Size Of Airy Disk Research Articles

Digital image correlation at long working distances: The influence of diffraction limits

Digital Image Correlation (DIC) is an optical measurement technique that can easily be adapted for high magnification applications. These high magnifications involve competing phenomena which must be balanced to produce the highest quality measurements. When out-of-plane displacements cause the specimen under investigation to move out of the depth of field, poor focus negatively affects the measurement. As a result, it is often recommended to reduce aperture size to improve the depth of field. However, smaller aperture sizes can also cause poor focus as the diffraction limit of light causes larger Airy disks, particularly at longer working distances. This work investigates the competing effects of both depth of field and Airy disk size in three test cases: higher magnification and shorter working distance, lower magnification and shorter working distance, and lower magnification and longer working distance. Different aperture sizes are found to change which effect dominates, and a recommendation for selecting the aperture setting to minimize measurement error from both phenomena is made.

Anomalous change of Airy disk with changing size of spherical particles

Use of laser diffraction is considered as a method of reliable principle and mature technique in measurements of particle size distributions. It is generally accepted that for a certain relative refractive index, the size of the scattering pattern (also called Airy disk) of spherical particles monotonically decreases with increasing particle size. This fine structure forms the foundation of the laser diffraction method. Here we show that the Airy disk size of non-absorbing spherical particles becomes larger with increasing particle size in certain size ranges. To learn more about this anomalous change of Airy disk (ACAD), we present images of Airy disk and curves of Airy disk size versus particle size for spherical particles of different relative refractive indices by using Mie theory. These figures reveal that ACAD occurs periodically for non-absorbing particles and will disappear when the absorbing efficiency is higher than certain value. Then by using geometrical optics (GO) approximation, we derive the analytical formulae for the bounds of the size ranges where ACAD occurs. From the formulae, we obtain laws of ACAD as follows: (1) for non-absorbing particles, ACAD occurs periodically, and when the particle size tends to infinity, the period tends to a certain value. As the relative refractive index increases, (2) the particle size ranges where ACAD occurs shift to smaller values, (3) the period of ACAD becomes smaller, and (4) the width of the size ranges where ACAD occurs becomes narrower. In addition, we can predict from the formulae that ACAD also exists for particles whose relative refractive index is smaller than 1.

Field scanner design for MUSTANG of the Green Bank Telescope

MUSTANG is a bolometer camera for the Green Bank Telescope (GBT) working at a frequency of 90 GHz. The detector has a field of view of 40 arcseconds. To cancel out random emission change from atmosphere and other sources, requires a fast scanning reflecting system with a few arcminute ranges. In this paper, the aberrations of an off-axis system are reviewed. The condition for an optimized system is provided. In an optimized system, as additional image transfer mirrors are introduced, new aberrations of the off-axis system may be reintroduced, resulting in a limited field of view. In this paper, different scanning mirror arrangements for the GBT system are analyzed through the ray tracing analysis. These include using the subreflector as the scanning mirror, chopping a flat mirror and transferring image with an ellipse mirror, and chopping a flat mirror and transferring image with a pair of face-to-face paraboloid mirrors. The system analysis shows that chopping a flat mirror and using a well aligned pair of paraboloids can generate the required field of view for the MUSTUNG detector system, while other systems all suffer from larger off-axis aberrations added by the system modification. The spot diagrams of the well aligned pair of paraboloids produced is only about one Airy disk size within a scanning angle of about 3 arcmin.

Maximum fiber coupling efficiency and optimum beam size in the presence of random angular jitter for free-space laser systems and their applications

Free-space laser communication systems use optical-fiber-based technology such as optical amplifiers, receivers, and high-speed modulators. In these systems using single-mode fibers, the fiber coupling efficiency is one of the most significant issues to be solved. Optimum relationships between a focused optical beam and mode field size of the optical fiber in the presence of random angular jitter are discussed in relation to fiber-coupled optical systems. Maximum fiber coupling efficiency is analytically derived with the optimum Airy disk radius normalized by the mode field radius as a function of random angular jitter. The fade level of fiber-coupled signals at desired fade probability is investigated. It is shown that the average bit error ratio significantly degrades with the random angular jitter normalized by the mode field radius larger than about 0.3 when the Airy disk size is optimally selected.

Spatial filtering of atmospheric decorrelation from wavefronts for interferometry

For aperture diameters greatly exceeding the Fried parameter r 0, the spatial frequency spectrum of an atmospherically degraded wavefront extends out to frequencies much greater than the Airy disk size characterizing a clean wavefront diffracting at the aperture. One may use a low-pass spatial filter like a pinhole to reject selectively the high spatial frequencies in a degraded wavefront and thereby dramatically increase its spatial coherence. We show that although a simple filter like a pinhole reduces the power throughput, that power reduction is in a sense more than made up for by the improved spatial coherence of the wavefronts. By analyzing a two-aperture Michelson stellar interferometer, which is the simplest aperture-synthesis array, we demonstrate a clear improvement of the performance of the interferometer when spatial filters are used.

Video-enhanced microscopy with a computer frame memory.

Video-enhanced microscopy combined with the use of a computer frame memory extends considerably the useful range of our video enhanced contrast (AVEC) methods for polarizing, double-beam interference and differential interference contrast microscopy. Increased visual contrast is achieved by two stages of amplifications: the first optical, by using high bias retardation settings, and the second electronic. These steps are followed by a reduction of background brightness by means of a clamp voltage applied to a DC restoration circuit of the video camera. One of the limitations of the AVEC method alone is the inevitable appearance under high gain conditions of a pattern of mottle due to inaccessible dirt and defects in the lenses even of high quality. This limitation has been circumvented by storing the mottle pattern in the frame memory (frame store) and continuously subtracting it from each succeeding frame to clear the image. A major gain in image quality has resulted. In polarizing microscopy, the frame memory can be used also to subtract the image at one compensator setting from that at the equivalent setting of opposite sign, thus removing from the final image not only most of the mottle pattern but also the contrast due to the bright-field contrast. In the polarizing microscope, these manipulations of the raw video image make it possible to observe and measure the birefringence of various organelles and elements such as microtubules, intermediate filaments and bundles of as few as a half dozen actin filaments. Since scattered light is also removed from the image, features hidden from view in the unprocessed image become visible. In differential interference microscopy, the AVEC method makes visible (i.e. detectable) many linear elements and particles that are an order of magnitude smaller than the resolution limit and not visible in the optical image. Such features are inflated by diffraction, however, to Airy disk size.