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For applications involving time varying optical phase distributions, fast cameras and/or pulsed lasers have to be used. To apply phase–shifting interferometry techniques (PSI) as well, single shot capture is required. Among others, modulation of polarization and phase grating interferometry is a possible technique to be considered. In this paper, a report about the use of this technique based on a double pulse laser system is presented. Single–pulse and twin–pulse operations are considered both in optical interferometers as well as in ESPI systems (mainly in subtraction mode). In ESPI a reduction of the degree of polarization appears due to scattering, so some measures have to be taken to prevent such deletereous effect. To show the feasibility of the proposed variants some experimental results are presented.
© 2015 Optical Society of America
1. Introduction
Conventional Phase Shifting Interferometry is a well known technique to extract phase information from interferograms with static phase distribution [1, 2]. Common techniques based on piezoelectric devices require to mantain as much as possible a constant phase distribution during phase–shift value changes introduced by the piezoelectric. Thus, for industrial applications where environmental disturbances strongly affect measurements, such as vibration and air turbulance [3], this technique is somewhat limited due to its sensitivity, and must be modified in order to perform properly under adverse environments. Several efforts toward avoiding piezoelectric devices have oriented to develop a great variety of phase shifting interferometric techniques to achieve simultaneous interferograms in one–shot. In order to obtain n–phase shifts in one–shot, some techniques utilize diffractive elements [4–7], some others employ holographic ones [8–11], as well as pixelated phase masks attached to a CCD (Charge Coupled Device) camera [12], among others [13–17]. These techniques are useful in studying phenomena with static phase distributions, but when describing applications involving time varying optical phase distributions, such as object deformations and full–field vibration measurements in harsh environmental conditions (appearing in the industry automotive, aerospace, shipping, railway, etc.), high speed cameras and/or pulsed lasers are required [18].
Pulsed lasers are useful when environmental conditions are such that coherent interferometric effects are destroyed for cw illumination [18]. In fact, pulsed lasers freeze object motion and other environmental disturbances in the measurements, and several methods with single–pulse and twin–pulse modes have been proposed in order to compose the history of the evolution of harmonic vibrations and repeatable transient events [19–24] (typically performed with stroboscopic or pulsed laser illumination). However, one of the main disadvantages of these methods is that they require to repeat many times an experiment in order to obtain the evolution of harmonic vibrations and repeatable transient events, each time with a different time delay between the beginning of the event and with the emission of the laser pulse [22]. Furthermore, due to low operation rates of previously conventional CCD (around 60 Hz [21]), double–pulse addition correlation fringes were required rather than single–pulse subtraction correlation fringes to observe deformations in very short periods of time, and to completely discard the influence of rigid body motion [22]; but, as is well known, addition correlation fringes have very poor fringe contrast and usually require highpass filtering to observe correlation fringes [25]. Thus, the evaluation is not only time consuming, but inadequate to obtain the evolution of nonrepeatable transient deformations [26].
The continuous development of pulsed lasers and increasing speed of high–speed CCD and CMOS (Complementary Metal–Oxide Semiconductor) cameras have afforded to begin the study of dynamical events without having to repeat several times the same event. A simply solution proposed in [26], was to employ rapid sophisticated equipment to obtain the deformation history of repeatable and non repeatable deformations; although certain limitations to measure harmonic vibrations were presented [27]. A high–speed CCD camera, with high framing rates and short exposure time, and a pulsed laser were employed. By firing laser pulses stroboscopically, with microsecond temporal resolution, it was possible to register repeatable and non repeatable events. But, the real system operation rate proposed in [26] was strongly restricted by the poor time response of a piezoelectric device employed as a phase shifter to obtain four phase–stepped fringe patterns; even though high framing rates were employed to register the evolution of the events, 4500 fps (frames per second) and 45 kfps. Nevertheless, in order to increase the operation rate of the system, the piezoelectric device was substituted in [28] by a waveguide phase modulator, achieving thus a high–frequency phase–shifting modulation technique working at 100 kHz. Other attempts toward this direction employing CCD cameras have been informed, at operation rates of 360 fps [29, 30], among others [31]. In [32] for instance, a faster phase modulator and a CCD high–speed camera have been employed; a Pockels cell manufactered device utilized as a phase modulator has afforded to achieve an operation rate up to 1 kHz. Methods based on the previous idea are strongly constrained by the time response of the phase shifter employed, and have been recently called high–speed phase–shifting speckle interferometry. Although these methods present certain advantages over repeatable ones, some phase errors due to phase–stepping techniques are introduced (and must be considered in high–speed dynamic tests) due to three sources: intensity errors, velocity errors, and speckle decorrelation [33].
