Laser frequency noise characterization using high-finesse plano-concave optical microresonators.

Characterizing laser frequency noise is essential for applications including optical sensing and coherent optical communications. Accurate measurement of ultra-narrow linewidth lasers over a wide frequency range using existing methods is still challenging. Here we present a method for characterizing the frequency noise of lasers using a high-finesse plano-concave optical microresonator (PCMR) acting as a frequency discriminator. To enable noise measurements at a wide range of laser frequencies, an array of PCMRs was produced with slight variations of thickness resulting in a series of discriminators operating at a series of periodical frequencies. This method enables measuring the frequency noise over a wide linewidth range (15 Hz to <100 MHz) over the 1440-1630 nm wavelength range. To assess the performance of the method, four different lasers were characterized, and the results were compared to the estimations of a commercial frequency noise analyzer.

Increasing the Q-factor of Fabry-Perot etalons using focused Bessel beam illumination.

Sensing and filtering applications often require Fabry-Perot (FP) etalons with an Interferometer Transfer Function (ITF) having high visibility, narrow Full Width at Half Maximum (FWHM), and high sensitivity. For the ITF to have these characteristics, the illumination beam must be matched to the modes of the FP cavity. This is challenging when a small illumination element size is needed, as typical focused beams are not matched to the FP cavity modes. Bessel beams are a potential alternative as their structure resembles the FP cavity modes while possessing a focused core. To study the feasibility of using Bessel beam illumination, in this Letter, ITFs of an FP etalon were measured using Bessel and Gaussian illumination beams. A Bessel beam with core size of 28 µm provided an ITF with visibility 3.0 times higher, a FWHM 0.3 times narrower, and a sensitivity 2.2 times higher than a Gaussian beam with waist 32 µm. The results show that Bessel beam illumination can provide ITFs similar to that of collimated beam illumination while also having with a focused core.

Spatially resolved readout of a Fabry-Perot ultrasound sensor interrogated through a multimode optical fiber using wavefront shaping.

The spatially resolved interrogation of a Fabry-Perot ultrasound sensor using a laser beam focused through a multimode fiber is demonstrated. To scan the beam across the sensor as required to read it out, optical wavefront shaping was employed to compensate for the scrambling of light in the fiber. By providing a means to map ultrasound through inexpensive, lightweight fibers, this could lead to new ultrasonic and photoacoustic imaging systems, such as endoscopes and flexible handheld probes.

ABCD transfer matrix model of Gaussian beam propagation in plano-concave optical microresonators.

Plano-concave optical microresonators (PCMRs) are optical microcavities formed of one planar and one concave mirror separated by a spacer. PCMRs illuminated by Gaussian laser beams are used as sensors and filters in fields including quantum electrodynamics, temperature sensing, and photoacoustic imaging. To predict characteristics such as the sensitivity of PCMRs, a model of Gaussian beam propagation through PCMRs based on the ABCD matrix method was developed. To validate the model, interferometer transfer functions (ITFs) calculated for a range of PCMRs and beams were compared to experimental measurements. A good agreement was observed, suggesting the model is valid. It could therefore constitute a useful tool for designing and evaluating PCMR systems in various fields. The computer code implementing the model has been made available online.

Numerical model of light propagation through Fabry-Perot etalons composed of interfaces with non-planar surface topography.

We present a model that calculates optical fields reflected and transmitted by a Fabry-Perot (FP) etalon composed of interfaces with non-planar surface topography. The model uses the Rayleigh-Rice theory, which predicts the fields reflected and transmitted by a single interface, to account for the non-planar surface topography of each interface. The Rayleigh-Rice theory is evaluated iteratively to account for all round trips that light can take within the FP etalon. The model predictions can then be used to compute Interferometer transfer function (ITF)s, by performing wavelength or angle resolved simulations enabling predictions of the bandwidth, peak transmissivity, and sensitivity of FP etalons. The model was validated against the Pseudospectral time-domain (PSTD) method, which resulted in good agreement. Since the model accuracy is expected to reduce as the Root mean square (RMS) of the topographic map increases, the error in the model's predictions was studied as a function of topographic map RMS. Finally, application of the model was exemplified by predicting the impact of roughness on ITFs and computing the changes in FP etalon transmissivity as cavity thickness is modulated by an ultrasonic wave.

