Inferring aerosol layer properties from the spatial structure of satellite images

Scattering from atmospheric aerosols causes blurring of satellite images. A study of this effect suggests that it might be possible to evaluate aerosol properties from these images. We consider an aerosol layer superimposed on a surface with a one-dimensional sinusoidal variation in reflectivity and with a half-plane reflectivity variation. A single scattering approximation is used to show that information about the aerosol layer height and optical depth can be extracted provided the variation in ground reflectivity is known.     

Enhanced three-dimensional deconvolution microscopy using a measured depth-varying point-spread function

We present a technique to systematically measure the change in the blurring function of an optical microscope with distance between the source and the coverglass (the depth) and demonstrate its utility in three-dimensional (3D) deconvolution. By controlling the axial positions of the microscope stage and an optically trapped bead independently, we can record the 3D blurring function at different depths. We find that the peak intensity collected from a single bead decreases with depth and that the width of the axial, but not the lateral, profile increases with depth. We present simple convolution and deconvolution algorithms that use the full depth-varying point-spread functions and use these to demonstrate a reduction of elongation artifacts in a reconstructed image of a 2 microm sphere.     

Sun and aureole spectrometer for airborne measurements to derive aerosol optical properties

We have designed an airborne spectrometer system for the simultaneous measurement of the direct Sun irradiance and aureole radiance. The instrument is based on diffraction grating spectrometers with linear image sensors. It is robust, lightweight, compact, and reliable, characteristics that are important for airborne applications. The multispectral radiation measurements are used to derive optical properties of tropospheric aerosols. We extract the altitude dependence of the aerosol volume scattering function and of the aerosol optical depth by using flight patterns with descents and ascents ranging from the surface level to the top of the boundary layer. The extinction coefficient and the product of single scattering albedo and phase function of separate layers can be derived from the airborne measurements.     

Focus measurement with a simple pattern design

The increasingly smaller depth of focus of advanced lithographic tools requires that the position of best focus be determined to ensure accuracy and efficiency. We present what we believe is a novel bar in bar that is drawn on a conventional chrome binary mask to translate focal errors into center-to-center shifts of outer and inner bars. An overlay measurement tool can easily measure this shift. A symmetrical center-to-center shift against best focus is created during defocus, and this shift can be well fitted by a second-order polynomial equation. Simply differentiating the fitted equation leads to an accurate and reliable focus value, with a maximum error of less than 0.05 mum. The proposed technique can also be employed to evaluate the tilt, field curvature, and astigmatism of advanced lithographic tools.     

Precision of measurement of tissue optical properties with optical coherence tomography

Accurate and noninvasive measurement of tissue optical properties can be used for biomedical diagnostics and monitoring of tissue analytes. Noninvasive measurement of tissue optical properties (total attenuation and scattering coefficients, optical thickness, etc.) can be performed with the optical coherence tomography (OCT) technique. However, speckle noise substantially deteriorates the accuracy of the measurements with this technique. We studied suppression of speckle noise for accurate measurement of backscattering signal and scattering coefficient with the OCT technique. Our results demonstrate that the precision of measurement of backscattering signals with the OCT technique can be 0.2% for homogeneously scattering media and 0.7% for skin, if spatial averaging of speckle noise is applied. This averaging allows us to achieve the precision of tissue scattering coefficient measurements of approximately +/-0.8%. This precision can be further improved by a factor of 2-3, upon optimization of OCT operating parameters.     

Fluorescence spectra provide information on the depth of fluorescent lesions in tissue

The fluorescence spectrum measured from a fluorophore in tissue is affected by the absorption and scattering properties of the tissue, as well as by the measurement geometry. We analyze this effect with Monte Carlo simulations and by measurements on phantoms. The spectral changes can be used to estimate the depth of a fluorescent lesion embedded in the tissue by measurement of the fluorescence signal in different wavelength bands. By taking the ratio between the signals at two wavelengths, we show that it is possible to determine the depth of the lesion. Simulations were performed and validated by measurements on a phantom in the wavelength range 815-930 nm. The depth of a fluorescing layer could be determined with 0.6-mm accuracy down to at least a depth of 10 mm. Monte Carlo simulations were also performed for different tissue types of various composition. The results indicate that depth estimation of a lesion should be possible with 2-3-mm accuracy, with no assumptions made about the optical properties, for a wide range of tissues.     

