Lloyd's Mirror Research Articles

Matched cross‐spectrum phase processing for source depth estimation in deep water

AbstractZhou et al. (2022) proposed a method for instantaneous source depth estimation in deep water using matched beam intensity processing (MBIP) that leverages depth‐related oscillatory features arising from Lloyd's mirror interference in the frequency domain (Appl. Acoust., 2022, 186, 108493). However, the efficacy of MBIP diminishes with a random source spectrum. To counteract the effect of a random source spectrum, a vertical line array (VLA) positioned near the sea bottom is employed and a cross‐spectrum is generated from the conventional beamforming output, which is achieved by dividing the VLA into upper‐half and lower‐half arrays. The authors find that the cross‐spectrum phase interference pattern is determined by the source depth and is unaffected by the source spectrum. Consequently, a matched cross‐spectrum phase processing method is proposed, which demonstrates appreciable depth estimation accuracy compared to that of the existing techniques, as evidenced by the results from both simulated and experimental data.

On the radiation of sound from an immersed cylindrical shell close to the sea surface

Numerical methods for the prediction of underwater radiated noise from immersed structures play a key role in the naval and offshore industry to ensure high acoustic performance of systems or to preserve natural habitats. Most of the approaches so far assume that the surrounding fluid is homogeneous and unbounded. However, in many situations the structure can be close to interfaces, namely the sea surface and the sea bottom, such as navigation of underwater vehicles in shallow waters. The Lloyd's mirror effect describes the interference phenomena occurring when a sound source is close to the sea surface. This effect is easily accounted for with a source image approach, while the strong vibro-acoustic coupling between the structure and the interface is more complicated to deal with. In this context, an analytical method has recently been developed to predict the vibro-acoustic behaviour of an infinite length cylindrical shell close to the surface, based on the shell equations and Graf's addition theorem. In the present work, we compare this approach to a simplified one where the strong interactions between the surface and the structure are not considered. Results highlight these effects on a typical underwater structure

Wide field 3D optical profilometry using a diffraction Lloyd's mirror interferometer.

Interference fringe projection is used as a non-contact optical profilometry method for accurate 3D measurements. In interferometric fringe projection schemes, the maximum measurable size of the test object is limited by the optics of the interferometer. In this work, we report the application of a diffraction Lloyd's mirror interferometer (DLMI) as a wide-field sinusoidal fringe projection system for 3D shape measurement. The DLMI works on diffracted light and therefore generates interference fringes over a large area. This enables measurement of large objects using DLMI as compared to a conventional Lloyd's mirror interferometer. The performance of the proposed system is evaluated in terms of its stability and reproducibility of the results through measurement of the standard deviation in the phase values.

Demonstration of a non-orthogonal Lloyd's mirror interferometer with a spatial light modulator for arbitrary two-dimensional pattern fabrication.

A new, to the best of our knowledge, method of generating interference patterns based on a non-orthogonal Lloyd's mirror interferometer with a spatial phase modulation is proposed. In the proposed method, a spatial light modulator (SLM) is introduced to a conventional non-orthogonal Lloyd's mirror interferometer so that arbitrary interference patterns, such as line interference patterns with varied line-spacing or two-dimensional patterns, can be generated by controlling the wavefronts of the laser beams at each position on the substrate. In this paper, as the first step of the research, the feasibility of the proposed method is theoretically confirmed by calculating interference patterns to be obtained when a spatial modulation of the phase delay is applied to the laser beams. A prototype of a non-orthogonal one-axis Lloyd's mirror interferometer with an SLM in its optical path is also designed and constructed. Some basic experiments are carried out to demonstrate the feasibility of the generation of interference patterns having varied line-spacing and two-dimensional patterns by the proposed method.

