Measuring wavelength of light

Abstract

To provide a wavelength measurement system that can measure a wavelength of light with high accuracy.SOLUTION: A wavelength measurement system 200 comprises an interferometer 226, a camera system 228, a sensor 206, and a control system 202. The interferometer includes two reflective surfaces and a transmission medium between the two reflective surfaces. The interferometer receives an optical signal from a laser and generates an interferogram in response. The camera system receives the interferogram from the interferometer and generates interferogram data in response. The interferogram data represents the interferogram received from the interferometer. The sensor senses an environmental parameter of the transmission medium and generates sensor data in response. The control system performs operations including: receiving the interferogram data from the camera system and the sensor data from the sensor and computing a wavelength of the laser on the basis of the interferogram data and the sensor data.SELECTED DRAWING: Figure 2A

Description

[Technical field]

[0001] This application claims priority to U.S. patent application Ser. No. 1 6 / 907,469, entitled "Measuring Wavelength of Light," filed Jun. 22, 2020, the contents of which are incorporated herein by reference.

[0002] The following description is directed to measuring the wavelength of light. [Background technology]

[0003] Lasers are precision tools for manipulating matter and making measurements. In many cases, the properties of lasers, such as frequency or wavelength, are required to be precisely tuned to atomic resonances for use in commercial devices. Examples of such devices include atomic clocks, gravimeters, electric and magnetic field sensors, and accelerometers. One of the major challenges for such devices is to measure accurate absolute frequencies with high precision (e.g., ~1 MHz) from the ultraviolet to the infrared. Currently, wavelength measurements with such precision rely on power-consuming environmental control and stabilization techniques, greatly limiting the use of such techniques outside of laboratory environments. [Brief description of the drawings]

[0004] [Figure 1] FIG. 1 is a schematic diagram of an exemplary system for measuring wavelength. [Figure 2A] FIG. 1 is a schematic diagram of an exemplary system for measuring wavelength. [Figure 2B] 1 is a schematic diagram of an exemplary interferometer. [Diagram 3] FIG. 1 is a top-view photograph of a prototype system for wavelength measurement. [Figure 4A] FIG. 1 shows exemplary interferogram data generated by the camera of the prototype system. [Figure 4B] 1 is a plot showing measured frequency before and after compensation for environmental effects. [Diagram 5] 4 is a flowchart illustrating an exemplary process for calibrating a wavelength measurement system. [Figure 6] 4 is a flowchart illustrating an exemplary process for performing wavelength measurements. [Figure 7A] 7A and 7B are schematic diagrams of reflected intensity models used in the exemplary processes of FIGS. 5 and 6, respectively. [Figure 7B] 7A and 7B are schematic diagrams of reflected intensity models used in the exemplary processes of FIGS. 5 and 6, respectively. [Figure 7C] 7A and 7B are schematic diagrams of reflected intensity models used in the exemplary processes of FIGS. 5 and 6, respectively. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0005] Measurement of laser light characteristics, such as wavelength or frequency, is increasingly important in many applications, for example in high-precision experiments and devices where the optical signal forms an integral part of the measurement or detection system. In some aspects described herein, the wavelength measurement system includes an optical system and one or more environmental sensors. In some implementations, the optical system includes a series of optical elements that define one or more beam paths between a laser source and a camera system. In some implementations, the optical system includes one or more interferometers that generate a spatial interferogram that can be used for wavelength measurement. In some implementations, the one or more interferometers are arranged with one or more environmental sensors that can monitor one or more environmental parameters of the transmission medium of the laser light. In some implementations, the one or more environmental parameters are used to determine the refractive index of the transmission medium and to compensate for environmental effects on the measured wavelength. In some implementations, the environmental parameters are used to compensate for thermal expansion of the interferometer.

[0006] In some implementations, the methods and systems described herein may provide improvements over or beyond existing technology. For example, the methods and systems may not require passive isolation, power-consuming environmental control, or active atmospheric stabilization for the system to achieve high precision and accuracy. In another example, the methods and systems may avoid the use of permanent reference lasers that are intermittently recalibrated to correct for long-term drift. In yet another example, the system may be suitable for small form factors, e.g., portable devices that occupy a small volume or footprint and where power consumption is a key design constraint. In some examples, a combination of these advantages and potentially other advantages and improvements may be obtained.

[0007] In some aspects of what is described herein, one or more interferometers of the wavelength measurement system can be implemented as dual Fizeau interferometers. However, other types and combinations of interferometers are possible. In some aspects of what is described herein, a dual Fizeau interferometer with two interferometer cavities is constructed and used simultaneously to provide a reliable and efficient wavelength measurement. In some implementations, a minimum chi-square based optimization model is performed on the interferogram obtained using two interferometer cavities with two different interferometer lengths, thereby allowing the unambiguous wavelength to be determined by finding the global minimum with high accuracy.

[0008] In some aspects of what is described herein, one or more environmental sensors are configured proximate to the interferometer cavity to monitor environmental parameters of the transmission medium within the interferometer cavity. In some implementations, the environmental parameters can include temperature (T), atmospheric pressure (P), and humidity (H). In some examples, the environmental sensor can monitor the concentration of CO2 in the transmission medium. TIFF2024099614000002.tif13150 may further include a carbon dioxide (CO2) sensor for determining

[0009] In some aspects described herein, the wavelength measurement system further includes a control system, which can be used to operate the optical system, for example, to switch between different laser sources. A reference laser source can be used in the calibration process, and a test laser source can be used in the wavelength measurement process. In some examples, the control system can receive data for signal processing. For example, the control system can communicate with a camera of the optical system to receive spatial interferogram data. The control system can also communicate with an environmental sensor to receive data representing environmental parameters of the transmission medium (e.g., air) in the interferometer cavity. In some implementations, the control system can use the data to estimate the refractive index of the transmission medium. In some examples, the control system can be used to implement one or more aspects of the systems and techniques described in connection with FIGS. 1-3 and 5-6. However, the control system can also perform other types of operations. In some variations, the control system can implement a thermal expansion model to compensate for thermal expansion of optical elements in the optical system.

[0010] 1 illustrates a schematic diagram of an exemplary wavelength measurement system 100. The exemplary wavelength measurement system 100 includes an optical system 102, an environmental sensor 104, and a control system 106. However, additional features may be implemented in the exemplary wavelength measurement system 100.

[0011] In some implementations, the optical system 102 can be coupled to two or more laser sources 120, such as a reference laser source and a test laser source. In some implementations, the reference laser source can be used to generate a reference laser beam having a known wavelength. In some implementations, the reference laser source can be used to calibrate the wavelength measurement system 100. In some implementations, the test laser source can generate a laser beam having an unknown wavelength that can be measured by the exemplary wavelength measurement system 100 before being used in other applications.

[0012] In some implementations, the optical system 102 may include a series of optical elements that define one or more beam paths between the two or more laser sources 120 and the camera system. In some examples, the series of optical elements of the optical system 102 may include an optical switch, one or more lenses, one or more mirrors, a beam splitter, and one or more interferometers. In some implementations, the optical system 102 may be implemented as the optical system 204 shown in FIG. 2. However, other implementations of the optical system 102 are possible. In some implementations, the optical switch may be configured to select and route an input laser beam at a first input port or a second laser beam at a second input port to an output port of the optical switch. In some implementations, the laser beam from the output port of the optical switch is collimated by one or more lenses.

[0013] In some implementations, the collimated laser beam exiting the one or more lenses can be directed through an interferometer. In some examples, an interferometer including at least two different interferometer lengths can facilitate reliable and efficient matching of the wavelength of the test laser beam. In some examples, the interferometer can include a dual Fizeau interferometer, a Fabry-Perot interferometer, a Michelson interferometer, or other types of interferometers. In certain implementations, the optical system 102 includes a camera system that can be configured in a position optically coupled to the interferometer. In some examples, the camera system can be used to detect one or more interferograms.

[0014] In some implementations, the environmental sensor 104 may include at least one of a temperature sensor, an atmospheric pressure sensor, and a humidity sensor. In some implementations, the environmental sensor 104 is configured proximate to the interferometer in the optical system 102. In some implementations, the environmental sensor 104 may be configured for in-situ monitoring of an environmental parameter of a transmission medium in the interferometer cavity to determine a refractive index of the transmission medium, e.g., air, in the interferometer. In some implementations, the sensor data representing the value of the environmental parameter may be generated by the environmental sensor including temperature (T), atmospheric pressure (P), and humidity (H). In some implementations, the environmental sensor 104 may further include a carbon dioxide (CO2) sensor to generate sensor data including CO2 concentration data in the transmission medium. In some implementations, the refractive index may be determined by the control system 106 using a refractive index calculation algorithm. In some implementations, the environmental sensor 104 may include an additional temperature sensor, for example, disposed in the interferometer, to compensate for thermal expansion effects in the interferometer.

[0015] In the example shown in FIG. 1, the control system 106 includes a processor 110, a memory 112, and a communication interface 114. The control system 106 may include additional components, such as, for example, an input / output controller, a communication link, power for the optical system or environmental sensors, a display, and an input device. In some examples, the control system 106 may be used to operate an optical switch in the optical system 102 to switch between different input laser sources. In some examples, the control system 106 may be used to communicate with the camera system and the environmental sensor 104 of the optical system 102 via the communication interface 114. For example, the control system 106 may receive the data 116 for signal processing (e.g., performing an example process 500 for calibrating a wavelength measurement system as described in connection with FIG. 5 or performing an example process 600 for wavelength measurement as described in connection with FIG. 6). In some implementations, the control system 106 may be used to implement one or more aspects of the systems and techniques described in connection with FIG. 2-FIG. 6 or to perform other types of operations.