Multiple scattering in optical coherence tomography. I. Investigation and modeling

We present a new model of optical coherence tomography (OCT) taking into account multiple scattering. A theoretical analysis and experimental investigation reveals that in OCT, despite multiple scattering, the field backscattered from the sample is generally spatially coherent and that the resulting interference signal with the reference field is stationary relative to measurement time. On the basis of this result, we model an OCT signal as a sum of spatially coherent fields with random-phase arguments--constant during measurement time--caused by multiple scattering. We calculate the mean of such a random signal from classical results of statistical optics and a Monte Carlo simulation. OCT signals predicted by our model are in very good agreement with a depth scan measurement of a sample consisting of a mirror covered with an aqueous suspension of microspheres. We discuss other comprehensive OCT models based on the extended Huygens-Fresnel principle, which rest on the assumption of partially coherent interfering fields.     

Horizon brightness revisited: measurements and a model of clear-sky radiances

Clear daytime skies persistently display a subtle local maximum of radiance near the astronomical horizon. Spectroradiometry and digital image analysis confirm this maximum's reality, and they show that its angular width and elevation vary with solar elevation, azimuth relative to the Sun, and aerosol optical depth. Many existing models of atmospheric scattering do not generate this near-horizon radiance maximum, but a simple second-order scattering model does, and it reproduces many of the maximum's details.     

Standoff determination of the particle size and concentration of small optical depth clouds based on double scattering measurements: concept and experimental validation with bioaerosols

A multiple-field-of-view (MFOV) lidar is used to characterize size and optical depth of low concentration of bioaerosol clouds. The concept relies on the measurement of the forward scattered light by using the background aerosols at various distances at the back of a subvisible cloud. It also relies on the subtraction of the background aerosol forward scattering contribution and on the partial attenuation of the first-order backscattering. The validity of the concept developed to retrieve the effective diameter and the optical depth of low concentration bioaerosol clouds with good precision is demonstrated using simulation results and experimental MFOV lidar measurements. Calculations are also done to show that the method presented can be extended to small optical depth cloud retrieval.     

Influence of scattering on transmission through long-period fiber gratings and tunable microstructure fibers

Controlled optical scattering within or around an optical fiber provides a potentially useful mean for adjusting its transmission characteristic. This approach can complement conventional methods based on the establishment of well-defined variations in the index of refraction of the core or the cladding of the fiber. We describe the use of a highly scattering submonolayer of nanoparticles deposited onto the fiber surface for adjusting the resonance wavelength, depth, and width of an in-fiber long-period grating filter. We also introduce a polymer-dispersed liquid-crystal material that has a thermally tunable scattering cross section and can be incorporated into the channels of a microstructure optical fiber; this system may provide the means for a fiber-based scattering switch.     

Telecentric three-dimensional sensor with a liquid mirror for large-object inspection

We describe a device that applies the advantages of the space invariance of telecentric triangulation with the measurement of large objects (1 m(3)). Because the scan motion of the laser beam is decoupled from the physical transport of the sensor head, the fast scanning of large volumes becomes feasible. The device consists of a triangulation laser telemeter head that uses a large liquid primary mirror and an aspheric secondary mirror to realize the telecentric f-theta objective. We propose using liquid-mirror technology to make low-cost large objectives that have low f numbers, a diffraction-limited performance, and low scattering in the visible. This new optical system is useful for 3-D measurement. We discuss the optical configuration of the system and the performance of a laboratory prototype. The prototype has a standoff distance of 1.5 m, a telecentric scan as long as 1 m, a depth of view of 1 m, and a relative depth resolution of 0.5-1 mm.     

