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Laser ultrasonics is a powerful technique for contactless investigation of important material parameters such as Young’s modulus or thin layer thickness. However, the often employed Gaussian beams result in diverging sound fields of quickly decreasing intensity. Conventionally, changing the laser beam profile requires the slow movement or exchange of optical elements. We present a laser ultrasonics setup for the creation of arbitrary intensity distributions by holographic projection using a MEMS spatial light modulator. High-intensity ultrasound foci with a focus width of 1.6 mm are scanned axially in a sample into depths of up to 7.4 mm by projecting ring-shaped intensity distributions of varying diameter without any mechanical movements. This technique is promising for highly spatially resolved flaw detection or a fast scanning investigation of biological tissue.
© 2016 Optical Society of America
Corrections
12 December 2016: A correction was made to Ref. 11.
1. Introduction
Laser-generated ultrasound has been under investigation since the early 1960s [1]. This unwavering interest stems from several advantages it provides over conventional ultrasonic testing using piezoelectric ultrasonic transducers, e.g. the contactless excitation of broadband ultrasonic waves with frequencies up to the GHz range [2]. Furthermore, the point-like laser sources are suited for the excitation of ultrasound in specimen which are very small or exhibit a complex shape which prevents them from attaching common transducers. The interferometric detection of laser-generated ultrasound also permits the investigation of specimen whose temperature would incapacitate piezoelectric transducers or which would be contaminated if directly exposed to the ultrasound-generating ceramics as in the case of hot melts.
Of the two regimes of laser-induced ultrasound generation [1], especially the thermoelastic regime is suited for the investigation of material parameters such as stress [3], speed of sound or Young’s modulus [4]. Scanning samples using ultrasound which is adaptively focused to varying depths promises enhanced spatial resolution in non-destructive testing. However, this requires the flexible tailoring of the laser intensity distribution to form the desired sound field.
Early on techniques utilizing non-Gaussian intensity profiles were employed to e.g. change the bandwidth or directivity of the generated ultrasound using axicons [5], cylinder lenses [6], fiber bundles [7] or masks [8]. At the same time, many of these techniques offer the benefit of enhancing the achievable ultrasound amplitude while remaining in the thermoelastic regime by distributing the laser energy over a wider area [5, 7]. Adaptive optics has proven another valuable means for wavefront shaping and beam shaping [9–11]. Recently, a liquid-crystal-on-silicon (LCoS) spatial light modulator was used to account for changing light absorption rates in composite materials [12] for a homogeneous excitation of ultrasound in fibers and matrix material, thus avoiding damage to the sample. Such modulators can greatly enhance the flexibility of a laser ultrasonics setup due to the ability to emulate many of the aforementioned optical elements with just one device.
We present a laser ultrasonics setup using a micro-electro-mechanical-system(MEMS)-based piston micro mirror array which enables polarization-independent phase-only modulation as well as pattern update frequencies of up to 250 Hz. We demonstrate the scanning of an ultrasound focus into varying depths of an aluminum sample utilizing the angled directivity of shear waves in solids. To the best of our knowledge, the proposed system is the first to achieve this by laser beam shaping from a deteriorated source to ring-shaped intensity distributions with varying diameters at a fixed distance and without the need for any mechanical movements.
