Dual photoelastic modulators and related methods

Abstract

In one embodiment, a method includes driving a photoelastic modulator optical element with at least two transducers, and control a phase difference between the driving signals applied to the at least two transducers based on a change in the resonant frequency of the photoelastic modulator optical element and a change in the vibration phase delay associated with a change in the temperature of the photoelastic modulator optical element. Related systems and devices are also disclosed.

Description

TECHNICAL FIELD

[0001] The field is photoelastic modulators and photoelastic modulation. BACKGROUND

[0002] A photoelastic modulator is a polarization modulation device that relies on photoelastic strain within an isotropic optical window to change the polarization state of light passing through the optical device. A photoelastic modulator is composed of two main parts: a piezoelectric transducer and an isotropic optical window. Using two piezoelectric transducers can allow for further enhanced operation, for example, as the operation of a rotating waveplate described in K. W. Li, L. M. Wang, R. Zhang, Z. B. Wang, "Modulation axis performs circular motion in a 45° dual-drive symmetric photoelastic modulator" https: / / doi.org / 10.106 3 / 1.4971302 (incorporated herein by reference). However, there remains a need for improved systems as further enhancements and modes of operation exhibit inconsistent operation in different environments or over time. SUMMARY

[0003] By using two piezoelectric transducers arranged at 45 degrees to each other and careful control of system parameters, a photoelastic modulator can be constructed that stably mimics the behavior of a rotating waveplate, or a standard single-transducer photoelastic modulator arranged at an arbitrary angle. The disclosed examples use amplitude and phase control to make these modes of operation robust over a reasonable temperature range.

[0004] The foregoing and other objects, features and advantages of the disclosed technology will be apparent from the following detailed description, which proceeds with reference to the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0005] Figure 1 is a schematic diagram of a photoelastic modulator (PEM) and related operation.

[0006] Figure 2 is a plot of voltage current waveforms at resonance and off-resonance.

[0007] Figure 3 is a plot of measured intensity of a PEM with modulation amplitude of π radians delay.

[0008] Figure 4 is a schematic diagram of a dual PEM example.

[0009] Figure 5is a schematic of a dual PEM with an exemplary drive circuit.

[0010] Figure 6 is a schematic of a dual PEM operating as a rotating waveplate.

[0011] Figure 7 is a plot of detected harmonic power of a dual transducer PEM placed between crossed polarizers.

[0012] Figure 8 is a plot of calibrated system parameter values over a selected temperature range.

[0013] Figure 9 is a plot of phase shift versus frequency for calibration.

[0014] Figure 10 is a schematic of a dual PEM operating with a fixed modulation axis different from the modulation axis along the two transducers.

[0015] Figure 11 is a plot showing adjustment of the modulation axis angle.

[0016] Figure 12 is a schematic of a dual PEM system.

[0017] Figure 13 is a schematic of a multi-transducer PEM system.