[0016] In some implementations, some of the processes and logic flows described herein may be performed by one or more programmable processors, such as processor 110, executing one or more computer programs to perform operations by operating on input data and generating output. For example, processor 110 may execute program 118 by executing or interpreting scripts, functions, executable files, or other modules included in program 118. In some implementations, processor 110 may perform one or more of the operations described with respect to Figures 5 and 6, for example.

[0017] In some implementations, the processor 110 may include various types of apparatuses, devices, and machines for processing data, including, by way of example, a programmable data processor, a system on a chip (SoC), or a plurality or combination of the foregoing. In certain examples, the processor 110 may include special purpose logic circuitry, such as a field programmable gate array (FPGA), an application specific integrated circuit (ASIC), or a graphics processing unit (GPU). In some examples, the processor 110 may include, in addition to hardware, code that creates an execution environment for the computer program, such as code that constitutes a processor firmware, a protocol stack, a database management system, an operating system, a cross-platform execution environment, a virtual machine, or one or more combinations thereof. In some examples, the processor 110 may include, by way of example, both general purpose and special purpose microprocessors, as well as processors of any type of digital computer.

[0018] In some implementations, the processor 110 can include both general purpose and special purpose microprocessors, as well as processors of any type of digital computer. Generally, the processor 110 will receive instructions and data from a read-only memory or a random access memory or both (e.g., memory 112). In some implementations, the memory 112 can include any form of non-volatile memory, media, and memory devices, including, by way of example, semiconductor memory devices (e.g., EPROM, EEPROM, flash memory devices, etc.), magnetic disks (e.g., internal hard disks, removable disks, etc.), magneto-optical disks, and CD-ROM and DVD-ROM disks. In some cases, the processor 110 and the memory 112 may be supplemented by, or incorporated in, special purpose logic circuitry.

[0019] In some implementations, the data 116 stored in the memory 112 may include data received from the camera system of the optical system 102 and from the environmental sensor 104. In some implementations, the data 116 stored in the memory 112 may include information related to the reference laser beam (e.g., wavelength or frequency, Gaussian envelope parameters, etc.). In some implementations, the program 118 may include a software application, script, program, function, executable file, or other module that is interpreted or executed by the processor 110. In some implementations, the program 118 may include machine-readable instructions for receiving data of environmental parameters of the transmission medium (e.g., air) in the interferometer and performing a wavelength measurement process to evaluate the refractive index of the transmission medium. In some implementations, the program 118 may include machine-readable instructions for controlling an optical switch of the optical system 102 to switch between different input laser sources.

[0020] In some implementations, the program 118 can access the data 116 from the memory 112, from another local source, or from one or more remote sources (e.g., via a communication link). In some examples, the program 118 can generate output data and store the output data in the memory 112, another local medium, or one or more remote devices (e.g., by transmitting the output data via the communication interface 114). In some examples, the program 118 (also referred to as software, software application, script, or code) can be written in any type of programming language, including compiled or interpreted languages, declarative or procedural languages. In some implementations, the program 118 can be deployed to run on one computer, or on multiple computers located at one site or distributed across multiple sites and interconnected by a communication network. For example, the program 118 may run in the cloud, and the control system 106 can access the program 118 via an Internet connection.

[0021] In some implementations, the communication interface 114 may include any type of communication channel, connector, data communication network, or other link. In some implementations, the communication interface 114 may provide a communication channel between the control system 106 and the optical system 102, the environmental sensor 104, or other systems or devices. In some examples, the communication interface 114 may include a wireless communication interface that provides wireless communication under various wireless protocols, such as, for example, Bluetooth, Wi-Fi, Near Field Communication (NFC), GSM voice calls, SMS, EMS, or MMS messages, wireless standards (e.g., CDMA, TDMA, PDC, WCDMA, CDMA2000, GPRS, etc.), among others. In some examples, such communication may occur, for example, via a radio frequency transceiver or another type of component. In some examples, the communication interface 114 may include a wired communication interface (e.g., USB, Ethernet, etc.) that may be connected, for example, via a network adapter, to one or more input / output devices, such as, for example, a keyboard, a pointing device, a scanner, or a network device such as a switch or router.

[0022] FIG. 2 is a schematic diagram of an exemplary wavelength measurement system 200 for wavelength measurements. In some examples, the exemplary wavelength measurement system 200 shown in FIG. 2 can be used to perform wavelength measurements, such as the processes described in connection with FIG. 5 and FIG. 6. In the example shown in FIG. 2, the wavelength measurement system 200 includes a control system 202, an optical system 204, and an environmental sensor 206. As shown in FIG. 2, the optical system 204 includes a series of optical elements that define one or more beam paths between one or more lasers and a camera system. In the illustrated example, the series of optical elements of the optical system 204 includes an optical switch 216, a lens assembly 218, a mirror 220, a beam splitter 222, a beam stop 224, an interferometer 226, and a camera system 228. In some examples, the wavelength measurement system 200 can include additional or different components, and the components can be arranged as shown or in another manner.

[0023] In some embodiments, the optical system 204 can receive one or more laser beams from a reference laser source 212 and a test laser source 214. In the example shown in FIG. 2, the reference laser source 212 can be used to generate a reference laser beam with a known frequency. In some implementations, the test laser source 214 can be used to generate a laser beam with an unknown frequency / wavelength that needs to be measured before being used in other applications. In some implementations, the reference laser source 212 can be used for recalibration or in-situ calibration purposes, for example, after a substantial reconfiguration to the system 200 has been performed. However, once the system 200 has been calibrated, it may not require recalibration with a reference laser source.

[0024] In some implementations, the reference laser source 212 can be actively stabilized and locked to an atomic frequency reference, for example, where the frequency interval between some atomic transitions may be known with high precision. For example, optical absorption by the D1 transition (62S1 / 2 → 62P1 / 2 transition) or D2 transition (62S1 / 2 → 62P3 / 2 transition) of cesium (Cs) atoms can be used as an absolute frequency reference to calibrate the example wavelength measurement system 200. In some examples, the reference laser source 212 can provide high precision and frequency stability better than 3 parts in 1010, or 100 kHz accuracy for a frequency of about 300 THz. In some other examples, the reference laser source 212 can include another type of laser source with a different precision. For example, a HeNe laser with reduced precision can be used as the reference laser source 212. In one example, the reference laser source 212 can output a reference laser beam having a wavelength at 852.356 nm, which corresponds to an optical frequency of 351.722 THz. In some embodiments, the reference laser source 212 is locked to an atomic transition of Cs using an ultrastable optical resonator with wavelength variations of less than 0.2 fm (eg, frequency variations of less than 100 kHz).

[0025] In some implementations, the optical switch 216 can selectively switch an optical signal from one input port to another. The optical switch 216 can be an optical router or a mechanically actuated mirror. In some variations, the optical switch 216 can be actuated by mechanical methods, such as shifting from one fiber coupled to a laser source (e.g., the reference laser source 212) to another fiber coupled to a different laser source (e.g., the test laser source 214). However, in many implementations, the optical switch 216 includes a microelectromechanical system (MEMS) optical switch. In some examples, the optical switch 216 can include one or more mirrors, the tilt angle of which can be digitally controlled by the control system 202. In some examples, the optical switch 216 can have two or more input ports and one or more output ports. In the exemplary system 200 shown in FIG. 2, the optical switch 216 can route the first laser beam at the first input port 230A or the second laser beam at the second input port 230B to the output port 232. In some examples, the optical switch 216 can provide the same optical path for the input laser beams. In certain embodiments, the optical switch can allow for measuring multiple lasers. In some embodiments, the optical switch 216 can be capable of coupling to various optical fibers, such as single mode optical fibers, multimode optical fibers, or polarization maintaining optical fibers. In some examples, the optical switch 216 can be selected according to the frequency range of the input laser beams. In some examples, the optical switch 216 can have low insertion loss and can operate at low voltages to prevent additional thermal load on the exemplary system 200.

[0026] In some implementations, the laser beam from the output port 232 of the optical switch 216 can be collimated by a lens assembly 218. In some implementations, the lens assembly 218 includes one or more collimating lenses oriented in a direction perpendicular to the incidence direction of the laser beam from the output port 232. In some implementations, the collimating lens 218 is achromatic to minimize beam divergence at different wavelengths.

[0027] In some implementations, an optical fiber may be used to direct the laser beam from the laser sources 212, 214 to the optical switch 216. In some implementations, the optical fiber may include a single mode optical fiber to improve the quality of the laser beam, or a multimode optical fiber to maintain the intensity of the laser beam. In some implementations, the optical fiber may also be used to direct the laser beam from the optical switch 216 to the lens assembly 218. In certain embodiments, the optical fiber may be implemented as a polarization maintaining optical fiber, a photonic crystal fiber, or another type of optical fiber.

[0028] In some implementations, the collimated laser beam exiting the lens assembly 218 is then directed through a beam splitter 222. In some implementations, the collimated laser beam can be redirected by a first mirror 220 along a different direction (e.g., from horizontal to vertical) before propagating through the beam splitter 222. In some examples, a partially reflective and partially transmissive beam splitter 222 is used to split the incident laser beam into two beams, each along a separate path (e.g., a transmission path and a reflection path). In some examples, a beam stop 224 can be placed in the path (e.g., the reflection path) of the beam splitter 222. In some examples, the beam stop 224 is a beam dump that prevents the laser on the reflection path from contributing to the interferogram. In some examples, an interferometer 226 can be placed on the other path (e.g., the transmission path) of the beam splitter 222.

