Light Diffraction Patterns Research Articles

Laser diffraction pattern analysis of various two-dimensional regular-shaped model particles

Effects of the particle shapes and dispersions on the equivalent particle sizes determined by the laser light diffraction pattern analysis are experimentally investigated. The sample model particles are prepared on slide film as photographic images having various shapes (round, rectangular and triangular) and having various concentration (from about 1 to 30%): defined as two-dimensionally dispersed particle images on the film. The results of experimental observation are compared with other equivalent sizes induced from the geometrical dimensions of the rectangular or triangular images. The overlapping effect of diffraction of several particles on the incident beam cross-section is discussed in terms of the particle shape or aspect ratio. This effect determines the light scattering diameter of the non-circular particles.

Optical analysis of finite-amplitude ultrasonic pulses

Finite-amplitude pulses are examined acousto-optically using a newly developed light-diffraction apparatus. Based on an optical analysis of ultrasonic transducer response to continuous-wave excitation at and near the fundamental frequency, pulse Fourier spectra are derived for input to a light-diffraction model, providing quantitative agreement between experiment and theory. The diffraction theory predicts that a light-diffraction pattern produced by a harmonically distorted acoustic pulse train will exhibit asymmetry in the intensity distribution with respect to the zero order. To simulate harmonic distortion, pulse frequency spectra are used for input to a computational model that is based on the Burgers’ equation for propagation of finite-amplitude acoustic waves in a nonlinear medium. The spectrum, propagation, and light-diffraction models give a complete description of light diffraction by finite-amplitude pulses and provide good agreement with experimentally obtained diffraction patterns.

Unified diagram for Fraunhofer diffraction and interference patterns from single, double, and multiple slits

A unified diagram is presented, based on the Huygens–Fresnel principle, which permits a construction of the Fraunhofer diffraction pattern of light from any combination of slits. The diagram employs a graphical evaluation of a line integral over a frozen-wave profile along a rotated slit configuration.

Optical probing of ultrasonic pulses

A description is given of an experimental set-up with which the predictions of a recently developed theory of light diffraction by pulsed ultrasonic waves was verified. The apparatus uses a long optical path which makes it possible to resolve diffraction orders produced by low MHz centre frequency pulses with repetition frequencies as low as 40 kHz. An empirical model of the transducer frequency response to continuous waves was established using light diffraction. The model was then used to predict the Fourier spectrum of an ultrasonic pulse in the liquid whose centre and repetition frequencies and pulse duration were known. The pulse frequency spectrum was used as input for the diffraction model to predict the shape of light diffraction patterns. The pulse modelling technique provides better agreement between measured and predicted light diffraction patterns.

Examination of finite amplitude ultrasonic pulses using light diffraction

Finite amplitude pulses are examined acousto‐optically with a light diffraction apparatus. Using an empirical model of transducer frequency response, ultrasonic pulse Fourier spectra are derived for input to a light diffraction model. To then simulate harmonic distortion, the pulse spectra are used for input to a computational model based on the Burgers' equation for propagation of finite amplitude acoustic waves in a nonlinear medium. Several examples are presented that illustrate good agreement between experimental light diffraction patterns and those predicted by the pulse spectrum, propagation, and light diffraction theories. [Work supported by ONR.]

Positron emission holography: A new method of creating positron camera images

By simulating the presence of a Fresnel zone plate in a camera designed for positron emission tomography (PET), a hologram can be synthesized which permits full three-dimensional images of the positron distribution in the original object to be rapidly constructed. The method requires no additional apparatus to a standard PET system, which is also operated in the usual way. The trajectory of each photon pair, detected in coincidence, is weighted as if it had passed through a zone plate optimised to suit the problem, before recording its intercept with a (single) plane to produce the hologram. The final image is created by calculating the diffraction pattern of monochromatic light passed through this hologram; it may also be created optically. The method is described in detail and its attractions discussed. Results are presented of some simple objects obtained from holograms produced from PET camera data, in comparison with images created by conventional back-projection processing of the same data.

Light‐scattering characterization of polyblends in the presence of multiple‐scattering conditions

AbstractA novel approach is described for the noncontact evaluation of structural morphology in polyblends by light scattering. Optical methods are attractive for the on‐line characterization of translucent materials because they are noninvasive, rapid, and applicable to high temperature materials. One limitation of conventional light‐scattering techniques is their requirement for relatively thin samples in order to avoid multiple‐scattering effects that smear out the details of the light diffraction pattern. The approach described in this paper is meant to circumvent this limitation by resorting to turbidimetric measurements, which provide useful information on the average size, shape, concentration, and orientation of the dispersed phase particles even in the presence of multiple scattering. The sample thickness is no longer restricted, and methods are described by which the near‐surface volume of infinitely thick parts may be inspected with access to a single side of the material. Results are presented for polypropylene‐polycarbonate (PP/PC) samples of different thicknesses and microstructural morphology, including fibrillar‐type oriented structures.

