Dual photoelastic modulators and related methods

Abstract

Methods include driving a photoelastic modulator optical element with at least two transducers and controlling a phase difference between driving signals applied to the at least two transducers based on a variation in resonant frequency of the photoelastic modulator optical element and a variation in vibrational phase delay associated with a change in temperature of the photoelastic modulator optical element. Related system and apparatus are also disclosed.

Description

[0001] DUAL PHOTOELASTIC MODULATORS AND RELATED METHODS

[0002] FIELD

[0003] The field is photoelastic modulators and photoelastic modulation.

[0004] BACKGROUND

[0005] 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 optic. Photoelastic modulators are built from two primary parts: a piezoelectric transducer and an isotropic optical window. Use of two piezo transducers can allow further enhancements to operation, such as operation as a rotating waveplate as described in “Modulation axis performs circular motion in a 45° dual-drive symmetric photoelastic modulator” K. W. Li, L. M. Wang, R. Zhang, Z. B. Wang https: / / doi.org / 10.1063 / 1.4971302” (incorporated herein by reference). However, a need remains for improved systems as further enhancements and operational modes exhibit inconsistent operation in different environments or over time.

[0006] SUMMARY

[0007] By using two piezo transducers aligned at 45 degrees to one another and carefully controlling system parameters, a photoelastic modulator can be built that stably imitates the behavior of a rotating waveplate, or a standard single transducer photoelastic modulator aligned at an arbitrary angle. Disclosed examples use amplitude and phase control to make these modes of operation robust over a reasonable temperature range.

[0008] The foregoing and other objects, features, and advantages of the disclosed technology will become more apparent from the following detailed description, which proceeds with reference to the accompanying figures.

[0009] BRIEF DESCRIPTION OF THE DRAWINGS

[0010] FIG. l is a schematic of a photoelastic modulator (PEM) and associated operation.

[0011] FIG. 2 is a graph of voltage current waveforms at-resonance and off-resonance.

[0012] FIG. 3 is a graph of measured intensities for a PEM with a modulation amplitude of TI radians of retardance.

[0013] FIG. 4 is a schematic illustration of a dual-PEM example.

[0014] FIG. 5 is a schematic illustration of a dual-PEM with example driving circuits.

[0015] FIG. 6 is a schematic illustration of a dual-PEM operating as a rotating waveplate. FIG. 7 is a graph of detected harmonic power of a dual transducer PEM placed between cross polarizers.

[0016] FIG. 8 is a graph of calibrated system parameters values over a selected temperature range.

[0017] FIG. 9 is a graph of phase offset vs. frequency for calibration.

[0018] FIG. 10 is a schematic illustration of a dual -PEM operating with a fixed modulation axis different from the modulation axes along the two transducers.

[0019] FIG. 11 is a graph illustrating adjustment of modulation axis angle.

[0020] FIG. 12 is a schematic of a dual-PEM system.

[0021] FIG. 13 is a schematic of a multi -transducer PEM system.

[0022] FIG. 14 is a schematic of another dual-PEM system.

[0023] DETAILED DESCRIPTION

[0024] Overview of PEM Technology

[0025] A single transducer photoelastic modulator (PEM) consists of a piezotransducer and an isotropic optical window coupled together. For example, FIG. 1 shows a photoelastic modulator assembly 100 of a PEM that includes a piezo transducer 102 attached to an optical window 104, which also can 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 is monitored (return current 110) to control the frequency and amplitude of modulation. The high voltage 106 applied to the piezoelectric transducer causes a small deformation of the transducer 102 and imparts stress onto the optical window 104. So long as both the transducer 102 and optical window 104 are sized to mechanically resonate at the same frequency and physically coupled to one another, the deformation in the transducer 102 imparts a strain onto the optical window 104. This strain in turn produces optical retardation through the photoelastic effect.

[0026] In order to optimize this resonance, the frequency of the high voltage driving signal 106 should be carefully controlled. Two example ways of accomplishing this frequency control include analog zero crossing detection and digital frequency synthesis. In either case, the PEM system (which includes processor feedback controls) operates by adjusting the frequency of modulation while using the current 110 passing through the transducer as an indicator of resonance.

[0027] The resonant frequency can continually change with small changes in temperature or the mechanical strain holding the piezotransducers 102 and optical windows 104 in place. These changes in resonant frequency can be tracked when using a zero-crossing detection driver. When using digital frequency synthesis, the driving frequency is continuously changed to maintain a constant phase relationship between the driving voltage waveform and the return current waveform. During the initial calibration of many PEM examples, the frequency of modulation of the high voltage signal 106 is adjusted so that the current 110 passing through the modulator is maximized. Then, the control electronics are used to measure the phase difference between the driving voltage signal 106 and the return current signal 110. In an ideal example, this difference will be zero. In practical examples, delays in the electronics or other system delays will result in a non-zero phase difference being measured. During normal operation, a PEM controller will continually measure this voltage-current phase relationship. When the voltage-current phase relationship changes substantially (e.g., past a selected threshold), the PEM controller will start to adjust the PEM's driving frequency (e.g., the frequency of the high voltage driving signal 106) in order to readjust the voltage-current phase difference back to the calibrated phase difference. This can maintain the PEM at its resonant frequency with temperature changes.

