Coherent Reflection Research Articles

The small-slope approximation for layered, fluid seafloors.

The small-slope approximation (SSA) for rough-interface scattering is most commonly applied to the upper boundary of either impenetrable media or uniform half-space media, but has been recently developed for layered media in the acoustic and electromagnetic cases. The present work gives an overview of three forms of the SSA for layered media. The first has been previously presented in the acoustics literature. The second is from the electromagnetics literature and in the present work is converted to the fluid-sediment problem. A missing proof is supplied of a key consistency condition demanded of the small-slope ansatz. As is usual, these small-slope results are expressed in k-space. A third SSA for layered seafloors follows from conversion of the usual half-space formulation from k-space to coordinate space. This form turns out to be useful for reverberation simulations. The three different approaches are compared with respect to scattering strength and the coherent reflection coefficient, but an assessment of their relative merits will require comparison with exact calculations.

Sea Ice Thickness Measurement Using Spaceborne GNSS-R: First Results With TechDemoSat-1 Data

In this article, an effective schematic is developed for estimating sea ice thickness (SIT) from the reflectivity ( $\Gamma$ ) produced with TechDemoSat-1 (TDS-1) Global Navigation Satellite System-Reflectometry data. Here, $\Gamma$ is formulated as the product of the propagation loss due to SIT and the reflection coefficient of underlying seawater. The effect of surface roughness on $\Gamma$ is neglected when only considering signals of coherent reflection. In practice, $\Gamma$ at the specular point is first generated using TDS-1 data. Afterwards, SIT is calculated from TDS-1 $\Gamma$ based on the proposed reflectivity model, and verified with two sets of reference SIT data; one is obtained by the Soil Moisture Ocean Salinity (SMOS) satellite, and the other is the combined SMOS/Soil Moisture Active Passive (SMAP) measurements. This analysis is performed on the data with SIT less than 1 m. Through comparison, good consistency between the derived TDS-1 SIT and the reference SIT is obtained, with a correlation coefficient ( $r$ ) of 0.84 and a root-mean-square difference (RMSD) of 9.39 cm with SMOS, and an $r$ of 0.67 and an RMSD of 9.49 cm with SMOS/SMAP, which demonstrates the applicability of the developed model and the utility of TDS-1 data for SIT estimation. In addition, this method is proved to be useful for improving existing sea ice detection accuracy.

Mikhail Vasilyevich Sechkin – Pianist, Conductor, Teacher

Mikhail Vasilyevich Sechkin – Pianist, Conductor, Teacher

Geostatistical characterization of internal structure of mass-transport deposits from seismic reflection images and borehole logs

SUMMARY Seismic reflection images of mass-transport deposits often show apparently chaotic, disorded or low-reflectivity internal seismic facies. The lack of laterally coherent reflections can prevent horizon-based interpretation of internal structure. This study instead inverts for geostatistical parameters which characterize the internal heterogeneity of mass-transport deposits from depth-domain seismic reflection images. A Bayesian Markov Chain Monte Carlo inversion is performed to estimate posterior probability distributions for each geostatistical parameter. If the internal heterogeneity approximates an anisotropic von Kármán random medium these parameters can describe the structural fabric of the imaged mass-transport deposit in terms of lateral and vertical dominant scale lengths and the Hurst number (roughness). To improve the discrimination between vertical and lateral dominant scale lengths an estimate of the vertical dominant scale length from a borehole is used as a prior in the inversion. The method is first demonstrated on a synthetic multichannel seismic reflection image. The vertical and lateral dominant scale lengths are estimated with lower uncertainty when data from a synthetic borehole data are included. We then apply the method to a real data example from Nankai Trough, offshore Japan, where a large mass-transport deposit is imaged in a seismic profile and penetrated by a borehole. The results of the inversion show a downslope shortening in lateral scale length, consistent with progressive down-slope disaggregation of the mass-flow during transport. The dominant scale lengths can be used as a proxy for strain history, which can improve understanding of post-failure dynamics and emplacement of subacqueous mass-movements, important for constraining the geohazard potential from future slope failure.