[0029] In some implementations, the interferometer 226 can include at least two pieces of glass facing each other. In some implementations, the interferometer 226 can include ultra-low expansion glass. In the example shown in FIG. 2, the first piece of glass 240A is configured perpendicular to the incident laser beam, and the second piece of glass 240B is angled at a wedge angle with respect to the perpendicular (e.g., as shown in the schematic ray diagrams of FIGS. 7A-7C). In some implementations, the first surface of the first piece of glass 204A facing the incident laser beam can be coated with one or more anti-reflective coatings to enhance operation at a particular wavelength or set of wavelengths. In some implementations, the thickness of each of the one or more anti-reflective coatings can be determined by the wavelength range and the refractive index of the transmission medium and the first piece of glass 204A. In some implementations, the first surface of the first piece of glass 240A can be uncoated for broadband operation. In some implementations, the second opposing surface of the first glass piece 240A and the first surface of the second glass piece 240B, which are configured to face each other, are coated with a reflective coating. In some implementations, the reflective coating can include a layer of a metal, a metal alloy, or a dielectric material. For example, the reflective coating can include aluminum, silver, gold, chromium, copper, nickel, titanium, and Inconel, or a layered dielectric including silicon dioxide (SiO2) and titanium dioxide (TiO2).

[0030] As shown in FIG. 2, by forming a step 244 on a first surface of the second glass piece 240B, two interferometer cavities 242A, 242B with two different interferometer lengths are created. In some implementations, a portion of the transmitted laser beam from the beam splitter 222 is incident on the wedge surface 246A of the step 244, and a portion of the transmitted laser beam is incident on the bottom wedge surface 246B. The bottom wedge surface 246B is displaced from the wedge surface 246A by the step 244. In some embodiments, the wedge surface 246A is displaced from the bottom wedge surface 246B by the step 244 by 0.39 mm, e.g., the height of the step 244 is 0.39 mm. The reflected laser beams from the wedge surface 246A and the bottom wedge surface 246B can effectively form two interferometer cavities 242A, 242B, e.g., a dual Fizeau interferometer. In some examples, the difference between the interferometer lengths of the dual Fizeau interferometer is the height of the step 244. For example, the two interferometer lengths are 20.00 mm and 19.61 mm. In some embodiments, the reflected laser beam from the interferometer may be spatially patterned with two separate interference patterns (e.g., interferograms) that may have different periodicity and / or phase due to the different interferometer lengths (e.g., interferograms 402a, 402b shown in FIG. 4A). Furthermore, the dual Fizeau interferometer may be constructed as a single monolithic piece, e.g., from a single piece of glass, or as several pieces fused together. In some implementations, the interferometer may include two or more interferometer cavities, and the interferometer cavities may be fabricated in other ways, e.g., with different wedge angles.

[0031] In some implementations, the interferograms from the interferometer 226 can be captured by the camera system 228. In some implementations, each of the interferograms can include a series of interferograms. To a first approximation, the series of interferograms is generated when the interferometer length is equal to mλ / 2, where m is an integer representing the interference order and λ is the wavelength of the laser beam. In some implementations, if the interferometer length is known, the spacing and position of the interferograms can be used to calculate the wavelength λ by inferring m. In some implementations, the interferometer length can be determined from a calibration process, such as the exemplary process 500 described in connection with FIG. 5, or in another manner.

[0032] In some examples, the camera system 228 can include an array of image sensors, each of which may be a charge-coupled device (CCD) sensor and a complementary metal-oxide semiconductor (CMOS) sensor. In a particular implementation, the camera system 228 can be configured at a location within the exemplary system 200 that receives the combined laser beam from the beam splitter 222 to record the complete spatial intensity profile of the interferogram from the beam splitter 222.

[0033] In some implementations, the environmental sensor 206 can include one or more temperature sensors, one or more atmospheric pressure sensors, and one or more humidity sensors. In some implementations, the environmental sensor 206 is disposed proximate to the interferometer 226. In some implementations, the environmental sensor 206 can be configured for in-situ monitoring of environmental parameters of the transmission medium in the interferometer cavities 242A, 242B, including temperature (T), atmospheric pressure (P), and humidity (H). In some implementations, the environmental parameters monitored by the environmental sensor 206 can be used to determine the refractive index of the transmission medium (e.g., air) in the interferometer cavities 242A, 242B of the interferometer 226.

[0034] The environmental sensors 206 can be selected according to design considerations including detection range, sensitivity, accuracy, response time, repeatability, size, and power consumption. In some implementations, the environmental sensors 206 are calibrated prior to a measurement operation or in-situ by comparison to respective precisely calibrated reference sensors.

[0035] In some implementations, the environmental sensor 206 may further include one or more separate temperature sensors for measuring the temperature of a single monolithic piece of glass of the interferometer. In some implementations, one or more separate temperature sensors may be used to measure the temperature of an interferometer spacer 250 used to separate the first and second pieces of glass 240A, 240B. In some implementations, the interferometer temperature data generated by the one or more separate temperature sensors may be used in a thermal expansion model to compensate for thermal expansion effects on the wavelength measurement. In some examples, the thermal expansion effects may be modeled for the entire monolithic piece of the interferometer with a linear model, a higher order model, or otherwise. In a particular example, a linear model ΔL=γΔT·L may be used, where ΔL is the change in interferometer length, γ is the thermal expansion coefficient, ΔT is the change in temperature, and L is the interferometer length. In some implementations, the thermal expansion coefficient in the linear model may be determined by applying a known laser frequency, holding the interferometer at different controlled temperatures, and determining the change in interferometer length as the interferometer resonance shifts. In some implementations, thermal expansion effects can be calibrated and thermal expansion coefficients determined before wavelength measurements are made. In some implementations, thermal expansion effects on other geometries of the interferometer 226, particularly if the interferometer is implemented in another way, for example, the angle of incidence of the incident laser on the second piece of glass 240B, can also be measured and calibrated.

[0036] In some implementations, the environmental sensor 206 may be configured within a housing (not shown) of the exemplary system 200, which may be used to enclose the exemplary system 200 from dust accumulation. The exemplary system 200 may or may not be sealed within a housing. In some examples, the exemplary system 200 is configured without a housing and is open to the environment.

[0037] In some implementations, different types of temperature sensors can be implemented, including contact and non-contact temperature sensors. In some implementations, the contact temperature sensor can be a thermostat, a thermistor, a thin film resistive sensor, or a thermocouple. In some implementations, the humidity sensor can be a capacitive sensor, a resistive sensor, or a thermal conductivity sensor. In some implementations, the atmospheric pressure sensor can be an absolute pressure sensor or a differential pressure sensor. In some examples, the atmospheric pressure sensor can be a MEMS air pressure sensor that can measure atmospheric pressure using a small and flexible structure. In some examples, the MEMS air pressure sensor can be used to measure dynamic or static air pressure in the interferometer cavities 242A, 242B. In some implementations, other types of environmental sensors can be used.

[0038] In some implementations, the environmental sensor 206 can further include one or more carbon dioxide (CO2) sensors. In some embodiments, the one or more CO2 sensors include a chemical gas sensor. In some embodiments, the chemical CO2 gas sensor can be a MEMS CO2 gas sensor that uses a chemically sensitive layer to measure the CO2 concentration level in the interferometer cavities 242A, 242B. In some implementations, other types of CO2 gas sensors can be used according to their detection range and selectivity to other gas molecules.

[0039] In some implementations, sensor data representing values ​​of environmental parameters can be generated by the environmental sensor 206. In some implementations, the sensor data can be used in a calibration process and a wavelength measurement process (e.g., exemplary processes 500 and 600 described in connection with FIGS. 5 and 6). In some examples, the sensor data can be used to determine the refractive index of the transmission medium (e.g., air) in the interferometer cavities 242A, 242B. As shown in FIGS. 5 and 6, the calibration and wavelength measurement processes can use the sensor data, the wavelength of the reference laser beam, and the geometric parameters of the interferometer cavity (e.g., the interferometer length and wedge angle) to determine the absolute wavelength of the test laser beam. However, other environmental parameters are possible.

[0040] In some implementations, the control system 202 can be used, for example, to operate an optical switch 216 in the optical system 204 to switch between receiving different laser input sources. In some implementations, the control system 202 receives data for signal processing. For example, the control system 202 can communicate with a camera system 228 in the optical system 204 to receive interferogram data. For example, the control system 202 can communicate with an environmental sensor 206 to receive sensor data. In some implementations, the control system 202 can be used to implement one or more aspects of the systems and techniques described with respect to FIGS. 5-6 or to perform other types of operations.

[0041] FIG. 3 shows a top view photograph of a prototype system 300 for wavelength measurement. In some embodiments, the prototype system 300 shown in FIG. 3 can be used to perform wavelength measurements, such as the processes described in connection with FIG. 5 and FIG. 6. In the example shown in FIG. 3, the prototype system 300 includes control electronics 302, an environmental sensor 304, and a series of optical elements that define one or more beam paths between a laser source (not shown) and a camera 322. In the example shown, the series of optical elements includes a MEMS fiber optic switch 310, a fiber coupler 312, a collimating lens 314, a mirror 316, a beam splitter 318, and a dual Fizeau interferometer 320. The prototype system 300 can also include a beam stop, which can be a cover (not shown) of the prototype system. In some examples, the prototype system 300 can receive a laser beam via an optical fiber 328 optically coupled to the MEMS fiber optic switch 310. The laser beam can be generated by a laser source (not shown). As shown in Figure 3, the physical footprint of the prototype system 300 is approximately 175mm x 175mm x 100mm (L x W x H), however, other dimensions are possible.

[0042] In some implementations, the array of optical elements is mounted on a base unit 324, which is further mounted on an optical table 326. In these implementations, the control electronics 302 can be located elsewhere (e.g., a remote location not on the base unit 324). In some implementations, the temperature of the base unit 324 can be actively stabilized using a low-power (<1 W) temperature controller (not shown). In some implementations, the low-power temperature controller is used to limit the temperature fluctuation of the base unit 324 to ±20 mK. In some implementations, the environmental sensor 304 has low power consumption during operation, for example, about 3 mW. In some implementations, the techniques and systems disclosed herein are suitable for portable devices where power consumption is an important design constraint.

