Distribution Of Optical Path Length Research Articles

Digital holographic imaging of thermal signatures and its use in inhomogeneity identification

Thermal diffusion results in spatiotemporally evolving temperature distribution in material mediums. In dielectric mediums it will also lead to change in local refractive index. Digital holographic interferometry can be used for high contrast quantitative phase imaging of spatially and temporally evolving refractive index variations in dielectric mediums, arising due to temperature changes. Phase retrieved from numerically processed digital holograms recorded at different time instances can be compared to obtain this information. Since the thermal conductivity varies for materials, the thermal diffusion and hence the refractive index across them will also vary. Time varying optical path length distributions of the test sample under thermal stress, obtained from the phase maps retrieved from the recorded holograms, can be used to obtain this information. This leads to detection of regions having different thermal conductivities and hence identification of inhomogeneities in the test sample. Lens less Fourier transform digital holographic interferometry is a perfect tool to quantify optical path length distributions with nanometre accuracy to quantify spatiotemporally evolving refractive index distributions. In this technique, a single Fourier transform of the recorded hologram yields the spatial distribution of object phase, making it ideal for real time imaging and applications. Here we describe our efforts in the development lens less Fourier transform digital holographic interferometric technique for the imaging and quantification of spatiotemporally evolving refractive index distributions in test samples under thermal stress and its application in detection of surface and sub-surface inhomogeneities.

Noncontact three-dimensional quantitative profiling of fast aspheric lenses by optical coherence tomography

Abstract The use of optical coherence tomography (OCT) for noncontact three-dimensional aspheric lens profiling and retrieval of aspheric surface parameters is demonstrated. Two commercially available aspheric lenses with different focal length-to-diameter ratio have been imaged using OCT, and the measured optical path length distribution has been least square fitted with the aspheric lens surface retrieving the radius of curvature, aspheric constant, and conic constants. The refractive index of these lenses has also been measured referencing with a standard Zerodur glass flat. The fitted aspheric surface coefficients of the lenses are in close agreement with the manufacturer’s values, thus, envisaging the potential of OCT in rapid screening, testing of aspheric lenses, and other micro-optical components such as those used in illumination optics.

Reduction of parasitic interferences in digital holographic microscopy by numerically decreased coherence length

Due to the large coherence length of laser light, optical path length (OPL) resolution in laser based digital holographic microscopy suffers from parasitic interferences caused by multiple reflections within the experimental setup. Use of partially coherent light reduces this drawback but requires precise and stable matching of object and reference arm’s OPLs and limits the spatial frequency of the interference pattern in off-axis holography. Here, we investigate if the noise properties of spectrally broadened light sources can be generated numerically. Therefore, holograms are coherently captured at different laser wavelengths and the corresponding reconstructed wave fields are numerically superimposed utilizing variable weightings. Gaussian and rectangular spectral shapes of the so synthesized field are analyzed with respect to the resulting noise level, which is quantified in OPL distributions of a reflective test target. Utilizing a Gaussian weighting, the noise level is found to be similar to the one obtained with the partially coherent light of a superluminescent diode. With a rectangular shaped synthesized spectrum, noise is reduced more efficient than with a Gaussian one. The applicability of the method in label-free cell analysis is demonstrated by quantitative phase contrast images obtained from living cancer cells.

Based on MDCE to simulate bell-shaped interferograms produced by a capillary tube interferometer

The vector theory to calculate the optical path length (OPL) of the rays passing through a capillary tube was given and the OPLs including the collimated lens in 3D space were calculated, the interferograms produced by the capillary tube were simulated. A pinhole localized at the focal point of the collimated lens was seen as a point source of light. Based on ray-tracing, the OPL distribution from the point source of light, passing by the collimated lens, a cylindrical lens, the capillary tube and a screen was calculated. Because the huge calculation in the ray-tracing, a distributed calculating net based on MATLAB Distributed Computing Engine (MDCE) was established to save time. In order to get the simulated interferograms from the envelope of the OPLs, Delaunay triangulation algorithm and cubic spline interpolation were used. We record the interferograms of the capillary tube filled with liquids with different refractive indices and compared with the simulated interferograms. The results showed the two coincided well.