Basal cell carcinoma treated with combined ablative fractional laser and ingenol mebutate – an exploratory study monitored by optical coherence tomography and reflectance confocal microscopy

Basal cell carcinomas (BCCs) have previously been treated off-label with ingenol mebutate (IM). Ablative fractional laser (AFL) may improve efficacy of IM by increasing drug uptake in the tumour. Optical coherence tomography (OCT) and reflectance confocal microscopy (RCM) detect BCC non-invasively. Our aim was to investigate BCC response and tolerability after combined AFL and IM treatment of low-risk BCCs. Twenty patients with histologically verified superficial (n=7) and nodular (n=13) BCCs were treated with combined fractional CO2 -laser (10600nm) and IM 0.015% or 0.05%, the concentration depending on anatomical location. BCC response was evaluated clinically, by OCT and RCM at day 29 and 90 after first treatment, and histologically at day 90. Treatment was repeated at day 29 if BCC persisted. Local skin reactions (LSRs) were assessed using LSR scale at all visits. At day 29, 18/20 patients received a second treatment due to residual BCC detected clinically, by OCT or RCM. OCT and RCM presented subclinical BCCs in five of 20 cases (25%). At day 90, overall histological cure rate was 70%, corresponding to clinical (65%) and OCT/RCM (60%) cure rates, and agreement between evaluation methods was substantial (kappa≥0.796, P<0.0001). Clearance rates were similar for sBCCs and nBCCs (P=0.354) and for lesions treated with IM 0.015% and 0.05% (P=0.141). LSRs were tolerable, but scarring was observed in the majority of cleared patients. Two treatments of combined AFL and IM show potential to treat low-risk BCCs with acceptable tolerability. OCT and RCM show promise to detect subclinical BCCs at short-term follow-up.

Clinical and Instrumental Objective Evidence of the Efficacy of a New Water-Based Nail-Strengthening Solution Containing Pistacia lentiscus and Hyaluronic Acid Applied for Up to 6 Months to Improve the Appearance of Weak, Brittle Nails.

IntroductionBrittle nails are fragile or split nails; they affect 20% of the population and may be primary or secondary to different conditions. The aim of our studies was to evaluate the efficacy and tolerability of a new water-based nail-strengthening treatment containing hyaluronic acid and Pistacia lentiscus with daily application for a period of 1–3 months for one study (n = 30) and up to 6 months for a second study (n = 30).MethodsIn total, we enrolled 60 patients of both sexes with brittle and weak nails due to primary or secondary causes and evaluated the efficacy of this new product using subjective and objective methods: clinical evaluation, assessment of photographs, onychoscopy evaluation, investigator and patient global assessment, dynamic optical coherence tomography (D-OCT) and reflectance confocal microscopy (RCM).ResultsStudies subjects presented a statistically significant improvement in global assessment scale (GAS) scores at 14 days (GAS = 1.7 ± 0.6), 1 month (GAS = 1.4 ± 0.7) and at 3 months (GAS = 1±0.7) versus the GAS score obtained before treatment (1.9 ± 0.5) (p < 0.0001). From the Italian study at 6 months (n = 30) 76% of the patients had an improvement in their nail appearance. Reduction in nail plate roughness with improved nail resistance and decreased distal breakage were the most evident benefits, demonstrated on clinical and instrumental evaluations. No side effects were reported. All patients reported an improvement in nail appearance after using the product for 1 month, 3 months and 6 months, and had a positive opinion on the product.ConclusionsThis new product is an effective, safe, and easy-to-use option for topical treatment of brittle nails and primary nail fragility and an adjuvant therapy in secondary nail fragility. Moreover, its ease of application and cosmetic qualities allow good compliance.FundingISDIN.

A CYGNSS‐Based Algorithm for the Detection of Inland Waterbodies

AbstractThe Cyclone Global Navigation Satellite System (CYGNSS) is a new constellation of eight low Earth orbiting spacecrafts that receive both direct and reflected signals from GPS satellites. Coherent reflection of the GPS signal from standing water over land results in a high surface reflectivity signal in the CYGNSS data. An image processing algorithm is presented, which leverages the surface reflectivity signal to produce a watermask of inland waterbodies at 0.01° × 0.01° spatial resolution. The watermask is compared to hand‐drawn maps of inland waterbodies, as well as to the MODIS watermask product. We find that the CYGNSS watermask provides accurate, time‐varying maps that are able to resolve changes in lake and river position and extent. With CYGNSS' short return time, watermasks can be generated using as little as half a month of data to produce near‐real‐time maps of flooding events.