In order to employ CMOS cameras, which usually are faster than CCD, certain characteristics must be fulfilled to avoid distortions due to the readout process of certain CMOS cameras. Its incorporation to measure time–dependent deformations with ESPI, requires cameras only with integrating sensors and global shutter in the field of CMOS cameras [34]. A proposal employing a high–speed CMOS camera with phase–stepping phase–shifting techniques have been proposed in [35], but errors associated with temporal phase–stepping are still presented. Related proposals have also been presented; in [36] for instance, a CMOS camera with a digital holographic interferometry system is proposed to evaluate transient deformations, however, phase extraction resulted complicated due to image decorrelation generated in the system. In [37], a digital holographic proposal avoiding the phase–stepping method is presented (although achieved operation rates and the employed sensor type are not mentioned). A phase shifting array device was employed in order to directly obtain phase–shifted patterns such that fast changes can be observed. But, these array devices require special manufacturing and commonly introduce phase errors due to misalignment.
The present paper describes a one–shot phase–shifting method based on modulation of polarization with pulsed lasers applied on optical systems and ESPI for studying dynamical phenomena. One–shot phase–shifting optical interferometry with modulation of polarization has shown to be a versatile and easy technique to extract static phase distributions without errors due to environmental disturbances by the instantaneous captura of different phase–shifted patterns [4,5]. By combining this technique with high–speed phase–shifting speckle interferometry, different phase–shifted speckle patterns per frame are generated. Thus, common interframe phase–stepping methods are avoided allowing higher operating rates in high–speed phase–shifting speckle interferometry. Besides, single–pulse subtraction correlation fringes can be achieved at different high speed operation rates generating thus, subtraction correlation fringes with very good fringe contrast at very short periods of time. In other words, deformations can be observed at very short periods of time in single–pulse operation mode, and the influence of rigid body motion is avoided. The system employs a twin–cavity Nd:YLF laser originally designed for particle image velocimetry (PIV) and a fast CMOS camera. In the following sections, a description of the system for optical and ESPI operations with modulation of polarization are described. The characterization of the system, some static and dynamic results achieved at different high framing rates, as well as some measures to prevent loss of polarization in ESPI systems are presented.
2. Experimental setup
Figure 1 presents an experimental system that can be employed for optical evaluation as well as ESPI incorporating modulation of polarization. The basic structure of the proposed system consists of a Mach–Zehnder interferometric arrangement, but different interferometric arrangements can be employed also as the basic arrangement of the system. In order to employ speckle effect, two scattering plates are incorporated in each arm of the arrangement for in–plane displacement measurement as reported in [38]; nevertheless, as usual, the interferometric arrangement can be rearranged for out–of–plane displacement measurement, as shown in Fig. 2.
Fig. 2 Interferometric Mach–Zehnder arrangement for a) in–plane and b) out–of–plane displacement measurement.
