Showing papers in "Applied Optics in 1964"

Off-Axis Paths in Spherical Mirror Interferometers

Abstract: When a spherical mirror interferometer is illuminated by an off-axis ray of light, the repeated reflections cause the ray to trace a path which lies on the surface of a hyperboloid, with the points of reflection on the mirrors on ellipses. Under special conditions, these ellipses may become circles, with the points of reflection displaced by an angle 2θ after every round trip. When 2νθ = 2μπ, ν and μ being integers, the rays retrace their paths. These ray paths give rise to additional resonances which were observed. Pictures of the points of reflection are reproduced. The theory is in good agreement with the experimental observations. In laser amplifiers these ray paths enable one to obtain long effective path lengths in the active medium which may be contained in a thin annular cylindrical or hyperboloidal shell.

Amplification in a Fiber Laser

Abstract: Fiber lasers of neodymium-doped glass have been used on a pulsed basis to amplify 1.06-μ radiation. To prevent oscillation, the ends are polished at an angle such that reflected light is lost from the cavity. With the high inversion which can then be obtained, gains as large as 5 × 104 have been observed in a 1-m long fiber. The gain was measured as a function of pumping energy and as a function of time during the pumping pulse at which the amplification was determined.

Scattering and Polarization Properties of Water Clouds and Hazes in the Visible and Infrared

Abstract: The extinction coefficient, albedo of single scattering, and differential scattering and polarization properties of water clouds and hazes in the visible and infrared have been computed using the complete Mie series. The results with three types of size distributions are presented and compared with observations. These show a strong dependence of angular intensity and polarization patterns on the size distribution, the size range, and the dielectric and absorbing properties of water droplets at each wavelength. A peculiarity of scattering at angles near 45°, observed experimentally and independently by two authors, is corroborated by the numerical results. Prominent observational features characteristic of natural fog, such as an extremely bright and narrow aureole, cloudbows, and glories, are reproduced in a model cloud of spherical water droplets, with a wide distribution in droplet radius and a maximum concentration at a 4-μ radius.

Forty Years of History of a Grating Interferometer

Abstract: The present paper deals with the development of studies concerning the employment of diffraction gratings as interferometers, starting in 1922 when they were used to test optical systems. After reporting how a concave surface was tested by means of gratings their elementary theory is described. The phenomenon is further studied from the interferential standpoint and a wave theory of shadows formulated which is analogous to Abbe’s theory on images. A series of studies follows demonstrating that interferential theory accounts for the form of the fringes recorded when a grating is placed on the path of a wave affected by any aberration. In conclusion some simple rules are derived which allow evaluation of both the quality and the amount of the aberration of the wave under test on the basis of the form of the fringes. The sensitivity of the method is then studied, and the most recent developments and better-known applications of the gratings reported concerning their employment as achromatic interferometers.

The use of a single plane parallel plate as a lateral shearing interferometer with a visible gas laser source.

Abstract: A high-intensity interference pattern can be obtained in a shearing interferometer with the use of a visible gas laser and a simple construction. The high intensity of the laser per unit of solid angle gives an interference pattern that is visible in room light. The narrow spectral width of the source allows a simple plane parallel plate to be used to obtain the desired shear.

Comparison of Models for Correlation of Total Band Absorption

Abstract: Use of the Goody model for spectral absorptivity is made to construct band models by assignment of intensity-to-line-spacing and line-width-to-spacing ratios vs wavenumber. The vibrating rigid rotator and the vibrating nonrigid rotator are employed to obtain spectral variations of the Goody parameters. An arbitrary assignment of spectral variation of the parameters is also made. The course of total band absorption vs mass path length and pressure is then obtained for each so-constructed model by integration over wavenumber. Asymptotic relations for the total band absorption vs mass path length and pressure obtained from each model are compared. Linear, square root, square root logarithmic, and logarithmic relations are found. Results of numerical calculations are also presented for comparison.

Frustrated Total Internal Reflection and Application of Its Principle to Laser Cavity Design

Abstract: A general treatment of the phenomenon of frustrated total internal reflection is presented and numerical results are given which are related to cavity resonator design parameters. A minimum loss, minimum alignment requirement resonator is described offering a maximum of versatility. Experimental results of quasi-cw and single-pulse Q switching with a ruby optical maser are presented.