ABCD transfer matrix model of Gaussian beam propagation in Fabry-Perot etalons.

A numerical model of Gaussian beam propagation in planar Fabry-Perot (FP) etalons is presented. The model is based on the ABCD transfer matrix method. This method is easy to use and interpret, and readily connects models of lenses, mirrors, fibres and other optics to aid simulating complex multi-component etalon systems. To validate the etalon model, its predictions were verified using a previously validated model based on Fourier optics. To demonstrate its utility, three different etalon systems were simulated. The results suggest the model is valid and versatile and could aid in designing and understanding a range of systems containing planar FP etalons. The method could be extended to model higher order beams, other FP type devices such as plano-concave resonators, and more complex etalon systems such as those involving tilted components.

Angular Airy function: a model of Fabry-Perot etalons illuminated by arbitrary beams.

Fabry-Perot (FP) etalons are used as filters and sensors in a range of optical systems. The reflected and transmitted fields associated with an FP etalon have traditionally been predicted by the Airy function, which assumes a plane wave illumination. FP etalons are, however, often illuminated by non-collimated beams, rendering the Airy function invalid. To address this limitation, we describe the angular Airy function which calculates the reflected and transmitted fields for arbitrary illumination beams, using angular spectrum decomposition. Combined with realistic models of the experimental illumination beams and detection optics, we show that the angular Airy function can accurately predict experimental wavelength resolved intensity measurements. Based on the angular Airy function, we show that the fundamental operating principle of an FP etalon is as an angular-spectral filter. Based on this interpretation we explain the asymmetry, broadening and visibility reduction seen on wavelength resolved intensity measurements from high Q-factor FP etalons illuminated with focused Gaussian beams.

Analysing the impact of non-parallelism in Fabry-Perot etalons through optical modelling.

Fabry-Perot (FP) etalons, composed of two parallel mirrors, are used widely as optical filters and sensors. In certain applications, however, such as when FP etalons with polymer cavities are used to detect ultrasound, the mirrors may not be perfectly parallel due to manufacturing limitations. As little is known about how the mirrors being non-parallel impacts upon FP etalon performance, it is challenging to optimize the design of such devices. To address this challenge, we developed a model of light propagation in non-parallel FP etalons. The model is valid for arbitrary monochromatic beams and calculates both the reflected and transmitted beams, assuming full-wave description of light. Wavelength resolved transmissivity simulations were computed to predict the effect that non-parallel mirrors have on the sensitivity, spectral bandwidth and peak transmissivity of FP etalons. Theoretical predictions show that the impact of the non-parallel mirrors increases with both mirror reflectivity and incident Gaussian beam waist. Guidelines regarding the maximum angle allowed between FP mirrors whilst maintaining the sensitivity and peak transmissivity of a parallel mirror FP etalon are provided as a function of mirror reflectivity, cavity thickness and Gaussian beam waist. This information, and the model, could be useful for guiding the design of FP etalons suffering a known degree of non-parallelism, for example, to optimize the sensitivity of polymer based FP ultrasound sensors.

Modelling Fabry-Pérot etalons illuminated by focussed beams.

Fabry-Pérot (FP) etalons are used as filters and sensors in a range of optical systems. Often FP etalons are illuminated by collimated laser beams, in which case the transmitted and reflected light fields can be calculated analytically using well established models. However, FP etalons are sometimes illuminated by more complex beams such as focussed Gaussian beams, which may also be aberrated. Modelling the response of FP etalons to these beams requires a more sophisticated model. To address this need, we present a model that can describe the response of an FP etalon that is illuminated by an arbitrary beam. The model uses an electromagnetic wave description of light and can therefore compute the amplitude, phase and polarization of the optical field at any position in the system. It can also account for common light delivery and detection components such as lenses, optical fibres and photo-detectors, allowing practical systems to be simulated. The model was validated against wavelength resolved measurements of transmittance and reflectance obtained using a system consisting of an FP etalon illuminated by a focussed Gaussian beam. Experiments with focal spot sizes ranging from 30 µm to 250 µm and FP etalon mirror reflectivities in the range 97.2 % to 99.2 % yielded excellent visual agreement between simulated and experimental data and an average error below 10% for a range of quantitative comparative metrics. We expect the model to be a useful tool for designing, understanding and optimising systems that use FP etalons.