2. Beam shaping from arbitrary wavefronts
Beam shaping is commonly understood as the formation of a certain field distribution from a light source, usually a laser beam. In general terms the resulting complex wave Ψ of the beam shaping process can be expressed as
where and In these equations, A0 and ϕ0 represent amplitude and phase of the original laser beam impinging on the modulator, ϕm and m are the phase shift and the amplitude attenuation induced by the modulator and is a linear operator describing the optical system between the planes (x, y, z) and (x′, y′, z′). Knowing the optical system and the desired field distribution and assuming a known (e.g. plane wave) illumination, one can easily calculate the required modulation to achieve the desired results. The efficiency of achieving the desired beam shape can be expressed by a number α with α ∈ [0, 1] [13]. The highest efficiency (α = 1) is achieved, when both amplitude and phase are modulated as in the general case of light modulation stated in equations 1–3. Undermining this restriction as with phase-only (α = π/4), binary phase (α = π−1) and intensity-only modulation (α = (2π)−1) [13], leads to successively lower efficiency. However, amplitude and phase modulation currently requires the use of two well-aligned modulators and results in a significant loss of input power, which is not always tolerable. If the phase distribution after the modulation is of minor importance as is the case in the laser-induced generation of ultrasound, phase-only modulation can be applied, which has the benefit of high throughput at a moderate loss of modulation efficiency and is therefore the type of modulation we utilised in our experiments.There are several possibilities to obtain phase holograms for the generation of the desired intensity distributions. Among these are iterative optimization algorithms [14, 15] that do not depend on knowledge of the optical system but require several thousand iterations to achieve an optimal solution, which may take several hours depending on the employed hardware. Other popular methods are based on the Gerchberg-Saxton algorithm, which uses known constraints in an optical system to reconstruct missing information [16–19]. Furthermore, there is the possibility to calculate holograms in one step [20], albeit with high noise, or directly by the summation of spherical waves [21, 22]. In our experiments, we used a standard input-output algorithm according to [17] and the angular spectrum method of light propagation [23] for the calculation of as they are well-documented, easily implemented and converge in a timely fashion. However, the input-output-algorithm requires the knowledge of amplitude and phase distribution of the original laser beam, since the former is required for the hologram calculation and the latter has to be compensated for when displaying the digital hologram on a phase-only modulator. Since the referencing of the impinging laser beam with Hartmann-Shack wavefront sensors or with holography data is experimentally quite difficult, we use another step of phase retrieval for the determination of the original amplitude and phase distribution according to [24]. In this method a number of known phase masks is added to the impinging laser beam and the modulated intensity distributions are recorded by a camera. The sets of known phase masks and camera pictures are then used as constraints for the retrieval of A0 and ϕ0 in equation 2, both readily aligned with the applied phase masks. In [24] a random phase mask etched into glass was traversed to generate the different required phase patterns. In our setup, we use our beam shaping modulator to display sets of overlapping sinusoidal patterns as depicted in Fig. 1 as phase masks. The so distorted laser beam is imaged onto a CCD camera by a lens to speed up the propagation calculation by using a single FFT (Fast Fourier Transform). To correctly match the modulator and camera plane for the FFT calculation, both have to be cropped or extended to a number of pixels N given by
where λ is the laser wavelength, f is the focal length of the lens, in our case 400 mm and ΔxC and ΔxM are the pixel pitches of the camera and modulator, respectively. For both phase retrieval steps, phase noise is reduced by averaging over the results of several iterations of the respective phase retrieval algorithm after it has reached a state when the solution oscillates with every iteration step. The whole process of beam shaping including the retrieval of the phase and intensity of the original beam as well as the hologram generation runs for 500 iterations and takes about 5 minutes to execute on a conventional PC in Matlab.
Fig. 1 An exemplary set of sinusoidal phase patterns (top) and the corresponding camera pictures of the diffracted beam (bottom) used as constraints for phase retrieval.
3. Experimental setup
The modulator used in our experiments is a MEMS-based piston micromirror array fabricated by the Fraunhofer Institute for Photonic Microsystems (Fraunhofer IPMS, Dresden, GER). Its 200 * 240 pixels are built monolithically from low-temperature sputtered amorphous TiAl with integrated CMOS address circuitry and have a pitch of 40 µm and a fill factor of at least 80 %. Phase patterns with low phase noise and 8 bit resolution can be uploaded to the modulator at 250 Hz maximum making the modulator ideal for fast scanning applications, the high frequency being an advantage over LCoS modulators which is inherent to MEMS devices and furthermore has the potential to be increased into the multi-kilohertz range [25]. Due to the piston stroke Δx of 425 nm and the resulting maximum optical path length difference of 850 nm, a phase shift of 2π*Δx/λ≈3.2π can be achieved independent of polarization. As phase shifts larger than 2π may be represented by wrapping them into the interval [0, 2π), the dynamic range of the modulator is thus effectively reduced in our experiment as the piston stroke has to be limited to 532 nm/2 = 216 nm at most. For reasons of strain relaxation the duty cycle of the modulator is limited to 5 %, so that it is well-suited for pulsed-laser applications.