[0018] Figure 14 is a schematic of another dual PEM system. DETAILED DESCRIPTION Overview of PEM technology A single transducer photoelastic modulator (PEM) consists of a piezoelectric transducer and an isotropic optical window coupled together. For example, Figure 1 A photoelastic modulator assembly 100 of a PEM is shown, which includes a piezoelectric transducer 102 attached to an optical window 104, which can also be referred to as a photoelastic modulator. A high voltage AC waveform 106 is applied to one side 108 of the transducer. The current through the transducer (return current 110) is monitored to control the frequency and amplitude of the modulation. The high voltage 106 applied to the piezoelectric transducer causes small deformations in the transducer 102 and applies stress onto the optical window 104. As long as the dimensions of the transducer 102 and the optical window 104 are designed to mechanically resonate at the same frequency and are physically coupled to each other, the deformations in the transducer 102 apply strain onto the optical window 104. This strain in turn creates an optical delay through the photoelastic effect. To optimize this resonance, the frequency of the high voltage drive signal 106 should be carefully controlled. Two exemplary ways to achieve this frequency control include analog zero-crossing detection and digital frequency synthesis. In either case, the PEM system, which includes a processor feedback control, operates by adjusting the modulation frequency while using the current 110 through the transducer as a sign of resonance. The resonance frequency can vary continuously with temperature or small changes in mechanical strain that hold the piezoelectric transducer 102 and optical window 104 in place. When using a zero-crossing detection driver, these changes in the resonance frequency can be tracked. When using digital frequency synthesis, the drive frequency is continuously varied to maintain a constant phase relationship between the drive voltage waveform and the return current waveform. During initial calibration of many PEM examples, the modulation frequency of the high voltage signal 106 is adjusted so that the current 110 through the modulator is maximized. Then, the control electronics are used to measure the phase difference between the drive voltage signal 106 and the return current signal 110. In an ideal example, this difference would be zero. In a real example, a delay in the electronics or other system delays will result in a non-zero phase difference being measured. During normal operation, the PEM controller will continuously measure this voltage-current phase relationship. When the voltage-current phase relationship changes significantly (e.g., beyond a selected threshold), the PEM controller will begin adjusting the drive frequency of the PEM (e.g., the frequency of the high voltage drive signal 106) in order to readjust the voltage-current phase difference back to the calibrated phase difference. This can maintain the PEM at its resonance frequency as temperature changes. Figure 2 This principle is further depicted. Referring to the voltage 202 and ideal current signal 204, at the resonance frequency, the phase difference between the drive high voltage 106 and the current 110 through the transducer 102 will be zero under ideal conditions. Also, the current 110 through the transducer 102 will be maximized at the resonance peak of the PEM assembly 100. At off-resonance, as shown with the current signal 206, the current through the transducer 102 will be reduced and the phase difference between the drive voltage 106 and the return current 110 will be increased. Under non-ideal conditions, due to delays in the electronics and mechanical phase delays, the detectable phase difference between the current 110 and the drive voltage 106 will not exactly be zero at the resonance peak. Despite these additional non-ideal delays, the current 110 through the transducer will still be maximized at resonance. This allows the digital system to calibrate the optimal resonance phase regardless of the non-ideal phase difference between the voltage and current caused by factors such as electronic delays, cable length, etc. To control the amplitude of the modulation, one can simply increase the amplitude of the drive voltage 106. Higher drive voltages result in a linear increase in the delay amplitude. Since the resonance frequency shifts due to temperature, a convenient method to vary the modulation amplitude is to carefully monitor and control the amplitude of the current 110 through the transducer 104 while maintaining a constant phase difference between the voltage 106 and the current 110. This ensures a linear relationship between the current 110 flowing through the modulator and the induced maximum delay of the light propagating through the optical window 104. The change in delay is not generally directly observable. Instead, the photoelastic modulator is typically placed between two polarizing filters, the light passes through all of the optics, and is detected at the end with an appropriate intensity detector. As shown in FIG. 1, depending on the relative angles of the polarizers and the photoelastic modulator, the resulting waveforms will be either a sine or cosine of the delay. Figure 3 Figure 3 The measurable sine 302 and cosine 304 intensity terms of a photoelastic modulator with a modulation amplitude of π radians of delay 306 are shown. The detected intensity depends on the sample being measured and the arrangement of optical components. Typically, the detected intensity of a single PEM placed between polarizing filters will be in the form of Equation 1. In Equation 1, δ is the instantaneous delay, ω is the phase velocity, which is 2π times the frequency, and δ 0 is the static delay of the optical window, which is typically taken to be zero. The constant coefficients DC , Y and X depend on the optical arrangement of the system, and I is the intensity as a function of time. For simplicity, a specific optical layout is now adopted, which consists of two crossed linear polarizers placed around a photoelastic modulator. In this arrangement, the ideal intensity equation is given by Equation 2. The waveforms generated by photoelastic modulators are typically analyzed using a lock-in amplifier, which can demodulate the signal amplitude at harmonics of the base frequency. The waveforms generated by photoelastic modulators are not simple sine or cosine waveforms, and therefore the Jacobi-Anger expansion is used to scale the measured amplitude of each harmonic. ​Accordingly, the Jones-Angele expansion shows that a single photoelastic modulator will produce a signal not only at the first harmonic of the modulation, but at all higher harmonics as well. Proper scaling of the measured harmonic amplitudes can be difficult, and the presence of additional harmonics is not intuitive. In addition to using the Jones-Angele expansion, a single