3.5. Sagnac Interferometer

Apart from the ‘classical’ two-beam interferometers discussed above of which the designs are constantly being improved, there is an additional Sagnac-type (or ring-type) interferometer, which has been in the shadow of others for decades. It has been recently reconsidered due to the development of fiber-optic technology that was essential for its proper functioning. This type of optical interferometers was not included in previous reviews and, therefore, we provide a more detailed description of its principle here.

The Sagnac interferometer, named after French physicist Georges Sagnac, represents a circular path along which two interfering beams propagate in opposite directions (Fig. 15). If the setup has no rotation, the position of interference fringes is stationary, whereas their position is shifted according to the angular velocity of the system. This effect has found important application in laser gyroscopes and metrology [58]. The Sagnac effect, for example, helps in synchronizing global navigation systems that are affected by the Earth’s rotation. There is an idea of using the Sagnac interferometer in detecting gravitational waves [59] because this could potentially serve a much simpler solution with a tremendously smaller detector footprint compared to currently exploiting Michelson Interferometer with gigantic 4 km arms.

Sagnac Interferometer for the detection of system rotation.

However, as it was noticed later, if a temporally short vibration is applied to the mirror located in the right bottom corner in Fig. 15, the detection signal will be non-zero although the interfering beams still propagate the same path without applied vibrations. Indeed, the vibration causes the same change in the path of both interfering beams, but the change is introduced at different time moments defined by the lengths of optical paths to the mirror (or the lengths of the interferometer arms). When the beams bounce off the mirror and propagate back to the detector, the difference in total propagation paths is compensated due to the same total propagation path for both beams. Thus, the intensity It of the modulated signal on the detector is proportional to the difference in the vertical displacement Dzt of the mirror measured over a small difference ∆t in time, i.e., the vertical component of the vibration speed vzt:

where ∆t=(llong−lshort)/c (c – is the speed of light, llong and lshort are the lengths of the interferometer arms).

In 2006, Tachizaki et al. [60] demonstrated the design of a conventional Sagnac interferometer capable of measuring surface acoustic wave (SAW) signals up to 1 GHz. The scheme of the interferometer is presented in Fig. 16a. In that design, the sample beam generated by the probe laser and linearly polarized at 45 degrees was split into horizontal and vertical beams using a polarization beam splitter PBS1. Both beams were reflected by mirrors M1 and M2 and projected onto the sample surface. The arm between PBS1 and mirror M2 was slightly longer than the arm between PBS1 and M2, therefore the second beam arrived at the surface after the first one. Both beams were then reflected from the surface, collected by the lens, and then followed a different path through the PBS1. For example, if a first beam traveled from the probe to the sample through PBS1-M1 arm, on the way back it traveled through the PBS1-M2 arm. In the end, both beams reflected from the surfaces were directed towards the quarter-wave plate QWP4 and the PBS2, where they interfered on a balanced photodetector. QWP4 introduced a shift of 90 degrees between the two beams to set the interferometer in a state of maximum phase sensitivity. Due to the time shift between the beams, the measurement of surface displacement on the sample was based on the difference between the signals reflected from the surface at two time instants. A femtosecond laser with a wavelength of 830 nm operating at a repetition rate of 76 MHz was used for the probe beam. In the presented system, the LUS was excited using a pump laser operating at the second harmonic of the probe beam (415 nm). During the measurement, the pump laser pulses were synchronized with the probe laser pulses. Therefore, the change between the two reflected probe beams was defined by the phase shift of the signal due to the out-of-plane displacement of the surface perturbed by the pump laser. The presented Sagnac interferometer was designed for a detection of high frequencies. The upper frequency limit was inversely proportional to the duration of the probe optical pulse. The authors indicated that the theoretical frequency range of up to 50 THz was possible.

(a) Gigahertz-range Sagnac interferometer scheme (reproduced with permission from Ref. [60]), (b) the result of SAW full-field measurement obtained using the Sagnac interferometer. Reproduced with permission from Ref. [61].