Sea Ice Transition Detection Using Incoherent Integration and Deconvolution

Currently, reflectometry-based sea ice detection methods rely on observables extracted from delay-Doppler maps (DDM)s, which are sensitive to ice in the specular zone. Due to the size of the glistening zone, the transition from open seas to sea ice in the specular zone can take up to 10 s for satellite platforms and no methods exist that can process this. In this article, using DDMs collected by TechDemoSat-1, we demonstrate that this transition is comprised of a response that is fixed in the spatial domain, at the ice edge, and moving in the delay-Doppler domain. This is the first observation of persistent nonspecular coherent reflections from sea ice. The delay-Doppler trajectory of the ice response is shown to correspond with a point that is located on the ambiguity free line. Furthermore, the response is point-like as it suffers from delay and Doppler walk suggesting that it originates from a small spatial footprint, i.e., the first (few) Fresnel zone(s). Exploiting these facts, we then propose a technique that integrates the ice response in the spatial domain after preprocessing. This results in the edges of the ice sheet being emphasized as all of the power received during the transition phase maps to the edge of the sheet. We also propose to compensate for the delay-Doppler walk during preprocessing by modifying Woodward's ambiguity function when deconvolution is performed.

Suggestion of coherent radio reflections from an electron-beam induced particle cascade

Testbeam experiment 576 (T576) at the SLAC National Accelerator Laboratory sought to make the first measurement of coherent radio reflections from the ionization produced in the wake of a high-energy particle shower. The >10 GeV electron beam at SLAC End Station A was directed into a large high-density polyethylene target to produce a shower analogous to that produced by an EeV neutrino interaction in ice. Continuous wave (CW) radio was transmitted into the target, and receiving antennas monitored for reflection of the transmitted signal from the ionization left in the wake of the shower. We detail the experiment and report on preliminary hints of a signal consistent with a radio reflection at a significance of 2.36$\sigma$. We recommend another test-beam measurement in order to verify the signal.

Coherent Matched-Filter Reflection Loss From a Moving Rough Surface as a Function of Pulse Duration and Ensonified Extent

In many applications of active sonar, the propagation paths connecting a source, an object of interest, and a receiver include reflection from the ocean surface. A classic result describes the coherent surface reflection loss (SRL) of an acoustic pulse solely as a function of the Rayleigh roughness parameter by requiring a large ensonified area (LEA) and a pulse short in duration relative to the surface wave period. At the other extreme are results accounting for motion of the surface throughout reflection of the pulse but requiring a small ensonified area (SEA) where, in effect, less than a correlation length of the surface contributes to the reflection. The pulse compression achieved by matched filtering broadband pulses enables the SEA while using a pulse that may be long in duration relative to the surface wave period. The coherent SRL for a medium ensonified area (MEA) is derived in this paper by extending the SEA results to account for the combination of multiple correlated components of the surface contributing to specular reflection. The derivation adds a dependence on both the ensonified area and the spatial correlation function of the surface. The model is seen to simplify to the classic LEA result when the ensonified area is large relative to the correlation length. A low-roughness approximation allows simple evaluation of the MEA SRL that, for long pulses, is a mixture of the SEA and LEA results. An example evaluation of SRL using a Pierson-Moskowitz wave spectrum is presented as a function of the duration and bandwidth of linear-frequency-modulated pulses to illustrate how the loss is near the LEA result for low bandwidths and tends to the SEA result as bandwidth increases.