Development of dielectric-film-based polarization modulation scheme for patterning highly uniform 2D array structures with periodic tunability

A passively polarized holographic lithography system is proposed for fabricating highly uniform 2D crossed-array structures with periodic tunability and high throughput. The dielectric-film-based polarization modulation scheme is applied to an orthogonal two-axis Lloyd's mirror interferometer to guide the polarization modulation at the interfaces of the mirrors and simplify the exposure-system configuration for large-area fabrication. The proposed polarization-modulation system can fabricate stable large-area (30 mm × 30 mm) array structures with a wide period range from 742 to 1500 nm. Moreover, the established polarization-modulation model could be expanded with multiple dielectric films for attaining higher periodic tunability.

Retrofit-induced changes in the radiated noise and monopole source levels of container ships.

The container shipping line Maersk undertook a Radical Retrofit to improve the energy efficiency of twelve sister container ships. Noise reduction, identified as a potential added benefit of the retrofitting effort, was investigated in this study. A passive acoustic recording dataset from the Santa Barbara Channel off Southern California was used to compile over 100 opportunistic vessel transits of the twelve G-Class container ships, pre- and post-retrofit. Post-retrofit, the G-Class vessels' capacity was increased from ~9,000 twenty-foot equivalent units (TEUs) to ~11,000 TEUs, which required a draft increase of the vessel by 1.5 m on average. The increased vessel draft resulted in higher radiated noise levels (<2 dB) in the mid- and high-frequency bands. Accounting for the Lloyd's mirror (dipole source) effect, the monopole source levels of the post-retrofit ships were found to be significantly lower (>5 dB) than the pre-retrofit ships in the low-frequency band and the reduction was greatest at low speed. Although multiple design changes occurred during retrofitting, the reduction in the low-frequency band most likely results from a reduction in cavitation due to changes in propeller and bow design.

Effect of quality of opto-mechanical components on fringes of diffraction Lloyd mirror interferometer

Diffraction Lloyd mirror interferometer (DLMI) is a relatively new interferometer where interference fringes are generated by superposition of two diffracted beams instead of two geometrical beams of light. The interferometer is suitable for performing basic investigations on diffraction and interference of light. In this work, a number of set-up parameters determining the performance of DLMI including characteristics of knife-edge, quality of mirror, quality of lenses, and effect of algorithm, are experimentally studied and reported for the first time. The effect of these parameters on interference fringes of DLMI is evaluated in terms of change in average intensity, signal to noise ratio (SNR) and contrast of the fringes. By optimizing above parameters, a DLMI set-up is realized and used for characterization of silicon optics fabricated using the single point diamond turning process. The validation results by a commercial optical profiler confirms the effectiveness of DLMI system. This study would provide useful reference for setting up the DLMI system for different applications such as optical profilometry, optical metrology, and to study the diffraction of light etc.

Source level and vocalizing depth estimation of two blue whale subspecies in the western Indian Ocean from single sensor observations.

The source level (SL) and vocalizing source depth (SD) of individuals from two blue whale (BW) subspecies, an Antarctic blue whale (Balaenoptera musculus intermedia; ABW) and a Madagascar pygmy blue whale (Balaenoptera musculus brevicauda; MPBW) are estimated from a single bottom-mounted hydrophone in the western Indian Ocean. Stereotyped units (male) are automatically detected and the range is estimated from the time delay between the direct and lowest-order multiply-reflected acoustic paths (multipath-ranging). Allowing for geometric spreading and the Lloyd's mirror effect (range-, depth-, and frequency-dependent) SL and SD are estimated by minimizing the SL variance over a series of units from the same individual over time (and hence also range). The average estimated SL of 188.5 ± 2.1 dB re 1μPa measured between [25-30] Hz for the ABW and 176.8 ± 1.8 dB re. 1μPa measured between [22-27] Hz for the MPBW agree with values published for other geographical areas. Units were vocalized at estimated depths of 25.0 ± 3.7 and 32.7 ± 5.7 m for the ABW Unit A and C and, ≃20 m for the MPBW. The measurements show that these BW calls series are stereotyped in frequency, amplitude, and depth.