The presented Sagnac interferometer was used in several applications, including measuring GHz-range surface waves in metamaterials [61] (an exemplary snapshot of the wavefield is presented in Fig. 16b) or recording zero-group velocity Lamb waves up to 10 GHz frequency in a silicon-nitride plate [62].

As can be seen, the first applications of the Sagnac interferometer were limited to the reception of US waves of very high frequency. Indeed, the detection bandwidth BW of the Sagnac interferometer is:

For example, a 1 m difference in path lengths results in a BW=300MHz. Reducing the bandwidth to the lower megahertz range (typical to conventional NDT studies) would result in a few tens of meters of Sagnac loop, which would be difficult to implement using open space optical components.

Bowers et al. [63] in 1982 (see Fig. 17) first introduced the Sagnac Interferometer using a fiber-optic design for the detection of ultrasound vibrations, where the tens of meters Sagnac loop length was no longer an issue. The study proposed an asymmetry in the Sagnac interferometer halves so that beams propagating into different directions of the Sagnac loop arrived at the measurement surface with the delay from each other (determined by the delay line) which was compensated on the way back from the surface to the detector when both beams complete the entire Sagnac loop. Unfortunately, the existing fiber-optic technology that existed at the time did not allow the Bowers’s innovation to work properly. The clockwise and counterclockwise beams were not encoded properly, and the single mode fibers used in the system were sensitive to environmental vibrations.

Schematic of Sagnac interferometer based on the original design by Bowers et al. [63] in 1982.

In 1997, Alcoz [64], [65] (see Fig. 18) introduced several advanced modifications of the Sagnac interferometer for the detection of US signals with the design using only polarization-maintaining (PM) fibers that allowed to properly encode clockwise and counter clockwise propagating beams with independent circular polarizations of light in the Sagnac loop. A polarization controller working as a quarter-wave plate was proposed to automatically rotate the paths of the propagation beams. The only drawback of the proposed design was in the use of the in-fiber quarter-wave plate. Although the Alcoz’s patent declared that the in-fiber polarization controller would work as a quarter-wave plate rotating the beams, to date, there are still no polarization controllers capable of changing the light polarization inside the PM fiber. In addition, a piece of fiber between the polarization controller and the detection head was used to propagate signals polarized along both slow and fast fiber axes, although the speed of light depends on the polarization in the PM fiber. Thus, an unbalanced difference for right and left circularly polarized signals was introduced, which dramatically reduced the sensitivity of the proposed method, especially in the case of using low-coherent probe light sources. However, the main reason that the method developed by Alcoz was forgotten for years is what it was only patented without clear demonstration of its advantages in literature.

One of the Sagnac interferometer designs proposed by Alcoz et al. [65] in 1997.

In 2014, Pelivanov, Buma and O’Donnell revisited the Sagnac technology to develop a fiber-optic interferometer independently of Alcoz. The proposed design, as shown in Fig. 19, was free of the drawbacks of previous approaches. In particular, modern fiber-optic components combining PM and single-mode (SM) fibers were used to build the interferometer. Instead of using circularly polarized light, the design [27] used linearly-polarized radiation which was controlled at all steps by two in-fiber polarization controllers. A quarter-wave plate to automatically switch the light propagation direction within the Sagnac loop after its reflection from the target was placed inside the detection head within the collimated beam so that the equivalence of propagation paths of the interfering beams was not violated. The detection head consisted of aspheric lenses minimizing aberrations and maximizing light reception back into the PM fiber. However, the major factor influencing the light reception from the sample surface is the surface roughness, reducing the amount of the recorded light from nearly 100 % down to the fraction covered by the transducer effective NA (in the worst situation of surface isotropic scattering).

Sagnac interferometer design proposed by Pelivanov et al. [27] in 2014.