Diffuse light propagation in a turbid medium with varying refractive index: Monte Carlo modeling in a spherically symmetrical geometry

We report on the development of Monte Carlo software that can model media with spatially varying scattering coefficient, absorption, and refractive index. The varying refractive index is implemented by calculating curved photon paths in the medium. The results of the numerical simulations are compared with analytical solutions obtained using the diffusion approximation. The model under investigation is a scattering medium that contains a spherically symmetrical inclusion (inhomogeneity) created by variation in optical properties and having no sharp boundaries. The following steady-state cases are considered: (a) a nonabsorbing medium with a spherically symmetrical varying refractive index, (b) an inclusion with varying absorption and scattering coefficients and constant refractive index, and (c) an inclusion with varying absorption, scattering, and refractive index. In the latter case it is shown that the interplay between the absorption coefficient and the refractive index may create the effect of a hidden inclusion.     

级联型波导中古斯-汉欣位移的增强

前期的工作已经证明,由于共振效应和渗透深度的增加,利用毫米尺度对称金属包覆波导和自由空间耦合技术,可获得毫米量级的古斯 -汉欣(Goos-H.nchen)位移。本文在此基础上,利用一对对称金属包覆波导组成级联型结构,研究了这种结构中古斯 -汉欣位移的增强效应。实验结果表明：当激光波长变化 43 pm时,由 CCD探测器测量得到的古斯 -汉欣位移达到了 2 215 μm,约为单级波导古斯 -汉欣位移的 2倍,实验结果与理论推导完全一致。     

Analysis of specular resonance in dielectric bispheres using rigorous and geometrical-optics theories

We have recently identified the resonant scattering from dielectric bispheres in the specular direction, which has long been known as the specular resonance, to be a type of rainbow (a caustic) and a general phenomenon for bispheres. We discuss the details of the specular resonance on the basis of systematic calculations. In addition to the rigorous theory, which precisely describes the scattering even in the resonance regime, the ray-tracing method, which gives the scattering in the geometrical-optics limit, is used. Specular resonance is explicitly defined as strong scattering in the direction of the specular reflection from the symmetrical axis of the bisphere whose intensity exceeds that of the scattering from noninteracting bispheres. Then the range of parameters for computing a particular specular resonance is specified. This resonance becomes prominent in a wide range of refractive indices (from 1.2 to 2.2) in a wide range of size parameters (from five to infinity) and for an arbitrarily polarized light incident within an angle of 40 degrees to the symmetrical axis. This particular scattering can stay evident even when the spheres are not in contact or the sizes of the spheres are different. Thus specular resonance is a common and robust phenomenon in dielectric bispheres. Furthermore, we demonstrate that various characteristic features in the scattering from bispheres can be explained successfully by using intuitive and simple representations. Most of the significant scatterings other than the specular resonance are also understandable as caustics in geometrical-optics theory. The specular resonance becomes striking at the smallest size parameter among these caustics because its optical trajectory is composed of only the refractions at the surfaces and has an exceptionally large intensity. However, some characteristics are not accounted for by geometrical optics. In particular, the oscillatory behaviors of their scattering intensity are well described by simple two-wave interference models.     

Coupling of surface roughness to the performance of computer-generated holograms

Computer-generated holograms (CGHs), such as those used in optical testing, are created by etching patterns into an optical substrate. Imperfections in the etching can cause small scale surface roughness that varies across the pattern. The variation in this roughness affects the phase and amplitude of the wavefronts in the various diffraction orders. A simplified model is developed and validated that treats the scattering loss from the roughness as an amplitude effect. We demonstrate the use of this model for engineering analysis and provide a graphical method for understanding the application. Furthermore, we investigate the magnitude of this effect for the application of optical testing and show that the effect on measurement accuracy is limited to 1 nm for typical CGHs.     