The system can be employed to investigate applications involving phase dynamic evolution in the optical mode as for instance flows with little absorption, transients and disturbances in fluids (flames, impacts, vibrations), movement of microscopic biological specimens, among others; meanwhile ESPI operation mode allows to study applications of non-transparent objects, principally of rapid events in mechanical surfaces, but also can be employed in the determination of elastic characteristics. For rapid object deformation research, the system can also be employed, nonetheless the interferometric arrangement would require to be changed. In [39] for instance, an interferometric arrangement to study object deformation utilizing a temporal phase–shifting technique based on modulation of polarization was proposed. The technique was employed to investigate static deformations but the interferometric arrangement could be coupled to our system instead of the Mach-Zehnder arrangement to investigate rapid varying object deformations.
Illumination comes from the Nd:YLF laser operating at 527 nm. Laser pulses coming from each cavity, denoted by Ps and Pp, are linearly polarized and orthogonal between them. The interferometric arrangement comprises two cube beam splitters (BS, BS′), two mirrors (M, M′), two scattering plates (SP, SP′), two linear polarizer filters (PLψ, PL′ψ), with polarizing angle ψ, and two zero–order wave plates (Q, Q′) of λ/4. In each arm of the interferometer, the combination of a polarizer filter PLψ and a zero–order wave plate Q, with an appropiate azimuth angle (45°), generates circularly polarized light rotating similarly in both arms of the interferometer; however, beam combiner BS′ introduces a phase change of π radians on the reflected beam passing through it, therefore, left circularly polarized light becomes right circularly and viceversa. In this way, at the output of the interferometric arrangement left and right circularly polarized light is always obtained, which is a necessary condition to incorporate modulation of polarization [4]. In order to generate several replicas of the same pattern produced in the interferometric arrangement, light emerging from the interferometer is conduced to a 4 f Fourier System (the modulation of polarization stage), where a phase grating (PG) of 110 ln/mm was set at the system’s Fourier plane. Four 1D diffracted orders generated in the Fourier system are then selected and passed through linear polarizer filters set at the image plane. Each linear polarizer filter, denoted by PLψi, is set with a distinct azimuth angle ψi, for i = 0,..., 3.
Interference occurs therefore after each linear polarizer filter, and each pattern contains a different phase–shift ξi = 2ψi. Azimuth angles are usually chosen such that maximum phase–shifts are introduced. Typical azimuth angles are ψ1 = 0, ψ2 = π/4, ψ3 = π/2 and ψ4 = 3π/4. In this way, four fringe patterns with different phase–shifts are obtained at the same moment, i. e., instantaneously. The fast camera square sensor has a maximum resolution of 1024 × 1024 pixels, but only a Region of Interest (ROI) is selected to reduce the size of the captured images, i.e., only a ROI where the four 1D horizontal diffracted orders are accommodated with the aid of a zoom is chosen. Phase–shifted patterns can be analyzed with usual four interferogram algorithms to recover the phase under study. One of the main advantages of this technique is that no phase–stepping interframe techniques are required to introduce phase–shifts; therefore, high operation rates of the system can be achieved. These operation rates are only limited by the laser performance at high operation frequencies and by the ROI of the fast camera; which decreases as higher operation rates are employed and certain size of the ROI must be kept in order to observe the diffracted orders.
2.1. System parameters
Synchronization of the system is performed with the aid of a BNC Pulse/Delay generator model 575 and an oscilloscope; as shown in the configuration of Fig. 1. Besides, a schematic flow control of the synchronization process is presented in Fig. 3. The fast camera employed in the system is a Photron Fast Cam CMOS 1024 PCI with operation rates since 500 fps up to 109.5 kfps; its gray level depth is in the range of [0, 255]. The fast camera has an integrating sensor and global shutter and is perfectly adequate to measure time–dependent deformations with ESPI. At any speed of operation, the fast camera generates a TTL output pulse signal corresponding with the exposure time of each frame. The camera exposure time varies as the selected shutter speed, being the default value (frame rate)−1. For instance, at a speed of 500 fps the pulse duration width default value of a TTL pulse is of 2 ms; but this value is reduced (1/shutter speed) with higher shutter speed options. The rising edge of this TTL output pulse signal is employed to trigger the Pulse/Delay generator. In this way, each of the eight available channel outputs of the generator are synchronized with the fast camera, and are employed to synchronize other devices.