Analysis of the Directivity of Glass-Etalon Fabry-Pérot Ultrasound Sensors.

Planar glass-etalon Fabry-Pérot (FP) optical ultrasound sensors offer an alternative to piezoelectric sensors for the measurements of high-intensity focused ultrasound (HIFU) fields and other metrological applications. In this work, a model of the frequency-dependent directional response of the FP sensor was developed using the global matrix method, treating the sensor as a multilayered elastic structure. The model was validated against the experimentally measured directional response of an air-backed cover-slip FP sensor with well-known material properties. In addition, the model was compared with the measurements of an all-hard-dielectric sensor suitable for HIFU measurements. The model was then used to calculate modal dispersion curves for both glass-etalon sensors, allowing the features of the directional response to be linked to specific wave phenomena. The features in the directivity of the air-backed cover-slip sensor are due to guided Lamb waves. Symmetric Lamb modes give rise to regions of high sensitivity, whereas anti-symmetric modes cause regions of low sensitivity. For the all-hard-dielectric sensor, two features correspond to the water-substrate and water-spacer compressional and shear critical angles. A region of high sensitivity close to the shear critical angle is associated with a leaky-Rayleigh wave, which has a frequency-dependent phase speed. At higher frequencies, this feature is counteracted by a region of low sensitivity, which occurs when there is no difference in the vertical displacement of the mirrors forming the FP cavity. The model may be used to improve and optimize the design of FP sensors or could be used to assist with the accurate deconvolution of the directional response from array measurements in metrological and imaging applications.

Quantitative bioluminescence tomography using spectral derivative data.

Bioluminescence imaging (BLI) is a non-contact, optical imaging technique based on measurement of emitted light due to an internal source, which is then often directly related to cellular activity. It is widely used in pre-clinical small animal imaging studies to assess the progression of diseases such as cancer, aiding in the development of new treatments and therapies. For many applications, the quantitative assessment of accurate cellular activity and spatial distribution is desirable as it would enable direct monitoring for prognostic evaluation. This requires quantitative spatially-resolved measurements of bioluminescence source strength inside the animal to be obtained from BLI images. This is the goal of bioluminescence tomography (BLT) in which a model of light propagation through tissue is combined with an optimization algorithm to reconstruct a map of the underlying source distribution. As most models consider only the propagation of light from internal sources to the animal skin surface, an additional challenge is accounting for the light propagation from the skin to the optical detector (e.g. camera). Existing approaches typically use a model of the imaging system optics (e.g. ray-tracing, analytical optical models) or approximate corrections derived from calibration measurements. However, these approaches are typically computationally intensive or of limited accuracy. In this work, a new approach is presented in which, rather than directly using BLI images acquired at several wavelengths, the spectral derivative of that data (difference of BLI images at adjacent wavelengths) is used in BLT. As light at similar wavelengths encounters a near-identical system response (path through the optics etc.) this eliminates the need for additional corrections or system models. This approach is applied to BLT with simulated and experimental phantom data and shown that the error in reconstructed source intensity is reduced from 49% to 4%. Qualitatively, the accuracy of source localization is improved in both simulated and experimental data, as compared to reconstruction using the standard approach. The outlined algorithm can widely be adapted to all commercial systems without any further technological modifications.

A Method for Measuring the Directional Response of Ultrasound Receivers in the Range 0.3-80 MHz Using a Laser-Generated Ultrasound Source.

A simple method for measuring the directivity of an ultrasound receiver is described. The method makes use of a custom-designed laser ultrasound source which generates a large diameter (>1 cm) broadband monopolar plane wave with a continuous frequency content extending from to . The plane wave is highly uniform in amplitude (±5% over >8 mm) and phase (equivalent to at 80 MHz over ). To measure directivity, the source is rotated around the receiver under test in a compact centimeter-scale setup. To demonstrate the method, it was used to measure the directivity of two broadband small aperture Fabry-Perot ultrasound sensors over an angular range of ±50° at frequencies up to 80 MHz. Measurements were found to be highly repeatable with an estimated typical repeatability <4% in the range of 0.5-25 MHz. Due to the broad bandwidth, large size, and adjustable nature of the source, the method is widely applicable and could aid the characterization of receivers used in medical ultrasound, ultrasonic nondestructive testing. and ultrasound metrology.

