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.

Diffuse Correlation Spectroscopy: A Review of Recent Advances in Parallelisation and Depth Discrimination Techniques.

Diffuse correlation spectroscopy is a non-invasive optical modality used to measure cerebral blood flow in real time, and it has important potential applications in clinical monitoring and neuroscience. As such, many research groups have recently been investigating methods to improve the signal-to-noise ratio, imaging depth, and spatial resolution of diffuse correlation spectroscopy. Such methods have included multispeckle, long wavelength, interferometric, depth discrimination, time-of-flight resolution, and acousto-optic detection strategies. In this review, we exhaustively appraise this plethora of recent advances, which can be used to assess limitations and guide innovation for future implementations of diffuse correlation spectroscopy that will harness technological improvements in the years to come.

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.

Application of a Taylor series approximation to the Debye-Wolf integral in time-domain numerical electromagnetic simulations.

Finite-difference time-domain (FDTD) and pseudospectral time-domain (PSTD) methods are numerical electromagnetic simulation techniques that have been employed to perform rigorous simulations of broadband illuminations in several contexts. However, the computational cost of calculating the incident source fields introduced into the FDTD/PSTD grid can be considerable. In some cases, this can exceed the computational cost of what might be considered the principal part of the FDTD/PSTD algorithm, which calculates the spatial derivative of fields throughout the computational grid. In this paper, we analyze an existing method that has been used to approximate broadband illumination, which uses knowledge of the field only at a central frequency of the spectrum. We then present a new, to the best of our knowledge, approximation of the broadband illumination, which is more accurate, while remaining computationally tractable. Finally, we present some examples to verify the accuracy and efficiency of the new method and compare these results with the existing method.

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.

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.

Speckle-dependent accuracy in phase-sensitive optical coherence tomography.

Phase-sensitive optical coherence tomography (OCT) is used to measure motion in a range of techniques, such as Doppler OCT and optical coherence elastography (OCE). In phase-sensitive OCT, motion is typically estimated using a model of the OCT signal derived from a single reflector. However, this approach is not representative of turbid samples, such as tissue, which exhibit speckle. In this study, for the first time, we demonstrate, through theory and experiment that speckle significantly lowers the accuracy of phase-sensitive OCT in a manner not accounted for by the OCT signal-to-noise ratio (SNR). We describe how the inaccuracy in speckle reduces phase difference sensitivity and introduce a new metric, speckle brightness, to quantify the amount of constructive interference at a given location in an OCT image. Experimental measurements show an almost three-fold degradation in sensitivity between regions of high and low speckle brightness at a constant OCT SNR. Finally, we apply these new results in compression OCE to demonstrate a ten-fold improvement in strain sensitivity, and a five-fold improvement in contrast-to-noise by incorporating independent speckle realizations. Our results show that speckle introduces a limit to the accuracy of phase-sensitive OCT and that speckle brightness should be considered to avoid erroneous interpretation of experimental data.

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.

Optimal compressive multiphoton imaging at depth using single-pixel detection.

Compressive sensing can overcome the Nyquist criterion and record images with a fraction of the usual number of measurements required. However, conventional measurement bases are susceptible to diffraction and scattering, prevalent in high-resolution microscopy. In this Letter, we explore the random Morlet basis as an optimal set for compressive multiphoton imaging, based on its ability to minimize the space-frequency uncertainty. We implement this approach for wide-field multiphoton microscopy with single-pixel detection, which allows imaging through turbid media without correction. The Morlet basis promises a route for rapid acquisition with lower photodamage.

Rigorous multi-slice wave optical simulation of x-ray propagation in inhomogeneous space.

The simulation of the propagation of divergent beams using Fourier-based angular spectrum techniques can pose challenges for ensuring correct sampling in the spatial and reciprocal domains. This challenge can be compounded by the presence of diffracting objects, as is often the case. Here, I give details of a method for robustly simulating the propagation of beams with divergent wavefronts in a coordinate system where the wavefronts become planar. I also show how diffracting objects can be simulated, while guaranteeing that correct sampling is maintained. These two advances allow for numerically efficient and accurate simulations of divergent beams propagating through diffracting structures using the multi-slice approximation. The sampling requirements and numerical implementation are discussed in detail, and I have made the computer code freely available.

Retrieval of weak x-ray scattering using edge illumination.

X-ray phase contrast imaging provides additional modes of image contrast compared to conventional attenuation-based x-ray imaging, thus providing additional structural and functional information about the sample. The edge-illumination (EI) technique has been used to provide attenuation, refraction, and scattering contrast in both biological and non-biological samples. However, the retrieval of low scattering signals by fitting a single Gaussian remains problematic, principally due to the inability of the EI system to achieve perfect dark-field illumination. We present a new retrieval method that fits three Gaussians, which successfully overcomes this limitation, and provide examples of the retrieval of such signals in highly absorbing, weakly scattering samples.

Three-dimensional full wave model of image formation in optical coherence tomography.

We demonstrate, what we believe to be, the first mathematical model of image formation in optical coherence tomography, based on Maxwell's equations, applicable to general three-dimensional samples. It is highly realistic and represents a significant advance on a previously developed model, which was applicable to two-dimensional samples only. The model employs an electromagnetic description of light, made possible by using the pseudospectral time-domain method for calculating the light scattered by the sample which is represented by a general refractive index distribution. We derive the key theoretical and computational advances required to develop this model. Two examples are given of image formation for which analytic comparisons may be calculated: point scatterers and finite sized spheres. We also provide a more realistic example of C-scan formation when imaging turbid media. We anticipate that this model will be important for various applications in OCT, such as image interpretation and the development of quantitative techniques.