For the generation of laser-induced ultrasound, we operate in the thermoelastic regime, meaning the surface of our sample is merely heated by impinging laser pulses and not ablated as in the plasma regime. We use a q-switched Nd:YAG laser with a wavelength of 532 nm, pulse width of 5 ns and a maximum repetition rate of 15 Hz. The 70 mJ pulses are attenuated to a maximum of 4 mJ to avoid damage to the optical components. A half-wave plate is used to adjust the polarisation for maximum transmission through a polarizing beam splitter as can be seen in Fig. 2. The beam splitter is required to illuminate the modulator perpendicularly. A quarter-wave plate is used to maximize the throughput of modulated light through the beam splitter whereas a polarisation-matching to the modulator like for LCoS devices is unnecessary. After the modulation, the main part of shaped laser beam is directed onto the sample via free space propagation whereas a fraction of 4 % is branched off by a beam sampler and imaged onto a CCD camera by a 400 mm lens which can be easily removed from the beam path using a hinged mount. We used a 3 mm thick aluminum plate as a sample. Both sample and CCD camera are positioned at twice the focal length of the hinged lens from the modulator to allow for the assessment of the shaped laser beam when the lens is not positioned in the beam path.
Fig. 2 Experimental setup. PBS: polarizing beam splitter, S: Aluminum sample, M: Mirror, LV: Laser vibrometer. The polarization Optics are used to reduce losses in the beam shaping part of the setup. The beam sampler is used to picture the beam onto the CCD camera to perform the phase retrieval and assess the result of the beam shaping. Note that sample and CCD are at the same distance from the modulator, this distance being twice the focal length of the hinged lens.
The ultrasound signal is detected on the backside of the aluminum sample by a Polytec OFV-503 laser vibrometer with 24 MHz frequency resolution which is mounted to translation stages. The velocities of shear waves and longitudinal waves in aluminum are about 3000 m/s and 6000 m/s, respectively. This significant difference leads to a temporal separation of both components after the propagation through the material and therefore allows to distinguish both otherwise undistinguishable components by their respective arrival time at the surface, where the out-of-plane component is registered by the laser vibrometer.
The setup is synchronized as follows: The modulator board triggers the laser pulse generation, the active time of the modulator at the set repetition rate being sufficiently long to allow for the pulse generation delay of 200 µs. The acquisition of surface displacement data generated by the laser vibrometer is triggered by a 200 MHz silicon avalanche photo diode which registers the laser pulses triggered by the modulator.
4. Measurements
The aim of our laser ultrasonic measurements is to demonstrate the ability to focus ultrasonic shear waves into a material using a flexible laser ultrasonics and beam shaping setup. The concept of the focusing of shear waves is outlined in Fig. 3 using the directivity of shear waves in aluminum as described in [26]. This rotationally symmetric directivity consists of a main lobe at a certain angle to the surface normal, the angle being determined by the Poisson ratio. By simultaneously illuminating two surface spots, the overlapping angled shear wave pulses focus to a spot at a distance d = Rtan−1(Θ) with R being half the distance between the spots and Θ being the main ultrasound directivity angle. The ideal case of this scenario corresponds to a simultaneous illumination of the sample with a ring-shaped intensity distribution which we want to achieve by beam shaping using a phase modulator since, in contrast to conventional optical elements, it allows to quickly change the ring diameters at an arbitrary distance without the need for slowly moving mechanical parts.
Fig. 3 Concept of focusing ultrasound waves in solids. The main lobes of the shear waves created by two thermoelastic ultrasound point sources overlap at a depth depending on the distance between the point sources.
Before the actual laser ultrasonic measurements can be conducted, the intensity profile and phase distribution of the laser beam impinging on the modulator have to be determined. Figure 4 shows the intensity distribution of our laser captured in the far field with a camera as well as the phase distribution of the laser beam at the modulator as a result of the phase retrieval. It is noteworthy that this phase also contains all aberrations of the setup, as the phase retrieval is performed under the idealistic assumption of an aberration-free light propagation through the optical setup. As can be seen, the sum of initial phase and aberrations mainly consist of a slight defocus.