Dynamic analysis of pathogen-infected host cells using quantitative phase microscopy

We present the real-time quantitative analysis of Vibrio vulnificus-infected host cells using quantitative phase microscopy (QPM) based on interferometric techniques. This provides the ability to retrieve the phase or optical path-length distribution over the cell with nanometer path-length sensitivity from a single interferogram image. We have used QPM to study dynamic cell morphologic changes and to noninvasively quantify the cell volumes of rat basophilic leukemia RBL-2H3 cells infected with V. vulnificus strains: wild type (MO6-24∕O) and RtxA1 toxin mutant (CMM770). During the process of V. vulnificus infection in RBL-2H3 cells, the dynamic changes of quantitative phase images, cell volumes, and areas were observed in real time using QPM. In contrast, dramatic changes were not detected in RBL-2H3 cells infected with the noncytotoxic RtxA1 toxin mutant. The results showed good correlation between QPM analysis and biochemical assays, such as lactate dehydrogenase assay or β-hexosaminidase release assay. We suggest that QPM is a powerful quantitative method to study the dynamic process of host cells infected with pathogens in a noninvasive manner.

In vivo optical path lengths and path length resolved doppler shifts of multiply scattered light

In laser Doppler measurements, perfusion values averaged over different and basically unknown path lengths are recorded. To facilitate quantitative path length resolved perfusion measurements, we developed a phase modulated Mach-Zehnder interferometer with spatially separated fibers for illumination and detection. The goal of this study is to measure in vivo optical path lengths and path length resolved Doppler shifts and to compare these with conventional laser Doppler perfusion measurements. With a phase modulated Mach-Zehnder interferometer, we performed path length resolved perfusion measurements on human skin and its variations to external stimuli and compared these with conventional laser Doppler perfusion measurements. The method was evaluated in three human subjects on the dorsal side of the forearm to establish inter-individual within-site variations. Measurements were performed at three different locations of one individual for observing intra-individual inter-site variations resulting from the heterogeneity of the tissue, both in the static matrix and in the microvascular architecture of the skin. In all measurements, perfusion was simultaneously measured with a conventional laser Doppler perfusion monitor. In this study, we show the first results of path length resolved perfusion measurements in skin and its variations to occlusion and Capsicum cream provocation. From our data, we deduced the Doppler shifted fraction of photons, which is related to the blood volume, and the path length dependent average Doppler shift, which is related to the mean velocities of red blood cells. The Doppler shifted fraction of photons is decreased from 28% to 18% during occlusion and increases to 41% when capsicum cream was applied to the skin. Inter- and intra-individual inter-site measurements demonstrated variations in optical path length distributions and path length resolved Doppler shifts. The Doppler shifted fraction of photons measured on the fingertip is about 38% and that measured on the dorsal and palmar sides of the forearm are 32% and 17%, respectively. The path length distributions depend on the skin site that is being probed and the intra-individual inter-site variability is higher than the inter-individual within-site variability measured on comparable sites between different individuals. In this study, we demonstrated, for the first time to our knowledge, that in vivo path length resolved perfusion measurements are feasible. Optical path length distributions of multiply scattered light, spanning a range of 0-6 mm, and their response to external stimuli such as occlusion and capsicum cream provocation have been measured. This method will enable better interpretation of inter- and intra-individual inter-site variations in the LDF readings that are introduced by the variance in tissue optical properties. The inter- and intra-individual inter-site variations measured with our setup results indicate that that these variations should be taken into account while comparing the perfusion readings from comparable sites between individuals and from different sites of the same individual. Furthermore, the observed inter- and intra-individual inter-site variations in path length resolved Doppler measurements indicate the inherent limitation of conventional LDPM that restrict its clinical usefulness, due to its dependence on the unknown photon path length. Consequently, this method will enable to correctly interpret or counter-act the inter- and intra-individual inter-site variations in the LDF readings introduced by the variance in tissue optical properties. This approach also enables to discriminate between the Doppler-shifted photons resulting from interaction with the moving red blood cells and the non-shifted light scattered only by the surrounding static tissue matrices.