[0043] In the prototype system 300, the dual Fizeau interferometer 320 in the monolithic block 330 is further mounted to a base unit 324 along with a low power temperature controller. In some implementations, thermal effects on the monolithic block 330 may simultaneously affect the geometry of the dual Fizeau interferometer 320. In some implementations, thermal effects on the geometry of the dual Fizeau interferometer 320 may affect the interferogram collected by the camera 322, which is used to determine the wavelength of the test laser beam. In some examples, changes in the geometry of the dual Fizeau interferometer 320 can be determined by monitoring the temperature of the interferometer. The temperature measurements can be used to correct the wavelength measurements.

[0044] In the prototype system 300 shown in FIG. 3, the environmental sensor 304 was obtained from Honeywell (BME280), the MEMS fiber optic switch 310 with custom connector was obtained from Thorlabs (OSW12-830-SM), the camera 322 was obtained from IDS systems (UI-5290SE), and the temperature controller was obtained from Koheron (TEC100L).

[0045] FIG. 4A is a plot 400 illustrating an example of interferogram data. As shown in FIG. 4A, the exemplary interferogram data is generated using a wavelength measurement system, such as the systems 200 and 300 shown in FIGS. 2-3. In some implementations, two interferometers 402A and 402B from two interferometer cavities (e.g., the interferometer cavities 242A and 242B shown in FIG. 2) in a complete spatial intensity profile are spatially separated and captured by a camera (e.g., the camera systems 228 and 322 shown in FIGS. 2-3). In some implementations, the camera can include a two-dimensional (2D) array of image sensors, each of which may be a charge-coupled device (CCD) sensor and a complementary metal-oxide semiconductor (CMOS) sensor. For example, the first interferogram 402A may be captured by a first row of pixels of the camera (e.g., between row 0 and row 180), and the second interferogram 402B may be captured by a second row of pixels of the camera (e.g., between row 420 and row 600). In some embodiments, a subset of the rows of each interferogram is used to determine the interferogram of the corresponding interferogram. As shown in FIG. 4A, the sum of the intensity values ​​of the pixels in the same column of the first subset of rows 404A (e.g., between row 0 and row 180) is used to determine the first intensity curve 406A of the first interferogram 402A. Similarly, the sum of the intensity values ​​of the pixels in the same column of the second subset of rows 404B (e.g., between row 420 and row 600) is used to determine the second intensity curve 406B of the second interferogram 402B. In some embodiments, the camera may include two line sensor arrays oriented in the same direction and separated by a distance to capture two spatially separated interferograms 402A, 402B.

[0046] FIG. 4B presents a plot 410 showing the measured frequency before and after compensation for environmental effects. As shown in FIG. 4, frequency measurements are made using a wavelength measurement system, for example, the prototype system 300 shown in FIG. 3. As shown in FIG. 4, the plot 410 includes six panels, including a first panel 412 showing frequency shift values ​​(Δf) over a time period (6 hours), a second panel 422 showing a probability density over a range of frequency shift values ​​(Δf), and a third panel 430 showing pressure values ​​over the same time period. A fourth panel 432 showing temperature values ​​over the same time period, a fifth panel 434 showing relative humidity over the same time period, and a sixth panel 436 showing calculated refractive index as a function of the measured environmental parameters shown in the third, fourth, and fifth panels 430, 432, and 434. The plot 410 can be obtained by performing a wavelength measurement process, for example, the exemplary process 600 described in FIG. 6.

[0047] In some embodiments, a laser source is used to deliver a laser beam having a wavelength of 1018.62 nm and an optical frequency of 294.52 THz to the optical system via an optical fiber, e.g., optical fiber 328 in Figure 3. The laser source is stabilized throughout the measurement period and locked to an ultra-stable optical resonator with wavelength fluctuations of less than 0.2 fm, e.g., corresponding to frequency fluctuations of less than 100 kHz, much lower than the measurement accuracy that prototype system 300 can provide.

[0048] In some implementations, curve 414 in the first panel 412 of Figure 4 shows the frequency shift (Δf) before compensation for environmental effects on the refractive index. In some embodiments, the refractive index of air at the wavelength of the laser beam, 1018.62 nm, is fixed at a value determined by the initial environmental conditions. As shown in curve 414 and corresponding histogram 424, the uncompensated frequency shift (Δf) values ​​vary significantly between +70 MHz and -35 MHz.

[0049] In some implementations, compensation is performed based on data of environmental parameters collected by environmental sensors during the same time period, as shown in sub-panels 430, 432, and 434. As shown in the third sub-panel 430, the pressure increases from 1014.5 to 1015.5 hPa during the time period between hours 1 and 3, decreases between hours 3 and 5, and eventually reaches a value below 1014.5 hPa at hour 5. Temperature and relative humidity remain constant with visible fluctuations and random noise in the signal, as shown in the fourth and fifth sub-panels 432, 434.

[0050] The data of the environmental parameters are used to correct the refractive index values. The calculated refractive index values ​​as a function of time (shown in the sixth sub-panel 436) show a similar shape with a generally consistent behavior over time, similar to the pressure shown in the third sub-panel 430. As shown in the curve 416 of the first panel 412 of FIG. 4, after correcting the refractive index, the frequency shift (Δf) values ​​are reduced to a range between −5 MHz and +5 MHz with a standard deviation of <2 MHz. As shown in the corresponding histogram 426 of the second panel 424 of FIG. 4, the probability density of the corrected frequency shift (Δf) values ​​shows an approximate Gaussianity with a bandwidth of <2 MHz, which corresponds to a variation of 6 / 109 of the frequency. In some implementations, the methods and techniques presented herein can effectively remove the environmental effects on the wavelength measurement without performing a recalibration process.

[0051] 5 is a flow chart illustrating an example process 500 for calibrating a wavelength measurement system. The example process 500 may be performed, for example, by a wavelength measurement system and a reference laser of known frequency. For example, the operations in the process 500 may be performed or implemented using components in the wavelength measurement systems 100, 200, and 300 shown in FIGS. 1-3 or another type of system. The example process 500 may include additional or different operations, including operations performed by additional or different components, and the operations may be performed in the order shown or in a different order.

[0052] In some implementations, the exemplary process 500 can be performed during an initial setup of a wavelength measurement system. In some implementations, the process 500 can be performed for recalibration purposes when a substantial reconfiguration to the wavelength measurement system occurs, such as after an optical realignment. In some implementations, the exemplary process 500 can be used to determine at least one interferometer length of at least one interferometer of the wavelength measurement system. The exemplary process 500 can also be used to determine a Gaussian envelope parameter or another parameter. In some examples, the at least one interferometer length and the Gaussian envelope parameter can be used in a wavelength measurement process (e.g., process 600 described in connection with FIG. 6) to determine the wavelength of the test laser beam.

[0053] At 502, information of a reference laser beam is provided. In some implementations, information including, for example, the wavelength, frequency, or other parameters of the reference laser beam can be provided by inputting information into the control system. For example, the information with high precision and accuracy can be input into the control system via an input device and stored in the memory of the control system. In some examples, the wavelength of the reference laser beam can be provided by a manufacturer, determined by theoretical calculation, or determined in another manner. In some implementations, the reference laser beam can be used only at 502 of the exemplary process 500. The techniques and systems disclosed herein do not require a permanent reference laser for intermittent recalibration to compensate for long-term drift. In some examples, multiple reference laser beams with different frequencies can be used.

[0054] At 504, an approximate interferometer length is measured. In some implementations, the approximate interferometer length of the interferometer can be measured using a mechanical method, such as a micrometer gauge. In some examples, the micrometer can provide an accuracy of ±10 micrometers (μm). In some examples, the interferometer is implemented as a dual Fizeau interferometer 226 as shown in FIG. 2 or in another manner. In some examples, the approximate interferometer length can be measured at two opposing ends of the dual Fizeau interferometer 226 or anywhere along the interferometer cavity. In some implementations, the difference between the interferometer lengths measured at the two opposing ends that is less than 10 micrometers is caused by the angled second glass piece 240B. In some implementations, the interferometer length measured here is used as a reference value to constrain the fit value in the exemplary process 500. In some examples, step 244 has a height of 390 μm.

[0055] At 506, data from the optics and the environmental sensor is received. The optics may include a camera (or camera system) and two lasers configured to generate respective laser beams. In some implementations, the camera may be configured at the output of a beam splitter (e.g., as shown in Figures 2 and 3), which combines the two laser beams to create one or more interferograms. In some implementations, the data generated by the camera upon detecting one or more interferograms includes interferogram data. In some examples, an environmental sensor is configured proximate to the interferometer to measure an environmental parameter within the cavity of the interferometer. In some examples, the environmental sensor may be implemented as an environmental sensor as shown in Figures 2 and 3, or in another manner. In some examples, the data received from the environmental sensor may include sensor data representing a value of an environmental parameter in the transmission medium, including at least one of temperature, pressure, humidity, and CO2 concentration level. In some implementations, the sensor data is received by a control system and stored in a memory, which may be implemented as the control system 202, 302 as shown in Figures 2 and 3, or in another manner.

[0056] At 508, the refractive index of the transmission medium in the interferometer is calculated. In some implementations, the sensor data received from the environmental sensor can be used to determine the refractive index of the transmission medium (e.g., air) in the cavity of the interferometer. In some implementations, the refractive index can be a function of temperature, pressure, humidity, and wavelength of the reference laser beam. In some implementations, the refractive index can also be a function of the CO2 concentration level in the transmission medium. In some implementations, the refractive index is determined by the control system according to a refractive index calculation algorithm. In some embodiments, the refractive index calculation algorithm can be executed by executing a program stored in the memory of the control system. In some embodiments, the refractive index can be used to determine the optical path length, which is the product of the interferometer length and the refractive index.