Fig. 4 Far field input intensity distribution of the unmodulated laser beam captured with a CCD camera (left) and the phase distribution of the input laser beam at the modulator. (right)
Using the retrieved information about the initial phase and intensity of the laser on the modulator, we calculated phase patterns for the forming of ring-shaped intensity distributions on the surface of the aluminum sample as described in section 2. Ten ring profiles were formed with outer diameters ranging from 1 mm to 10 mm in steps of 1 mm. The ring width was kept fixed at 250 µm to ensure comparability of the generated sound fields. Four rings imaged with the camera are shown exemplarily in Fig. 5. The sharply accentuated intensity distributions demonstrate a successful compensation of the deteriorated intensity and phase of the input beam, which should not be expected with usual optics. It is noticeable that the rings mainly consist of evenly distributed speckles, a problem well known in the field of computer-generated holograms which in part stems from the use of a random phase distribution as a starting condition for most Gerchberg-Saxton-based phase retrieval algorithms [27].
Fig. 5 Output of the beam shaping: The laser is shaped into rings with diameters of 1 mm (top left), 2 mm (top right), 3 mm (bottom left) and 4 mm (bottom right) and a width of 250 µm each. Laser ultrasonic excitation was investigated with rings of up to 10 mm in diameter.
The laser power transmitted to the aluminum sample was attenuated for an operation just below the plasma regime. The laser energy was measured to be 880 µJ per pulse at a repetition rate of 12 Hz, resulting in radiant fluences ranging from 1.1 MJ/cm2 to 13 MJ/cm2 depending on the ring diameter. The laser ultrasound generated under these conditions was measured on the backside of the aluminium sample by detecting surface displacements using the laser vibrometer. For each ring diameter the maximum displacement at the center of the excitation ring was measured, where a maximum should occur when the lobes of the shear waves overlap.
Figure 6 shows the result of all conducted measurements. All results are normalized by the overall beam intensity to account for the intensity dependence of ultrasound generation. It can easily be seen that the normalized ultrasound amplitude reaches a maximum corresponding to an excitation ring diameter of 4 mm. Taking into account a sample thickness of 3 mm, this corresponds to an ultrasound propagation angle of 34° and thus fits well to reported shear wave propagation angles in aluminum [1]. This clearly demonstrates the ability to adaptively focus ultrasound into different depths of a sample for non-destructive testing. For the assessment of the achieved focal width, a cross-section of the sound field was measured for a ring diameter of 4 mm. The highest surface displacement is depicted in Fig. 7. From the data a maximum focal width of 1.6 mm can be estimated.
Fig. 6 Normalized maximum recorded surface displacement due to transverse ultrasound waves in dependency of the diameter of the ultrasound-exciting laser beam ring. A maximum surface displacement can be observed for a ring diameter of 4 mm, which corresponds to a propagation angle of 34° for the transverse waves.
Fig. 7 Cross-section of the measured sound field at the back of the sample at the time of highest surface displacement. From the data a maximum focal width of 1.6 mm can be estimated.
5. Conclusion
We have demonstrated a setup for the adaptive intensity redistribution from near arbitrary input beams for the use in laser ultrasonics. Phase retrieval provides both beam shaping and aberration correction. Phase modulation was performed by a polarization-independent MEMS-based piston micro-mirror device. We used our setup to shape our input laser beam into rings of varying diameters. For the first time, we demonstrated the adaptive focusing of shear waves and the scanning of this focus without moving elements. With the foreseeable future development of MEMS devices, this scanning can potentially be performed at several kilohertz. A focus of 1.6 mm is generated at an excitation ring diameter of 4 mm, which fits well with the shear wave directivity reported in literature. Lateral scans can easily be implemented by adding a phase-grating-like structure to the projected phase holograms. This is a prerequisite for the adaptive and contactless scanning for flaws with high spatial resolution with shorter laser pulses promising ever smaller focal widths. As the setup is capable of forming almost any intensity distribution for the excitation of ultrasound, different ultrasonic measurements requiring different sound fields may be fused into one device including the investigation of biological tissue.
Funding
German Research Foundation (DFG) Reinhart Koselleck project (CZ 55/30).
Acknowledgment
We would like to thank Thomas Windisch and Robert Kuschmierz for their valuable support and discussions. We would furthermore like to acknowledge the supplying of the MEMS piston micro-mirror modulator by the Fraunhofer Institute for Photonic Microsystems (IPMS) in Dresden.
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