photoelastic modulator is used to modulate the polarization of light along only one axis. In order to measure the entire Stokes vector of the light or the entire Mueller matrix of a sample, multiple photoelastic modulators must be placed in the optical path. Given these two factors, the disclosed examples can address these difficulties and deficiencies by using a multi-PEM system (i.e., multiple transducers) on a single optical window. Figure 4 One such example is shown using two transducers ("dual-PEM"). In Figure 4 The dual-PEM assembly 400 includes a first transducer 402 and a second transducer 404 configured to induce strain in the attached optical window 410 along respective modulation axes 406, 408. Each transducer 402, 404 is labeled with the angle at which the strain is induced. Operating each transducer 402, 404 in turn is the simplest mode of operation for such a photoelastic modulator. In this way, the modulator can act as a standard photoelastic modulator arranged at zero or forty-five degrees. While this trivial case can seem unnecessary, using a single optical window 410 in the optical path provides several advantages over multiple optical devices; for example, a smaller and lighter optical system with fewer components, less back-reflection, and no need to physically rotate the PEM to measure the entire Stokes vector or Mueller matrix. Dual transducer PEM Driving both modulators simultaneously can provide at least two different modes of operation; a rotating waveplate and an arbitrary angle modulation. However, in these modes of operation, non-ideal modulation behavior can lead to application complexity. While the dual-transducer PEM provides substantially greater flexibility in its operation, with this flexibility comes additional complexity. In a photoelastic modulator, the strain induced by the piezoelectric transducer directly leads to the optical retardation of interest. With the addition of another transducer, another set of phase retardations must also be tracked. Figure 5An exemplary dual PEM 500 is shown, highlighting the different phase delays that can be taken into account in order to properly manipulate the behavior of the induced delays. The dual PEM 500 includes a first transducer 502 and a second transducer 504 configured to vibrate along respective axes 506, 508 and thereby induce strain in the attached photoelastic optical element 510. A drive square wave 512 generated by a controller is converted into a high voltage sine wave 514 using a resonant LLC circuit 516. The example shown is used here to illustrate a first source of phase delay within the system and is not intended to be exhaustive, as it should be understood that the high voltage waveform can be generated in a variety of ways. Since each transducer 502, 504 has its own set of electronics, the phase delay induced by the electronics will be close but not identical, and thus should be taken into account in actual operation. This can correspond to the drive electronics phase delay. After the drive square wave 512 has been converted into a high voltage sine wave 514, the high voltage signal will induce acoustic oscillations in the piezoelectric transducers due to the piezoelectric effect. This acoustic oscillation will also take time to propagate into the optical window 510, where the acoustic strain will induce the delay of interest. The acoustic delay between the two transducers will be similar but not identical. In the following, this acoustic phase delay will be α A and α B which will be referred to as the vibration phase delay, and is the quantity of interest, as the phase relationship between the acoustic waves will determine the optical behavior of the modulator. The electronics phase delay can be addressed to a large extent by actively monitoring the high voltage signal and comparing it to the known drive signal. The vibration phase delay can be monitored via a change in the polarization of the light beam sent through the optical window. Since changing the polarization state of the light beam is the purpose of the device, continuously monitoring this signal can be largely counterproductive. Instead, the difference in the vibration phase delay between the two transducers can be addressed by a calibration prior to operation. In some examples, an alternative to calibration may include placing a piezoelectric sensor on the distal side of the optical window. A piezoelectric sensor is a piezoelectric transducer in which vibrations of the optical window are converted back into an alternating voltage. This signal can then be measured and used to actively monitor changes in the phase delay of the vibrations. However, placing a piezoelectric sensor on the optical window suppresses oscillations and introduces additional changes in the resonant frequency, which is undesirable. Thus, calibration is generally preferred over active monitoring, although both are applicable according to the disclosed techniques. In other examples, alternative detection paths (e.g., from a separate light source) may be used, and a detection path through the PEM optical window 510 can be used to verify the operation or modulation of the dual PEM 500 (e.g., using the method described in US 6,867,863, granted to Kadlec, which is incorporated herein by reference), and thus can be used to calibrate the performance or operation of the dual PEM 500. Using a separate detection path can be an alternative to using a piezoelectric sensor on the distal side of the optical window, thereby eliminating the disadvantages associated with attaching a piezoelectric transducer. At the resonant frequency, current flows through the transducer and can be monitored by control electronics. An additional delay exists in the detection of this current. Ideally, at resonance, the phase delay between the voltage applied to the transducer and the current flowing through it would be zero. In reality, as mentioned above, a small phase delay exists, for example, due to the electronics required to convert the current through the transducer into a measurable voltage. This current-to-voltage phase delay is also a calibration quantity. Any phase change between the current and voltage flowing through the transducer at PEM resonance can be used as a signal to adjust the modulation frequency in order to maintain the ideal resonant frequency. The strain induced in an isotropic optical window using two transducers is shown in Equation 3. In equation 3, P A and P B It is the amplitude of the stress wave that is proportional to the drive voltage of each transducer. α A and α B It is a vibration phase delay. ɸ It is the angular spatial position in polar coordinates, where, π / 4 represents the angle difference between the two transducers, and It is the controlled phase difference of the transducer. This generates three effective control parameters; the phase difference between the AC waveforms. and the modulation amplitude of each transducer P A andP B Vibration phase