[0028] FIG. 2 further depicts this principle. With reference to the voltage and ideal current signals 202, 204, at the resonant frequency, the phase difference between the driving high voltage 106 and the current 110 passing 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. Off resonance, as shown with current signal 206, the current passing through the transducer 102 will diminish and the phase difference between the driving voltage 106 and return current 110 will increase.

[0029] In the non-ideal case, the detectable phase difference between the current 110 and the drive voltage 106 will not be exactly zero at the resonance peak due to delays in the electronics and the mechanical phase delay. The current 110 passing through the transducer will still be maximized at the resonance regardless of these additional non-ideal delays. This allows for a digital system to calibrate the optimal resonance phase regardless of the non-ideal phase difference between the voltage and current caused by factors like electronic delays, cable lengths, etc.

[0030] To control the amplitude of modulation, the amplitude of the driving voltage 106 can simply be increased. A higher driving voltage induces a linear increase in the amplitude of the retardance. Due to temperature induced shifts in resonance frequency, a convenient way to change the amplitude of modulation is to carefully monitor and control the amplitude of the current 110 passing through the transducer 104 while maintaining a constant phase difference between the voltage 106 and current 110. This can ensure a linear relationship between the current 110 passing through the modulator and the induced maximum retardation on light propagating through the optical window 104.

[0031] The changes in retardance are generally not directly observed. Instead, the photoelastic modulator is generally placed between two polarization filters, light is passed through all the optics, and detected at the end with a suitable intensity detector. As shown in FIG. 3, depending upon the relative angles of the polarizers and the photoelastic modulator, the waveform produced will be the sine or cosine of the retardation. FIG. 3 shows the measurable sine and cosine intensity terms 302, 304 for a photoelastic modulator with a modulation amplitude of TI radians of retardance 306.

[0032] The detected intensity depends on the sample under test and the arrangement of the optical components. In general, the detected intensity for a single PEM placed between polarization filters will take the form of Equation 1.

[0033] In Equation 1, 0 is the instantaneous retardance, co is the phase velocity which is 2TI times the frequency, and do is the static retardance of the optical window often taken as zero. The constant coefficients, DC, Y and X depend upon the optical arrangement of the system, and I is the time varying intensity.

[0034] For the sake of simplicity, we will now assume a specific optical path composed of two crossed linear polarizers placed around a photoelastic modulator. In this arrangement, the ideal intensity equation is given by Equation 2.

[0035] The waveform generated from a photoelastic modulator is often analyzed using a lock-in amplifier which can demodulate the amplitude of a signal at a harmonic of a base frequency. The waveform generated by a photoelastic modulator is not a simple sine or cosine waveform, and so the Jacobi-Anger expansion is used to scale the measured amplitudes at each harmonic. The Jacobi-Anger expansion thereby dictates that a single photelastic modulator will give rise to signals at not only the 1st harmonic of modulation, but all higher harmonics. Proper scaling of the measured harmonic amplitudes can be difficult and the presence of additional harmonics is not intuitive. In addition to the use of the Jacobi-Anger expansion, a single photoelastic modulator only acts to modulate the polarization of light along one axis. In order to measure a complete Stokes vector of light or a complete Mueller matrix of a sample, multiple photoelastic modulators must be placed in the optical path. In view of these two factors, disclosed examples can address these difficulties and deficiencies through the use of multi-PEM systems, i.e., multiple transducers on a single optical window. One such example using two transducers (“dual-PEM”) is illustrated in FIG. 4.

[0036] In FIG. 4, a dual-PEM assembly 400 includes first and second transducers 402, 404 configured to induce strain along respective modulation axes 406, 408 in an attached optical window 410. Each transducer 402, 404 is labeled with the angle at which strain is induced. Operating each transducer 402, 404 in turn is the simplest operating mode for such a photoelastic modulator. As such, the modulator can act as a standard photoelastic modulator aligned at zero degrees or forty-five degrees. While this trivial case may seem needless, the use of a single optical window 410 as opposed to multiple optics in the beam path offer several advantages; such as smaller and lighter optical systems, with fewer components, less back reflections, and no need to physically rotate the PEM to measure the complete Stokes vector or Mueller matrix.

[0037] Dual-transducer PEMs

[0038] Driving both modulators simultaneously can offer at least two distinct modes of operation; rotating waveplate and arbitrary angle modulation. However, practical complications arise from non-ideal modulation behavior in these operating modes. While the dual transducer PEM offers substantially more flexibility in its operation, along with this flexibility comes additional complexity. In a photoelastic modulator, the strain induced by the piezotransducers is directly responsible for the optical retardance of interest. With the addition of another transducer, there are also another set of phase delays that need to be tracked.

