Abstract: The solution of electromagnetic scattering by a homogeneous prolate (or oblate) spheroidal particle with an arbitrary size and refractive index is obtained for any angle of incidence by solving Maxwell's equations under given boundary conditions. The method used is that of separating the vector wave equations in the spheroidal coordinates and expanding them in terms of the spheroidal wavefunctions. The unknown coefficients for the expansion are determined by a system of equations derived from the boundary conditions regarding the continuity of tangential components of the electric and magnetic vectors across the surface of the spheroid. The solutions both in the prolate and oblate spheroidal coordinate systems result in a same form, and the equations for the oblate spheroidal system can be obtained from those for the prolate one by replacing the prolate spheroidal wavefunctions with the oblate ones and vice versa. For an oblique incidence, the polarized incident wave is resolved into two components, the TM mode for which the magnetic vector vibrates perpendicularly to the incident plane and the TE mode for which the electric vector vibrates perpendicularly to this plane. For the incidence along the rotation axis the resultant equations are given in the form similar to the one for a sphere given by the Mie theory. The physical parameters involved are the following five quantities: the size parameter defined by the product of the semifocal distance of the spheroid and the propagation constant of the incident wave, the eccentricity, the refractive index of the spheroid relative to the surrounding medium, the incident angle between the direction of the incident wave and the rotation axis, and the angles that specify the direction of the scattered wave.

Abstract: The differential scattering characteristics of closed three-dimensional dielectric objects are theoretically investigated. The scattering problem is solved in a spherical basis by the Extended Boundary Condition Method (EBCM) which results in a system of linear equations for the expansion coefficients of the scattered field in terms of the incident field coefficients. The equations are solved numerically for dielectric spheres, spheroids, and finite cylinders to study the dependence of the differential scattering on the size, shape, and index of refraction of the scattering object. The method developed here appears to be most applicable to objects whose physical size is on the order of the wavelength of the incident radiation.

Abstract: The penetration depth of light in the sea is defined for remote sensing purposes as the depth above which 90% of the diffusely reflected irradiance (excluding specular reflectance) originates. It is demonstrated that for a homogeneous ocean, this is the depth at which the downwelling in-water irradiance falls to 1/e of its value at the surface. Penetration depths as a function of wavelength are presented for a variety of water types, and a mean penetration depth z (90) for a broadband sensor is defined and applied to the MSS on ERTS-1. The maximum z (90) expected for ERTS-l is found to be somewhat less than 20 m.

Abstract: Mode coupling theory is applied to the study of multimode optical fibers with graded-index cores. For coupling caused by random bends in the waveguide axis, the results predict the dependence of the induced losses on the fiber's characteristics. The impulse response is determined for fibers with random bends having several different power spectra. The results are used to predict the transmitted power, the delay time, and the rms pulse width in fibers with graded-index cores.

Abstract: We present further calculations of the three-dimensional mode patterns and power outputs from a high-power gas-dynamic laser, including a nonuniform flowing, saturable gain medium plus index inhomogeneities (shocks) inside the laser. The calculations are carried out using a plane-wave or k-space expansion together with the fast Fourier transform. A new expanding-beam coordinate transform converts all diverging or converging sections of the resonator mode into equivalent collimated beam sections. The resulting FFT propagation code is significantly faster than earlier propagation codes using other eigenmode expansions.

Abstract: where co is the angular velocity of the chopper, r the distance from the rotating center to the laser beam axis, and t2-t, the time interval for a variation of P(x)/P0 from 0.9 to 0.1. Figure 1 shows the experimental arrangement. In this experiment, we use a He-Ne laser oscillating in the TEMoo mode. The wavelength is 0.63 m. The position of the beam waist is located at the output mirror of the laser oscillator, and the beam radius w, at the waist is 0.4 mm. The focal length of lens A is 367 mm. The distance from lens A to the output mirror surface of the laser is 600 mm. Lens A transforms the beam from the oscillator to a beam that has a more accessible waist. The radius and the posi-

Abstract: The theoretical precision attainable from a number of types of ideal null and photometric ellipsometers is investigated quantitatively. Photometric and modulated null ellipsometer systems are shown to be approximately comparable with respect to precision when operating under shot-noise limited conditions. Differences are due principally to intrinsic detector noise levels, which are more significant in null designs. The equations derived can be used to estimate practical measurement limits or to choose components to achieve a specific objective.