delay cannot usually be directly controlled, but it can be addressed by adjusting the controllable phase difference. In this way, the difference in vibration phase delay can be reduced to a single variable, as shown in the following equation. Rotating waveplate operation By setting the modulation amplitude of each transducer to be equal, And adjust the phase delay so that the delay is changed from Given that the equation for a dual transducer waveplate can be simplified to the case of a rotating waveplate as given below. In this mode, the controller adjusts the phase delay and drive voltage of each axis of the PEM to match the conditions described above. When these conditions are met, the delay of the optical window remains constant in time, but the angle of this delay rotates continuously. Figure 6 A double PEM 600 is depicted as a rotating waveplate operation, wherein the delay remains constant in time while the angle of the delay rotates at twice the fundamental frequency of the PEM. The matching of drive voltage and phase delay can be tested by placing a dual transducer modulator (e.g., dual PEM 400, 500, 600) between cross polarizers and adjusting the phase delay and drive voltage ratio while measuring the harmonic amplitudes of the modulation frequency. For example, for a 50 kHz dual transducer PEM between cross polarizers, the amplitudes of the 50 kHz (1F) harmonic, 150 kHz (3F) harmonic, and 200 kHz (4F) harmonic should be zero, while the amplitude of the 100 kHz (2F) harmonic should be maximized. Figure 7 The graph 700 shows the results of this optimization across a temperature range. As shown, the temperature 702 of the dual transducer modulator is controlled from 2°C to 40°C, and at each temperature, the phase delay and drive ratio are adjusted to maximize the amplitude of the 2F harmonic 704 while minimizing the amplitudes of the 1F harmonic 706, 3F harmonic 708, and 4F harmonic 710. The harmonic power is detected at 633 nm using a dual transducer PEM placed between cross polarizers. It should be understood that calibration can also be performed in other temperature ranges, which may be smaller, larger, and / or centered on other temperatures, including negative temperatures. As examples, ranges may include -10°C to 60°C, 5°C to 30°C, -40°C to 80°C, etc. Typically, the calibrated temperature range corresponds to the range in which operation may occur, which can be determined by the environment. For example, the temperature variation in a space or outdoor environment may be much greater compared to a laboratory facility or factory. Figure 8It shows the use of Figure 6 The graph 800 shows the optimized system parameters for the rotating waveplate operation. These two system parameters are the drive ratio 802 and the phase delay 804, where the drive ratio 802 remains largely constant throughout the temperature range, while the phase delay 804 varies significantly with temperature. The system parameters were obtained through calibration performed at two temperature ramps from 2°C to 40°C. The drive ratio 802 is the voltage ratio of each axis of the PEM, and the phase delay 804 is the phase difference in the AC waveform of each transducer. The change in phase delay is caused by α A and α B Caused by changes, α A and α B This is the vibration phase delay when adjusting the temperature of the PEM. The linear relationship between the temperature of the PEM and the resonant frequency takes into account the mapping between the resonant frequency and the necessary adjustment of the phase shift. Figure 9 The graph 900 illustrates such a mapping over a selected temperature range of 2°C to 40°C. This mapping between frequency and phase shift can then be fed into the controller responsible for driving the PEM. As the resonant frequency changes, the controller can automatically adjust the phase delay between the transducers to maintain optimal operation. Alternative modulation axis operation In addition to operating the dual-transducer PEM as a rotating waveplate, each axis of the modulator can be simply disabled. This allows for baseline single-transducer operation, which enables the dual-transducer PEM to operate as PEMs arranged at zero or forty-five degrees. In another operating mode, the power of each modulator can be adjusted by matching the phase delay between the modulators to the vibration phase delay, allowing the dual-transducer PEM to operate as PEMs arranged at arbitrary angles. Figure 10 As described, the dual transducer modulator 1000 is driven by a phase delay to address vibration delay, and the voltage is adjusted on each axis of the modulator to allow modulation along any selectable angle. For example, it should be understood that the dual PEM may have this operating mode, with or without the rotating waveplate mode discussed above. The modulation angle can be set by adjusting the voltage, and thus the strain induced along each axis of the modulator. Using Equation 3 above, and taking into account the difference in vibration phase delay, it is possible to... And specify the power on each axis of the modulator as and ,in, PNow a calibrated constant ratio is used to obtain the same strain caused by each PEM, and the angle of the modulation axis can be adjusted between the two nominal modulation axes provided by the respective transducers. Using Equation 3 above, and expressing the strains caused along 0° / 90° and 45° / 135° as two separate components, the equation can be rewritten as follows. By selecting the ratio of the drive voltage directed to each PEM and adjusting the phase delay to eliminate vibration delay, the modulation axis can be shifted at any position between transducers arranged at zero degrees and transducers arranged at 45 degrees. In experiments confirming arbitrary angle selection, dual transducers (PEMs) were placed between cross-polarizers, which were aligned at zero degrees. Harmonic amplitude data were then collected over an angular range from 0 to 180 degrees to demonstrate the expected behavior of maximum modulation at a given angle, and zero modulation when the cross-polarizers were aligned at 45° to the maximum modulation angle. For example, Figure 11 Graph 1100 shows the adjustment of the axis angle. It shows the harmonic power of two runs to illustrate the shift along the modulation axis by adjusting the drive voltage of each modulator. Harmonic power can be collected while the cross polarizer is rotated around the dual PEM transducers, with harmonic data collected at each angle. If the phase delay is not set correctly, the modulation amplitude will not be zero at 45 degrees from the maximum modulation position. Conversely, a considerable amplitude will still exist at 45 degrees from the maximum modulation angle. Under this uncalibrated condition, a hybrid behavior exists where the PEM delay never reaches zero during PEM cycling, and the operating mode becomes a mixture of rotating waveplates and PEMs arranged at arbitrary angles. Therefore, in