Theoretical Fraunhofer light diffraction patterns calculated from three-dimensional sarcomere arrays imaged from isolated cardiac cells at rest

Sarcomere striation positions have been obtained throughout the volumes of calcium-tolerant resting heart cells by direct computer interfaced high-resolution optical imaging. Each sarcomere position is stored in a three-dimensional (3-D) matrix array from which Fraunhofer light diffraction patterns have been calculated using numerical methods based on Fourier transforms. Diffraction patterns have been calculated from heart cell data arrays oriented normal to a theoretical laser beam. Twelve characteristic features have been identified and described from these diffraction patterns that correlate to diffraction phenomena observed from both cardiac and skeletal muscle. This numerical approach provides the means to directly assess diffraction pattern formulation, the precision of layer line angular separation, layer-line intensity and angular asymmetries, line widths and fine structures in terms of the known diffracting source structures. These results confirm that theoretical calculations can predict real muscle diffraction patterns and their asymmetries.

Acousto-optic method for ultrasonic pulse characterization

The light distribution in a diffraction pattern produced by a sequence of ultrasonic pulses depends on a number of parameters characterizing the pulse shape, modulation and sequencing as well as changes in the spectral composition due to non-linearities in the propagation medium. Based on calculations of such light diffraction patterns it is possible to consider the inverse problem, i.e. the determination of parameters mentioned above by evaluating certain features of the diffraction pattern produced by the pulses. A number of examples are given to illustrate these possibilities.

Light diffraction patterns and sarcomere length variation in striated muscle fibers of Limulus.

Light diffraction patterns produced by Limulus striated muscle fibers were examined. Segments of fibers were glycerinated, fixed or bathed in relaxing solution. Profiles of the intensity of a diffracted order vs. the angle of incidence of the laser beam often exhibited narrow peaks with the fiber at rest length. The incident angles at which the intensity of left and right orders is greatest are used to calculate the sarcomere length, supporting the notion that regions of the fiber are organised into Bragg reflecting planes. These profiles developed subpeaks and broadened upon stretch of the fiber. The broad angle scan profiles are suggested to result from a decrease in the regular packing of myofibrils as the fiber is lengthened. The angular width of the subpeaks is used to estimate the thickness of clusters of myofibrils. The variation in sarcomere length along the fiber, as determined by the 0th to 1st diffraction order spacing, was dependent upon the fiber preparation. Glycerinated fibers and those bathed in relaxing solution showed more variation than fixed fibers. The variation of sarcomere length is compared to the variation in thick filament lengths in Limulus reported by Dewey et al. (1982). These results are compared to those obtained from frog fiber segments.

Measurement of Diffraction and Interference Patterns of Light : Making Use of Personal Computer

Measurement of Diffraction and Interference Patterns of Light : Making Use of Personal Computer

Sarcomeric domain organization within single skinned rabbit psoas fibers and its effects on laser light diffraction patterns

Total intensity and fine structure of first-order laser light diffraction maxima from single skinned rabbit psoas fibers were studied. Total intensity of the diffraction maxima was measured as a function of the incidence angle (omega-scan). In the most homogeneous fibers, most of the intensity in the diffraction maxima is confined to a rather narrow range of incidence angles. Fibers with less homogeneous striation patterns, apparently composed of several regions of distinct sarcomere length and tilt of striation (domains), give rise to several narrow intensity peaks in their omega-scans. Left and right first-order diffraction lines produce omega-scans of almost identical shape, composed of one or more intensity peaks, with each pair of corresponding peaks separated by about the same angle. The data indicated that in single skinned rabbit psoas fibers, light diffraction is dominated by Bragg diffraction and that the peaks within omega-scans can be directly correlated with domains within the illuminated fiber segment. In the most homogeneous fiber segments the diameter of domains, estimated from the width of the corresponding maxima in the omega-scans, could almost be as large as the fiber diameter. On average, from the number of peaks in the omega-scans two to three domains with an average length of approximately 250-350 microns can be identified in a fiber cross-section. Therefore, on average only a small number of domains (8 per mm) are found within skinned rabbit psoas fiber segments. In contrast, the number of substructural lines within the diffraction maxima is large even for microscopically homogeneous fibers. Substructural lines appear to be present only when several domains are illuminated simultaneously. Separation and width of these substructural lines are approximately inversely proportional to the length of the illuminated region of the fiber. These data suggest that the substructural lines are due to interference between domains, illuminated simultaneously by a light source with a high degree of spatial coherence (laser). The relevance of these findings for measurements of sarcomere length by laser light diffraction is discussed.

Fine structures in the light diffraction pattern of striated muscle.

Single skeletal muscle fibres of frog were illuminated with a He-Ne, argon-ion or rhodamine 6G dye laser. The fine structures lying within the diffraction columns moved parallel to the fibre axis without changing their pattern when either the wavelength or the incident angle of the laser beam was varied, or when the fibre was stretched slightly. However, their pattern remained nearly constant when the fibre was submerged in hypotonic or hypertonic solution. As the illumination of about 1 mm or 0.1 mm width scanned along the length of the fibre, new structures emerged while others faded away giving rise to the notion that the diffraction columns were moving in the direction of the scan. A decrease in the illumination width caused the structures lying on the periphery of the diffraction column to disappear and the width of the remaining structures to increase. Measurements rule out the existence of large diffraction planes in these muscles. In addition, they indicate that the fine structures come from the diffraction of the whole rather than independent components of the illuminated volume. The origin of the fine structures is explained by two diffraction models.