[0039] FIG. 5 shows an example dual-PEM 500 highlighting the different phase delays that can be considered in order to properly manipulate the behavior of the induced retardance. The dual-PEM 500 includes first and second transducers 502, 504 configured to vibrate along respective axes 506, 508 and thereby cause strain in an attached photoelastic optical element 510. A driving square wave 512 generated by a controller is transformed into a high voltage sine wave 514 using a resonant LLC circuit 516. The example shown serves here to illustrate a first source of phase delay within the system and is not meant to be exhaustive, as it will be appreciated that high voltage waveforms can be generated in many ways. As each transducer 502, 504 has its own set of electronics, the phase delay induced by the electronics will be close but not identical and so should be accounted for in practical operation. This can correspond to a driving electronics phase delay.

[0040] After the driving square wave 512 has been transformed into the high voltage sine wave 514, the high voltage signal will induce an acoustic oscillation in the piezotransducer due the piezoelectric effect. This acoustic oscillation will also take time to propagate into the optical window 510 where the acoustic strain will result in the retardance of interest. This acoustic delay will be similar but not identical between the two transducers. In the text below, this acoustic phase delay will be OA and which will be called the vibrational phase delay, and is a quantity of interest as the phase relationship between the acoustic waves will dictate the optical behavior of the modulator.

[0041] The electronic phase delay can largely be accounted for by actively monitoring the high voltage signal and comparing that signal to the known driving signal. The vibrational phase delay can be monitored via the changes in polarization of an optical beam sent through the optical window. As changing the polarization state of an optical beam is the purpose of this device, continuously monitoring this signal can be largely self-defeating. Instead, the difference in vibration phase delay between the two transducers can be accounted for by calibration prior to operation.

[0042] In some examples, an alternative to calibration can include the placement of a piezo-sensor on a far side of the optical window. A piezo-sensor is a piezo-transducer where the vibrations of the optical window are turned back into an alternating voltage. This signal can then be measured and used to actively monitor the changes in vibrational phase delay. However, the placement of a piezo sensor on the optical window can dampen the oscillations and induce additional changes in the resonant frequency, which may be undesirable. Thus, calibration is generally preferred over active monitoring, though each may be suitable in accordance with the disclosed technology. In further examples, an alternative detection path can be used, e.g., from a separate light source and detection path through the PEM optical window 510, can be used to confirm operation or modulation of the dual-PEM 500 (e.g., using the approaches described in US 6,867,863 to Kadlec, which is incorporated by reference herein) and therefore can be used to calibrate performance or operation of the dual-PEM 500. Using a separate detection path can be an alternative to using a piezo-sensor on the far side of the optical window, thereby eliminating downsides associated with attaching piezo-sensors. At the resonance frequency, current will pass through the transducer and can be monitored by control electronics. There also can be an additional delay in the detection of this current. At resonance, the ideal phase delay between the voltage applied to the transducer and the current passing through the transducer would be zero. In reality, as discussed above, there is a small phase delay, e.g., due to the electronics needed to convert the current passing through the transducer into a measurable voltage. This current to voltage phase delay is also a calibrated quantity. As the PEM resonates, any changes in the phase between the current and voltage passing through the transducer can be used as a signal to adjust the frequency of modulation in order to maintain the ideal resonance frequency.

[0043] With two transducers, the strain induced in the isotropic optical window is shown in Equation 3.

[0044] In Equation 3, PA and PB are the amplitudes of the stress wave which are proportional to the drive voltage of each transducer, O and O are the vibrational phase delay, <[) is the angular space position in polar coordinates with TT / 4 representing the angular difference between the two transducers, and (o is the controlled phase difference of the transducers.

[0045] This yields three effective parameters of control; the phase difference between the AC waveforms, (o, and the amplitude of modulation for each transducer, PA and PB. The vibrational phase delay generally cannot be directly controlled but it can be accounted for by adjusting the controllable phase difference. In this fashion, the difference in vibrational phase delay can be reduced to one variable as in the following equation.

[0046] Rotating Waveplate Operation

[0047] By setting the amplitude of modulation of each transducer to be equal, , and adjusting the phase delay such that the delay is given by, , the dual transducer waveplate equation can be simplified to the case of a rotating waveplate given below. P = 2P. A?" A-A ± 2^>)

[0048] In this mode, the controller adjusts the phase delay and the drive voltage for each axis of the PEM to match the above conditions. When these conditions are met, the retardance of the optical window remains constant in time, but the angle of this retardation rotates continuously. FIG. 6 depicts a dual-PEM 600 operating as a rotating waveplate in which the retardance remains constant in time while the angle of the retardance rotates at twice the fundamental frequency of the PEM.