each case, proper phase delay between modulators and the drive voltage ratio of each PEM must be maintained very carefully. A calibration can be generated by measuring the appropriate phase delay and power ratio over a wide temperature range, mapping the modulation frequency to the optimal phase delay and drive ratio to maintain stable operation with temperature fluctuations. Selected applications Some exemplary dual or multi-PEM systems and methods may involve or provide Stokes vector measurements. A Stokes vector is a complete description of coherent and incoherent light. Measuring the Stokes vector of light includes the total intensity of the light being measured, the amount of light polarized along 0° / 90° and 45° / 135°, and the amount of light with circular polarization, whether left- or right-handed. To measure the Stokes vector of light, any operating mode utilizing a dual-transducer PEM can be used, but each mode has a different set of equations used to solve for the Stokes vector. Using the disclosed multi-transducer PEM as a rotating waveplate, the Stokes vector of the incident light can be solved as follows: Compared to rotating waveplates, PEMs provide a superior polarization modulator for Stokes polarization measurements. The significantly higher "rotation" frequency of the dual-transducer PEM allows for the use of a lock-in amplifier, which can collect more oscillations each time and reduce the signal-to-noise ratio. In fact, optimal delay for a rotating waveplate-based Stokes polarimeter requires a fully achromatic waveplate with a 90° delay. The disclosed dual-transducer PEM polarimeter allows for continuous adjustment of the delay to enable optimal measurement of the incident light. The complexity that can arise with a rotating waveplate Stokes polarimeter is that the total intensity component consists of the DC component of the signal and the proportional cosine of the rotating fourth harmonic. One of the most important components of concern to most users of Stokes polarimeters is the total polarization factor. The total polarization factor is defined as follows. When measuring a polarization factor close to 1, the contribution of the rotating fourth harmonic to the measured intensity introduces errors, which significantly contribute to the measured total polarization factor in the presence of linearly polarized light Q along 0° / 90°. Here, it is advantageous to use a dual-transducer PEM and a dual detector (where the polarizers are each arranged at 0° and 45°). Alternatively, a single polarizer can be rotated to 0° and 45°. For such a polarimeter, the PEM first oscillates at 45°, with the polarizer at 0° used for detection, and then the PEM operates at 0°, with the polarizers arranged at 0°. This method of detecting the Stokes vector avoids any contribution of the measured harmonics to the measurement of the total intensity, and therefore the measured total polarization factor avoids errors from other polarization components. A highly complex series of equations were generated using a Miller polarimeter with a rotating waveplate having arbitrary rotation speed (“Absolute Mueller Polarimeters Based on Dual-Rotating Imperfect Retarders and Arbitrary Ratio of Angular Velocities”, Gil, Dynamics 2023, 3(2), 250-271, https: / / doi.org / 10.3390 / dynamics3020015 (This is incorporated herein by reference), where the measurement of each Miller matrix element depends on the measurements of many harmonic components. The need to measure multiple frequency components of each Miller matrix element leads to significantly larger errors and artifacts. Here, using a dual-transducer PEM as a PEM arranged at arbitrary angles also brings similar advantages to the Stokes vector case, since the measurement of each Miller matrix element comes directly from a single frequency component. Furthermore, very similar to the Stokes polarimeter case, the rotating waveplate Miller polarimeter has a specific delay at each wavelength to obtain optimal measurements. In the case of the Miller polarimeter, the optimal delay is a highly non-standard 126° delay. Achromatic waveplates with this delay must be custom-made. The dual-transducer PEM avoids this complexity by simply adjusting its delay according to the needs of each wavelength. In other examples, exemplary multi-PEM systems and methods may involve or provide polarization scramblers. Dual-transducer PEMs are particularly well-suited for applications involving polarization perturbation. Since many intensity detectors exhibit polarization sensitivity (i.e., the detector is more sensitive to one polarization of light than another), perturbing the polarization state of light in an optical system can reduce the overall signal-to-noise ratio by more effectively “averaging” the polarization state. Polarization perturbation typically utilizes the rapid modulation of the polarization state of a beam. This modulation can be accomplished using a range of methods. A common application is a purely fiber-based solution where an electro-optic crystal acts as a polarization modulator to rapidly and randomly change the polarization state of light passing through the fiber. In free-space applications, for large beams, electro-optic crystals are limited by their useful aperture and high cost. For these free-space applications, PEMs coupled with additional polarization optics have been used to modulate polarization states, as in Illing (“Design and development of the PolZero Time Domain Polarization Scrambler”, Illing, Proceedings Volume 7461, Polarization Science and Remote Sensing IV; 746104 (2009). https: / / doi.org / 10.1117 / 12.826217 The additional polarizing optics applied by Illing allow the PEM to modulate the polarization of light along both the 0° and 45° axes. As an alternative to additional static polarizing optics, polarization perturbation can be achieved by placing a pair of PEMs in the optical path; one at 0° and one at 45°. Dual-transducer PEMs eliminate the need for these additional optics. Dual-transducer PEMs effectively scramble the polarization state of light in both directions, producing, for example, a time-domain polarization scrambler, and the precise calibration of the PEM becomes significantly less critical. The reduction in weight, reflective surfaces, and number of components required using such PEMs makes them particularly suitable for space- or weight-constrained applications (e.g., aerospace). Additional examples Figure 12 An exemplary dual PEM system 1200 is illustrated, comprising a PEM assembly 1202, which itself includes a first transducer 1204 and a second transducer 1206. The first transducer 1204 and the second transducer 1206 are coupled to a photoelastic optical element 1208 and configured to vibrate the photoelastic optical element 1208 along respective first modulation axes 1210 and second modulation axes 1212. System 1200 can be used in a variety of polarization measurement applications, which