The linear polarization design also allowed the balanced detection to remove the non-birefringent component from the detected signal and reduce the common noise. A little footprint super-luminescent diode (SLD) was used as a stable low-coherent source, which provided more than 50 dB dynamic range of the detection and did it insensitive to in-fiber reflections due to the short coherence length. The only constraint on the coherence length in the proposed design is that it should be larger compared to variations in the topography of sample surface to provide coherent reflections within the area covered by the probe beam. Finally, a fully PM-fiber design with an in-fiber polarization controllers (OZ Optics) made of short piece of SM fiber was commercialized by LuxSonics Inc.

The modern fiber-optic design makes the Sagnac interferometer competitive with other designs and even outperforms them in several characteristics. Indeed, most designs discussed above require a reference arm, which adds complexity into the system and requires complex stabilization techniques. In the Sagnac approach, both interfering beams come from the sample surface and no reference arm is required. Because the same surface is used to reflect both interfering beams that are reflected from the same target spatial point, the thermal lensing effect introduced by the pump beam is almost eliminated for frequencies above a few kHz. In addition, in interferometers that use a reference arm, it is necessary to “protect” it from environmental vibrations. The Sagnac interferometer is free of noise coming from the reference arm. However, in two-beam interferometers, the most serious negative effect is driven by the principle difference between the ideal mirror-like reflector of the reference arm and the speckle-based reflection introduced by most surfaces of untreated materials. This leads to the dramatic decrease of sensitivity of conventional designs; and most innovations in two-beam interferometer designs (discussed above) were aimed to compensate for the speckle effect. In contrast, the phase retardation effect has no influence on the Sagnac interferometer made of PM fibers. Indeed, optical fields of both Sagnac beams are the same without surface vibration. PM fibers propagate both fields with minor distortions and make them interfere in the second polarization controller. Only the difference between the fields of the two beams is important, and not the phase compound of the individual fields. Note that the amount of detected light is still affected by surface roughness. This problem can potentially be solved by increasing the probe light source power up to 300 mW (damage limit for PM components), but unfortunately, stable low coherent 1550 nm sources with the power of more than 40 mW are currently not available on the market.

The Sagnac loop automatically equalizes the paths of the interfering beams, which will be stable under any environmental conditions except for the rotation of the interferometer. This maximizes the interference to the theoretical limit because interfering beams travel exactly the same distance and meet at exactly the same time. This allows using a very compact, low coherent SLD source to greatly reduce the effects of parasitic interferences within the interferometer itself and minimizes speckles when examining regular rough surfaces.

A unique feature of the Sagnac design is the ability to quickly tune the detection bandwidth over an extremely broad range (from kHz to GHz) by changing the fiber length within the same device and without additional adjustment. This allows to apply the interferometer for both low and high-frequency measurements. Using PM fibers makes it possible to focus the probe beam spot to the diffraction limit, which enable its potential application for spectroscopy of microscale objects, such as single cells.

Traditionally, the noise figure of interferometers is compared to the shot noise of photodetectors, which is also an intrinsic characteristic of the detector. Such estimations are important and represent the ultimate sensitivity of the detector, but these estimations do not indicate how large the detection signal is compared to the ambient noise. Indeed, Johnson-Nyquist noise defines the thermal noise power, which is the minimum acoustic signal power that can be detected regardless the type of the detector used. The authors of Ref. [27] , estimated the Sagnac noise power and found that it was about 12 dB greater than the Johnson-Nyquist noise power. That figure overestimated the noise factor of the interferometer itself since it included all the electronics in the signal path. Note that an unvarnished aircraft composite surface with less than 1 % reflectance was used as the target for evaluation. Later, the noise figure was further improved to around 8 dB.

Despite the fact that the noise figure of the Sagnac detector is quite small, the overall NEP of the detection system is still modest compared to contact US probes because of the small detection area (probe light focusing spot). For a mirror-like sample surface, the probe beam diameter can be increased, and the overall optical power can be increased to significantly reduce the NEP. However, the main problem with LU inspection of industrial materials is that their surface is usually quite rough, which requires a focused probe beam and high NA optics to efficiently collect backscattered light. On the other hand, the larger the NA, the shorter the depth of field. The trade-off between a high NA and sufficient depth of field is a subject for future optimizations of confocal systems, such as the Sagnac detector.