[0049] A drive voltage and phase delay match can be tested by placing the dual transducer modulator, such as dual-PEM 400, 500, 600, between crossed polarizers and adjusting the phase delay and drive voltage ratio while measuring the amplitude of the harmonics of the modulation frequency. For instance, with a 50kHz dual transducer PEM between crossed polarizers, the amplitude of the 50kHz (IF), 150kHz (3F), and 200kHz (4F) harmonics should be zero while the 100kHz (2F) harmonic should be maximized.

[0050] FIG. 7 is a graph 700 of results of such an optimization across a temperature range. As shown, a 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 is adjusted in order to maximize the magnitude of the 2F harmonic 704 while the IF, 3F and 4F magnitudes 706, 708, 710 are minimized. The harmonic power was detected with the dual transducer PEM being placed between cross polarizers at 633nm. It will be appreciated that calibrations can occur over other temperature ranges as well, which may be smaller, larger, and / or centered on other temperatures (including negative ones). By way of example, ranges can include -10 °C to 60 °C, 5 °C to 30 °C, -40 °C to 80 °C, etc. In general, calibrated temperature ranges can correspond to ranges over which operation may occur, which can be determined by the environment. For example, a space-based or outdoor environment may have considerably larger temperature variation than a lab facility or factory.

[0051] FIG. 8 shows a graph 800 of optimized system parameters for the rotating waveplate operation shown in FIG. 6. The two system parameters are the drive ratio 802 which largely stays constant across the whole temperature range, and the phase delay 804 which varies significantly with temperature. The system parameters are found for the calibration between 2 °C and 40 °C over two temperature ramps. The drive ratio 802 is the ratio of voltages to each axis of the PEM, and the phase offset 804 is the phase difference in the AC waveform to each transducer.

[0052] The change in phase delay arises from the change in OCA and an which are the vibrational phase delays as the temperature of the PEMs is adjusted. The linear relationship between the temperature of the PEM and the resonant frequency allows for a mapping between the frequency of resonance and the necessary adjustment of the phase offset. One such mapping throughout the selected temperature range of 2 °C and 40 °C is shown in the graph 900 in FIG. 9. This map between frequency and phase offset can then be loaded 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.

[0053] Selectable Modulation Axis Operation

[0054] In addition to the operational mode of using a dual transducer PEM as a rotating waveplate, each axis of the modulator can simply be disabled. This allows baseline single-transducer operation which allows the dual transducer PEM to operate as a PEM aligned at zero degrees or at forty-five degrees. In a further mode of operation, by having the phase delay between the modulators match the vibrational phase delay, the power to each modulator can be adjusted to allow the dual transducer PEM to operate as a PEM aligned at an arbitrary angle. As depicted in FIG. 10, a dual transducer modulator 1000 is driven with a phase delay to account for a vibrational delay, and the voltage is adjusted at each axis of the modulator to allow for modulation along an arbitrary selectable angle. It will be appreciated, for example, that dual PEMs can have such a mode of operation with or without a rotating waveplate mode discussed previously.

[0055] The angle of modulation can be set by adjusting the voltage and hence the strain induced along each axis of the modulator. In taking Equation 3 from above and accounting for the difference in vibrational phase delay such that =°, and assigning the power at each axis of the modulator to be = cos(2S)F and Pe= s (2e)F where P is now a calibrated constant ratio to attain the same strain induced by each PEM, the angle of the axis of modulation can be adjusted between the two nominal modulation axes provided by the respective transducers.

[0056] Taking Equation 3 from above and denoting the induced strain along 0° / 90° and 45° / 135° as two separate components, the equation can be rewritten as given below.

[0057] By choosing the ratio of drive voltage directed to each PEM and tuning the phase delay to cancel the vibrational delay, the modulation axis can be shifted anywhere between the transducer aligned at zero degrees to the transducer aligned at 45°.

[0058] In an experiment confirming arbitrary angle selection, the dual transducer PEM is placed between crossed polarizers with the crossed polarizers aligned at zero. Then harmonic amplitude data is collect at a range of angles between zero and 180 degrees to illustrate that the modulation has the expected behavior of maximum modulation at a given angle, and zero modulation when the crossed polarizers are aligned at forty five degrees away from the angle of maximum modulation. For example, FIG. 11 is a graph 1100 showing adjustment of modulation axis angle. Harmonic power is shown for two runs to illustrate the shift in modulation axis by adjusting the driving voltage to each modulator. The power of the harmonics can be collected while rotating crossed polarizers around the dual PEM transducer, with harmonic data being collected at each angle.

[0059] If the phase delay is not set correctly, the amplitude of modulation will not be zero at forty five degrees away from the maximum modulation position. Instead, there will still be a significant magnitude at the forty five degree position to the maximum modulation. In this miscalibrated condition, there is a mixed behavior where the retardation of the PEM never reaches zero during the PEM cycle and the mode of operation becomes a mix of a rotating waveplate and a PEM aligned at an arbitrary angle. Hence, in each case, great care must be taken to maintain the appropriate phase delay between the modulators and the ratio of driving voltage to each PEM. By measuring the appropriate phase delay and power ratio across a wide temperature range, a calibration can be generated that maps the frequency of modulation to the optimal phase delay and drive ratio in order to maintain stable operation as temperature fluctuates.