typically involve modulating the polarization characteristics of input light. Examples of dual PEMs are described in U.S. Patent Nos. 11,054,672 and 11,686,957, which are incorporated herein by reference. System 1200 and other disclosed systems may include various components of the systems described herein, although generally without asymmetrical element lengths. In a representative embodiment, the first modulation axis 1210 and the second modulation axis 1212 extend at a 45-degree angle relative to each other. A first transducer 1204 and a second transducer 1206 are coupled to a dual PEM optics element 1208 to vibrate the dual PEM optics element 1208 along the respective first modulation axis 1210 and second modulation axis 1212. The dual PEM system 1200 also includes a controller 1214 coupled to the transducers 1204 and 1206 to control the timing and frequency of the transducer vibrations of the dual PEM optics element 1208 along the first modulation axis 1210 and the second modulation axis 1212. The timing and frequency of the transducer vibrations along the first modulation axis 1210 and the second modulation axis 1212 can be controlled independently of the other of the first modulation axis 1210 and the second modulation axis 1212, allowing the dual PEM system 1200 to operate in multiple modes. The controller 1214 is also coupled to a detector (not shown) to receive signals associated with detected modulated beams. During operation, one or both of modulation axes 1210 and 1212 can be vibrated to produce photoelastic modulation of the dual PEM optical element 1202. In some examples, one of the first transducer 1204 and the second transducer 1206 can operate without the other, such that one of the first modulation axis 1210 and the second modulation axis 1212 is active while the other is inactive. In other examples, the dual PEM system 1200 can provide a rotating waveplate mode 1216, wherein the phase and drive voltage relationship is controlled such that the photoelastic optical element effectively operates as a rotating waveplate. In other operating modes, the dual PEM system 1200 can provide a selection 1218 of an effective axis mode that differs from the axis angle of the first modulation axis 1210 or the second modulation axis 1212. In many examples, the dual PEM system 1200 can be configured to provide a selectable amount of delay based on a selectable PEM operating setpoint 1220. In representative examples, different modes can provide stable operation over a temperature range based on calibration data 1222 (e.g., a lookup table), which associates applied frequency adjustments with phase and drive voltage adjustments. In some examples, feedback from detected optical data or from an additional transducer configured to operate as a detector can be used to provide mode operation. Controller 1214 may include a computing environment having one or more processors 1224 and memory 1226. In some examples, processor 1224 may be configured based on a reduced or complex instruction set computing architecture and may include one or more general-purpose central processing units, application-specific integrated circuits, graphics or coprocessor units, or other processing units. In many examples, the computing environment may be distributed as a separate processor and / or other computing or controller device communicating with the computing environment of the dual PEM system 1200 or one or more other components, including one or more FPGAs, PLCs, PLDs, CPLDs, PALs, ASICs, PLLs, control logic, relays, detectors, amplifiers, digitizers, etc. Memory 1226 may be volatile memory (e.g., registry, cache, RAM), non-volatile memory (e.g., ROM, EEPROM, flash memory, etc.), or a combination of volatile and non-volatile memory. Memory 1226 is generally accessible to processor 1224 and may store software in the form of computer-executable instructions that can be executed by processor 1224 coupled to memory 1226. The memory 1226 may also include removable or non-removable memory (including magnetic media, CD-ROM, DVD) or any other medium that can be used to store information in a non-transitory manner and can be accessed within a computing environment. In a typical example, memory 1226 may store instructions, data arrays, lookup tables (e.g., calibration data 1222), etc., for implementing one or more method steps and algorithms described herein. For example, controller 1214 may adjust the transducer drive frequency and / or phase to provide operating modes 1216, 1218 based on calibration data. In some examples, control and adjustment may be provided or supplemented based on signals received from one or more (optical and / or electrical) detectors, one or more lock-in amplifiers, etc. In some examples, the characteristics of the detected light may be correlated based on, for example, Miller matrix calculations to determine Stokes polarization measurement parameters Q, U, and V. In some examples, dual PEM system 1200 may include one or more translation and / or rotary stages coupled to one or more components (e.g., analyzer, waveplate, sample container, etc.). Controller 1214 may include a rotation / translation controller coupled to the translation and / or rotary stage to command the corresponding translation and / or rotary stage to move. The overall structure of the dual PEM system 1200 and its various operating modes eliminate the need for angular adjustments to the actual angles of the photoelastic optical element 1208 or the first modulation axis 1210 and the second modulation axis 1212, which are positioned relative to each other at a fixed angular orientation. However, in some examples, the dual PEM assembly 1202 can be rotated as needed. In some examples, the controller 1214 may include a waveform digitizer capable of sampling and capturing a waveform or a portion of a waveform associated with the modulated beam. In some examples, the controller 1214 may include or be coupled to a display configured to display one or more waveforms or PEM data associated with operation. Figure 13 An exemplary PEM system 1300 is provided, configured to provide a stable, selectable modulation axis operating mode 1302 and / or a stable rotating waveplate operating mode 1304. The PEM system 1300 includes a photoelastic optical element 1306 and a plurality of coupled transducers (including at least a second transducer 1308). To provide stable operation in modes 1302, 1304, the PEM system 1300 includes a temperature (frequency) versus vibration phase delay map 1310 and a temperature (frequency) versus drive ratio map 1312, which may contain different data for different maps. During operation, the PEM system 1300 may provide a controllable phase shift 1314 for a voltage signal 1316 applied to transducer 1308 and a controllable voltage amplitude 1318 for the voltage signal 1316 based on maps 1310, 1312, the selected operating mode, and other system parameters (e.g., a user-selected delay setpoint, sensed current, applied