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.

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.

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.

Simulation of statistically accurate time-integrated dynamic speckle patterns in biomedical optics.

The simulation of statistically accurate time-integrated dynamic speckle patterns using a physics-based model that accounts for spatially varying sample properties is yet to be presented in biomedical optics. In this Letter, we propose a solution to this important problem based on the Karhunen-Loève expansion of the electric field and apply our method to the formalisms of both laser speckle contrast imaging and diffuse correlation spectroscopy. We validate our technique against solutions for speckle contrast for different forms of homogeneous field and also show that our method can readily be extended to cases with spatially varying sample properties.

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.

REEP6 deficiency leads to retinal degeneration through disruption of ER homeostasis and protein trafficking.

Retinitis pigmentosa (RP) is the most common form of inherited retinal dystrophy. We recently identified mutations in REEP6, which encodes the receptor expression enhancing protein 6, in several families with autosomal recessive RP. REEP6 is related to the REEP and Yop1p family of ER shaping proteins and potential receptor accessory proteins, but the role of REEP6 in the retina is unknown. Here we characterize the disease mechanisms associated with loss of REEP6 function using a Reep6 knockout mouse generated by CRISPR/Cas9 gene editing. In control mice REEP6 was localized to the inner segment and outer plexiform layer of rod photoreceptors. The Reep6-/- mice exhibited progressive photoreceptor degeneration from P20 onwards. Ultrastructural analyses at P20 by transmission electron microscopy and 3View serial block face scanning EM revealed an expansion of the distal ER in the Reep6-/- rods and an increase in their number of mitochondria. Electroretinograms revealed photoreceptor dysfunction preceded degeneration, suggesting potential defects in phototransduction. There was no effect on the traffic of rhodopsin, Rom1 or peripherin/rds; however, the retinal guanylate cyclases GC1 and GC2 were severely affected in the Reep6 knockout animals, with almost undetectable expression. These changes correlated with an increase in C/EBP homologous protein (CHOP) expression and the activation of caspase 12, suggesting that ER stress contributes to cell death. Collectively, these data suggest that REEP6 plays an essential role in maintaining cGMP homeostasis though facilitating the stability and/or trafficking of guanylate cyclases and maintaining ER and mitochondrial homeostasis.

Rescue of mutant rhodopsin traffic by metformin-induced AMPK activation accelerates photoreceptor degeneration.

Protein misfolding caused by inherited mutations leads to loss of protein function and potentially toxic 'gain of function', such as the dominant P23H rhodopsin mutation that causes retinitis pigmentosa (RP). Here, we tested whether the AMPK activator metformin could affect the P23H rhodopsin synthesis and folding. In cell models, metformin treatment improved P23H rhodopsin folding and traffic. In animal models of P23H RP, metformin treatment successfully enhanced P23H traffic to the rod outer segment, but this led to reduced photoreceptor function and increased photoreceptor cell death. The metformin-rescued P23H rhodopsin was still intrinsically unstable and led to increased structural instability of the rod outer segments. These data suggest that improving the traffic of misfolding rhodopsin mutants is unlikely to be a practical therapy, because of their intrinsic instability and long half-life in the outer segment, but also highlights the potential of altering translation through AMPK to improve protein function in other protein misfolding diseases.

Mutations in REEP6 Cause Autosomal-Recessive Retinitis Pigmentosa.