Measurements of the correlation of the frequency-difference autoproduct with acoustic and predicted-autoproduct fields in the deep ocean

Frequency-domain spatial-correlation analysis of recorded acoustic fields is typically limited to the bandwidth of the recordings. A previous study [Lipa, Worthmann, and Dowling (2018) J. Acoust. Soc. Am. 143(4), 2419-2427] suggests that limiting such analysis to in-band frequencies is not strictly necessary in a Lloyd's mirror environment. In particular, below-band field information can be retrieved from the frequency-difference autoproduct, a quadratic product of measured complex pressure-field amplitudes from two nearby frequencies. The frequency-difference autoproduct is a surrogate field that mimics a genuine acoustic field at the difference frequency. Here, spatial-correlation analysis is extended to deep-ocean acoustic fields measured during the PhilSea10 experiment. The frequency-difference autoproduct, at difference frequencies from 0.0625 to 15 Hz, is determined from hundreds of Philippine Sea recordings of 60 or 100 Hz bandwidth signals with center frequencies from 172.5 to 275 Hz broadcast to a vertical receiving array 129-450 km away. The measured autoproducts are cross correlated along the array with predicted acoustic fields and with predicted autoproduct fields at corresponding below-band frequencies. Stable measured cross correlations as high as 80%-90% are found at the low end of the investigated difference-frequency range, with consistent correlation loss due to mismatch at the higher below-band frequencies.

On the use of the Lloyd's Mirror effect to infer the depth of vocalizing fin whales.

The interference between the direct path and the sea surface reflection of a signal as measured by a receiver is called Lloyd's Mirror effect (LME). It results in a frequency-dependent interference pattern that can be observed in a spectrogram. LME depends on the receiver depth, signal source depth, signal frequency, and slant range between source and receiver. Knowing three of these parameters a priori, LME can be used to estimate the third parameter, such as source depth. Here, the work in Pereira et al. (2016) was expanded to estimate the depth of a vocalizing fin whale recorded by an ocean-bottom seismometer (OBS). In Pereira et al. (2016), the depth of a vocalizing fin whale was inferred by manually comparing spectrograms of LME transmission loss models with observed LME. This study developed an automated procedure to perform the same task using the LME interference pattern observed in the spectrograms of the hydrophone and the vertical channel of the OBS. The results show that the joint use of the two channels was the best approach to estimate a source depth using LME. LME provides a non-intrusive approach for estimating the depth at which a fin whale was vocalizing.

Comparison of sensitivity to beam collimation of the holographic shearing interferometer with the wedge plate shearing interferometer and the Talbot shearing interferometer.

High sensitivity of collimation testing equipment is desirable where collimated beams are used for precise and accurate measurements. Precision in the setting of collimation depends on the sensitivity of the testing equipment. In the present work, sensitivity to beam collimation of the recently reported holographic shearing interferometer (HSI) [J. Opt.20, 055603 (2018)JOOPDB0150-536X10.1088/2040-8986/aab6dc] is measured and compared with sensitivities of other collimation testing techniques based on the wedge plate shearing interferometer and the Talbot shearing interferometer. For a test beam of diameter 25 mm from an He-Ne laser and displacement of the collimating lens by 1 mm from the collimation position, the Talbot shearing interferometer shows a rotation of interference fringes from the horizontal direction by 2°, the wedge plate shearing interferometer shows 20°, and the HSI shows 25°. Sensitivity is also presented in terms of measured slopes of phase maps of the recorded interferograms for a 1 mm displacement of the collimating lens and is obtained as 0.98 mrad, 15 mrad, and 19 mrad corresponding to the Talbot shearing interferometer, the wedge plate shearing interferometer, and HSI, respectively. The effect of decollimation of the laser beam on the interference fringes of diffraction of the Lloyd mirror interferometer is also demonstrated. Theoretical concepts and experimental results are presented and discussed for the above-mentioned beam collimation testing techniques.