Choroba i strata jako regulator tożsamości: Rok magicznego myślenia Joan Didion

&#x0D; Cel badań. Celem artykułu było omówienie wpływu ekspresywnego pisania na sposób przeżywania żałoby i żalu po stracie. Analiza stanowi przyczynek do dyskusji o terapeutycznej mocy ekspresywnego pisania.&#x0D; Metodologia. Analizie poddano książkę Rok magicznego myślenia Joan Didion, w której autorka opisuje swoje zmagania z codziennością po nagłej śmierci jej męża. Pamiętnik został zanalizowany zgodnie z koncepcją autobiografistyki Georges’a Gusdorfa (2009). W kontekście książki omówiono również koncepcje odnoszące się do psychologii zdrowia i choroby: teorię pięciu etapów przeżywania żałoby według Elisabeth Kübler-Ross (2007) oraz sposoby radzenia sobie ze stresem Endlera i Parkera (1990).&#x0D; Wyniki. Analiza wykazała, iż myślenie magiczne, którym posługuje się autorka pamiętnika, służy jej za normatywny mechanizm obronny. Styl pisarski Joan Didion, zakorzeniony w tzw. nowym dziennikarstwie, przeplata się z refleksjami na temat śmierci, co czyni go jeszcze bardziej ekspresywnym i szczerym. Można zauważyć, że Didion sukcesywnie przechodzi przez kolejne etapy przeżywania żałoby, a sposobem radzenia sobie, z którego pisarka korzysta najczęściej, jest działanie. Odejście od myślenia magicznego pod koniec książki oraz ostateczne pogodzenie się ze śmiercią męża sugeruje, iż ekspresywne pisanie było jednym z czynników, który pomógł autorce w zmaganiach z żalem po stracie.&#x0D; Wnioski. Rok magicznego myślenia stanowi przykład tanatografii oraz jest logicznym i spójnym odbiciem przeżyć osoby zmagającej się z traumą po śmierci bliskiej osoby. W celu pełniejszego zbadania wpływu ekspresywnego pisania na samopoczucie i dobrostan wskazana byłaby podobna analiza książki Blue Nights, w której Didion zmaga się ze śmiercią córki.&#x0D; Słowa kluczowe: life writing, psychologia zdrowia i choroby, style radzenia sobie, tożsamość&#x0D; &#x0D;

Laser cleaning of paintings: in situ optimization of operative parameters through non-invasive assessment by optical coherence tomography (OCT), reflection FT-IR spectroscopy and laser induced fluorescence spectroscopy (LIF)

Nowadays the use of laser technology as a highly precise tool for the cleaning of paintings is gaining ground. The development of a non-invasive analytical protocol aimed at thorough assessment of the treated surfaces and real time monitoring of the laser cleaning action is thus becoming imperative. This ensures that no side effects (e.g. discoloration, darkening, blackening) will occur on the painting surfaces due to laser ablation. In the present study the potential of the combined use of optical coherence tomography (OCT) and reflection FT-IR spectroscopy for in situ non-invasive assessment of laser cleaning procedures has been investigated on a historical easel painting donated to science. Specifically, OCT and FT-IR analyses were carried out before and after each cleaning test in order to carefully assess the condition of the painting surfaces upon their irradiation with a KrF excimer laser and evaluate the removal of weathered and/or non-original materials (i.e. waxes, aged natural varnishes, oxalates, deposition/migration compounds). This specific laser radiation, operating in the ultraviolet region (λ = 248 nm), is highly absorbed by coating materials (i.e. oxidized natural varnishes) and thus high selectivity and control of the cleaning process can be pursued. A systematic integration of the information on the chemical changes of the molecular composition of the painting surface provided by reflection FT-IR spectroscopy with the visualization of the stratigraphical changes by OCT allowed the evaluation of the sensitivity of the painting materials to different operative parameters of the laser treatment, such as laser fluence and number of pulses. In parallel, laser induced fluorescence (LIF) spectroscopic measurements, recorded with the same laser beam at significantly attenuated energy density values, were exploited to provide information on the fluorescence properties of the irradiated varnish surfaces. The combination of the results obtained by OCT and FT-IR complemented with those from LIF measurements are discussed with the aim of developing an efficient methodology for assessing in situ the irradiated painting surfaces after the laser cleaning treatments and, thus, setting the basis for a future monitoring scheme that would ensure optimum cleaning interventions.

Generalized statistical dynamical theory of x-ray diffraction by imperfect multilayer crystal structures with defects

The generalized statistical dynamical theory of x-ray scattering by imperfect single crystals with randomly distributed Coulomb-type defects has been extended to characterize structure imperfections in the real multilayers of arbitrary thickness in Bragg diffraction geometry. The recurrence relations for the coherent amplitude reflection and transmission coefficients of such multilayers, which consist of any number of layers with constant strain and randomly distributed defects in each one, have been derived within the concept of the dynamical wave field, i.e., the so-called Ewald-Bethe-Laue approach, with rigorous accounting for boundary conditions at layer interfaces. The analytical expression for the differential dynamical diffuse component of the reflection coefficient of an imperfect multilayer system has been obtained as well. This expression establishes direct connection between the distribution of the diffuse scattering intensity in a momentum space and statistical characteristics of defects in each layer. In addition, the integrals from differential diffuse scattering intensity over the Ewald sphere and over vertical divergence have been found, which correspond to diffuse components in measurements of rocking curves and reciprocal space maps, respectively. The developed theory provides the dynamical description for the one- and two-dimensional angular distributions of the mutually consistent coherent and diffuse components of x-ray scattering intensities, which are measured by the high-resolution double- and triple-crystal diffractometers, respectively, from imperfect films, multilayer structures, superlattices, etc. Examples of simulated rocking curves for the imperfect superlattice with defects of several types and reciprocal space map for the ion-implanted sample of yttrium iron garnet film with defects are given and discussed.