Retinitis pigmentosa (RP) is the most frequent form of inherited retinal dystrophy. RP is genetically heterogeneous and the genes identified to date encode proteins involved in a wide range of functional pathways, including photoreceptor development, phototransduction, the retinoid cycle, cilia, and outer segment development. Here we report the identification of biallelic mutations in Receptor Expression Enhancer Protein 6 (REEP6) in seven individuals with autosomal-recessive RP from five unrelated families. REEP6 is a member of the REEP/Yop1 family of proteins that influence the structure of the endoplasmic reticulum but is relatively unstudied. The six variants identified include three frameshift variants, two missense variants, and a genomic rearrangement that disrupts exon 1. Human 3D organoid optic cups were used to investigate REEP6 expression and confirmed the expression of a retina-specific isoform REEP6.1, which is specifically affected by one of the frameshift mutations. Expression of the two missense variants (c.383C>T [p.Pro128Leu] and c.404T>C [p.Leu135Pro]) and the REEP6.1 frameshift mutant in cultured cells suggest that these changes destabilize the protein. Furthermore, CRISPR-Cas9-mediated gene editing was used to produce Reep6 knock-in mice with the p.Leu135Pro RP-associated variant identified in one RP-affected individual. The homozygous knock-in mice mimic the clinical phenotypes of RP, including progressive photoreceptor degeneration and dysfunction of the rod photoreceptors. Therefore, our study implicates REEP6 in retinal homeostasis and highlights a pathway previously uncharacterized in retinal dystrophy.

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.

Strain hardening and anisotropy in tensile fracture properties of sheared model Mozzarella cheeses.

We studied the tensile fracture properties of model Mozzarella cheeses with varying amounts of shear work input (3.3-73.7 kJ/kg). After manufacture, cheeses were elongated by manual rolling at 65°C followed by tensile testing at 21°C on dumbbell-shaped samples cut both parallel and perpendicular to the rolling direction. Strain hardening parameters were estimated from stress-strain curves using 3 different methods. Fracture stress and strain for longitudinal samples did not vary significantly with shear work input up to 26.3 kJ/kg and then decreased dramatically at 58.2 kJ/kg. Longitudinal samples with shear work input <30 kJ/kg demonstrated significant strain hardening by all 3 estimation methods. At shear work inputs <30 kJ/kg, strong anisotropy was observed in both fracture stress and strain. After a shear work input of 58.2 kJ/kg, anisotropy and strain hardening were absent. Perpendicular samples did not show strain hardening at any level of shear work input. Although the distortion of the fat drops in the cheese structure associated with the elongation could account for some of the anisotropy observed, the presence of anisotropy in the elongated nonfat samples reflected that shear work and rolling also aligned the protein structure.

The severity of retinal pathology in homozygous Crb1rd8/rd8 mice is dependent on additional genetic factors.

Understanding phenotype-genotype correlations in retinal degeneration is a major challenge. Mutations in CRB1 lead to a spectrum of autosomal recessive retinal dystrophies with variable phenotypes suggesting the influence of modifying factors. To establish the contribution of the genetic background to phenotypic variability associated with the Crb1(rd8/rd8) mutation, we compared the retinal pathology of Crb1(rd8/rd8)/J inbred mice with that of two Crb1(rd8/rd8) lines backcrossed with C57BL/6JOlaHsd mice. Topical endoscopic fundal imaging and scanning laser ophthalmoscopy fundus images of all three Crb1(rd8/rd8) lines showed a significant increase in the number of inferior retinal lesions that was strikingly variable between the lines. Optical coherence tomography, semithin, ultrastructural morphology and assessment of inflammatory and vascular marker by immunohistochemistry and quantitative reverse transcriptase-polymerase chain reaction revealed that the lesions were associated with photoreceptor death, Müller and microglia activation and telangiectasia-like vascular remodelling-features that were stable in the inbred, variable in the second, but virtually absent in the third Crb1(rd8/rd8) line, even at 12 months of age. This suggests that the Crb1(rd8/rd8) mutation is necessary, but not sufficient for the development of these degenerative features. By whole-genome SNP analysis of the genotype-phenotype correlation, a candidate region on chromosome 15 was identified. This may carry one or more genetic modifiers for the manifestation of the retinal pathology associated with mutations in Crb1. This study also provides insight into the nature of the retinal vascular lesions that likely represent a clinical correlate for the formation of retinal telangiectasia or Coats-like vasculopathy in patients with CRB1 mutations that are thought to depend on such genetic modifiers.

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.