Matched beam-intensity processing for a deep vertical line array

A vertical line array can be deployed in deep water below the critical depth, the depth where the sound speed equals the sound speed at the surface, to take advantage of the lower ambient noise level (compared with above the critical depth) for target detection. To differentiate a submerged source from a surface source, a Fourier transform based method [McCargar and Zurk, J. Acoust. Soc. Am. 133, EL320-325 (2013)] was proposed for a narrowband signal that exploits the depth-related harmonic (oscillation) feature of the beam power time series associated with the target arrival. In this paper, incoherent matched beam processing is used to estimate the target depth. Where the replica (calculated) beam intensity or amplitude time series best matches that of the data is used to estimate the source depth. This method is shown, based on simulated data, to provide a better depth resolution in general and better ability to estimate the depth of a very shallow source (say at 10 m) and can be used to complement the Fourier transform based method. It can be extended to process (random) broadband signals and to environments where the Lloyd's mirror theory is not valid.

Convolutional neural network for single-sensor acoustic localization of a transiting broadband source in very shallow water

When a broadband source of radiated noise transits past a fixed hydrophone, a Lloyd's mirror constructive/destructive interference pattern can be observed in the output spectrogram. By taking the spectrum of a (log) spectrum, the power cepstrum detects the periodic structure of the Lloyd's mirror fringe pattern by generating a sequence of pulses located at the fundamental quefrency and its multiples. The fundamental quefrency, which is the reciprocal of the frequency difference between adjacent destructive interference fringes, equates to the multipath delay time. An experiment is conducted where a motorboat transits past a hydrophone located about 1 m above the seafloor in very shallow water (20 m deep). The hydrophone has a frequency bandwidth of 90 kHz, and its output is sampled at 250 kHz. A cepstrogram database is compiled from multiple vessel transits, and its cepstrum-based feature vectors (along with ground-truth range data) form the input to train a convolutional neural network (CNN) so that it can predict the source range relative to the hydrophone for other ("unseen") vessel transits. The CNN provides an accurate prediction of the instantaneous source range even when the range estimate from conventional multipath passive ranging is biased, which occurs at low grazing angles (<12°).

Reflective metamaterial polarizer enabled by solid-immersion Lloyd's mirror interference lithography

Metamaterials with induced form birefringence arising from orderly arrangements of subwavelength structures can realize effective refractive indices that do not exist in nature. Using lithographically-defined thin film or multilayered metasurfaces, such form birefringence can be used for polarization and phase control in thin-film elements. In this work, the authors experimentally demonstrate a highly birefringent omnidirectional broadband reflective metamaterial polarizer (RMP), fabricated using a solid-immersion Lloyd's mirror interference lithography (SILMIL) technique. This technique can create 55 nm half-pitch gratings, up to 200 nm tall, using single 405 nm exposures. Angle-resolved reflection spectra of SILMIL-fabricated subwavelength dual-silver grating RMPs exhibit excellent omnidirectionality over a broad spectral bandwidth in the optical range. The behavior and mechanism of the double-layer RMP has been analyzed with finite-difference time domain and rigorous coupled wave analysis simulations, showing coupling between excited surface plasmon polaritons and multiple Fabry–Perot resonances. Furthermore, the authors propose via simulation that by switching from a dielectric resonator to a metallic resonator, the SILMIL technique can be used to fabricate dual-layer thin-film metamaterials that have the capability of phase retardation control, providing a new scheme for reflective thin-film waveplates.

Design optimization of a non-orthogonal two-axis Lloyd's mirror interferometer for fabrication of large-area two-dimensional scale gratings

An optimized beam expansion assembly is newly designed for a non-orthogonal two-axis Lloyd's mirror interferometer to fabricate large-area two-dimensional (2D) diffraction scale gratings in a small-scale manufacturing facility or a research laboratory. Theoretical calculations are at first carried out to quantitatively estimate the influences of the coherence length and the Gaussian light intensity distribution of a collimated laser beam, which is projected onto a mirror-substrate assembly for the generation of interference fringe fields on a substrate. Design optimization of the interferometer is then carried out in such a way that a beam shaper, which contributes to obtain a flat-top light intensity distribution in the collimated laser beam and is expected to reduce the amplitude deviation of the developed pattern structures as well as the pattern exposure time, is integrated into the beam expansion assembly. The feasibility of the newly developed beam expansion assembly is demonstrated through fabricating a 100 mm × 100 mm 2D scale grating having pattern structures with uniform amplitude of approximately 500 nm and a short period of 1 μm.