The Nd:YLF laser can be operated in continuous and Q-switch mode; in order to get synchronized, second option must be selected. Once the laser has been connected to the Pulse/Delay generator, pulsed illumination is immediately achieved (necessary to record information at each frame). It is important to mention that for the Nd:YLF laser employed in our test, only the trigger of each laser pulse can be controlled, since the pulse width is fixed for all pulses with a pulse duration of 150 ns. A laser pulse is then straddled at each frame and with the aid of the oscilloscope it can be easily accomodated for single–pulse mode. For twin–pulse mode, two channel outputs of the Pulse/Delay generator have to be employed to fire two pulses by frame (one channel per cavity). Several other pulse configurations can be achieved by multiplexing several outputs into another one. Due to the Pulse/Delay generator, the minimum pulse separation time that can be achieved for twin–pulse mode is of 25 ps.
Operation rate range of the system depends principally on the following parameters: frequency range operation of the laser and the frame rate range of the fast camera with its associated maximum resolution. The fast camera can operate from 500 fps up to 109.5 kfps, while the operation range of each cavity of the Nd:YLF laser in Q-switched mode goes from 300 Hz (or 300 pulses per second) up to 10 kHz. The minimum operation rate of the system is then limited by the minimum operation rate of the fast camera; therefore this value is set at 500 fps or 500 Hz, indistinctly. On the other side, the maximum operation rate of the system is limited by the maximum operation rate of the laser, and thus, this value is set at 10 kfps. Then, the operation rate range of the system is 500 fps–10 kfps. At 10 kfps, the maximum achieved resolution by the fast camera is 256 × 256 pixels, which still is an appropiate ROI in order to employ modulation of polarization. With a 2 GB memory, the record duration at 10 kfps is of 2.61 seconds, recording up to 26, 112 frames. These parameters are enough to compose a complete history of a rapid event.
At an operation rate of 500 fps the maximum resolution is of 1024 × 1024 pixels. If this resolution is not required, a reduced ROI can be selected. Thus, depending on the size of the selected ROI, an increase of the record duration time and consequently an increase of the number of recorded frames are afforded. Besides, as is well known, an increase of the operation rate of the system can be achieved if working in twin–pulse mode. Unlike single–pulse mode where a single pulse is straddled at each frame, in twin–pulse mode two different pulses can be straddled into the same frame or perhaps they can be straddled one at the end of a certain frame and the other at the beggining of the next frame, reducing in this way the time of observation between pulses [22].
2.2. Optical systems and ESPI with modulation of polarization
Optical systems can be operated in both, single–pulse or twin–pulse modes. Table 1 shows coded configuration of the interferometric arrangement in order to operate optical systems. For single–pulse mode, pulses Ps or Pp can be employed without distinction, and only linear polarizer filters must be oriented properly to work with either pulse. For twin–pulse mode operation, linear polarizer filters before the zero–order wave plates must be oriented at 45° in order to work with the component of pulses Ps or Pp at this angle, and both zero–order wave plates Q and Q′ must be oriented at 0° or 90°, indistinctly, in order to have circularly polarized light in each arm of the arrangement. The price of employing the twin–pulse mode is that more energy is required, because half of the energy of each pulse is lost at linear polarizer filters at 45°.
Table 1. Configuration for optical and ESPI evaluation with modulation of polarization (y denotes the pulse is employed meanwhile × denotes the corresponding pulse is not employed).