[0060] Selected Applications

[0061] Some example dual- or multi-PEM systems and methods can relate to or provide Stokes vector measurement. The Stokes vector is a complete description of both coherent and incoherent light. Measuring the Stokes vector of light involves measuring the overall intensity of light, the amount of light polarized along 0790° and 457135°, and the amount of left or right handed light with circular polarization.

[0062] To measure the Stokes vector of light, either mode of operation with the dual transducer PEM can be used, but each mode has a different set of equations used to solve for the Stokes vector. Using disclosed multi-transducer PEMs as a rotating waveplate, the Stokes vector of incident light can be solved as given below:

[0063]

[0064] The PEM can offer a superior polarization modulator for Stokes polarimetry as compared to a rotating waveplate. The much higher frequency of “rotation” of a dual transducer PEM allows for the use of lock-in amplifiers that can collect many more oscillations per time and lower the signal to noise. In practical terms, the optimal retardance of a rotating waveplate-based Stokes polarimeter requires a perfectly achromatic waveplate at 90° of retardance. Disclosed dual transducer PEM polarimeters can continuously adjust retardance to allow for optimal measurement of the incident light.

[0065] A complication that can arise with a rotating waveplate Stokes polarimeter is that the overall intensity component is composed of both the signal’s DC component and the scaled cosine of the fourth harmonic of rotation. One of the most important components of interest for most users of a Stokes polarimeter is the total polarization factor. The definition of total polarization factor is given below.

[0066] When measuring the polarization factor near unity, the contribution of the fourth harmonic of rotation to the measured intensity can result in errors that contribute significantly to the measured total polarization factor in the presence of linearly polarized light along 0790°, Q. Here, the use of a dual transducer PEM and dual detectors with a polarizer each aligned at 0° and 45° can be advantageous. Alternatively to dual detectors, 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° for detection, and then the PEM operates at 0° with the polarizer aligned at 0°.

[0067] Such methods of detecting the Stokes vector can avoid any contribution of the measured harmonics to the measurement of the overall intensity, and hence the measured total polarization factor can avoid errors from other polarization components.

[0068] Mueller polarimeters using rotating waveplates with arbitrary rotation speeds generates a highly complex series of equations (“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, incorporated by reference herein ) where the measurement of each Mueller matrix element depends on the measured values of many harmonic components. The need to measure multiple frequency components for each Mueller matrix element results in significantly larger errors and artifacts. Here, using a dual transducer PEM as a PEM aligned at an arbitrary angle also brings a similar advantage as the Stokes vector case, since each Mueller matrix element measurement results directly from a single frequency component. Also, much like the Stokes polarimeter case, a rotating waveplate Mueller polarimeter has a specific retardance at each wavelength for optimal measurements. For the Mueller polarimeter case, the optimal retardance is a highly non-standard 126° of retardance. Achromatic waveplates with such a retardance must be custom made. Dual transducer PEMs can avoid this complication by simply adjusting their retardance as needed for each wavelength.

[0069] In further examples, example multi-PEM systems and methods can relate to or provide polarization scramblers. The dual transducer PEM is particularly well-suited to the application of polarization scrambling. As many intensity detectors exhibit polarization sensitivity (i.e., a detector being more sensitive to one polarization of light than another), scrambling the polarization state of light in an optical system can lower the overall signal to noise by more effectively “averaging” the polarization state. Polarization scrambling typically leverages a rapid modulation of the polarization state of a beam. This modulation can be accomplished in a range of methods. One common application is purely fiber-based solutions where an electro-optic crystal acts as a polarization modulator to rapidly and randomly alter the polarization state of light passing through a fiber optic. In free space applications, electro-optic crystals can be limited by their useful aperture and high cost for large beams. For these free space applications, PEMs coupled with extra polarization optics have been used to modulate the polarization state, as in tiling (“Design and development of the PolZero Time Domain Polarization Scrambler,” Uling, Proceedings Volume 7461, Polarization Science and Remote Sensing IV; 746104 (2009), https: / / doi.org / 10. 1117 / 12,826217, incorporated by reference). The extra polarization optics applied by tiling allows the PEM to modulate the polarization of light along both the 0° and 45° axis. Alternatively to extra static polarization optics, polarization scrambling can be accomplished by placing a pair of PEMs in the optical path; one at 0° and one at 45°.

[0070] A dual transducer PEM can eliminate the need for these extra optics. The dual transducer PEM can effectively scramble the polarization state of light in both directions creating, for example a time domain polarization scrambler, and the precise calibration of the PEM can become significantly less important. The reduction in weight, reflective surfaces, and number of components required with such a PEM makes it particularly well-suited in applications areas that are space or weight-constrained, such as aeronautics and space.