Light diffraction studies of single muscle fibers as a function of fiber rotation

Light diffraction patterns from single glycerinated frog semitendinosus muscle fibers were examined photographically and photoelectrically as a function of diffraction angle and fiber rotation. The total intensity diffraction pattern indicates that the order maxima change both position and intensity periodically as a function of rotation angle. The total diffracted light, light diffracted above and below the zero-order plane, and light diffracted into individual orders gives information about the fiber's longitudinal and rotational structure and its noncylindrical symmetry.

LASER DIFFRACTION ANALYSIS FOR TWO-DIMENSIONAL MODEL PARTICLES PHOTOGRAPHED ON THE SLIDE FILM

ABSTRACT In order to investigate the influence of particle parameters on the light diffraction pattern analysis, a model particle was prepared by photographing the round particles and the rectangular ones separately on the slide film, and experimentally analysed with the He-Ne Laser diffraction system. The parameters analysed in this experiment are size, concentration, and shape of the particle images photographed on the film. The analysis provided a good coincidence with the results of microscopic observations; the standard deviation was within 1–5 %. The influence of the particle size of the sample on the results evaluated is negligible or in the acceptable range of measurement error. The results of observation suggests that the lowest limit of particle concentration will be suggested not to be less than 2 % in order to eliminate any possible errors in analysing the intensity of the diffraction pattern of round particles. For rectangular particles which are homogeneously and randomly dispersed on the film, the equivalent size evaluated approachs only to the magnitude of the breadth of the particle.

Optical method for fatigue crack detection

A 1-D optical Fourier spectrum analyzer system is used to detect fatigue cracks as small as 0.5 microm in titanium test samples. Signatures obtained from scans of reflected laser light diffraction patterns show features linked to the presence of surface cracks. Signature characteristics are preserved without a need for critical focusing or optics-to-sample positioning. Analytic modeling of a crack surface profile is used to explain the primary cause of the observed signature properties.

Digital data acquisition and analysis of striated muscle diffraction patterns with a direct memory access microprocessor system.

A microprocessor based data acquisition computing system has been developed to examine dynamic changes in light diffraction patterns from single skeletal muscle fibers. A significant improvement in digital data acquisition rate compared to previous designs has been achieved by utilizing a fast dedicated analog to digital converter and direct memory access data storage. Diffraction patterns from muscle fibers are imaged onto a 256 element charge-coupled device. The analog output of a full 256 point frame of data may be digitized and stored in 2.2 ms (128 point half frame in 1.1 ms) with a spatial resolution of up to 5.0 nm/sarcomere. This computing system can transfer up to 28 full frames of data as one continuous block directly between the CCD and memory leaving the CPU free for experimental control and closed-loop processing. The computing system calibrates and analyzes diffraction data under sofware control for sarcomere length, dispersion, and peak intensity. The operation of this data acquisition computing system is superior to previous digital designs with its increased data acquisition rate and to analog designs with its data manipulation, analysis, experimental control, and processing capabilities.

Light diffraction by magnetic domain gratings and its applications

Magnetic domains arranged in a regular domain grating give rise to light optical diffraction patterns. The diffractions are examined at a stripe domain grating and a hexagonal bubble domain grating. Applications of the diffraction for light deflection and data processing are discussed.

Light diffraction study of single skeletal muscle fibres

Light diffraction patterns from isolated frog semitendinosus muscle fibers were examined. When transilluminated by laser light, the muscle striations produce a diffraction pattern consisting of a series of lines that are projected as points onto an optical detector by a lens system. Diffraction data may be sequentially stored every 18 ms for later processing by digital computer systems. First- and second-order diffraction line intensities were examined from intact, chemically skinned, and glycerinated single fibers. The diffraction line intensities demonstrated a strong length dependence upon passive stretch from reference length to 3.6 micrometer. The first-order intensity linearly increased an average of 15-fold over the range examined. The magnitude of the second order intensity was less than the first order and showed an exponential rise with increasing length. Both first- and second-order intensities decreased upon muscle activation. Data from chemically skinned and glycerinated single fibers were not significantly different from intact fibers, indicating that the membrane structure has little effect upon the diffraction phenomenon in muscle. Theoretical model systems are examined in an attempt to find the basis of these results. Neither an analysis based on a diffraction grating with variable spacing nor the unit cell model of Fujime provides an explanation for the observed length dependency of intensity. Though the origin of the intensity decrease upon stimulation is not known, we have suggested that it could result from lateral misalignment of myofibrils and can occur upon activation.

White light diffraction patterns of amplitude and phase zone plates

The polychromatic properties of the Fresnel zone plate, Gabor zone plate, phase reversal zone plates and kinoform lens are studied. The polychromatic intensity in the diffraction patterns on these plates has been computed and the influence of Gaussian spectral filters is shown. Also, the distributions of illuminance and chromaticity in the diffraction patterns and along the optical axis, have been calculated for several zone numbers. The results obtained are discussed and compared for the different plates.