[0057] At 510, the interferometer lengths are fitted. In some implementations, the interferometer lengths are determined by fitting a reflected intensity model to the interferogram data received by the camera. For example, the reflected intensity model can be implemented as the reflected intensity models 700A-700C described in connection with FIGS. 7A-7C or in another manner. In some implementations, the interferogram data can include parameters such as phase difference and reflected electric field amplitude for the reflected laser beam (e.g., zeroth, first and second order reflections described in connection with FIGS. 7A-7C) at the inner surface of the interferometer. The geometric parameters of the reflected intensity model can be determined using the known wavelength of the reference laser beam and sensor data received from the environmental sensor. In some implementations, the fitted interferometer lengths are compared to the measured interferometer lengths at 504. In some implementations, the interferometer lengths are fitted with a least squares minimization algorithm. In some instances, the least squares minimization algorithm may use the least chi-square method by minimizing the chi-square function.

[0058] At 512, Gaussian envelope parameters of the reference laser beam are fitted. In some implementations, the Gaussian envelope parameters can be determined by fitting a reflected intensity model to the interferogram data received from the camera. For example, the Gaussian envelope parameters can be determined according to the refractive index, the fitted interferometer length, and the wavelength of the reference laser beam.

[0059] 6 is a flow chart illustrating an example process 600 for performing wavelength measurements. The example process 600 may be performed, for example, by a wavelength measurement system. For example, the operations in the example process 600 may be performed or implemented using components in the wavelength measurement systems 100, 200, and 300 shown in FIGS. 1-3, or another type of system. The example process 600 may include additional or different operations, including operations performed by additional or different components, and the operations may be performed in the order shown or in a different order.

[0060] In some implementations, the exemplary process 600 is performed after a calibration process, which may be performed as the exemplary process 500 described in connection with FIG. 5 or in another manner. In some implementations, prior to performing the exemplary process 600, the test laser beam may be directed to a wavelength measurement system (e.g., the wavelength measurement systems 200, 300 described in connection with FIG. 2 and FIG. 3, respectively).

[0061] At 602, data from optics and environmental sensors is received. In some implementations, the optics and environmental sensors may be configured as shown in Figures 2 and 3 or in another manner. In some examples, operation 602 may be implemented as operation 506 of Figure 5 or in another manner.

[0062] At 604, the refractive index of the transmission medium in the interferometer is calculated. In some examples, operation 604 may be implemented as operation 508 in FIG. 5 or in another manner. In some implementations, the refractive index may be determined using an initial guess for the wavelength of the test laser beam. In some implementations, the initial guess for the wavelength of the test laser beam may be guessed from the number of fringes in the interferogram data received from a camera system of the optical system, may be obtained from previous measurements, or may be obtained in another manner.

[0063] At 606, a first value for the wavelength of the test laser beam is determined using the local optimization model. In some implementations, the interferogram data received from the camera system is fitted according to a reflection intensity model, such as the reflection intensity models 700A-C described in connection with Figures 7A-C. The reflection intensity model can be represented by a function f based on multiple variables, as shown below:

number

[0064] In some implementations, the local optimization mode can be based on a least-squares minimization algorithm. In some examples, the least-squares minimization algorithm can use the minimum chi-square method by locally minimizing a chi-square function defined as follows:

number

[0065] At 608, a second value of the wavelength of the test laser beam is determined using the global optimization model. In some implementations, the second value of the wavelength is the wavelength value at the global minimum of the chi-squared value. In some implementations, the global optimization model is used to determine the global minimum using a cavity-free spectral range that separates the local minimum and adjacent local minima. In some examples, by varying the wavelength according to the cavity-free spectral range, the method allows "hopping" between local minima which further reduces the chi-squared value to efficiently search for the global minimum. In some implementations, the global optimization model can provide a fast, accurate, and reliable approach to determining the true value of the wavelength. In some implementations, a dual Fizeau interferometer with two different interferometer lengths can provide a reliable and efficient fitting of the wavelength. For example, the local minima corresponding to the two different interferometer lengths are separated by an integer multiple of the cavity-free spectral range. In some implementations, the least chi-squared method can be performed on two interferograms created from two corresponding interferometer cavities. In some implementations, the second value of the wavelength obtained during operation 608 can be further used in operation 606 to allow fine tuning the fitting of the true wavelength of the test laser beam. In some implementations, other methods for fitting local or global optimization models can be used.

[0066] In some implementations, the sensor data can be used with a thermal expansion model to compensate for the thermal expansion of the interferometer glass piece. In some implementations, the thermal expansion model can be determined according to the structure and geometry of the interferometer. In some implementations, the thermal expansion model is a linear function of temperature and can be determined using a laser with a known wavelength. In some implementations, the thermal expansion effect is determined prior to the wavelength measurement, as shown in FIG.

[0067] It will be appreciated that a model (e.g., a reflected intensity model) may be used to represent the optical properties of the interferometer. The model may be based on the configuration of the interferometer and can be used to fit data generated by light traversing the interferometer. Examples of interferometers with well-defined configurations include the Michelson interferometer, the Fabry-Perot interferometer, the Twyman-Green interferometer, the Mach-Zehnder interferometer, the Sagnac interferometer, and the Fizeau interferometer. Other types of interferometers are possible. The model can function as part of a process to determine the properties of the light (e.g., the wavelength of the light), such as the models described in connection with the exemplary processes 500, 600 of Figures 5 and 6, respectively.

[0068] 7A-7C show schematic diagrams 700A-700C of exemplary reflected intensity models for a Fizeau interferometer. In some examples, the reflected intensity models of FIGS. 7A-7C are used for wavelength measurements using wavelength measurement systems such as those shown in FIGS. 1-3. In some examples, when a different wavelength measurement system is used, for example, when using a different interferometer such as a Michelson interferometer or a Fabry-Perot interferometer, a different reflected intensity model can be constructed based on ray optics. In each of FIGS. 7A-7C, the schematic diagrams 700A-700C include reference axes defined by the x-axis, y-axis, and z-axis. The x-axis is perpendicular to the schematic diagram, and the positive direction extends in the schematic diagram. The y-axis and z-axis define a plane parallel to the schematic diagrams of FIGS. 7A-7C. In the examples shown in FIGS. 7A-7C, three rays 710, 712, 714 corresponding to the zeroth, first, and second order reflections at two internal air / glass interfaces in the interferometer are evaluated for illustrative purposes. All other rays with higher order reflections may be determined in the same way or in different ways. In some implementations, a similar analysis can be applied to a dual Fizeau interferometer with different interferometer lengths. In some implementations, parameters such as the path length, phase difference, and reflected electric field amplitude of each of the three rays can be determined according to a schematic ray diagram. More sophisticated models based on wave optics can also be used to model the interferometer.

[0069] In the example shown in FIG. 7A, a ray diagram is used to illustrate a specific example. The interferometer in this example is a Fizeau interferometer as shown in FIG. 3, where the first inner surface 708A and the second inner surface 708B are coated with Inconel to provide a reflectivity at each surface of 33%. The first outer surface 708C has a broadband dielectric coating to minimize reflection. The reflectivity of the first outer surface of the interferometer 320 shown in FIG. 3 is less than 0.5% in the wavelength range between 800 and 1100 nm. All three rays 710, 712, 714 are received by a detector, such as the camera system 228 of the wavelength measurement system 200, opposite the first inner surface 708A of the interferometer to create an interferometer. In some implementations, the detector can be located on a detector plane that is spaced from the first inner surface 708A of the interferometer by a distance d720. In some implementations, the distance d720 can include the thickness of the first piece of glass, the beam splitter, and the transmission medium between the detector and the first piece of glass. The distance d can be characterized as a physical distance with a path-dependent refractive index. An exemplary derivation assumes that the refractive index of the gap 704 and d720 is air. When a722 is small and d720 is large, the exiting rays are nearly parallel, and d only introduces a small relative phase shift between the different beams. In general, an infinite number of rays, such as 710, 712, 714, contribute to an interferogram. In many cases, a finite number of rays is sufficient to describe an interferogram. Each reflection introduces some loss, so the contribution of each ray decreases with the number of reflections.

[0070] In some implementations, the evaluation of the reflection of the light beam can be simplified according to certain assumptions. For example, the reflection losses at the first external surface 708C can be ignored by depositing an anti-reflection coating. In some examples, these assumptions can result in small shifts in amounts such as the optical path length difference of the laser beams used to calculate the interferogram. For example, the first piece of glass adds an approximately constant phase difference to all reflected laser beams, which acts as an offset to the value of d720 used.

[0071] In some implementations, the incident laser beam may be a plane wave; TIFF2024099614000008.tif7150 direction, the three rays 710, 712, 714 may have no initial phase difference before reaching the first inner surface 708a. In some examples, the first inner surface 708A lies on the xy plane and the second inner surface 708B lies on the xy plane. It is angled in the xy plane at a wedge angle α722 with respect to the TIFF2024099614000009.tif13150 axis.

[0072] In the example shown in FIG. 7A, the reflectance of the first and second inner surfaces 708A, 708B is expressed by the following equation:

number

[0073] In some implementations, the path length of the first light ray 710 corresponding to the zero-order reflection from the first inner surface 708A is equal to the distance d 720, and the reflected electric field of the first light ray 710 is expressed as:

number

[0074] According to an exemplary diagram 700B of the second light ray 712 shown in FIG. 7B, the distance between the first inner surface 708A and the point at which the second light ray 712 reflects off the second inner surface 708B is The distance e'734 along the TIFF2024099614000013.tif13150 axis can be expressed as follows:

number

[0075] This corresponds to the point on the camera where the second light ray 712 reflects off the second inner surface 708B to interfere with the first light ray 710. The distance △y1742 along the TIFF2024099614000015.tif7150 axis can be expressed as follows:

number

[0076] In the example shown in FIG. 7B, the total path length l1 of the second ray 712 can be determined as follows:

number

[0077] Moreover, the reflected electric field E1 of the second light ray 712 can be calculated as follows.

number

[0078] According to the example ray diagram of the third light ray 714 shown in FIG. 7C, the distance e″ 736 along the Z axis between the first inner surface 708A and the first point where the third light ray 714 reflects off the second inner surface 708B can be expressed as follows:

number

number

number

[0079] Define z=0 to be the first inner surface 708A and use the following equation:

number

[0080] In some implementations, the interferogram can be determined as follows. TIFF2024099614000033.tif7150 Here, I R can be expressed in terms of e, d, α, n, and λ or f. In some implementations, λ is the reflection intensity I R can be determined by the interferometer geometry (e.g., e, d, and α) and the refractive index n.