Abstract: The various theories of diffuse reflectance spectroscopy are compared mathematically, and it is concluded that the modified particle model theory is probably the most nearly correct. If so, the comparison shows that the simple, easily applied simplified particle model theory is approximately valid for relative index of refraction values of 1.5-2.5 and that the Kubelka-Munk remission function is approximately applicable in the traditional sense. Expressions were obtained for the Kubelka-Munk constants in terms of the fundamental optical parameters, and the depth of penetration of radiation into a powdered sample was investigated.

Abstract: The residual surface roughness of diamond-turned optics is expected to contain significant periodic components. The optical properties of such surfaces are explored as a special case of Rayleigh-Rice vector scattering theory applied to periodic roughness with vertical amplitudes much smaller than the wavelength of light. Expressions are given for the interpretation of differential-scatter, total-integrated-scatter, reflectometry, and ellipsometric measurements in the limit of a highly conducting. surface. In general, such measurements give varying degrees of information about the two-dimensional power spectral density of the surface roughness within the nominal range from the wavelength of light to the diameter of the probing beam spot. Such information may be useful for the practical characterization of mirror surfaces.

Abstract: We have measured the velocity of blood flow in the femoral vein of a rabbit by detecting the Doppler shift of laser light introduced into the vein by means of a fiber optic catheter. A 0.5-mm diam optical monofiber inserted in the vein transmits both the incident light and collects the light scattered from the moving erythrocytes. The spectrum of heterodyne beat notes between the local oscillator, which originates at the end of the fiber, and the scattered light are measured using optical mixing spectroscopy.

Abstract: We consider the effects of signal and local oscillator phase front misalignment, beam spot sizes, and electric field distributions on heterodyne detection. The signal and local oscillator fields that we consider are various combinations of Airy, Gaussian, and uniform distributions. We show that the values of the beam radii that maximize the heterodyne SNR are sensitive to phase front misalignment and that the degradation with misalignment angle is somewhat less severe for Airy received signals than for uniform. We also prove that for small optical spot sizes and perfect alignment, the optimal ratio of local oscillator Gaussian l/e field radius to signal Airy F number is approximately 0.7lambda. We next consider the effects of nonuniform detector quantum efficiency. Simple examples show that quantum efficiencies averaged over the detector surface give only crude estimates of the sensitivity of a heterodyne system. For accurate estimates full account must be made of the electric field parameters and the detector re ponse at each point on its photosurface.

Abstract: Long-path measurements of carbon monoxide in the atmosphere are described. The technique of resonance absorption was used in which the wavelength of radiation from a PbS0.82Se0.18 semiconductor diode laser was tuned into coincidence with an absorption line of CO in its fundamental band around 4.7 μm. By employing rapid frequency modulation of the laser emission to overcome atmospheric turbulence effects, it was possible to achieve a minimum detectable concentration of 5 parts per billion over a 0.61-km path. Continuous around-the-clock monitoring was also performed and permitted increases in the ambient CO level due to commuter traffic to be observed.

Abstract: Optoacoustic detectors are used to measure pressure changes occurring in enclosed gases, liquids, or solids being excited by intensity or frequency modulated electromagnetic radiation. Radiation absorption spectra, collisional relaxation rates, substance compositions, and reactions can be determined from the time behavior of these pressure changes. Very successful measurements of gaseous air pollutants have, for instance, been performed by using detectors of this type together with different lasers. The measuring instrument consisting of radiation source, modulator, optoacoustic detector, etc. is often called spectrophone. In the present paper, a thorough optoacoustic detector optimization analysis based upon a review of its theory of operation is introduced. New quantitative rules and suggestions explaining how to design detectors with maximal pressure responsivity and over-all sensitivity and minimal background signal are presented.