In order to work in ESPI with modulation of polarization two scattering plates SP and SP′ with the same characteristics are incorporated in the interferometric arrangement presented in Fig. 1. Through some experimental results, we have inferred that there is a gradual, and sometimes total loss of polarization degree in speckle patterns so that in order to introduce expected phase–shifts ξi = 2ψi, as described by [4], certain steps must be taken to introduce phase changes according to the theory of modulation of polarization. In fact, according with [40–44], depolarization of speckle patterns depends mainly on two factors. The first one concerns the scattering process, and is connected with the microstructure of the scattering plate. The second factor is related with the angular aperture of the detector employed to register the speckle pattern.
In order to understand speckle polarization dependency on the scattering process and the angular aperture, consider fully polarized light before being scattered. Depending on the microstructure of the scattering plate, single, multiple or completely diffusive scattering processes can occur [42]. For a single scattering process the state of polarization of the speckle pattern will strongly resemble the incident state of polarization [40–42]. Meanwhile, for a completely diffusive process, global polarization is totally lost. In fact, roughness of the scattering plate is the parameter affecting depolarization and has been entirely characterized, from a statistical point of view, as the quadratic surface slope s, which is defined as the ratio between the height root mean square, denoted by hrms and the correlation length, Lcor, of the scattering plate. Therefore, low quadratic surface slope values represent scattering plates depolarizing light less than those with high quadratic slope values, [43]. On the other side, once fully polarized light has been scattered with a certain scattering plate, light depolarizes as the contribution from multiple scattering increases [41,44]. In other words, a polarization dependency on the angular aperture of the detector can be observed, such that the more open the angular aperture, the greater the amount of speckle grains of different polarization states collected into the detector, causing then gradual loss of polarization in the registered pattern; theorically, an angular aperture at the speckle size perfectly mantains the original polarization state [43].
In our system, in order to prevent depolarization the following measures are taken. Angular aperture is controlled with a varying diaphragm from a commercial TV zoom lens. Thus, by closing the lens diaphragm until an f – number of 16, is sufficient to register fully polarized speckle patterns, one for each selected diffracted order, each one mantaining the induced linear polarization ψi of the linear polarizer filters at the output of the 4 f Fourier system. Obviously, as an f – number of 16 represents a very small aperture, the use of higher power laser is required to record results with a good visibility. On the other side, in order to prevent depolarization by the scattering plate and to have a single scattering process, several manufactered scattering samples with distinct surface roughness were tested until an appropriate sample was chosen.
Under the previous mentioned considerations, we employ then, the mechanism of modulation of polarization to describe speckle patterns generated in our system presented in Fig. 1. As is well known, in one–shot, certain number of reference speckle patterns (with different induced phase–shift ξi = 2ψi, according with [4]), can be registered and denoted by
where ϕ(x, y) represents the reference phase of the specimen under study before deformation. Once the deformation has been induced, a composed history of the evolution of the specimen is registered in each frame until the register process ends. The patterns carrying this information are denoted by where Δϕ is the phase difference caused by the deformation of specimen at each frame.Addition or subtraction between reference (Eq. (1)) and deformed speckle patterns (Eq. (2)) can be carried out. But, in order to obtain good correlation fringe contrast, subtraction is prefered. There are two ways in which subtraction correlation fringes can be analyzed [21]. The first consists in carrying out traditional subtraction between reference and deformed frames, i. e.,
which in terms of the trigonometric property, can be written asIn order to observe the effect of modulation of polarization, the following trigonometric property is employed
thus, we have For azimuth angles ψ1 = −π/4, ψ2 = 0, ψ3 = π/4 and ψ2 = π/2, four phase–shifted patterns are obtained. These patterns areProfiles of the expected patterns are presented in Fig. 4. As expected, introduced phase–shifts between speckle patterns are of ξ = 2ψ = π/2. We consider this procedure is useful to carry out a visual or computational verification of adequate introduced phase–shifts in ESPI with modulation of polarization, and will be employed in this paper to show instantaneos phase–shifting in speckle patterns due to modulation of polarization.