Characterization and modeling of Fabry-Perot ultrasound sensors with hard dielectric mirrors for photoacoustic imaging.

A Fabry-Perot ultrasound sensor with nonhygroscopic dielectric mirrors made out of Ta2O5 and SiO2 for use in photoacoustic tomography is described. The sensor offers flat frequency response up to 36 MHz, low noise-equivalent pressure (70 Pa), and near-omnidirectional response up to 20 MHz as well as optical transparency for near-infrared illumination. A numerical model was developed to predict its frequency response, and the results were validated experimentally. An image of the human palm was acquired to demonstrate in vivo imaging capabilities.

Rapid Spatial Mapping of Focused Ultrasound Fields Using a Planar Fabry-Pérot Sensor.

Measurement of high acoustic pressures is necessary in order to fully characterize clinical high-intensity focused ultrasound (HIFU) fields, and for accurate validation of computational models of ultrasound propagation. However, many existing measurement devices are unable to withstand the extreme pressures generated in these fields, and those that can often exhibit low sensitivity. Here, a planar Fabry-Pérot interferometer with hard dielectric mirrors and spacer was designed, fabricated, and characterized, and its suitability for measurement of nonlinear focused ultrasound fields was investigated. The noise equivalent pressure (NEP) of the scanning system scaled with the adjustable pressure detection range between 49 kPa for pressures up to 8 MPa and 152 kPa for measurements up to 25 MPa, over a 125 MHz measurement bandwidth. Measurements of the frequency response of the sensor showed that it varied by less than 3 dB in the range 1-62 MHz. The effective element size of the sensor was 65 and waveforms were acquired at a rate of 200 Hz. The device was used to measure the acoustic pressure in the field of a 1.1 MHz single-element spherically focused bowl transducer. Measurements of the acoustic field at low pressures compared well with measurements made using a Polyvinylidene difluoride needle hydrophone. At high pressures, the measured peak focal pressures agreed well with the focal pressure modeled using the Khokhlov-Zabolotskaya-Kuznetsov equation. Maximum peak positive pressures of 25 MPa and peak negative pressures of 12 MPa were measured, and planar field scans were acquired in scan times on the order of 1 min. The properties of the sensor and scanning system are well suited to measurement of nonlinear focused ultrasound fields, in both the focal region and the low-pressure peripheral regions. The fast acquisition speed of the system and its low NEP are advantageous, and with further development of the sensor, it has potential in application to HIFU metrology.

Time resolved diffuse optical spectroscopy with geometrically accurate models for bulk parameter recovery.

A novel straightforward, accessible and efficient approach is presented for performing hyperspectral time-domain diffuse optical spectroscopy to determine the optical properties of samples accurately using geometry specific models. To allow bulk parameter recovery from measured spectra, a set of libraries based on a numerical model of the domain being investigated is developed as opposed to the conventional approach of using an analytical semi-infinite slab approximation, which is known and shown to introduce boundary effects. Results demonstrate that the method improves the accuracy of derived spectrally varying optical properties over the use of the semi-infinite approximation.

Photoacoustic imaging of human lymph nodes with endogenous lipid and hemoglobin contrast.

Lymph nodes play a central role in metastatic cancer spread and are a key clinical assessment target. Abnormal node vascularization, morphology, and size may be indicative of disease but can be difficult to visualize with sufficient accuracy using existing clinical imaging modalities. To explore the potential utility of photoacoustic imaging for the assessment of lymph nodes, images of ex vivo samples were obtained at multiple wavelengths using a high-resolution three-dimensional photoacoustic scanner. These images showed that hemoglobin based contrast reveals nodal vasculature and lipid-based contrast reveals the exterior node size, shape, and boundary integrity. These two sources of complementary contrast may allow indirect observation of cancer, suggesting a future role for photoacoustic imaging as a tool for the clinical assessment of lymph nodes.

Quantitative surface radiance mapping using multiview images of light-emitting turbid media.