Analysis of Optical Resonators Involving Focusing Elements

Abstract: The electromagnetic fields in optical resonators involving focusing elements are considered. The work is restricted to cases where the electromagnetic fields are small at the edges of any optical elements so that there is no significant aperturing. The paper presents the analytical solution for the fields across two reference surfaces (often the end mirrors) within the resonator, and describes graphically the fields inside and outside the resonator. The analytical solution uses Huygens’ principle, but maintains generality in that the expressions relating the geometry of the particular optical resonator are left in terms of constants, which can be simply evaluated for the particular resonator. The expressions for the fields (over the reference surfaces), resonant frequencies, and stability conditions are given. The graphical description of the fields inside and outside the resonator is in terms of two experimentally observable variables: the radius of curvature of phase fronts and the spot size. A chart is utilized which permits a simple numerical presentation of those variables as a function of position along the axis, and enables a simple calculation of the higher-order transverse mode frequencies.

A Scanning Spherical Mirror Interferometer for Spectral Analysis of Laser Radiation

Abstract: The results of a theoretical and experimental investigation of a scanning spherical mirror interferometer designed specifically for analysis of laser radiation are given. It is shown that the high degree of spatial coherence and monochromaticity of laser radiation makes it possible to excite individual interferometer modes selectively. A theory of single-mode excitation is presented, and a specific example treated. The mechanical construction of the instrument and the dynamics of the scanning system are described. The capability of the instrument for observation of laser mode separation, amplitudes, and frequency shifts is illustrated by specific experiments. It is shown that the instrument can easily be used in both the visible and infrared. Results of simultaneous observation of beats between laser modes with an rf spectrum analyzer and of the laser optical field with the scanning interferometer are given, and it is shown that the combined system, in certain cases, will permit determination of the relative phases of the laser modes. Experiments illustrating the use of the scanning interferometer for observation of mode competition and the effects of magnetic fields on laser output are recounted, as is also the operation of an active scanning interferometer with which resolving powers of 2.5 × 109 and finesses of 1040 were obtained. Effects of coupling between laser and interferometer are shown, and a polarization isolator for decoupling is described.

The Infrared Transmittance of Water Vapor

Abstract: The infrared transmittance of water vapor has been calculated over a wide range of path lengths, pressures, and temperatures. All contributing lines whose relative intensity is greater than 10−8 times that of the strongest line in any particular band have been included in the calculation. In addition, the contributions from the four major isotopic species have been included. Although the vibrational analysis has been done exactly, the rotational contributions for some of the weaker lines have been calculated from the symmetric rotator approximation. This approximation was not used for the frequencies and intensities of the stronger lines below 3400 cm−1 which are correctly included in the calculations. The final transmittance tables have been generated using the quasi-random model of molecular band absorption.

Attenuation by Ozone and the Earth’s Albedo in the Middle Ultraviolet

Abstract: An approximate analytical expression is developed for the attenuation of middle ultraviolet radiation along slant paths through the atmosphere. The independent variables are wavelength, altitude of source (the detector is assumed to be above the atmosphere), angle of path with respect to zenith, and three parameters which characterize the ozone distribution. An approximate analytical expression is also developed for the scattered solar radiance seen by a satellite. Here the independent variables are the wavelength, the look angle and the sun angle with respect to the zenith, the scattering angle, and again three parameters which characterize the ozone distribution. The results based upon the formula are compared with previous studies and an experimental measurement.

Beat Frequencies Between Modes of a Concave-Mirror Optical Resonator

Abstract: The beat frequencies between modes of an optical resonator with concave mirrors have been studied by the photomixing technique. Lasers operating on the 6328 A He–Ne transition were used. The results agree well with theory. Removal of degeneracy by resonator irregularities and mode repulsion effects have been observed. The technique of partially blocking the external laser beam in order to observe all the beat frequencies is pointed out.

Principles of Self-Modulating Derivative Optical Spectroscopy

Abstract: This paper presents the theoretical principles underlying a new technique of optical spectroscopy, by the fact that the record of a spectrum, differentiated and efficiently purified of noise, is characterized in a direct and simple way. The interest of derivative optical spectroscopy is evidenced by obtained calculations showing for a typical case the gain to be expected. A set of equations is then given showing the dependence of the new spectrometer performance on the principal design parameters. Experimental results will be reported in another paper.

Resonant Optical Faraday Rotator

Abstract: Faraday rotation of the plane of polarization of light can be greatly enhanced by placing the Faraday rotating material in a resonant cavity. The transmission characteristics of a resonant rotator are analyzed, and observation of resonant rotation is reported. Under suitable conditions, the resonant rotation can be two orders of magnitude larger than the single-pass Faraday rotation. Bandwidth limitations are discussed, and a resonant rotation-bandwidth product is determined.

