in the array, and then obtain h1′ and h2′ respectively. cal1 and h cal2 The cavity length at that position in the array is calculated by averaging the two values ​​to obtain the final calibrated cavity length h. cal .

[0013] Furthermore, the acquisition of the interference fringe pattern in step 1 is achieved based on a Fizeau interferometric optical path system. This Fizeau interferometric optical path system includes an optical fiber port, a concave mirror, a first reflecting mirror, a second reflecting mirror, a Fizeau single-stage cavity, a first cylindrical mirror, a first linear array detector, a Fizeau multi-stage cavity, a second cylindrical mirror, and a second linear array detector. Laser light of a known wavelength enters the system through the optical fiber port, which is positioned at the focal point of the concave mirror. The outgoing light from the optical fiber port becomes collimated light after passing through the concave mirror. After collimation, the beam is split into two beams, one of which is collimated along the first sub-beam. The first beam of light is reflected by the first mirror and enters the Fizeau single-stage cavity. Part of the light is reflected multiple times within the Fizeau single-stage cavity and then exits, while the rest is transmitted directly. The exiting light passes through the first cylindrical mirror and converges the interference fringes onto the target surface of the first linear array detector. The second beam of collimated light is reflected by the second mirror along the second sub-path and enters the Fizeau multi-stage cavity. Part of the light is reflected multiple times within the Fizeau multi-stage cavity and then exits, while the rest is transmitted directly. The exiting light passes through the second cylindrical mirror and converges the interference fringes onto the target surface of the second linear array detector.

[0014] Furthermore, the formulas for calculating the interference orders m1 and m2 of the two interference fringes at their initial positions in step 4 are as follows:

[0015]

[0016]

[0017] Furthermore, the calculation formulas for h1 and h2 in step 5 are as follows:

[0018]

[0019]

[0020] Furthermore, the system of equations relating h1 and h2 to the actual cavity length in step 6 is as follows:

[0021]

[0022] In the formula, h1 and h2 are the cavity lengths at the (m+k) interference order, k is any integer, and the range of k is [-p, p+1] when solving, p is an integer, and h1′ and h2′ are the preliminary calibration cavity lengths obtained.

[0023] Furthermore, step 7 specifically includes:

[0024] By replacing h0 with h1′ and h2′, and repeating steps 4 and 5 above, we obtain:

[0025]

[0026]

[0027] In the formula, h cal1 and h cal2 This is the final calculated value of the calibration cavity length;

[0028] For h cal1 h cal2 The difference between the two sets of data h1′ and h2′ is calculated using least squares to obtain the minimum difference. The position of this minimum difference in the array is recorded as i. The final calibration cavity length is:

[0029]

[0030] In the formula, h cal1 (i) and h cal2 (i) are h respectively cal1 and h cal2 The i-th value of the array, h cal This is the final calibrated cavity length value.

[0031] Compared with the prior art, the significant advantages of this invention are:

[0032] 1) The calibration method is simple, the calculation process is convenient and fast, the calculation results are highly accurate, the experimental optical path is simple, and it is easy to operate.

[0033] 2) By processing the data using the least squares method, the final calibrated cavity length value has high accuracy. The Fizeau wavelength meter will not exhibit skipping fringes during wavelength measurement, thus ensuring the measurement accuracy of the Fizeau wavelength meter during wavelength measurement.

[0034] 3) The cavity length calibration method of the Fizeau wavelength meter of the present invention only requires two lasers with known wavelengths, which greatly reduces the number of lasers and costs, and the calibrated cavity length is more accurate. The wavelength measurement accuracy of the wavelength meter is improved by two orders of magnitude compared with the existing wavelength measurement accuracy.

[0035] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0036] Figure 1 This is a flowchart of a method for calibrating the cavity length of a Fizeau wavelength meter interferometer cavity in one embodiment.

[0037] Figure 2 This is a schematic diagram of the Fizeau interferometer system in one embodiment.

[0038] Figure 3 This is a schematic diagram of interference fringes from a single-stage cavity collected in one embodiment.