A disadvantage of the current Sagnac principle is the difficulty of measuring the absolute displacement without calibration, which is sometimes impossible due to highly variable light reflection properties of the target. Another disadvantage is its sensitivity to a possible depolarization of the probe light induced by its reflection from the target surface.

A laser-ultrasound scanner with a Sagnac interferometer on receive (see Fig. 20) was first introduced in by Pelivanov et al. in [27]. An improved sensitivity of the Sagnac detector allowed using low energy fiber or diode-pumped ns lasers with about a 1 mJ pulse energy (compared to other systems using tens and even hundreds of mJ). Such lasers have compact footprints with possibility of operation at kHz pulse rates, which make the LU system working as fast as conventional contact ultrasound systems, at that enabling a fully non-contact approach with an unprecedented resolution. The low pulse energy and a smooth Gaussian beam shape produced by the diode-pumped solid state (DPSS) laser [67] allows to avoid overheating of the target surface even for highly absorbing graphite/epoxy composites enabling the thermoelastic regime of LU signal generation. Another advantage of using the DPSS laser type is in its ability to operate at variable repetition rates with a small (less than 2 ns) jitter in triggering. Thus, a position-based trigger can be utilized at scanning where the trigger signal comes from the translator. This allows LU scanning without stopping, which dramatically reduces the scanning time. As such, LUT NDT of aircraft composites was demonstrated in Ref. [67] in a single-shot regime with a 100 μm resolution at 100 mm/s scanning rate (see Fig. 21a,b).

LU scanner with a Sagnac interferometer on receive [67].

Summary of recent results obtained using the LU scanner with a Sagnac interferometer on receive [27]. LU scan of a 19-ply fiber reinforced graphite-epoxy composite sample from the front side, regular quality surface: (a) - full-bandwidth (1–10 MHz), (b) – low-pass (1–5 MHz) filtered to remove the regular composite structure from the image. (c) LU scan of the same sample from its opposite (very rough) surface. Demonstration of the impact damage detection [68] (d) – photograph of the impacted sample, (e) – LU C-scan at the depth of 0.5 mm from the sample surface, (f) C-scan obtained from X-ray tomograph. Visualization of wrinkles and local ply angle orientation [69]: (h) - photograph of wrinkled sample, (i) – LU image of the sample structure overlapped with the locally computed ply angle. Evaluation of disbonds in adhesively bounded aluminum plates using laser-generated shear acoustic waves [70]: (j) – diagram of the sample, (k) – measurement diagram, (l) – LU C-scan at the depth of plate bounding, indicating a Teflon inclusion in the structure.

The reduced sensitivity of the Sagnac detector to surface roughness was demonstrated in Ref.[66] , where the detection was performed from an extremely rough (∼ 200 μm mean height) surface. Despite the reduced quality of images and very blurred structural signal, the defects were still well detected (Fig. 21c).

The broadband nature of generated LU signals and their non-contact detection with a high spatial resolution made it possible to not only detect the flaws, but to visualize the material structure, which in turn enabled new imaging capabilities not available to reach with conventional UT. Consequently, the LUT scanner was then demonstrated in the evaluation of material porosity [71], imaging of heat [72] and impact damage [68] (see also Fig. 21d-f), and wrinkles [69] (see also Fig. 21 h,i) in aircraft composites. Authors [70] modified the scanner to receive shear waves (see Fig. 21k) and used it to inspect adhesion in aluminum sandwich plates (see Fig. 21j-l). A possibility of LU signal generation and detection at the same spot was used in Ref [73] for the excitation of zero group velocity waves which were shown to be very sensitive to variations in the system structure.