The McMath Solar Telescope of Kitt Peak National Observatory

Abstract: The mechanical and optical arrangement of the 160-cm aperture, 90-m focal length, McMath Solar Telescope is described. Efforts have been made to obtain good images by thermal control of the optical paths and by selection of fused quartz or metal-based mirrors for the optical components. The optical paths and performances of a vacuum double-pass spectrometer and single-pass spectrograph are illustrated. Resolution of 600,000 and a total scattered light of 3% are obtained in double-pass.

Transmission of Isotropic Radiation Across an Interface Between Two Dielectrics

Abstract: Expressions for the transmissivity of an interface between two dielectrics, averaged over all directions of incidence and over all polarization directions, are given, and the results are tabulated and graphed. When the radiation is incident from the medium with lower index of refraction, the average transmissivity Tav(n) differs from the transmissivity at normal incidence by less than 6% for values of the ratio of the indices of refraction, n, between 1 and 8. The average transmissivity when the light is incident from the high-index side of the interface is smaller than Tav(n) by a factor n−2. The connection of the results with the blackbody flux in a dielectric is noted. The results are used to estimate the energy density in a dielectric when isotropic radiation is generated internally.

Superresolution for Nonbirefringent Objects

Abstract: The theory of a superresolution experiment is developed. To achieve superresolution one must know in advance some properties of the objects, e.g., nonbirefringence, time independence, or wavelength independence. Assuming that the objects are nonbirefringent, it would be wasteful to use the two possible states of independent linear polarization of the light for simultaneously carrying the same information twice through the image-forming system. One can avoid this waste by inserting polarizers and certain double-refracting components into the system, so that the two states of polarization instead carry different information through the conventional image-forming system. The transfer function of such a superresolution system is derived for coherent and incoherent object illumination. It confirms qualitatively the results of previously reported experiments. A modification of the system is then proposed so that the one-dimensional restriction of the original concept is eliminated. The transfer function for the modified system is derived and numerical examples are presented. The modification imposes a further constraint on the class of allowed objects: the objects must be time-independent or only slowly time-varying.

The Infrared Transmittance of Carbon Dioxide

Abstract: The infrared transmittance of carbon dioxide has been calculated over a wide range of path lengths, pressures, and temperatures from 500 to 10,000 cm−1. Values of the transmittance are given at intervals of 2.5 cm−1. In addition, transmittance values are also given which have been averaged over larger intervals. All contributing spectral lines whose relative intensity is greater than 10−8 that of the strongest line in any particular band have been included in the calculation. In addition, the contributions from the eight major isotopic species have been included. The calculation of the vibrational energy levels included terms through the third power of the vibrational quantum number and also the effects of Fermi resonance. The final transmittance tables were generated using the quasi-random model of molecular band absorption.

Parameters for Attenuation in the Atmospheric Windows for Fifteen Wavelengths

Abstract: A model of a Clear Standard Atmosphere for determining attenuation in the visible and infrared windows is useful for the interpretation of the optical properties of the atmosphere. It can be used, like the U.S. Standard Atmosphere, as an information source for many technical requirements. First, a Clear Standard Atmosphere is defined. A model is then derived based on a molecular atmosphere with an aerosol component determined by sea level and high-altitude measurements. The format of the model is a series of tabulations for fifteen wavelengths from 0.4 μ to 4.0 μ with molecular and aerosol parameters arrayed at kilometer intervals to an altitude of 30 km. Horizontal, vertical, and slant path transmission from sea level, transmission between two altitudes, and transmission to space are readily calculated from the model. A sample tabulation for 0.55 μ is presented. Tabulations for the other wavelengths are contained in ref. 17 [ L. Elterman , Rept. AFCRL-63-675 ( July1963)].

Balanced Optical Discriminator

Abstract: A balanced optical discriminator for detection of angle modulation on a light beam is discussed. The device is similar, in principle, though different in form, to bridge-type microwave discriminators and optical birefringent crystal discriminators. An angle-modulated system at optical frequencies, employing a balanced discriminator, has advantages over intensity modulated systems which are familiar at radio frequencies. In addition, an angle modulated system is not as sensitive to strains, due to heating or crystal growth, in the modulating medium or to inhomogeneities in the transmission medium.

A Compact Radial Shearing Interferometer Based on the Law of Refraction

Abstract: A brief review of radial shearing interferometers as well as a logical development of various types of these interferometers is presented. The discussion considers two types of interferometers. One type essentially introduces a radial shear in collimated light while in the other type a radial shear is introduced in converging light. Finally, a compact interferometer is described. This interferometer uses the Snell’s law of refraction for obtaining radial shear and consists of two identical prisms which make up a pentaprism. In one of the prisms, a hemispherical depression is made, and this is the basic element that introduces radial shear.