[0071] Additional Examples

[0072] FIG. 12 shows an example dual -PEM system 1200 that includes a PEM assembly 1202 itself including first and second transducers 1204, 1206 coupled to a photoelastic optical element 1208 and configured to vibrate the photoelastic optical element 1208 along respective first and second modulation axes 1210, 1212. The system 1200 can be used for various polarimetric applications which typically involve modulating polarization characteristics of input light. Dual PEM examples are described in U.S. Patents No. 11,054,672, and 11,686,957, which are incorporated by reference herein. The system 1200 and other disclosed systems can include various components of systems described therein though typically without asymmetric element lengths.

[0073] In representative embodiments, the first and second modulation axes 1210, 1212 extend at 45 degrees with respect to each other. First and second transducers 1204, 1206 are coupled to the dual PEM optical element 1208 so as to vibrate the dual PEM optical element 1208 along the respective first and second modulation axes 1210, 1212. The dual-PEM system 1200 further includes a controller 1214 that is coupled to the transducers 1204, 1206 so as to control the timing and frequency of the transducer vibration of the dual PEM optical element 1208 along the first and second modulation axes 1210, 1212. The timing and frequency of the transducer vibration of the first and second modulation axis 1210, 1212 can be controlled independently from the other of the first or second modulation axis 1210, 1212 so that the dual-PEM system 1200 can operate in various modes. The controller 1214 is also coupled to the detector (not shown) so as to receive a signal associated with a detected modulated beam.

[0074] During operation, one or both of the modulation axes 1210, 1212 can be vibrated to produce a photoelastic modulation of the dual PEM optical element 1202. In some examples, one of the first and second transducers 1204, 1206 can operate without the other so that one of first and second modulation axes 1210, 1212 is effective while the other is not. In further examples, the dual -PEM system 1200 can provide a rotational waveplate mode 1216 in which the phase and driving voltage relationship is controlled so that the photoelastic optical element effectively operates as a rotating waveplate. In a further mode of operation, the dual -PEM system 1200 can provide selection of an effective axis mode 1218 that is different from the axis angle of the first or second modulation axes 1210, 1212. In many examples, the dual-PEM system 1200 can be configured to provide a selectable amount of retardance based on selectable PEM operational setpoints 1220. In representative examples, the different modes can provide stable operation over a temperature range based on calibration data 1222, such as a look-up table, relating applied frequency adjustments to phase and driving voltage adjustments. In some examples, feedback from detected optical data or additional transducers configured to operate as detectors can be used to provide mode operation.

[0075] The controller 1214 can include a computing environment having one or more processors 1224 and memories 1226. In some examples, the processor 1224 can be configured based on reduced or complex instruction set computing architectures, and can include one or more general purpose central processing units, application specific integrated circuits, graphics or co-processing units or other processing units. In various examples, the computing environment can be distributed in the form of separate processors and / or other computing or controller devices in communication with one or more other components of the computing environment or dual-PEM system 1200, including one or more FPGA, PLC, PLD, CPLD, PAL, ASIC, PLL, control logic, relay, detector, amplifier, digitizer, etc. The memory 1226 can be volatile memory (e.g., registers, cache, RAM), non-volatile memory (e.g., ROM, EEPROM, flash memory, etc.), or a combination of volatile and non-volatile memory. The memory 1226 is generally accessible by the processor 1224 and can store software in the form of computer executable instructions that can be executed by the processor 1224 coupled to the memory 1226. The memory 1226 can also include removable or non-removable storage including magnetic media, CD-ROMS, DVDs, or any other medium that can be used to store information in a non-transitory way and which can be accessed within the computing environment. In typical examples, the memory 1226 can store instructions, data arrays, look-up tables (such as calibration data 1222), etc., implementing one or more method steps and algorithms described herein. For example, the controller 1214 can adjust transducer driving frequency and / or phase to provide operational modes 1216, 1218 based on calibration data. In some examples, control and adjustment can be provided or supplemented based on signals received from one or more detectors (optical and / or electrical), one or more lock-in amplifiers, etc. In some examples, characteristics of detected light can be correlated to determine Stokes polarimetry parameters Q, U, and V, based on, e.g., Mueller matrix calculus. In some examples, the dual-PEM system 1200 can include one or more translation and / or rotation stages coupled to one or more components, such as the analyzers, waveplates, sample receptacles, etc. The controller 1214 can include a rotate / translate control coupled to the stage so as to command the corresponding stage movement. The unitary structure of the dual-PEM system 1200 and its various modes of operation can eliminate the need for an angular adjustment of the photoelastic optical element 1208 or actual angle of the first and second modulation axes 1210, 1212, which are situated in a fixed angular orientation relative to each other. However, in some examples, the dual PEM assembly 1202 can be rotated as needed. In some examples, the controller 1214 can include a waveform digitizer that can sample and capture the waveform or a portion of a waveform associated with a modulated beam. In some examples, the controller 1214 can include or be coupled to a display configured to show one or more waveforms or PEM data associated with operation.