Estimation of inner surface profile of a tube by two-wavelength phase-shifting digital holography

A novel phase-shifting digital holographic method for estimation of inner surface profiles of tubes is proposed. For surface contouring, a two-wavelength method using injection-current-induced wavelength changes of a laser diode is used. To obtain inner surface information on a tube, a cone-shaped mirror is set inside the tube. Speckle noise occurring in the reconstructed phase difference image is effectively suppressed by an adaptive filtering technique consisting of exponential averaging and masking filtering processes. Distribution of optical path length in the experimental alignment is calculated and well explains the experimental results. It is shown that the calculation of optical path length by a simple model can remove the distortion of profiles occurring in the experimental results and enable the estimation of the inner surface profile of an aluminum tube.

A Method for Measuring the Three-Dimensional Refractive-Index Distribution of Single Cells Using Proximal Two-Beam Optical Tweezers and a Phase-Shifting Mach—Zehnder Interferometer

This paper describes a method for measuring the three-dimensional (3D) refractive-index distribution in a single cell. The method can be used to observe the distribution of cell components without fluorescence staining. The two-dimensional optical path length distributions from multiple directions are obtained by non-contact rotation of the cell. These optical path lengths are converted into the line integrals of the refractive index, and the 3D refractive-index distribution is reconstructed by means of computed tomography. The refractive-index distribution in a breast cancer cell can be measured using a phase-shifting Mach—Zehnder interferometer in conjunction with proximal two-beam optical tweezers.

Quantification of optical Doppler broadening and optical path lengths of multiply scattered light by phase modulated low coherence interferometry

We show experimental validation of a novel technique to measure optical path length distributions and path length resolved Doppler broadening in turbid media for different reduced scattering coefficients and anisotropies. The technique involves a phase modulated low coherence Mach-Zehnder interferometer, with separate fibers for illumination and detection. Water suspensions of Polystyrene microspheres with high scattering and low absorption levels are used as calibrated scattering phantoms. The path length dependent diffusion broadening or Doppler broadening of scattered light is shown to agree with Diffusive Wave Spectroscopy within 5%. The optical path lengths are determined experimentally from the zero order moment of the phase modulation peak around the modulation frequency in the power spectrum and the results are validated with Monte Carlo simulations.

Path-length-resolved measurements of multiple scattered photons in static and dynamic turbid media using phase-modulated low-coherence interferometry

In optical Doppler measurements, the path length of the light is unknown. To facilitate quantitative measurements, we develop a phase-modulated Mach-Zehnder interferometer with separate fibers for illumination and detection. With this setup, path-length-resolved dynamic light scattering measurements of multiple scattered light in static and dynamic turbid media are performed. Optical path length distributions spanning a range from 0 to 11 mm are measured from the area under the phase modulation peak around the modulation frequency in the power spectrum. A Doppler-broadened phase modulation interference peak is observed that shows an increase in the average Doppler shift with optical path length, independent of absorption. Validation of the estimated path length distributions is done by measuring their deformation for increasing absorption and comparing these observations with predictions based on Lambert-Beer's law.

전기장에 의한 Bi12SiO20단결정의 변화된 광행로길이 계산

The formula to calculate a variation of optical path length of single crystal by the electric field was derived by this study. The formula was applied to single crystal. The results are as follows. In case of the applied electric field in the body diagonal direction and the passing light along the same direction, the variation of optical path length had the largest value. The symmetry of the space distribution of optical path length satisfied , the set of elements of the symmetry of single crystal. The property which gave the largest influence to the variation of optical path length is the strain of length by the Inverse piezoelectric effect. The second influence, is the variation of the refractive index by the electro-optic effect. The variation of optical path length by the inverse piezoelectric effect and by the electro-optic effect have a reverse sign each other.

Optical path-length spectroscopy of wave propagation in random media

We propose optical path-length spectroscopy as a new approach to obtaining information from media that exhibit multiple light scattering. By using a backscattering technique based on low-coherence interferometry, we are able to determine the optical path-length distribution for light reflected from a random medium and to infer the value of the transport mean free path. We illustrate how a diffusion approximation model leads to a satisfactory description of depth-resolved profiles of the backscattered intensity and discuss potential applications of this technique.

Path-length-resolved dynamic light scattering in highly scattering random media: The transition to diffusing wave spectroscopy

We used low coherence interferometry to measure Brownian motion within highly scattering random media. A coherence gate was applied to resolve the optical path-length distribution and to separate ballistic from diffusive light. Our experimental analysis provides details on the transition from single scattering to light diffusion and its dependence on the system parameters. We found that the transition to the light diffusion regime occurs at shorter path lengths for media with higher scattering anisotropy or for larger numerical aperture of the focusing optics.