Compensation for temperature-dependent phase and velocity of guided wave signals in baseline subtraction for structural health monitoring

Baseline subtraction is commonly used in guided wave structural health monitoring to identify the signal changes produced by defects. However, before subtracting the current signal from the baseline, it is essential to compensate for changes in environmental conditions such as temperature between the two readings. This is often done via the baseline stretch method that seeks to compensate for wave velocity changes with temperature. However, the phase of the signal generated by the transduction system is also commonly temperature sensitive and this effect is neglected in the usual compensation procedure. This article presents a new compensation procedure that deals with both velocity and phase changes. The results with this new method have been compared with those obtained using the standard baseline stretch technique on both a set of experimental signals and a series of synthetic signals with different coherent noise levels, feature reflections, and defect sizes, the range of noise levels and phase changes being chosen based on initial experiments and prior field experience. It has been shown that the new method both reduces the residual signal from a set baseline and enables better defect detection performance than the conventional baseline signal stretch method under all conditions examined, the improvement increasing with the size of the temperature and phase differences encountered. For example, in the experimental data, the new method roughly halved the residual between baseline and current signals when the two signals were acquired at temperatures 15°C apart.

Snow Depth Estimation Based on Combination of Pseudorange and Carrier Phase of GNSS Dual-Frequency Signals

Global navigation satellite system reflectometry (GNSS-R) is a new remote sensing technique, which can be used to measure a wide range of geophysical parameters. GNSS-R makes use of the simultaneous reception of the direct transmission and the coherent surface reflections of the GNSS signal with either a single antenna or multiple separate antennas. This paper presents a new snow depth estimation method using a combination of pseudorange and carrier phase of GNSS dual-frequency signals. The proposed method is geometry-free and is not affected by ionospheric delays. The formulas of the amplitude attenuation factor of reflected signals, multipath-induced carrier-phase error, and pesudorange error for ground-based GNSS receivers are used to describe the combined signals. Using theoretical formulas instead of in situ measurement data, analytical linear models are established in advance to describe the relationship between snow depth and main frequency of combined signal time series. When the main frequency of the combined measurements is obtained by spectrum analysis, the model is used to determine snow depth. Two experimental data sets recorded in two different environments were used to test the proposed method. The results demonstrate that there exists good agreement between the proposed method and the ground-truth measurements.

New Estimates of Ice and Oxygen Fluxes Across the Entire Lid of Lake Vostok From Observations of Englacial Radio Wave Attenuation

AbstractOver deep Antarctic subglacial lakes, spatially varying ice thickness and the pressure‐dependent melting point of ice result in distinct areas of melting and freeze‐on at the ice‐water interface, that is, at the lake lid. These ice mass fluxes drive lake circulation and, because basal Antarctic ice contains air clathrate, affect the input of oxygen to the lake, with implications for subglacial life. Inferences of rates of melting and freeze‐on, that is, accretion rates, from radar layer tracking and geodesy are limited in spatial coverage and resolution. Here we develop a new method to estimate accretion rate, and the resulting oxygen input at a lake lid, using airborne radar data over Lake Vostok together with ice‐temperature and chemistry data from the Vostok ice core. Because the lake lid is a coherent reflector of known reflectivity (at our radar frequency), we can infer depth‐averaged radio wave attenuation in the ice, with a spatial resolution of ~1 km along flight lines. Spatial variation in attenuation depends mostly on variation in ice temperature near the lid, which in turn varies strongly with ice mass flux at the lid. We model ice temperature versus depth with ice mass flux as a parameter, thus linking that flux to observed depth‐averaged attenuation. The resulting map of melt and accretion rates independently reproduces features known from earlier studies but now covers the entire lid. We find that freeze‐on is dominant when integrated over the lid, with an ice imbalance of 0.05 to 0.07 km3/year, which is robust against uncertainties.