Fabrication of micrometer-scale surface relief gratings in azobenzene molecular glass films using a modified Lloyd's mirror interferometer

Large-scale surface relief diffraction gratings with pitches up to 20 μm were fabricated in thin films of azobenzene molecular glass using a single-step and mask-less photolithography process. A modified Lloyd's mirror interferometer having two degrees of freedom generated an interference pattern that was incident on the azobenzene films. Some of the fabricated gratings had non-periodic profiles resulting from the superposition of multiple sine waves, while others had periodic blazed sawtooth and Dirac comb profiles. Furthermore, careful selection of the experimental parameters resulted in gratings with a beat interference profile having a clearly-visible modulation envelope. A theoretical framework was developed to successfully explain the obtained grating profiles.

A compact two-axis Lloyd's mirror interferometer for scale grating fabrication

A compact two-axis Lloyd's mirror interferometer for scale grating fabrication

Flexible and stretchable guided-mode resonant optical sensor: single-step fabrication on a surface engineered polydimethylsiloxane substrate

We present an unconventional yet simple and effective surface re-engineering method to hydrophilize the polydimethylsiloxane (PDMS) surface for the direct fabrication of a flexible and stretchable guided mode resonance (GMR) sensor. It enables us to directly spin coat photoresist as a planar waveguide on a PDMS substrate without any oxygen or UV treatment. To fabricate a GMR structure, a 1D grating is surface-patterned on this coated photoresist layer through Lloyd mirror interference lithography. A sensing experiment is performed with the obtained GMR structure and is validated by FDTD simulations. The sensor performance is consistent over repeated measurements, making the PDMS surface highly resistant to hydrophobic recovery.

Optical spectrometer based on continuously-chirped guided mode resonance filter.

In this work we introduce a tunable GMR filter based on continuously period-chirped (ΔP = 130 nm) gratings using a Ta2O5 waveguide layer with graded thickness (ΔT = 36 nm). The structure of the gradient-period grating is defined using a modified Lloyd's mirror interferometer with a convex mirror, and Ta2O5 film used for the gradient is deposited using masked e-beam evaporation. The as-realized chirped GMR filter provides sharp transmission dips at resonant wavelengths with a filter bandwidth of approximately 4.2 nm and 0.78 nm when respectively applied to TE and TM polarized light under normal incidence. Gradually sweeping the chirped GMR filter makes it possible to monotonically sweep through resonant wavelengths from 500 to 700 nm, while maintaining stable filter bandwidth and transmission intensity. The optical spectrum of the incoming light can then be loyally reconstructed accordingly. We successfully demonstrate the spectrum reconstruction of a white light emitting diode and a dual-peak laser beam using the proposed chirped GMR filter as a dispersive device.

Modeling acoustic interactions with a dynamic rough sea surface boundary

The acoustic wave scattering properties of a dynamic pressure-release surface boundary are analyzed using a numeric technique based on the finite-difference time-domain (FDTD) method. Of primary interest is to study the impact of assuming a “frozen” sea-surface on long duration sonar transmissions. Although relatively uncommon in ocean acoustics, the FDTD approach is well suited for modeling boundary roughness and motion. This technique has the additional benefit that the pressure fields are resolved over time, which allows for transient analysis of the observed wave scattering effects. The method is adapted from electromagnetic wave scattering and can properly model the physics of the observed system, which shows a frequency modulated reflection that includes a double-Doppler effect. First, a traditional analytic solution for the static smooth surface boundary ocean half-space model, the Lloyd Mirror, is compared to an equivalent simulation using the FDTD method. Then a dynamic smooth surface boundary is investigated using a modified Lloyd-mirror solution and the FDTD method. Finally, surface roughness for both static and dynamic boundary cases will be considered. Agreement is shown between FDTD simulations and the modified Lloyd Mirror model for both one-dimension and two-dimension cases. [Work supported by the Office of Naval Research.]