frequency, etc.). Figure 14This is an exemplary dual PEM system 1400. In various examples, the dual PEM system can be configured to provide a temperature-stable selective modulation axis mode 1402 and / or a stable rotating waveplate mode 1404. The dual PEM system 1400 includes a photoelastic optical element 1406, wherein a first transducer 1408 and a second transducer 1410 are coupled to the photoelastic optical element 1406. The first transducer 1408 and the second transducer 1410 each receive separate voltage drive signals 1412, 1414, which cause the first transducer 1408 and the second transducer 1410 to vibrate in response, and thus vibrate the photoelastic optical element 1406. The drive signals 1412, 1414 are shaped by voltage amplitude adjustments 1416, 1418, frequency adjustments 1420, 1422, and a controllable phase shift 1424 of at least one of the two transducers (e.g., transducer 1410). The dual PEM system 1400 may include a first current sensor 1426 and a second current sensor 1428 that measure the current characteristics of the first and second transducers when the first transducer 1408 and the second transducer 1410 are driven using voltage signals 1412, 1414. During operation, the first transducer 1408 may be driven at a delayed, selectable setpoint, resulting in a selected amplitude target for the adjustable voltage amplitude 1416. A drive current setpoint comparison 1430 may be used to compare the sensed current with the setpoint of the first transducer 1408. In response to the comparison, the drive voltage 1412 may be adjusted to maintain it within an error range. The frequency of the voltage signal 1412 can be controllably adjusted to maintain suitable drive characteristics over time (e.g., with temperature fluctuations). For example, the measured current-voltage phase difference 1432 can be compared with a calibrated phase difference / offset 1434 associated with the first transducer 1408 to controllably adjust the frequency using frequency adjustment 1420. The calibrated phase offset comparison 1434 can also be used to adjust the frequency of the voltage signal 1414 using frequency adjustment 1422. The second transducer 1410 can also be controlled based on current sensing 1428 and a drive current setpoint. Voltage amplitude adjustment 1418 can operate in response to a drive current setpoint comparison 1436. For different operating modes, such as when the temperature varies within a predetermined range, the frequency-drive ratio map 1438 can be used to adjust the drive current setpoint adjustment 1440. The drive current setpoint adjustment 1440 of the second transducer can be partially based on the current sensing 1426 of the first transducer 1408. The drive ratio map 1438 can be based on selected operating modes 1402, 1404, phase calibration data 1442, and drive ratio calibration data 1444. In the stable selectable modulation axis mode 1402, an angle selection value 1446 is provided to the drive ratio map 1438 to command the corresponding effective modulation axis. For each mode, the voltage signal 1414 is adjusted using different vibration phase delay maps 1448 in conjunction with the controllable phase offset 1424. Generalities As used in this application and claims, the singular forms “a,” “an,” and “the” include the plural forms unless the context clearly specifies otherwise. Furthermore, the term “comprising” means “including.” Additionally, the term “coupled” does not exclude the presence of intermediate elements between coupled items. The systems, apparatuses, and methods described herein should not be construed as limiting in any way. Rather, this disclosure relates to all novel and non-obvious features and aspects of the various disclosed embodiments, including their individual forms and forms presented in various combinations and sub-combinations with each other. The disclosed systems, methods, and apparatuses are not limited to any particular aspect or feature or combination thereof, nor are they required to have any one or more particular advantages or problems solved. Any operational theory is provided for ease of interpretation, but the disclosed systems, methods, and apparatuses are not limited to such operational theory. Although some operations of the disclosed methods are described in a specific order for ease of presentation, it should be understood that this descriptive approach encompasses rearrangement unless the specific language used below requires a particular order. For example, operations described sequentially may be rearranged or performed simultaneously in certain situations. Furthermore, for simplicity, the accompanying drawings may not show the various ways in which the disclosed systems, methods, and apparatus can be used in conjunction with other systems, methods, and apparatuses. Additionally, the specification sometimes uses terms such as "produce" and "provide" to describe the disclosed methods. These terms are high-level abstractions of the actual operations performed. The actual operations corresponding to these terms will vary depending on the specific implementation and are readily discernible to those skilled in the art. In some examples, values, processes, or devices are referred to as “lowest,” “best,” “smallest,” etc. It should be understood that such descriptions are intended to indicate that there are many functional alternatives to choose from, and that this choice does not need to be better, smaller, or more preferred than other choices. By describing and illustrating the principles of the disclosed technology with reference to the illustrated embodiments, it will be appreciated that modifications can be made to the illustrated embodiments in terms of arrangement and details without departing from these principles. For example, elements of the illustrated embodiments shown in software may be implemented in hardware, and vice versa. Furthermore, techniques from any example may be combined with techniques described in any one or more other examples. It should be understood that processes and functions such as those described with reference to the illustrated examples may be implemented in a single hardware or software module, or may be provided as separate modules. For ease of illustration, the specific arrangement structure described above is provided, and other arrangement structures may be used. Given the many possible embodiments to which the principles of the disclosed technology can be applied, it should be understood that the illustrated embodiments are merely representative examples and should not be considered as limiting the scope of this disclosure. The alternatives specifically presented in these sections are merely exemplary and do not constitute all possible alternatives to the embodiments described herein. For example, various components of the system described herein can be combined in function and use. Therefore, we claim protection for all contents within the scope of the appended claims.