A second procedure to obtain the phase of the specimen under study consists on separately analyzing the reference and deformed set of speckle patterns, and then by subtraction obtaining the corresponding deformation, i. e.,
thus This procedure has some advantages over traditional subtraction [21], but it should be employed only after expected polarization due to the modulation of polarization process has been verified in speckle patterns, which can be carried out with traditional subtraction. This procedure has been employed in instantaneous phase–shifted ESPI for static tests with a micropolarizer array [45], and with a multi–camera system [46]; although considerations on depolarization of speckle patterns were neither discussed or considered in these papers.3. Static and dynamic experimental results
In order to verify adequate performance in ESPI with modulation of polarization, Fig. 5 shows some experimental results obtained both in optical and ESPI operation with modulation of polarization obtained with our proposed system operating at 500 fps for a same plane wavefront with tilt. Linear polarizer filters PLψi with azimuth angles ψ1 = 0, ψ2 = π/4, ψ3 = π/2 and ψ4 = 3π/2 have been employed (these angles are mantained for ESPI operation). Figure 5(a) shows four phase–shifted interferograms captured in one–shot for a tilted wavefront, generated in one arm, tilting mirror M′ of the Mach–Zehnder interferometer (the size of the ROI selected for the optical and ESPI test is of 512 × 208 pixels). The generated phase–shifts of ξ = 2ψi = 2(π/4) = π/2, between the shown patterns, are sequentially introduced, as expected. Now, by incorporating scattering plates in the interferometric arrangement as mentioned previously, ESPI operation is achieved. We have additional care in following the measures presented in the previous section. Under these conditions, Fig. 5(b) shows the phase–shifted correlation fringes formed by subtraction of the reference speckle patterns captured in one–shot (untilted wavefront) and between the deformed speckle patterns captured in one–shot at a different instant of time (patterns obtained with a tilted wavefront). Expected phase–shifts of ξ = π/2 are then induced between correlation fringes. Thus, a phase–shift of π is induced between patterns coming from linear polarizer filters with azimuth angles 0 and π/2, and between patterns coming from π/4 and 3π/2, as predicted in Fig. 4. In this way, it is verified that the mechanism of modulation of polarization properly works in ESPI operation. Phase extraction for optical and ESPI results presented in Fig. 5 was carried out with a conventional algorithm presented in [47]; obtaining similar results, as observed in this figure.
Fig. 5 Optical and ESPI phase–shifted experimental results due to modulation of polarization for a tilted wavefront. For linear polarizer filters with azimuth angles ψ1 = 0, ψ2 = π/4, ψ3 = π/2 and ψ4 = 3π/4, the induced phase–shifts ξi = 2ψi are shown at the top of each figure. (a) Optical results and its corresponding wrapped and unwrapped phase; (b) phase–shifted correlation fringes and its corresponding wrapped and unwrapped phase.
In order to verify proper operation of the system for dynamic phase distributions, an optical test at a rate of 3 kHz was carried out; i. e., the laser and the fast camera were synchronized at the mentioned operation rate (for this test, the scattering plates have been removed from the interferometric arrangement). Mirror M′ shown in Fig. 1 was replaced by an aluminized ethanoate sample of size 3 × 3 cm and served to simulate a transient event. The transient event was then induced by slightly impacting behind the ethanoate sample with a controlled solenoid (controlled with the Pulse/Delay generator). Information about this event was then registered with our system. Figure 6 shows a representative frame for this dynamic event; the original frame size or ROI for this test is of 768 × 256 pixels. The azimuth angles of the linear polarizer filters and induced phase–shifts are the same as those employed in the static test presented in Fig. 5. Visualization 1 shows the animation of some of the one–shot captured interferograms at different instants of time after the impact on the ethanoate sample was applied; Visualization 2 shows the corresponding dynamic unwrapped phase.