Estimates of coherent reflection loss inclusive of the effects of near-surface bubbles on sound speed

Through simplification of the authors’ model “JBZ” of coherent reflection loss at the ocean surface, a revised model has been obtained in extremely simple form. This model provides descriptions of the loss obtained at a wind-roughened surface, adhering to a Pierson-Moskowitz surface wave frequency spectrum, inclusive of the effects of near-surface bubbles on sound speed. A very compact form of the model has been obtained for application to surface ducted sound for a wide range of wind speed and frequency combinations, with the result that the dB loss with range is the same for all modes within the duct. The derivation of the model from the authors’ earlier JBZ is described, and the conditions for equivalence are detailed. In a limited range of comparisons, descriptions of reflection loss per bounce obtained with the original JBZ and the compact version are shown to be nearly identical to corresponding values obtained by the “Relay” model described by Ainslie [JASA 118, 3513–3523 (2005)]. Through simplification of the authors’ model “JBZ” of coherent reflection loss at the ocean surface, a revised model has been obtained in extremely simple form. This model provides descriptions of the loss obtained at a wind-roughened surface, adhering to a Pierson-Moskowitz surface wave frequency spectrum, inclusive of the effects of near-surface bubbles on sound speed. A very compact form of the model has been obtained for application to surface ducted sound for a wide range of wind speed and frequency combinations, with the result that the dB loss with range is the same for all modes within the duct. The derivation of the model from the authors’ earlier JBZ is described, and the conditions for equivalence are detailed. In a limited range of comparisons, descriptions of reflection loss per bounce obtained with the original JBZ and the compact version are shown to be nearly identical to corresponding values obtained by the “Relay” model described by Ainslie [JASA 118, 3513–3523 (2005)].

Supercurrent carried by nonequilibrium quasiparticles in a multiterminal Josephson junction

We theoretically study coherent multiple Andreev reflections in a biased three-terminal Josephson junction. We demonstrate that the direct current flowing through the junction consists of supercurrent components when the bias voltages are commensurate. This dissipationless current depends on the phase in the superconducting leads and stems from the Cooper pair transfer processes induced by non-local Andreev reflections of the quasiparticles originating from the superconducting leads. We identify supercurrent-enhanced lines in the current and conductance maps of the recent measurement [Y. Cohen, et al., PNAS 115, 6991 (2018)] on a nanowire Josephson junction and show that the magnitude of the phase-dependent current components is proportional to the junction transparency with the power corresponding to the component order.

Systematic Errors in Measurements of the Optical-Ranging Characteristics of Small Objects with Nonlocal Coherent Reflection

Adjustments in the phase structure of optical radiation reflected from a small object with nonlocal coherent reflection and detected by an objective with spherical aberration are examined. The conditions for the appearance of peripheral “bright zones” within the limits of the objective aperture are determined and their contribution to the formation of the reflected signal in a path of finite length is estimated. The systematic errors in measuring the effective scattering area of the central “bright zone” and the line density of the effective scattering area of the peripheral “bright zone” are estimated.

Optical method for sensing surface coverage by unicellular organisms

A theoretical and experimental assessment of an optical technique for the rapid quantification of the density of biological cells adsorbed on a flat surface, as well as for monitoring in real time the surface coverage is presented. The method relies on the high sensitivity of the optical reflectivity of a surface near grazing incidence to the presence of particles large compared to the wavelength of light, a fact mostly unknown and not yet utilized in optical sensing. First, we perform a theoretical assessment of the method for sensing surface-coverage by biological-cell type particles. For this, we use a recently developed analytical model for the coherent reflection of light from a flat interface partially covered by a disordered monolayer of particles. Then, we investigate the viability of the technique experimentally with spores of Penicillium digitatum (PD) deposited on microscope slide. These fungus spores, along with those of Penicillium italicum (PI) are the main cause of losses in the citrus industry. We illustrate the possibility of monitoring in real time, the detachment of spores from a surface by an air flow. Experimental measurements are found to follow qualitatively theoretical predictions, showing that the theoretical model can be used for general sensor design purposes. From the experimental tests performed, we conclude that resolutions better than 1% in surface coverage of a flat surface by unicellular organisms are achievable without difficulty.