Estimates of leaf vein density are scale dependent.

Leaf vein density (LVD) has garnered considerable attention of late, with numerous studies linking it to the physiology, ecology, and evolution of land plants. Despite this increased attention, little consideration has been given to the effects of measurement methods on estimation of LVD. Here, we focus on the relationship between measurement methods and estimates of LVD. We examine the dependence of LVD on magnification, field of view (FOV), and image resolution. We first show that estimates of LVD increase with increasing image magnification and resolution. We then demonstrate that estimates of LVD are higher with higher variance at small FOV, approaching asymptotic values as the FOV increases. We demonstrate that these effects arise due to three primary factors: (1) the tradeoff between FOV and magnification; (2) geometric effects of lattices at small scales; and; (3) the hierarchical nature of leaf vein networks. Our results help to explain differences in previously published studies and highlight the importance of using consistent magnification and scale, when possible, when comparing LVD and other quantitative measures of venation structure across leaves.

Exploiting data redundancy in computational optical imaging.

We present an algorithm which exploits data redundancy to make computational, coherent, optical imaging more computationally efficient. This algorithm specifically addresses the computation of how light scattered by a sample is collected and coherently detected. It is of greatest benefit in the simulation of broadband optical systems employing coherent detection, such as optical coherence tomography. Although also amenable to time-harmonic data, the algorithm is designed to be embedded within time-domain electromagnetic scattering simulators such as the psuedo-spectral and finite-difference time domain methods. We derive the algorithm in detail as well as criteria which ensure accurate execution of the algorithm. We present simulations that verify the developed algorithm and demonstrate its utility. We expect this algorithm to be important to future developments in computational imaging.

Full wave model of image formation in optical coherence tomography applicable to general samples.

We demonstrate a highly realistic model of optical coherence tomography, based on an existing model of coherent optical microscopes, which employs a full wave description of light. A defining feature of the model is the decoupling of the key functions of an optical coherence tomography system: sample illumination, light-sample interaction and the collection of light scattered by the sample. We show how such a model can be implemented using the finite-difference time-domain method to model light propagation in general samples. The model employs vectorial focussing theory to represent the optical system and, thus, incorporates general illumination beam types and detection optics. To demonstrate its versatility, we model image formation of a stratified medium, a numerical point-spread function phantom and a numerical phantom, based upon a physical three-dimensional structured phantom employed in our laboratory. We show that simulated images compare well with experimental images of a three-dimensional structured phantom. Such a model provides a powerful means to advance all aspects of optical coherence tomography imaging.

Phase and absorption retrieval using incoherent X-ray sources.

X-ray phase contrast imaging has overcome the limitations of X-ray absorption imaging in many fields. Particular effort has been directed towards developing phase retrieval methods: These reveal quantitative information about a sample, which is a requirement for performing X-ray phase tomography, allows material identification and better distinction between tissue types, etc. Phase retrieval seems impossible with conventional X-ray sources due to their low spatial coherence. In the only previous example where conventional sources have been used, collimators were employed to produce spatially coherent secondary sources. We present a truly incoherent phase retrieval method, which removes the spatial coherence constraints and employs a conventional source without aperturing, collimation, or filtering. This is possible because our technique, based on the pixel edge illumination principle, is neither interferometric nor crystal based. Beams created by an X-ray mask to image the sample are smeared due to the incoherence of the source, yet we show that their displacements can still be measured accurately, obtaining strong phase contrast. Quantitative information is extracted from only two images rather than a sequence as required by several coherent methods. Our technique makes quantitative phase imaging and phase tomography possible in applications where exposure time and radiation dose are critical. The technique employs masks which are currently commercially available with linear dimensions in the tens of centimeters thus allowing for a large field of view. The technique works at high photon energy and thus promises to deliver much safer quantitative phase imaging and phase tomography in the future.

A compact source condition for modelling focused fields using the pseudospectral time-domain method.

The pseudospectral time-domain (PSTD) method greatly extends the physical volume of biological tissue in which light scattering can be calculated, relative to the finite-difference time-domain (FDTD) method. We have developed an analogue of the total-field scattered-field source condition, as employed in FDTD, for introducing focussed illuminations into PSTD simulations. This new source condition requires knowledge of the incident field, and applies update equations, at a single plane in the PSTD grid. Numerical artifacts, usually associated with compact PSTD source conditions, are minimized by using a staggered grid. This source condition's similarity with that used by the FDTD suggests a way in which existing FDTD codes can be easily adapted to PSTD codes.

A simplified approach to quantitative coded aperture X-ray phase imaging.

We recently demonstrated how quantitative X-ray phase contrast imaging may be performed with laboratory sources using the coded aperture technique. This technique required the knowledge of system parameters such as, for example, the source focal spot size and distances between elements of the imaging system. The method also assumes that the absorbing regions of the apertures are perfectly absorbing. In this paper we demonstrate how quantitative imaging can be performed without knowledge of individual system parameters and with partially absorbing apertures. We also show that this method is analogous to that employed in analyser based imaging which uses the rocking curve of an analyser crystal.

A quantitative, non-interferometric X-ray phase contrast imaging technique.

We present a quantitative, non-interferometric, X-ray differential phase contrast imaging technique based on the edge illumination principle. We derive a novel phase retrieval algorithm which requires only two images to be acquired and verify the technique experimentally using synchrotron radiation. The technique is useful for planar imaging but is expected to be important for quantitative phase tomography also. The properties and limitations of the technique are studied in detail.