[0081] In some implementations, the total reflected intensity across the beam can be determined by replacing e in the above equation with e+ytan(α), where y is an array of points representing each pixel on the detector, and multiplying the entire array by a Gaussian envelope function: TIFF2024099614000034.tif13150, where y c ,σ,O are the parameters of the Gaussian envelope. For example, y c , σ, O are respectively the center, 1 / e width and offset (background level) of the Gaussian signal detected on the detector.

[0082] 7A-7C are presented in the context of a Fizeau interferometer, it will be appreciated that other types of interferometers may serve as a basis for determining the reflected intensity model. For example, a Michelson interferometer, a Fabry-Perot interferometer, a Twyman-Green interferometer, a Mach-Zehnder, a Sagnac interferometer, a Fizeau interferometer, or other types of interferometers may serve as a basis for generating the reflected intensity model. Additionally, methods other than ray analysis may be used to generate the reflected intensity model.

[0083] In a first embodiment, the wavelength measurement system includes an interferometer, a camera system, a sensor, and a control system. The interferometer includes two reflective surfaces and a transmission medium between the two reflective surfaces. The interferometer is configured to receive an optical signal from the laser and generate an interferogram in response thereto. The camera system is configured to receive an interferogram from the interferometer and generate interferogram data in response thereto. The interferogram data is representative of the interferogram received from the interferometer. The sensor is configured to sense an environmental parameter of the transmission medium and generate sensor data in response thereto. The sensor data is representative of a value of the environmental parameter. The control system is configured to perform operations including receiving the interferogram data from the camera system and receiving sensor data from the sensor, and calculating a wavelength of the laser based on the interferogram data and the sensor data.

[0084] Implementations of the first embodiment may include one or more of the following features: The interferometer is a Fizeau interferometer. The interferometer includes a first cavity and a second cavity. The first cavity has a first interferometer length and the second cavity has a second interferometer length different from the first interferometer length. The interferogram data includes a spatially dependent intensity profile of the first interferometer produced by the first cavity and the second interferometer produced by the second cavity.

[0085] Implementations of the first embodiment may include one or more of the following features: The camera system includes a photodiode array; The sensor is a temperature sensor, and the sensor data includes data representative of a temperature of the transmission medium; The sensor is a pressure sensor, and the sensor data includes data representative of a pressure of the transmission medium; The sensor is a humidity sensor, and the sensor data includes data representative of a humidity of the transmission medium; The sensor is a carbon dioxide sensor, and the sensor data includes data representative of a concentration of carbon dioxide of the transmission medium; The sensor is a first sensor, the environmental parameter is a first environmental parameter, and the wavelength measurement system includes a second sensor. The second sensor is configured to sense a second environmental parameter of the transmission medium and generate second sensor data in response thereto; The first and second sensors correspond to respective different sensors selected from a group of sensors consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor; The wavelength measurement system includes a third sensor. The third sensor is configured to sense a respective third environmental parameter of the transmission medium and generate third sensor data in response thereto. The first, second, and third sensors correspond to different sensors selected from a group of sensors consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor, and the first, second, and third sensors correspond to different sensors selected from a group of sensors consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor, and the sensor is a temperature sensor, and the wavelength measurement system includes a pressure sensor, a humidity sensor, and a carbon dioxide sensor, respectively, configured to sense respective environmental parameters of the transmission medium.

[0086] Implementations of the first example may include one or more of the following features: the sensor is a first temperature sensor, and the sensor data includes first sensor data representative of a first temperature of the transmission medium; the system includes a second temperature sensor configured to sense a second temperature of the interferometer spacer and generate second sensor data in response thereto; the second sensor data representative of a value of the second temperature; and the operation includes determining a thermal expansion value of the interferometer according to the second sensor data.

[0087] Implementations of a first embodiment may include one or more of the following features: Operations include calibrating a wavelength measurement system using a reference laser prior to receiving interferogram data and sensor data; the interferogram data includes first interferogram data; the laser includes a test laser; the optical signal includes a first optical signal; and the wavelength of the test laser includes a first wavelength. Calibrating the wavelength measurement system includes: receiving interferometer geometric data, receiving second interferogram data from a camera system and sensor data from a sensor, and calculating a first refractive index of a transmission medium based on the sensor data; calculating fitted interferometer lengths of the first and second cavities by performing a least-squares fitting of a reflected intensity model based on the first refractive index and a second wavelength of the reference laser; and calculating Gaussian envelope parameters of the reference laser by performing a least-squares fitting of the reflected intensity model based on the fitted interferometer lengths and the second wavelength of the reference laser. The geometric data includes first and second interferometer lengths and a wedge angle. The second interferogram data is generated by the interferometer based on a second optical signal from a reference laser. The second optical signal is simultaneously injected into the first and second cavities.

[0088] Implementations of the first example may include one or more of the following features: Calculating the wavelength of the test laser includes calculating a second refractive index of the transmission medium based on the sensor data, performing a least-squares fitting of a reflected intensity model based on the fitted interferometer length, the wedge angle, the second refractive index, and a Gaussian envelope parameter, and calculating the first wavelength of the test laser using a global optimization algorithm.

[0089] In a second embodiment, a wavelength measurement method includes receiving an optical signal from a laser and generating an interferogram by an interferometer, receiving the interferogram from the interferometer and responsively generating interferogram data by a camera system, sensing an environmental parameter of a transmission medium and responsively generating sensor data by a sensor, receiving the interferogram data and the sensor data from the camera system by operation of a control system, and wavelength calculating the laser based on the interferogram data and the sensor data. The interferometer includes two reflective interfaces and a transmission medium between the two reflective surfaces. The interferogram data represents the interferogram. The sensor data represents a value of the environmental parameter.

[0090] Implementations of the second embodiment may include one or more of the following features: Generating the interferogram is performed by a Fizeau interferometer. Generating the interferogram comprises generating a first interferogram by a first cavity of the interferometer and generating a second interferogram by a second cavity of the interferometer, the first cavity having a first interferometer length and the second cavity having a second interferometer length different from the first interferometer length.

[0091] Implementations of the second embodiment may include one or more of the following features: Sensing the environmental parameter includes operating a temperature sensor to obtain sensor data including data representative of a temperature of the transmission medium; Sensing the environmental parameter includes operating a pressure sensor to obtain sensor data including data representative of a pressure of the transmission medium; Sensing the environmental parameter includes operating a humidity sensor to obtain sensor data including data representative of a humidity of the transmission medium, and sensing the environmental parameter includes operating the humidity sensor to obtain sensor data including data representative of the humidity of the transmission medium; Sensing the environmental parameter includes operating a carbon dioxide sensor to obtain sensor data including data representative of a concentration of carbon dioxide in the transmission medium; Sensing the environmental parameter includes operating a first sensor to obtain first sensor data; and operating a second sensor to obtain second sensor data. The first and second sensors correspond to different sensors selected from a group of sensors consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor. Sensing the environmental parameter includes operating a third sensor to obtain third sensor data. The first, second, and third sensors correspond to different sensors selected from a group of sensors consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor. Sensing the environmental parameter includes operating a fourth sensor to obtain fourth sensor data. The first, second, third, and fourth sensors correspond to different sensors selected from a group of sensors consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor.

[0092] Implementations of the second embodiment may include one or more of the following features. The method further includes operating a first temperature sensor to obtain first sensor data representative of a value of a first temperature of the transmission medium; and sensing a second temperature of an interferometer spacer of the interferometer by a second temperature sensor. The second temperature sensor is configured to generate second sensor data representative of a value of the second temperature. The method further includes determining a thermal expansion value of the interferometer according to the second sensor data.

[0093] Implementations of the second embodiment may include one or more of the following features: The method further includes performing a calibration using a reference laser prior to receiving the interferogram data and the sensor data; Receiving an optical signal from a laser includes receiving a first optical signal from a test laser; Receiving interferogram data includes receiving first interferogram data; Calculating a wavelength includes calculating a first wavelength of the test laser; Performing a calibration includes receiving interferometer geometric data, receiving second interferogram data from a camera system and sensor data from a sensor, and calculating a first refractive index of a transmission medium based on the sensor data; Calculating fitted interferometer lengths of the first and second cavities by performing a least-squares fitting of a reflected intensity model based on the first refractive index and a second wavelength of the reference laser; and Calculating Gaussian envelope parameters of the reference laser by performing a least-squares fitting of the reflected intensity model based on the fitted interferometer lengths and the second wavelength of the reference laser. The geometric data includes first and second interferometer lengths and a wedge angle. The second interferogram data is generated by the interferometer based on a second optical signal from the reference laser. The second optical signal is simultaneously injected into the first and second cavities. Calculating the first wavelength of the test laser includes calculating a second refractive index of the transmission medium based on the sensor data, performing a least-squares fitting of a reflected intensity model based on the fitted interferometer length, wedge angle, second refractive index, and Gaussian envelope parameters, and calculating the wavelength of the test laser using a global optimization algorithm.