A novel method is presented for accurately reconstructing a spatially resolved map of diffuse light flux on a surface using images of the surface and a model of the imaging system. This is achieved by applying a model-based reconstruction algorithm with an existing forward model of light propagation through free space that accounts for the effects of perspective, focus, and imaging geometry. It is shown that flux can be mapped reliably and quantitatively accurately with very low error, <3% with modest signal-to-noise ratio. Simulation shows that the method is generalizable to the case in which mirrors are used in the system and therefore multiple views can be combined in reconstruction. Validation experiments show that physical diffuse phantom surface fluxes can also be reconstructed accurately with variability <3% for a range of object positions, variable states of focus, and different orientations. The method provides a new way of making quantitatively accurate noncontact measurements of the amount of light leaving a diffusive medium, such as a small animal containing fluorescent or bioluminescent markers, that is independent of the imaging system configuration and surface position.

Simultaneous multiple view high resolution surface geometry acquisition using structured light and mirrors.

Knowledge of the surface geometry of an imaging subject is important in many applications. This information can be obtained via a number of different techniques, including time of flight imaging, photogrammetry, and fringe projection profilometry. Existing systems may have restrictions on instrument geometry, require expensive optics, or require moving parts in order to image the full surface of the subject. An inexpensive generalised fringe projection profilometry system is proposed that can account for arbitrarily placed components and use mirrors to expand the field of view. It simultaneously acquires multiple views of an imaging subject, producing a cloud of points that lie on its surface, which can then be processed to form a three dimensional model. A prototype of this system was integrated into an existing Diffuse Optical Tomography and Bioluminescence Tomography small animal imaging system and used to image objects including a mouse-shaped plastic phantom, a mouse cadaver, and a coin. A surface mesh generated from surface capture data of the mouse-shaped plastic phantom was compared with ideal surface points provided by the phantom manufacturer, and 50% of points were found to lie within 0.1mm of the surface mesh, 82% of points were found to lie within 0.2mm of the surface mesh, and 96% of points were found to lie within 0.4mm of the surface mesh.

Multi-modal molecular diffuse optical tomography system for small animal imaging.

A multi-modal optical imaging system for quantitative 3D bioluminescence and functional diffuse imaging is presented, which has no moving parts and uses mirrors to provide multi-view tomographic data for image reconstruction. It is demonstrated that through the use of trans-illuminated spectral near infrared measurements and spectrally constrained tomographic reconstruction, recovered concentrations of absorbing agents can be used as prior knowledge for bioluminescence imaging within the visible spectrum. Additionally, the first use of a recently developed multi-view optical surface capture technique is shown and its application to model-based image reconstruction and free-space light modelling is demonstrated. The benefits of model-based tomographic image recovery as compared to 2D planar imaging are highlighted in a number of scenarios where the internal luminescence source is not visible or is confounding in 2D images. The results presented show that the luminescence tomographic imaging method produces 3D reconstructions of individual light sources within a mouse-sized solid phantom that are accurately localised to within 1.5mm for a range of target locations and depths indicating sensitivity and accurate imaging throughout the phantom volume. Additionally the total reconstructed luminescence source intensity is consistent to within 15% which is a dramatic improvement upon standard bioluminescence imaging. Finally, results from a heterogeneous phantom with an absorbing anomaly are presented demonstrating the use and benefits of a multi-view, spectrally constrained coupled imaging system that provides accurate 3D luminescence images.

Compressive sensing based reconstruction in bioluminescence tomography improves image resolution and robustness to noise.

Bioluminescence Tomography attempts to quantify 3-dimensional luminophore distributions from surface measurements of the light distribution. The reconstruction problem is typically severely under-determined due to the number and location of measurements, but in certain cases the molecules or cells of interest form localised clusters, resulting in a distribution of luminophores that is spatially sparse. A Conjugate Gradient-based reconstruction algorithm using Compressive Sensing was designed to take advantage of this sparsity, using a multistage sparsity reduction approach to remove the need to choose sparsity weighting a priori. Numerical simulations were used to examine the effect of noise on reconstruction accuracy. Tomographic bioluminescence measurements of a Caliper XPM-2 Phantom Mouse were acquired and reconstructions from simulation and this experimental data show that Compressive Sensing-based reconstruction is superior to standard reconstruction techniques, particularly in the presence of noise.