[0039] Figure 4 This is a schematic diagram of multi-cavity interference fringes collected in one embodiment. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0041] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0042] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0043] In one embodiment, combined Figure 1A method for calibrating the cavity length of a Fizeau wavelength meter interferometer is provided, the method comprising the following steps:

[0044] Step 1: Using two frequency-stabilized lasers of known wavelengths as light sources, acquire two interference fringe patterns after they pass through two Fizeau interferometer cavities respectively;

[0045] Step 2: Extract interference signals I1 and I2 from the two interference fringe patterns, respectively;

[0046] Step 3: Based on the interference signals I1 and I2, extract the fractional initial phase of the interference fringes respectively. and

[0047] Step 4: Using the ideal cavity length h0 of the Fizeau interferometer cavity and two known wavelengths λ1 and λ2, calculate the interference orders m1 and m2 of the two interference fringes at the initial position and round them down;

[0048] Step 5, based on the fractional initial phase Given the interference orders m1 and m2 and the known λ1 and λ2, calculate the cavity lengths h1 and h2 of the two Fizeau interferometer cavities;

[0049] Step 6: Based on the relationship between h1 and h2 and the actual cavity length, construct a system of equations and solve for the initial calibration cavity lengths h1′ and h2′. h1′ and h2′ are both one-dimensional arrays composed of n data points.

[0050] Step 7: Replace h0 with h1′ and h2′ respectively, and repeat steps 4 and 5 above to calculate the final calibration cavity length h. cal1 and h cal2 The array will yield h. cal1 and h cal2 After subtracting the array from arrays h1′ and h2′, perform least squares calculation to obtain the position of the minimum difference between the two arrays in the array, and then obtain h1′ and h2′ respectively. cal1 and h cal2 The cavity length at that position in the array is calculated by averaging the two values ​​to obtain the final calibrated cavity length h. cal .

[0051] Furthermore, in one embodiment, the acquisition of the interference fringe pattern in step 1 is achieved based on a Fizeau interferometer optical path system, such as... Figure 2As shown, the Fizeau interferometric optical path system includes an optical fiber port 1, a concave mirror 2, a first reflecting mirror 3, a second reflecting mirror 4, a Fizeau single-stage cavity 5, a first cylindrical mirror 6, a first linear array detector 7, a Fizeau multi-stage cavity 8, a second cylindrical mirror 9, and a second linear array detector 10. Laser light of a known wavelength enters the system through the optical fiber port 1, which is located at the focal point of the concave mirror 2. The outgoing light from the optical fiber port 1 is collimated by the concave mirror 2. After collimation, the beam is split into two beams. One collimated beam is reflected along the first sub-path by the first reflecting mirror 3. A beam of light enters the Fizeau single-stage cavity 5. Part of the light exits after multiple reflections within the Fizeau single-stage cavity 5, while the rest is directly transmitted. The emitted light passes through the first cylindrical mirror 6, converging the interference fringes onto the target surface of the first linear array detector 7. Another collimated beam is reflected along the second sub-optical path by the second reflecting mirror 4 and enters the Fizeau multi-stage cavity 8. Part of the light exits after multiple reflections within the Fizeau multi-stage cavity 8, while the rest is directly transmitted. The emitted light passes through the second cylindrical mirror 9, converging the interference fringes onto the target surface of the second linear array detector 10. Both the first linear array detector 7 and the target surface of the second linear array detector 10 have 2048 pixels. The acquired single-stage cavity interference fringe pattern is shown below. Figure 3 As shown, the multi-level cavity interference fringe pattern is as follows: Figure 4 As shown.

[0052] Furthermore, in one embodiment, step 3 involves extracting the initial phase of the interference fringes based on the interference signals I1 and I2, respectively. and Specifically, this includes: extracting the phases of the two interference fringes from the interference signals I1 and I2, respectively. Then, the initial terms of the phases of the two interference fringes are taken respectively to obtain the fractional initial phases of the two interference fringes. and

[0053] Furthermore, in one embodiment, the formula for calculating the interference orders m1 and m2 of the two interference fringes at the initial positions in step 4 is as follows:

[0054]

[0055]

[0056] Furthermore, in one embodiment, the calculation formulas for h1 and h2 in step 5 are as follows:

[0057]

[0058]

[0059] Furthermore, in one embodiment, the system of equations relating h1 and h2 to the actual cavity length in step 6 is as follows:

[0060]

[0061] In the formula, h1 and h2 are the cavity lengths at the (m+k) interference order, k is any integer, and the range of k is [-499, 500], for a total of 1000 numbers. h1′ and h2′ are the preliminary calibration cavity lengths obtained.

[0062] Furthermore, in one embodiment, step 7 specifically includes:

[0063] By replacing h0 with h1′ and h2′, and repeating steps 4 and 5 above, we obtain:

[0064]

[0065]

[0066] In the formula, h cal1 and h cal2 This is the final calculated value of the calibration cavity length;

[0067] For h cal1 h cal2 The difference between the two sets of data h1′ and h2′ is calculated using least squares to obtain the minimum difference. The position of this minimum difference in the array is recorded as i. The final calibration cavity length is:

[0068]

[0069] In the formula, h cal1 (i) and h cal2 (i) are h respectively cal1 and h cal2 The i-th value of the array, h cal This is the final calibrated cavity length value.