[0094] In some embodiments, the wavelength measurement system described can be illustrated by the following examples. Example 1. A wavelength measurement system, comprising: an interferometer including at least two reflective surfaces and a transmission medium between the reflective surfaces, the interferometer configured to receive an optical signal from a laser and to produce an interferogram in response thereto; a camera system configured to receive the interferogram and in response generate interferogram data representative of the interferogram; a sensor configured to sense an environmental parameter of the transmission medium and in response generate sensor data representative of a value of the environmental parameter; A control system; Including, The control system includes: receiving the interferogram data from the camera system and the sensor data from the sensor; computing a wavelength of the laser based on the interferogram data and the sensor data; and 23. A wavelength measurement system configured to perform operations including: Example 2. The wavelength measurement system of example 1, wherein the interferometer is a Fizeau interferometer. Example 3. A wavelength measurement system as described in Example 2, wherein the interferometer includes a first cavity and a second cavity, the first cavity having a first interferometer length, and the second cavity having a second interferometer length different from the first interferometer length. Example 4. A wavelength measurement system as described in Example 3, wherein the interferogram data includes a spatially dependent intensity profile of a first interferogram generated by the first cavity and a second interferogram generated by the second cavity. Example 5. The wavelength measurement system according to any one of Example 1 or Examples 2 to 4, wherein the camera system includes a photodiode array. Example 6. The wavelength measurement system according to example 1 or any one of examples 2 to 5, wherein the sensor is a temperature sensor, and the sensor data includes data representing a temperature of the transmission medium. Example 7. A wavelength measurement system as described in Example 6, wherein the sensor is a first temperature sensor, the sensor data includes first sensor data representative of a first temperature of the transmission medium, and the system includes a second temperature sensor configured to sense a second temperature of the interferometer and generate second sensor data representative of a value of the second temperature in response thereto. Example 8. The wavelength measurement system of example 7, wherein the operation includes determining a thermal expansion value of the interferometer according to the second sensor data. Example 9. The wavelength measurement system according to example 1 or any one of examples 2 to 8, wherein the sensor is a pressure sensor, and the sensor data includes data representative of a pressure of the transmission medium. Example 10. The wavelength measurement system according to example 1 or any one of examples 2 to 9, wherein the sensor is a humidity sensor, and the sensor data includes data representing the humidity of the transmission medium. Example 11. The wavelength measurement system according to example 1 or any one of examples 2 to 10, wherein the sensor is a carbon dioxide sensor, and the sensor data includes data representing a concentration of carbon dioxide in the transmission medium. Example 12. A wavelength measurement system as described in any one of Example 1 or Examples 2 to 5, wherein the sensor is a first sensor, the environmental parameter is a first environmental parameter, and the wavelength measurement system includes a second sensor configured to sense a second environmental parameter of the transmission medium and generate second sensor data in response thereto, and the first and second sensors correspond to different respective sensors selected from a sensor group consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor. Example 13. The wavelength measurement system of Example 12, wherein the wavelength measurement system includes a third sensor configured to sense a third environmental parameter of each of the transmission media and generate third sensor data in response thereto, and the first sensor, the second sensor, and the third sensor correspond to different respective sensors selected from a group of sensors consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor. Example 14. A wavelength measurement system as described in any one of Example 1 or Examples 2 to 5, wherein the sensor is a temperature sensor, and the wavelength measurement system includes a pressure sensor, a humidity sensor, and a carbon dioxide sensor, each configured to sense a respective environmental parameter of the transmission medium. Example 15. A wavelength measurement system as described in any one of Examples 1 or 2 to 14, wherein the operation includes calibrating the wavelength measurement system using a reference laser prior to receiving the interferogram data and the sensor data. Example 16. The interferogram data includes first interferogram data, the laser includes a test laser, the optical signal includes a first optical signal, and the wavelength of the test laser includes a first wavelength; Calibrating the wavelength measurement system includes: receiving geometric data of the interferometer, the geometric data including the first and second interferometer lengths and wedge angles; receiving second interferogram data from the camera system and the sensor data from the sensor, the second interferogram data being generated by the interferometer based on a second optical signal from the reference laser, the second optical signal being simultaneously incident on the first and second cavities; calculating a first refractive index of the transmission medium based on the sensor data; and calculating fitted interferometer lengths of the first and second cavities by performing a least squares fitting of a reflected intensity model based on the first refractive index and a second wavelength of the reference laser; calculating Gaussian envelope parameters of the reference laser by performing a least squares fitting of a reflected intensity model based on the fitted interferometer length and a second wavelength of the reference laser; 16. The wavelength measurement system of claim 15, Example 17. Calculating the wavelength of the test laser calculating a second refractive index of the transmission medium based on the sensor data; performing a least-squares fitting of the reflected intensity model based on the fitted interferometer length, the wedge angle, the second refractive index, and a Gaussian envelope parameter; calculating a first wavelength of the test laser using a global optimization algorithm; 17. The wavelength measurement system of claim 16, comprising:

[0095] In some embodiments described herein, the wavelength measurement method can be illustrated by the following examples. Example 18. A wavelength measurement method comprising the steps of: receiving an optical signal from a laser and generating an interferogram by operation of an interferometer, the interferometer having at least two reflective interfaces and a transmission medium between the reflective surfaces; receiving an interferogram from the interferometer by operating a camera system and responsively generating interferogram data representative of the interferogram; operating a sensor to sense an environmental parameter of said transmission medium and responsively generate sensor data representative of a value of said environmental parameter; receiving, by operation of a control system, interferogram data from the camera system and sensor data from the sensor; calculating a wavelength of the laser based on the interferogram data and the sensor data; A method comprising: Example 19. The wavelength measurement method according to example 18, wherein the step of generating the interferogram is performed by a Fizeau interferometer. Example 20. The step of generating the interferogram includes generating a first interferogram by a first cavity of the interferometer and a second interferogram by a second cavity of the interferometer; 20. The wavelength measurement method of example 19, wherein the first cavity has a first interferometer length and the second cavity has a second interferometer length different from the first interferometer length. Example 21. A wavelength measurement method as described in any one of Example 18 or Examples 19 to 20, wherein the step of sensing the environmental parameter includes a step of operating a temperature sensor to obtain sensor data including data representative of a temperature of the transmission medium. Example 22. A method for detecting a temperature of a transmission medium, comprising: operating a first temperature sensor to obtain first sensor data representative of a first temperature value of the transmission medium; sensing a second temperature of an interferometer spacer of the interferometer with a second temperature sensor, the second temperature sensor configured to generate second sensor data representative of a value of the second temperature; The wavelength measuring method according to any one of Example 18 or Examples 19 to 20, comprising: Example 23. The wavelength measurement method of example 22, further comprising determining a thermal expansion value of the interferometer according to the second sensor data. Example 24. Calibrating using a reference laser prior to receiving the interferogram data and the sensor data; calculating the wavelength of the test laser using a global optimization algorithm; The wavelength measurement method according to Example 23, comprising: Example 25. A wavelength measurement method as described in Example 18 or any one of Examples 19 to 24, wherein the step of sensing the environmental parameter includes a step of operating a pressure sensor to obtain sensor data including data representative of the pressure of the transmission medium. Example 26. A wavelength measurement method as described in Example 18 or any one of Examples 19 to 25, wherein the step of sensing the environmental parameter includes a step of operating a humidity sensor to obtain sensor data including data representative of humidity of the transmission medium. Example 27. A wavelength measurement method as described in Example 18 or any one of Examples 19 to 26, wherein the step of sensing the environmental parameter includes a step of operating a carbon dioxide sensor to obtain sensor data including data representative of a concentration of carbon dioxide in the transmission medium. Example 28 The step of sensing the environmental parameter includes: operating a first sensor to obtain first sensor data; operating a second sensor to obtain second sensor data; Including, The wavelength measurement method according to any one of Example 18 or Examples 19 to 20, wherein the first and second sensors correspond to different sensors selected from a sensor group consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor. Example 29. The step of sensing the environmental parameter includes a step of operating a third sensor to obtain third sensor data; 29. A wavelength measurement method as described in Example 28, wherein the first sensor, the second sensor, and the third sensor correspond to different sensors selected from a group of sensors consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor. Example 30. The step of sensing the environmental parameter includes a step of operating a fourth sensor to obtain fourth sensor data; 30. The wavelength measurement method of claim 29, wherein the first sensor, the second sensor, the third sensor, and the fourth sensor correspond to different sensors selected from a group of sensors consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor.

[0096] Although the present specification contains many details, these should not be understood as limitations on the scope of what may be claimed, but rather as descriptions of features specific to particular embodiments. Certain features described in this specification or shown in the drawings in the context of separate implementations may also be combined. Conversely, various features described or shown in the context of a single implementation may be implemented in multiple embodiments separately or in any suitable subcombination.

[0097] Similarly, although operations are depicted in the figures in a particular order, this should not be understood as requiring such operations to be performed in the particular order or sequence shown, or to perform all of the operations shown, to achieve desirable results. In certain circumstances, multitasking and parallel processing may be advantageous. Furthermore, the separation of various system components in the embodiments described above should not be understood as requiring such separation in all embodiments, and it should be understood that the program components and systems described may generally be integrated together in a single product or packaged into multiple products.