Fig. 6 One–shot single–frame excerpts from video recording of experimental results of a varying optical phase distribution; captured interferograms (see Visualization 1) and their corresponding extracted phase (see Visualization 2) are shown. For this test, scattering plates are removed from the interferometric arrangement shown in Fig. 1. Results of the ethanoate sample under study before a vibration was induced and after the ethanoate sample was perturbed are presented.
A test on the same ethanoate sample was carried out this time in ESPI operation mode again at a rate of 3 kHz. Once again scattering samples are incorporated in the interferometric arrangement to employ speckle effect and, as it has been mentioned, special measures need to be taken to introduce proper phase–shifts. Figure 7 presents a representative frame showing different phase–shifted correlation fringes formed by subtraction of reference and deformed speckle patterns (not shown) captured in one–shot at different instants of time. The original frame size or ROI selected for this test is of 768 × 304 pixels.This time three diffracted orders are only selected and the azimuth angles of the linear polarizer filters that were employed are ψ1 = 0, ψ2 = π/4 and ψ3 = π/2; thus the induced phase–shifts are of ξ1 = 0, ξ2 = π/2 and ξ3 = π, respectively. As it can be observed, proper phase–shifts and correlation is mantained at different instants of time. Visualization 3 presents results at different instants of time once the ethanoate sample was impacted and Visualization 4 presents the corresponding unwrapped phase. This time, the phase was calculated with the Fourier Transfer Function (FTF) for a 3–step phase shifting algorithm as proposed by Servin-Estrada in [47]. In this way, we verified appropiateness of the system to study dynamic varying phase distributions at different operation rates.
Fig. 7 One–shot single–frame excerpts from video recording of experimental results of a varying speckle phase distribution. For this test, scattering plates are incorporated in the interferometric arrangement shown in Fig. 1. As usual, reference speckle patterns correspond to the sample before being perturbed while speckle deformed patterns correspond to those patterns registered after the perturbation was applied. Correlation fringes (see Visualization 3) and their corresponding phase (see Visualization 4) are presented. As it can be noted, correlation is mantained for different instants of time.
4. Final remarks
In this work, we presented a system operating at different high framing rates for optical systems and ESPI incorporating modulation of polarization which has not been reported previously. The system has the ability to record multiple phase–shifted optical or speckle patterns at the same instant of time. This affords to measure rapid changes generated from rapid varying phenomena such that a compose history of the phenomena can be registered. The penalty paid, however, for the greatly improved temporal resolution of the method is a reduction of spatial resolution. Nevertheless, this limiting can be overcome through selecting an appropriate frequency for the phase grating employed in the 4 f Fourier system, for which a desirable resolution can be achieved.
We presented for the first time a discussion on several considerations that must be fulfilled in order to introduce phase–shifts in ESPI incorporating modulation of polarization. Under these considerations, we presented results for static and dynamic samples at different high framing rates that have not been achieved previously. The system can be employed in measuring both repeatable and non repeatable dynamic events and can be operated in single–pulse or twin–pulse modes. Operation of the system in ESPI with single–pulse mode at high framing rates affords to measure deformations corresponding to very short periods of time avoiding rigid body motion and other external perturbations and has the main advantage of generating subtraction correlation fringes with very good contrast instead of addition fringes with poor fringe contrast achieved with conventional CCD to measure deformations in short periods of time. Higher operation rates of the system can be achieved if more robust and faster equipment is employed. In other words, the present technique can work at higher operation rates if a faster laser is employed, but, special consideration on the ROI of the fast camera operating above 10 kfps must be taken into account.
Acknowledgments
A. G. A. thanks the National Council of Science and Technology (CONACyT) for Posdoctoral Scholarship support under call “Estancias Posdoctorales Vinculadas al Fortalecimiento del Posgrado Nacional 2013(3)”. Two of the authors (G. R. Z. and O. M. B.) acknowledge partial support from SENESCYT (Ecuador). We also thank Gerardo Calderón–Hernández and José F. Vázquez–Castillo for technical support during the development of this work.
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