[0076] FIG. 13 is an example PEM system 1300 configured to provide a stable selectable modulation axis operational mode 1302 and / or a stable rotating waveplate operational 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 the modes 1302, 1304, the PEM system 1300 includes a temperature (frequency) to vibrational phase delay map 1310 and a temperature (frequency) to drive ratio map 1312, which can contain different data for the different mappings. During operation the PEM system 1300 can provide a controllable phase offset 1314 for a voltage signal 1316 applied to the transducer 1308 and a controllable voltage amplitude 1318 for the voltage signal 1316, based on the mappings 1310, 1312, the selected mode of operation, and other system parameters, such as user-selected retardance setpoints, sensed currents, applied frequencies, etc.

[0077] FIG. 14 is an example dual-PEM system 1400. In various examples, the dual-PEM system can be configured to provide a temperature stable selection modulation axis mode 1402 and / or a stable rotating waveplate mode 1404. The dual-PEM system 1400 includes a photoelastic optical element 1406 with first and second transducers 1408, 1410 coupled to the photoelastic optical element 1406. The first and second transducers 1408, 1410 each receive separate voltage driving signals 1412, 1414 that cause the first and second transducers 1408, 1410 to vibrate in response and therefore to vibrate the photoelastic optical element 1406. The driving signals 1412, 1414 are shaped through voltage amplitude adjustments 1416, 1418, frequency adjustments 1420, 1422, and a controllable phase offset 1424 for at least one of the two transducers, e.g., transducer 1410.

[0078] The dual-PEM system 1400 can include first and second current senses 1426, 1428 that measure current characteristics of the first and second transducers 1408, 1410 as they are being driving with the voltage signals 1412, 1414. During operation the first transducer 1408 can be driven at a selectable setpoint for retardance, resulting in a selected target for the amplitude of the adjustable voltage amplitude 1416. A driving current setpoint comparison 1430 can be used to compare the sensed current to a setpoint of the first transducer 1408. In response to a comparison, driving voltage 1412 can be adjusted to maintain within an error margin.

[0079] A frequency of the voltage signal 1412 can be controllably adjusted to maintain suitable driving characteristics over time, e.g., as temperature fluctuates. For example, a measured currentvoltage phase difference 1432 can be compared to a calibrated phase difference / offset 1434 associated with the first transducer 1408 to controllably adjust the frequency with the frequency adjust 1420. The calibrated phase offset compare 1434 can also be used to adjust frequency of the voltage signal 1414 with the frequency adjustment 1422. The second transducer 1410 can also undergo control based on the current sense 1428 and a driving current setpoint. The voltage amplitude adjust 1418 can be operated in response to a driving current setpoint compare 1436.

[0080] For the different modes of operation, a frequency to driving ratio map 1438 can be used to adjust a driving current setpoint adjust 1440, e.g., as temperature varies over a predetermined range. The driving current setpoint adjust 1440 for the second transducer can be based in part on the current sense 1426 of the first transducer 1408. The driving ratio map 1438 can be based on the selected mode of operation 1402, 1404, phase calibration data 1442, and drive ratio calibration data 1444. In the stable selectable modulation axis mode 1402, an angle select value 1446 is provided to the drive ratio map 1438 in order to command the corresponding effective modulation axis. For each mode a different vibrational phase delay map 1448 is used in connection with the controllable phase offset 1424 to adjust the voltage signal 1414.

[0081] General Considerations

[0082] As used in this application and in the claims, the singular forms “a,” “an,” and “the” include the plural forms unless the context clearly dictates otherwise. Additionally, the term “includes” means “comprises.” Further, the term “coupled” does not exclude the presence of intermediate elements between the coupled items.

[0083] The systems, apparatus, and methods described herein should not be construed as limiting in any way. Instead, the present disclosure is directed toward all novel and non-obvious features and aspects of the various disclosed embodiments, alone and in various combinations and subcombinations with one another. The disclosed systems, methods, and apparatus are not limited to any specific aspect or feature or combinations thereof, nor do the disclosed systems, methods, and apparatus require that any one or more specific advantages be present or problems be solved. Any theories of operation are to facilitate explanation, but the disclosed systems, methods, and apparatus are not limited to such theories of operation.

[0084] Although the operations of some of the disclosed methods are described in a particular, sequential order for convenient presentation, it should be understood that this manner of description encompasses rearrangement, unless a particular ordering is required by specific language set forth below. For example, operations described sequentially may in some cases be rearranged or performed concurrently. Moreover, for the sake of simplicity, the attached figures may not show the various ways in which the disclosed systems, methods, and apparatus can be used in conjunction with other systems, methods, and apparatus. Additionally, the description sometimes uses terms like “produce” and “provide” to describe the disclosed methods. These terms are high- level abstractions of the actual operations that are performed. The actual operations that correspond to these terms will vary depending on the particular implementation and are readily discernible by one of ordinary skill in the art.