[0070] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to perform the following steps:

[0071] Step 1: Using two frequency-stabilized lasers of known wavelengths as light sources, acquire two interference fringe patterns after they pass through two Fizeau interferometer cavities respectively;

[0072] Step 2: Extract interference signals I1 and I2 from the two interference fringe patterns, respectively;

[0073] Step 3: Based on the interference signals I1 and I2, extract the fractional initial phase of the interference fringes respectively. and

[0074] Step 4: Using the ideal cavity length h0 of the Fizeau interferometer cavity and two known wavelengths λ1 and λ2, calculate the interference orders m1 and m2 of the two interference fringes at the initial position and round them down;

[0075] Step 5, based on the fractional initial phase Given the interference orders m1 and m2 and the known λ1 and λ2, calculate the cavity lengths h1 and h2 of the two Fizeau interferometer cavities;

[0076] Step 6: Based on the relationship between h1 and h2 and the actual cavity length, construct a system of equations and solve for the initial calibration cavity lengths h1′ and h2′. h1′ and h2′ are both one-dimensional arrays composed of n data points.

[0077] Step 7: Replace h0 with h1′ and h2′ respectively, and repeat steps 4 and 5 above to calculate the final calibration cavity length h. cal1 and h cal2 The array will yield h. cal1 and h cal2 After subtracting the array from arrays h1′ and h2′, perform least squares calculation to obtain the position of the minimum difference between the two arrays in the array, and then obtain h1′ and h2′ respectively. cal1 and h cal2 The cavity length at that position in the array is calculated by averaging the two values ​​to obtain the final calibrated cavity length h. cal .

[0078] For specific limitations on each step, please refer to the limitations on the cavity length calibration method of the Fizeau wavelength meter interferometer cavity mentioned above, which will not be repeated here.

[0079] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0080] Step 1: Using two frequency-stabilized lasers of known wavelengths as light sources, acquire two interference fringe patterns after they pass through two Fizeau interferometer cavities respectively;

[0081] Step 2: Extract interference signals I1 and I2 from the two interference fringe patterns, respectively;

[0082] Step 3: Based on the interference signals I1 and I2, extract the fractional initial phase of the interference fringes respectively. and

[0083] Step 4: Using the ideal cavity length h0 of the Fizeau interferometer cavity and two known wavelengths λ1 and λ2, calculate the interference orders m1 and m2 of the two interference fringes at the initial position and round them down;

[0084] Step 5, based on the fractional initial phase Given the interference orders m1 and m2 and the known λ1 and λ2, calculate the cavity lengths h1 and h2 of the two Fizeau interferometer cavities;

[0085] Step 6: Based on the relationship between h1 and h2 and the actual cavity length, construct a system of equations and solve for the initial calibration cavity lengths h1′ and h2′. h1′ and h2′ are both one-dimensional arrays composed of n data points.

[0086] Step 7: Replace h0 with h1′ and h2′ respectively, and repeat steps 4 and 5 above to calculate the final calibration cavity length h. cal1 and h cal2 The array will yield h. cal1 and h cal2 After subtracting the array from arrays h1′ and h2′, perform least squares calculation to obtain the position of the minimum difference between the two arrays in the array, and then obtain h1′ and h2′ respectively. cal1 and h cal2 The cavity length at that position in the array is calculated by averaging the two values ​​to obtain the final calibrated cavity length h. cal .

[0087] For specific limitations on each step, please refer to the limitations on the cavity length calibration method of the Fizeau wavelength meter interferometer cavity mentioned above, which will not be repeated here.

[0088] In summary, this invention employs a Fizeau interferometer system. By using two lasers of known wavelengths to acquire the fringe interference pattern after passing through the Fizeau interferometer cavity, and then analyzing and processing the fringe interference pattern, the cavity length of the Fizeau interferometer cavity is calibrated. This ensures that the Fizeau wavelength meter will not cause skipping steps in wavelength calculation due to inaccurate interference cavity length, thus guaranteeing the measurement accuracy of the Fizeau wavelength meter.

[0089] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention without departing from its spirit and scope should be included within the protection scope of the present invention.