Mie scattering and absorption cross sections of aluminum oxide and magnesium oxide

Abstract: The scattering and absorption cross sections for electromagnetic radiation incident upon spherical particles of aluminum oxide and magnesium oxide were calculated from the Mie theory. The complex index of refraction was taken from the best available experimental data. The calculations were made for particle radii from 0.1 μ to 10 μ and a range of wavelengths from 0.5 μ to 10 μ. The results are presented in the form of tables and graphs.

Correlations for Absorption by Methane and Carbon Dioxide Gases

Abstract: Correlations of band absorption based on the Goody model for average spectral absorptivity and an arbitrary band structure model are presented for the 7.6-μ and 3.3-μ methane bands and the 15-μ, 4.3-μ, and 2.7-μ carbon dioxide bands. The correlation gives band absorption as a smooth function of path length, pressure, and temperature. Correlation parameters were obtained from data at temperatures of 300°K, 555°K, and 833°K in the case of CH4 and 300°K, 555°K, 833°K, 1110°K, and 1390°K in the case of CO2. Comparisons of the correlations with data of various investigators are presented.

An Atlas of the Absorption Spectrum of the Lower Atmosphere from 5400Å to 8520Å

Abstract: This paper presents microphotometer traces which show, as film density vs wavelength, the absorption spectrum of an uncontaminated 16-km path in the lower atmosphere. The spectra were recorded with a small grating spectrograph over the spectral range from 5400A to 8520A with a resolution of about 0.2A. Wavelengths are presented for the absorption lines, and most lines are identified by absorbing species which are considered to be either water vapor or molecular oxygen.

John William Strutt, third Baron Rayleigh

Abstract: This paper presents a sketch of the life and principal scientific contributions of Lord Rayleigh, with emphasis on his research in optics.

Improvements in Design and Performance of the Large Aperture Lyman Flashtube

Abstract: A short duration flash source of high and reproducible intensity with usable continuum in the far ultraviolet is described. Electrical and optical studies of the source and its use to obtain absorption coefficients of argon between 450 A and 800 A are reported.

Exfocal Pumping of Optical Masers in Elliptical Mirrors

Abstract: An efficiency near unity can be achieved in optical pumping devices for lasers, where unabsorbed light is refocused at the light source, leading to multiple passes of pumping energy through source and laser. In properly dimensioned elliptical mirrors this can, in principle, be done by placing source and laser outside of the focal points. Furthermore, in these “exfocal” elliptical designs the light density of the source is transformed into the laser at a ratio of 1:1, resulting in very low-threshold energies. The lowest value observed for ruby lasers up to 7.6 cm in length was 50 W-sec at room temperature in a rotational-ellipsoidal mirror where the axis of source and laser are oriented in the rotational axis of the ellipsom, while their lengths are equal to the distance between focus and wall. Alternative designs are exfocal elliptical and circular cylinders. In exfocal ellipsoids the pump light distribution is of exactly rotational symmetry which leads to symmetrical absorption of pumping light in the laser. As a result, quasi-periodic relaxation oscillations of 5000-μsec duration and a component of continuous emission have been observed at room temperature with 300 W-sec pumping energy.

The Extreme Values of Reflectivity and the Conditions for Zero Reflection from Thin Dielectric Films on Metal

Abstract: The equations for the film thickness necessary to achieve the maximum and minimum values of reflectivity and the conditions for zero reflection for systems with one or two dielectric films over a metallic substrate are derived. Extension of results to multilayer systems are made on the basis of simple relationships obtained for the single- and double-layer systems in order to improve the effectiveness and the practical applicability of the systems. A simple system requiring an impractical value for film thickness or refractive index can be substituted by an equivalent symmetric multilayer system consisting of films with optical parameters within practical range of use.

Infrared-Optical Techniques Applied to Oceanography I. Measurement of Total Heat Flow from the Sea Surface

Abstract: The heat flow from the sea surface at night by evaporation and air conduction is from the interface. The radiation loss comes from the top 0.02 mm. Water temperature at greater optical depths was measured experimentally by infrared radiometry with wavelength regions selected for 1/k = 0.06 and 0.50 mm. Calculation of the heat flow by conduction through this half-millimeter layer is within experimental error of the total heat flow from the surface. This result indicates that the heat transfer by convection in this layer is small compared to conduction, and that such equipment, preferably airborne, can be used to measure the total heat flow from the sea at night.