[0085] In some examples, values, procedures, or apparatus are referred to as “lowest,” “best,” “minimum,” or the like. It will be appreciated that such descriptions are intended to indicate that a selection among many used functional alternatives can be made, and such selections need not be better, smaller, or otherwise preferable to other selections.

[0086] Having described and illustrated the principles of the disclosed technology with reference to the illustrated embodiments, it will be recognized that the illustrated embodiments can be modified in arrangement and detail without departing from such principles. For instance, elements of the illustrated embodiments shown in software may be implemented in hardware and vice-versa. Also, the technologies from any example can be combined with the technologies described in any one or more of the other examples. It will be appreciated that procedures and functions such as those described with reference to the illustrated examples can be implemented in a single hardware or software module, or separate modules can be provided. The particular arrangements above are provided for convenient illustration, and other arrangements can be used. In view of the many possible embodiments to which the principles of the disclosed technology may be applied, it should be recognized that the illustrated embodiments are only representative examples and should not be taken as limiting the scope of the disclosure.

[0087] Alternatives specifically addressed in these sections are merely exemplary and do not constitute all possible alternatives to the embodiments described herein. For instance, various components of systems described herein may be combined in function and use. We therefore claim all that comes within the scope of the appended claims.

Claims

We claim:

1. A method, comprising: driving a photoelastic modulator optical element with at least two transducers; and controlling a phase difference between driving signals applied to the at least two transducers based on a variation in resonant frequency of the photoelastic modulator optical element and a variation in vibrational phase delay associated with a change in temperature of the photoelastic modulator optical element.

2. The method of claim 1, wherein the controlling the phase difference comprises: adjusting the phase difference to compensate for a variation in a temperature dependent vibrational phase delay difference between the at least two transducers.

3. The method of claim 1, wherein the controlling the phase difference comprises adjusting the phase difference to cause the photoelastic modulator optical element to operate as a rotating waveplate.

4. The method of claim 1, further comprising controlling a ratio of the amplitudes of the driving signals in response to the varying vibrational phase delay.

5. The method of claim 4, wherein the adjusting of the phase difference and the controlling of the relative amplitudes of the driving signals are configured to cause the photoelastic modulator optical element to operate as a rotating waveplate producing an optical retardance that is constant in time at an angle that rotates continuously.

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

7. The method of claim 1, wherein the driving is configured to produce light depolarization or time domain polarization scrambling.

8. The method of claim 1, further comprising detecting light modulated by the driven photoelastic modulator optical element.

9. An apparatus, comprising: at least two transducers coupled to a photoelastic modulator optical element and configured to drive the photoelastic optical element; and a controller coupled to the at least two transducers and configured to control operation of the at least two transducers with respective driving signals, wherein the controller is configured to control a phase difference between the driving signals applied to the at least two transducers based on a variation in resonant frequency of the photoelastic modulator optical element and a variation in vibrational phase delay associated with a change in temperature of the photoelastic modulator optical element.

10. The apparatus of claim 9, wherein the controller is configured to control the phase difference including by adjusting the phase difference to compensate for a variation in a temperature dependent vibrational phase delay difference between the at least two transducers.

11. The apparatus of claim 9, wherein the controller is configured to control the phase difference including by adjusting the phase difference to cause the photoelastic modulator optical element to operate as a rotating waveplate.

12. The apparatus of claim 9, wherein the controller is configured to control a ratio of the amplitudes of the driving signals in response to the varying vibrational phase delay.

13. The apparatus of claim 12, wherein the controller is configured to adjust the phase difference and to control the relative amplitudes of the driving signals to cause the photoelastic modulator optical element to operate as a rotating waveplate producing an optical retardance that is constant in time at an angle that rotates continuously.

14. The apparatus of claim 12, wherein the controller is configured to control the phase difference and ratio of amplitudes to produce an effective modulation axis at an angle between the angles of respective modulation axes of the at least two transducers.

15. The apparatus of claim 11, wherein the operation is configured to produce light depolarization or time domain polarization scrambling.

16. The apparatus of claim 9, further comprising an optical detector configured to detect light modulated by the driven photoelastic modulator optical element.

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

18. The computer readable medium of claim 17, wherein the controlling the phase difference comprises: adjusting the phase difference to compensate for a variation in a temperature dependent vibrational phase delay difference between the at least two transducers.

19. The computer readable medium of claim 17, wherein the controlling the phase difference comprises adjusting the phase difference to cause the photoelastic modulator optical element to operate as a rotating waveplate.

20. The computer readable medium of claim 17, wherein the stored processorexecutable instructions are further configured to cause the controller to control a ratio of the amplitudes of the driving signals in response to the varying vibrational phase delay.

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