Accurate estimation of the boundaries of a structured light pattern

Depth recovery based on structured light using stripe patterns, especially for a region-based codec, demands accurate estimation of the true boundary of a light pattern captured on a camera image. This is because the accuracy of the estimated boundary has a direct impact on the accuracy of the depth recovery. However, recovering the true boundary of a light pattern is considered difficult due to the deformation incurred primarily by the texture-induced variation of the light reflectance at surface locales. Especially for heavily textured surfaces, the deformation of pattern boundaries becomes rather severe. We present here a novel (to the best of our knowledge) method to estimate the true boundaries of a light pattern that are severely deformed due to the heavy textures involved. First, a general formula that models the deformation of the projected light pattern at the imaging end is presented, taking into account not only the light reflectance variation but also the blurring along the optical passages. The local reflectance indices are then estimated by applying the model to two specially chosen reference projections, all-bright and all-dark. The estimated reflectance indices are to transform the edge-deformed, captured pattern signal into the edge-corrected, canonical pattern signal. A canonical pattern implies the virtual pattern that would have resulted if there were neither the reflectance variation nor the blurring in imaging optics. Finally, we estimate the boundaries of a light pattern by intersecting the canonical form of a light pattern with that of its inverse pattern. The experimental results show that the proposed method results in significant improvements in the accuracy of the estimated boundaries under various adverse conditions.     

Direct calculation with a finite-element method of the Laplace transform of the distribution of photon time of flight in tissue

Reconstruction methods for optical tomographic imaging require the development of models of light transport in highly scattering materials. While the simulation of the full temporal response function arising from a short source light pulse is computationally expensive, there are methods to evaluate efficiently certain transforms of the temporal profile. We previously presented methods to obtain directly the Mellin Transform, which is related to the moments of the temporal intensity distribution; We introduce a similar method to calculate directly the Laplace transform. This method provides an addtional, largely independent measurement type that can be combined with the moments to improve image quality in optical tomography, in particular with respect to the simultaneous reconstruction of absorption and scattering distribution.     

Reduced depth of field in incoherent hybrid imaging systems

A hybrid imaging system combines a modified optical imaging module and a digital postprocessing step. We define what to our knowledge is a new metric to quantify the blurring of a defocused image that is more suitable than the defocus parameter for describing defocused hybrid imaging systems. We use this metric to design a pupil phase grating to reduce the depth of field, thereby increasing the axial resolution, of an incoherent hybrid imaging system using quasi-monochromatic illumination. By introducing this grating at the exit pupil and digitally processing the output of the detector, we reduce the depth of field by more than a factor of 2. Finally, we examine the effect of using a CCD optical detector, instead of an ideal optical detector, on the reduction of the depth of field.     

Distortion of particulate extinction profiles measured with lidar in a two-component atmosphere

Distortions of particular extinction-coefficient profiles measured with lidar in a two-component (molecular and aerosol) scattering atmosphere are analyzed. The error of the extinction coefficient measured at range r depends on the location of the point r(b), where a boundary value is specified, and the particulate optical depth of the atmosphere between r and r(b); the particulate backscatter-to-extinction ratio; and the ratio of particulate and molecular scattering extinction. If the near-end solution is used, small measurement errors can produce a significant divergence between the actual and the retrieved extinction-coefficient profiles, even if the boundary value and the particulate backscatter-to-extinction ratio are specified accurately. This effect is exacerbated at small values of the particulate scattering coefficient and the backscatter-to-extinction ratio. When reasonable criteria are used, feasible minimum and maximum boundary values can be specified to restrict the range of lidar equation solutions from below and from above.     

Visible and near infrared reflectances measured from laboratory ice clouds

We present laboratory results of the 0.68 microm visible (VIS) and 1.617 microm near infrared (NIR) reflectances typically used for inferring optical depth and ice crystal size from satellite radiometers, from ice clouds generated in a temperature controlled column cloud chamber. Two types of ice crystals were produced in this experiment: small columns and dendrites with mean maximum dimensions of about 17 and 35 microm. Within experimental uncertainty, the measured reflectances from ice clouds at both wavelengths agree reasonably well with the theoretical results computed from the plane-parallel adding-doubling method for radiative transfer using the measured ice particle morphology. We demonstrate that laboratory scattering and reflectance data for thin ice clouds with optical depths less than 0.4 can be used for validation of the thin cirrus optical depth and ice crystal size that have been routinely retrieved from the satellite VIS-NIR two channel pair.