[0098] Although several embodiments have been described, it will be understood that various modifications are possible and, therefore, other embodiments are within the scope of the following claims. [Explanation of symbols]

[0099] 200 Wavelength Measurement System 202 Control System 204 Optical system 206 Environmental Sensor 212 Reference Laser Source 214 Test Laser Source 216 Optical Switch 218 Lens Assembly 220 First Mirror 222 Beam splitter (BS) 224 Beam Stop 226 Fizeau Interferometer 228 Camera 230A First Input Port 230B Second Input Port 232 output ports 240A First Glass Piece 240B Second piece of glass 242A,B Interferometer Cavity 244 Multilayered section 246B Bottom wedge surface 250 Interferometer Spacer

Claims

1. 1. A wavelength measurement system comprising: an interferometer configured to receive an optical signal from a laser and, in response thereto, generate an output optical signal comprising a first interferogram and a second interferogram, a first pair of reflecting surfaces and a second pair of reflecting surfaces disposed adjacent to each other; a first cavity extending between the first pair of reflecting surfaces and having a first interferometer length, the first cavity being used to generate the first interferogram; a second cavity extending between the second pair of reflecting surfaces and having a second interferometer length different from the first interferometer length, the second cavity being used to generate the second interferogram; and a transmission medium present within the first cavity and the second cavity; an interferometer including: a camera system configured to receive the output light signal and to generate interferogram data in response thereto, the interferogram data representing the first interferogram and the second interferogram; a sensor configured to sense an environmental parameter of the transmission medium in the first cavity and the second cavity and to generate sensor data in response thereto, the sensor being disposed proximate to the first cavity or the second cavity, the sensor data representing a value of the environmental parameter; and 1. A control system comprising: receiving the interferogram data from the camera system and the sensor data from the sensor; determining a refractive index of the transmission medium based on the sensor data and a model of the transmission medium including the environmental parameters; determining first and second correction values ​​for the first and second interferometer lengths, respectively, based on the sensor data and a thermal expansion model of the interferometer that includes the environmental parameters; and calculating a wavelength of the laser based on the interferogram data and the sensor data, the determined refractive index, the first correction value, and the second correction value; a control system configured to perform operations including:

1. A wavelength measurement system comprising:

2. 10. The wavelength measurement system of claim 1, wherein the interferometer is a Fizeau interferometer.

3. 3. The wavelength measurement system of claim 2, wherein the interferogram data includes spatially dependent intensity profiles of a first interferogram produced by the first cavity and a second interferogram produced by the second cavity.

4. The wavelength measurement system according to any one of claims 1 to 3, wherein the camera system includes a photodiode array.

5. 4. The wavelength measurement system according to claim 1, wherein the sensor is a temperature sensor, and the sensor data includes data representing a temperature of the transmission medium.

6. the sensor is a first temperature sensor, and the sensor data is first temperature data representing temperatures of the transmission medium in the first cavity and the second cavity; the wavelength measurement system includes a second temperature sensor configured to sense a temperature of the interferometer and to generate second temperature data in response thereto, the second temperature data representing the temperature of the interferometer; the control system processing includes receiving the second temperature data from the second temperature sensor; The wavelength measurement system of claim 5 , wherein the first correction value and the second correction value are determined based on the second temperature data and a thermal expansion model of the interferometer.

7. 7. The wavelength measurement system of claim 6, wherein the second temperature sensor is in contact with an interferometer spacer of the interferometer, and the temperature of the interferometer is the temperature of the interferometer spacer.

8. 4. The wavelength measurement system according to claim 1, wherein the sensor is a pressure sensor, and the sensor data includes data representing a pressure of the transmission medium.

9. 4. The wavelength measurement system according to claim 1, wherein the sensor is a humidity sensor, and the sensor data includes data representing humidity of the transmission medium.

10. 4. The wavelength measurement system according to claim 1, wherein the sensor is a carbon dioxide sensor, and the sensor data includes data representing a concentration of carbon dioxide in the transmission medium.

11. the sensor is a first sensor, the environmental parameter is a first environmental parameter, and the sensor data is first sensor data; the wavelength measurement system includes a second sensor configured to sense a second environmental parameter of the transmission medium and to generate second sensor data in response thereto, the second sensor being disposed proximate to the first cavity or the second cavity; 4. The wavelength measurement system according to claim 1, wherein the first sensor and the second sensor correspond to different sensors selected from the group consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor.

12. the wavelength measurement system includes a third sensor configured to sense a third environmental parameter of each of the transmission media and to generate third sensor data in response thereto, the third sensor being disposed proximate to the first cavity or the second cavity; 12. The wavelength measurement system of claim 11, wherein the first sensor, the second sensor, and the third sensor correspond to different respective sensors selected from a group of sensors consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor.

13. the sensor is a temperature sensor; the wavelength measurement system includes a pressure sensor, a humidity sensor, and a carbon dioxide sensor, each configured to sense a respective environmental parameter of the transmission medium; The wavelength measurement system according to any one of claims 1 to 3.

14. 4. The wavelength measurement system of claim 1, wherein the operation of the control system includes calibrating the wavelength measurement system using a reference laser before receiving the interferogram data and the sensor data at the control system.

15. the sensor generates reference sensor data in response to the interferometer receiving a reference optical signal from the reference laser; calibrating the wavelength measurement system receiving geometric data of the interferometer, the geometric data including the first and second interferometer lengths and wedge angles; receiving reference interferogram data from the camera system and the reference sensor data from the sensor, the reference interferogram data being generated by the interferometer in response to receiving a reference optical signal from the reference laser, the reference optical signal being simultaneously incident on the first cavity and the second cavity; calculating a reference refractive index of the transmission medium based on the reference sensor data; calculating fitted interferometer lengths of the first cavity and the second cavity by performing a least-squares fitting of a reflected intensity model based on the reference refractive index and a reference wavelength of the reference laser; and calculating Gaussian envelope parameters of the reference laser by performing a least-squares fitting of a reflected intensity model based on the fitted interferometer length and a reference wavelength of the reference laser.

16. Calculating the wavelength of the laser comprises: performing a least-squares fit of the reflected intensity model based on the fitted interferometer length, the wedge angle, the refractive index, and the Gaussian envelope parameters; calculating the wavelength of the laser using a global optimization algorithm; 16. The wavelength measurement system of claim 15, comprising:

17. A wavelength measurement method, comprising: an interferometer configured to receive an optical signal from a laser and responsively generate an output optical signal comprising a first interferogram and a second interferogram by interferometric operation, a first pair of reflecting surfaces and a second pair of reflecting surfaces disposed adjacent to each other; a first cavity extending between the first pair of reflecting surfaces and having a first interferometer length, the first cavity being used to generate the first interferogram; a second cavity extending between the second pair of reflecting surfaces and having a second interferometer length different from the first interferometer length, the second cavity being used to generate the second interferogram; and a transmission medium present within the first cavity and the second cavity; an interferometer including: operating a camera system to receive the output optical signal from the interferometer and responsively generate interferogram data representative of the first interferogram and the second interferogram; operating a sensor to sense an environmental parameter of the transmission medium in the first cavity and the second cavity and to generate sensor data in response thereto, the sensor being disposed proximate to the first cavity or the second cavity, the sensor data representing a value of the environmental parameter; The operation of the control system receiving, at the control system, the interferogram data from the camera system and the sensor data from the sensor; determining a refractive index of the transmission medium based on the sensor data and a model of the transmission medium including the environmental parameters; determining first and second correction values ​​for the first and second interferometer lengths, respectively, based on the sensor data and a thermal expansion model of the interferometer that includes the environmental parameters; and calculating a wavelength of the laser based on the interferogram data and the sensor data, the determined refractive index, the first correction value, and the second correction value; A wavelength measurement method comprising:

18. 18. The wavelength measurement method of claim 17, wherein the interferometer is a Fizeau interferometer.

19. 19. The wavelength measurement method of claim 17 or 18, wherein sensing the environmental parameter comprises operating a temperature sensor to obtain sensor data including data representative of a temperature of the transmission medium.

20. the sensor is a first temperature sensor, and the sensor data is first temperature data representing temperatures of the transmission medium in the first cavity and the second cavity; a second temperature sensor is operated to sense a temperature of the interferometer and responsively generate second temperature data, the second temperature data representing the temperature of the interferometer; receiving the second temperature data from the second temperature sensor at the control system; 19. The wavelength measurement method according to claim 17, wherein the first correction value and the second correction value are determined based on the second temperature data and a thermal expansion model of the interferometer.

21. 21. The wavelength measurement method of claim 20, wherein the second temperature sensor is in contact with an interferometer spacer of the interferometer, and the temperature of the interferometer is the temperature of the interferometer spacer.

22. the interferometer, the camera system, the sensor, and the control system are part of a wavelength measurement system; calibrating the wavelength measurement system using a reference laser prior to receiving the interferogram data and the sensor data at the control system; Calculating the wavelength of the laser includes calculating the wavelength of the laser using a global optimization algorithm; 19. The wavelength measurement method according to claim 17 or 18, comprising:

23. 19. The wavelength measurement method of claim 17 or 18, wherein sensing the environmental parameter comprises operating a pressure sensor to obtain sensor data including data representative of a pressure of the transmission medium.

24. 19. The wavelength measurement method of claim 17 or 18, wherein sensing the environmental parameter comprises operating a humidity sensor to obtain sensor data including data representative of humidity of the transmission medium.

25. 19. The wavelength measurement method of claim 17 or 18, wherein sensing the environmental parameter includes operating a carbon dioxide sensor to obtain sensor data including data representative of a concentration of carbon dioxide in the transmission medium.

26. Sensing the environmental parameter comprises: operating a first sensor disposed proximate to the first cavity or the second cavity to obtain first sensor data; operating a second sensor disposed proximate to the first cavity or the second cavity to obtain second sensor data; Including, 19. The wavelength measurement method according to claim 17, wherein the first sensor and the second sensor correspond to different sensors selected from a group of sensors consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor.

27. sensing the environmental parameter includes operating a third sensor disposed proximate to the first cavity or the second cavity to obtain third sensor data; 27. The wavelength measurement method of claim 26, wherein the first sensor, the second sensor, and the third sensor correspond to different sensors selected from a group of sensors consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor.

28. sensing the environmental parameter includes operating a fourth sensor disposed proximate to the first cavity or the second cavity to obtain fourth sensor data; 28. The wavelength measurement method of claim 27, wherein the first sensor, the second sensor, the third sensor, and the fourth sensor correspond to different sensors selected from a group of sensors consisting of a temperature sensor, a pressure sensor, a humidity sensor, and a carbon dioxide sensor.

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