Measurement-based evaluation of optical pathlength distributions reconstructed from simulated differential interference contrast images.

Recently a method was presented for reconstructing optical pathlength distributions (OPDs) from images of weak phase objects obtained by a conventional differential interference contrast (DIC) microscope. A potential application of this technique is the determination of the mass of biological objects: by integrating the optical pathlength over the projected surface of the image of an object, a measure of the dry mass, i.e. the total mass of all solid constituents present in the object, is obtained. To assess the possibilities of DIC microscopy for this application, simulations were performed on computer-generated DIC images of objects of various sizes, shapes and orientation angles. After reconstructing the OPDs from these images, the integrated optical pathlength of each of the test objects was determined, and compared with the expected results. The parameter settings used in the reconstruction algorithm were found to be very important in obtaining a reliable measurement. Using optimal parameter settings, errors in the integrated OPD could be limited to a few per cent for circular objects within the investigated size range. For non-circular objects, however, the orientation angle of the object relative to the lateral shift was found to influence the measured values. Ellipses with their long axes perpendicular to the shift direction had a significantly higher integrated OPD than ellipses orientated parallel to the shift. By adjusting the reconstruction parameters the effect could be limited, but complete elimination of the artefact was not possible within the parameter range investigated.

Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope.

An image processing algorithm is presented to reconstruct optical pathlength distributions from images of nonabsorbing weak phase objects, obtained by a differential interference contrast (DIC) microscope, equipped with a charge-coupled device camera. The method is demonstrated on DIC images of transparent latex spheres and unstained bovine spermatozoa. The images were obtained with a wide-field DIC microscope, using monochromatic light. After image acquisition, the measured intensities were converted to pathlength differences. Filtering in the Fourier domain was applied to correct for the typical shadow-cast effect of DIC images. The filter was constructed using the lateral shift introduced in the microscope, and parameters describing the spectral distribution of the signal-to-noise ratio. By varying these parameters and looking at the resulting images, an appropriate setting for the filter parameters was found. In the reconstructed image each grey value represents the optical pathlength at that particular location, enabling quantitative analysis of object parameters using standard image processing techniques. The advantage of using interferometric techniques is that measurements can be done on transparent objects, without staining, enabling observations on living cells. Quantitative use of images obtained by a wide-field DIC microscope becomes possible with this technique, using relatively simple means.

Observation of the concentration distribution around a growing lysozyme crystal

The optical path length distribution of the solution around a growing lysozyme crystal was observed in situ using a Michelson interferometer of the reflection type. From the interferograms, a concentration profile around a growing crystal and the growth rate were obtained and thus, we could evaluate the diffusion coefficient of the lysozyme molecules to be 1.59 × 10 -10 m 2/s. The measurement of the viscosity of the solution rendered it possible to estimate the Stokes radius of the diffusing entities which coincided with the crystallographic size of a lysozyme molecule.

Picosecond time of flight measurement of living tissue: time resolved Beer-Lambert law.

In the turbid systems such as living tissues, the optical pathlength differs significantly from geometrical pathlength due to the effect of multiscattering. With living tissues, optical absorbers, for example, hemoglobin and myoglobin coexist together with the scattering materials. And, there are several arguments concerning the effect of such absorber on the distribution of optical pathlength. Previously, we showed that, using picosecond photometry, light intensity along the nonlinear path taken by photons through scattering media is exponentially attenuated (Nomura, et al. 1989). Present paper expands this conclusion into living tissues of rat in situ in the range from visible to near-infrared region.

Photon path length distributions for an isotropically scattering planar medium

The optical path length concept is employed to determine path length distributions by an approximate numerical inversion of the Laplace transform. Six-term or 13-term closed-form representations of the hemispherical reflectance and transmittance optical path length distributions are presented. The mean path lengths and the distributions integrated over path length are found to be in excellent agreement with known results for a scattering optical depth range of 0.001 to 50.0. Any absorption feature of a medium is easily included in a scattering calculation using the results presented. Internal directional heat flux optical path length distributions are shown to exhibit the effects of higher orders of scattering.