Claims

1. A method comprising: At least two transducers are used to drive the optical elements of the photoelastic modulator. as well as The phase difference between the drive signals applied to the at least two transducers is controlled based on the change in the resonant frequency of the photoelastic modulator optical element and the change in the vibrational phase delay associated with the temperature change of the photoelastic modulator optical element.

2. The method as described in claim 1, wherein, The control of the phase difference includes: The phase difference is adjusted to compensate for the temperature-dependent vibration phase delay difference between the at least two transducers.

3. The method as described in claim 1, wherein, Controlling the phase difference includes adjusting the phase difference to cause the photoelastic modulator optics to operate as a rotating waveplate.

4. The method of claim 1, wherein, The method further includes controlling the amplitude ratio of the drive signal in response to the changing vibration phase delay.

5. The method of claim 4, wherein, The adjustment of the phase difference of the drive signal and the control of the relative amplitude of the drive signal are configured to cause the photoelastic modulator optical element to operate as a rotating waveplate, thereby producing a time-constant optical delay with a continuously rotating angle.

6. The method of claim 4, wherein, The control of the phase difference and amplitude ratio is configured to generate an effective modulation axis between the angles of the respective modulation axes of the at least two transducers.

7. The method of claim 1, wherein, The drive is configured to generate optical depolarization or temporal polarization perturbation.

8. The method of claim 1, wherein, The method also includes detecting light modulated by the driven optical element of the photoelastic modulator.

9. An apparatus comprising: At least two transducers are coupled to a photoelastic modulator optics element and configured to drive the photoelastic optics element. and A controller, coupled to the at least two transducers and configured to control the operation of the at least two transducers using corresponding drive signals, wherein the controller is configured to control the phase difference between the drive signals applied to the at least two transducers based on a change in the resonant frequency of the photoelastic modulator optics and a change in the vibrational phase delay associated with a temperature change of the photoelastic modulator optics.

10. The device as claimed in claim 9, wherein, The controller is configured to control the phase difference, the control of the phase difference including adjusting the phase difference to compensate for variations in temperature-dependent vibration phase delay difference between the at least two transducers.

11. The device as claimed in claim 9, wherein, The controller is configured to control the phase difference, the control of the phase difference including adjusting the phase difference to cause the photoelastic modulator optics to operate as a rotating waveplate.

12. The device as claimed in claim 9, wherein, The controller is configured to control the amplitude ratio of the drive signal in response to the changing vibration phase delay.

13. The device as claimed in claim 12, wherein, The controller is configured to adjust the phase difference and control the relative amplitude of the drive signal, such that the photoelastic modulator optical element operates as a rotating waveplate, thereby producing a time-constant optical delay with a continuously rotating angle.

14. The device as claimed in claim 12, wherein, The controller is configured to control the phase difference and amplitude ratio to generate an effective modulation axis between the angles of the respective modulation axes of the at least two transducers.

15. The device as claimed in claim 11, wherein, The operation is configured to generate optical depolarization or temporal polarization perturbation.

16. The device as claimed in claim 9, wherein, The device also includes an optical detector configured to detect light modulated by the driven optical elements of the photoelastic modulator.

17. A computer-readable medium comprising stored processor-executable instructions configured to cause a controller to: Using at least two transducers to drive the optical elements of a photoelastic modulator; and The phase difference between the drive signals applied to the at least two transducers is controlled based on the change in the resonant frequency of the photoelastic modulator optical element and the change in the vibrational phase delay associated with the temperature change of the photoelastic modulator optical element.

18. The computer-readable medium of claim 17, wherein, The control of the phase difference includes: The phase difference is adjusted to compensate for the temperature-dependent vibration phase delay difference between the at least two transducers.

19. The computer-readable medium of claim 17, wherein, Controlling the phase difference includes adjusting the phase difference to cause the photoelastic modulator optics to operate as a rotating waveplate.

20. The computer-readable medium of claim 17, wherein, The stored processor-executable instructions are also configured to cause the controller to control the amplitude ratio of the drive signal in response to the changing vibration phase delay.

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