Claims

1. A method for calibrating the cavity length of a Fizeau wavelength meter interferometer cavity, characterized in that, The method includes the following steps: Step 1: Using two frequency-stabilized lasers of known wavelengths as light sources, acquire two interference fringe patterns after they pass through two Fizeau interferometer cavities respectively; Step 2: Extract the interference signals from the two interference fringe patterns respectively. and ; Step 3, based on the interference signal and Extract the fractional initial phase of the interference fringes respectively. and ; Step 4, determine the ideal cavity length of the Fizeau interferometer cavity. and two known wavelengths , Calculate the interference order of the two interference fringes at their initial positions. and And round down; Step 5, based on the fractional initial phase , Interference level , and known , Calculate the cavity lengths of the two Fizeau interferometer cavities. and ; Step 6, based on the above and A system of equations was constructed to determine the relationship between the cavity length and the actual cavity length, and the initial calibration cavity length was obtained by solving the equations. and , and All are one-dimensional arrays consisting of n data points; Step 7, Replace with , Repeat steps 4 and 5 above to calculate the final calibration cavity length. and The array will be obtained and Arrays and and After subtracting the arrays, perform least squares calculations to find the position of the minimum difference between the two sets of differences in the array, and then obtain the minimum difference value from each array. and The cavity length at that position in the array is calculated by averaging the two values ​​to obtain the final calibrated cavity length. .

2. The method for calibrating the cavity length of the Fizeau wavelength meter interferometer cavity according to claim 1, characterized in that, In step 1, the acquisition of the interference fringe pattern is based on the Fizeau interferometric optical path system, which includes an optical fiber port (1), a concave mirror (2), a first reflector (3), a second reflector (4), a Fizeau single-stage cavity (5), a first cylindrical mirror (6), a first linear array detector (7), a Fizeau multi-stage cavity (8), a second cylindrical mirror (9), and a second linear array detector (10). A laser of known wavelength enters the system through the optical fiber port (1), which is located at the focal point of the concave mirror (2). The light emitted from the optical fiber port (1) becomes collimated light after passing through the concave mirror (2). After collimation, the beam is split into two beams, one of which is collimated light. The light beam is reflected by the first mirror (3) along the first sub-light path and enters the Fizeau single-stage cavity (5). Part of the light is reflected multiple times in the Fizeau single-stage cavity (5) and then emitted. Part of the light is directly transmitted out. The emitted light passes through the first cylindrical mirror (6) and then converges the interference fringes on the target surface of the first linear array detector (7). The other collimated light is reflected by the second mirror (4) along the second sub-light path and enters the Fizeau multi-stage cavity (8). Part of the light is reflected multiple times in the Fizeau multi-stage cavity (8) and then emitted. Part of the light is directly transmitted out. The emitted light passes through the second cylindrical mirror (9) and then converges the interference fringes on the target surface of the second linear array detector (10).

3. The method for calibrating the cavity length of the Fizeau wavelength meter interferometer cavity according to claim 2, characterized in that, The first linear array detector (7) and the second linear array detector (10) each have 2048 pixels on their target surfaces.

4. The method for calibrating the cavity length of the Fizeau wavelength meter interferometer cavity according to claim 3, characterized in that, Step 3, based on the interference signal and The initial phase of the interference fringes was extracted separately. and Specifically, this includes: from the interference signal and The phases of the two interference fringes were extracted separately. Then, the initial terms of the phases of the two interference fringes are taken respectively to obtain the fractional initial phases of the two interference fringes. and .

5. The method for calibrating the cavity length of the Fizeau wavelength meter interferometer cavity according to claim 4, characterized in that, In step 4, the interference order of the two interference fringes at their initial positions is calculated. and The formula is as follows: 。 6. The method for calibrating the cavity length of the Fizeau wavelength meter interferometer cavity according to claim 5, characterized in that, The steps described in step 5 and The calculation formula is: 。 7. The method for calibrating the cavity length of the Fizeau wavelength meter interferometer cavity according to claim 6, characterized in that, In step 6 and The system of equations relating to the actual cavity length is as follows: In the formula, and Let k be the cavity length at the (m+k) interference order, where k is any integer. When solving, k is taken in the range [-p, p+1], where p is an integer. and To obtain the preliminary calibration cavity length.

8. The method for calibrating the cavity length of the Fizeau wavelength meter interferometer cavity according to claim 7, characterized in that, Step 7 specifically includes: Depend on and replace Repeat steps 4 and 5 above to obtain: 、 、 In the formula, and This is the final calculated value of the calibration cavity length; right , and , The difference between the two sets of data is calculated using least squares to obtain the minimum difference, and the position of this value in the array is recorded as i. The final calibration cavity length is: In the formula, and (j) are respectively and The values ​​of the i-th and j-th elements of the array, This is the final calibrated cavity length value.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the content of the method according to any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the content of the method according to any one of claims 1 to 8.

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