Abstract: A new microscope imaging system, modulation contrast, has been devised that reveals phase gradients; the image intensity is proportional to the first derivative of the optical density in the object. The modulator, a special filter, is placed in the Fourier plane, a plane conjugate with a slit aperture. The image of the slit aperture is registered within a gray region of the modulator; on one side of the gray region is a region of low transmittance and on the other side, a region of maximum transmittance. The modulator processes opposite gradients to produce opposite intensities, creating an optical shadowing effect. The dark region may be outside the optical system when the gray region is offset to the edge of the Fourier plane, to achieve maximum resolution. Modulation contrast is directional and capable of optical sectioning, revealing details without obscuring effects of structures above and below the plane of focus. The imaging theory of microscope optics has been extended to include effects of phase gradients. Phase gradients distribute the zero order across the Fourier plane. Intensity of the gradient's image is controlled by the zero order of the gradient diffraction pattern.

Abstract: Response calculations for five commercial light-scattering aerosol particle counters have been carried out that take into account the emissive power of the light source, the spectral sensitivity of the phototube, and the specific geometrical factors for each instrument. Earlier calculations had been published for two of these instruments, but these had not considered each of these factors appropriately. The results indicate a strong dependence of response upon both the real and imaginary part of the refractive index and, for a given refractive index, a multivalued response in the submicrometer range for three of the five instruments.

Abstract: A high resolution near ir Fourier spectrometer with the same general design as previously described laboratory instruments has been built for astronomical observations at a coude focus. Present spectral range is 0.8–3.5 μm with PbS and Ge detectors and maximum path difference 1 m. The servo system can accommodate various recording modes: stepping or continuous scan, path difference modulation, sky chopping. A real time computer is incorporated into the system, which has been set up at the Hale 500-cm telescope on Mount Palomar. Samples of the results are given.

Abstract: Inversion of measurements of optical pathlength through strongly refracting, radially symmetric phase objects, such as plasmas, is discussed. An exact inversion scheme, based upon methods originally applied in seismology is developed and applied to interferometry. It is shown that Abel inversion, which assumes that the probing rays are straight lines, yields rather accurate results if the interferogram is formed with appropriate imaging.

Abstract: An improved speckle-shearing interferometric method is presented that allows simultaneous determination of derivatives of surface displacements of a structure with respect to four different directions. The technique relaxes several limitations associated with conventional interferometry and thus is adaptable to nonlaboratory environments. The relevant theory is presented, and the method demonstrated by determining spatial derivatives of in-plane and out-of-plane displacements of statically loaded and vibrated structures.

Abstract: The radiance in the earth's atmosphere and ocean is calculated for a realistic model including an ocean surface with waves. Individual photons are followed in a Monte Carlo calculation. In the atmosphere, both Rayleigh scattering by the molecules and Mie scattering by the aerosols as well as molecular and aerosol absorption are taken into account. Similarly, in the ocean, both Rayleigh scattering by the water molecules and Mie scattering by the hydrosols as well as absorption by the water molecules and hydrosols are considered. Separate single-scattering functions are used which are calculated separately for the aerosols and the hydrosols from the Mie theory with appropriate and different size distributions in each case. The scattering angles are determined from the appropriate scattering function including the strong forwardscattering peak when there is aerosol or hydrosol scattering. Both the reflected and refracted rays, as well as the rays that undergo total internal reflection, are followed at the oceanc surface. The wave slope is chosen from the Cox-Munk distribution. Graphs show the influence of the waves on the upward radiance at the top of the atmosphere and just above the ocean surface and on the downward radiance just below the ocean surface as well as deeper within the ocean. The radiance changes are sufficient at the top of the atmosphere to determine the sea state from satellite measurements. Within the ocean the waves smooth out the abrupt transition that occurs at the edge of the allowed cone for radiation entering a calm ocean. The influence of the waves on the contrast between the sky and sea at the horizon is discussed. It is shown that the downward flux just below the surface increases with wind speed at all solar angles.

Abstract: Vector components of alternating electric and magnetic fields can be measured with excellent sensitivity and time resolution using a laser system employing Pockels effect or Faraday effect materials as field sensors. This technique offers the advantages of being passive and remote; the sensor material requires no power source and can be interrogated by a remotely located laser transmitter and receiver with no connecting wires or electrodes. This paper analyzes the sensitivity of the electrooptic and magnetooptic methods and derives new figures of merit for materials used as sensors in these applications. Experiments evaluating the temperature coefficients of sensitivity and demonstrating that sensitivities of 0.06 V/cm and 0.5 G can be achieved easily are described.

Abstract: A calculation is made of the luminance and polarization of light due to single and double reflections from the faces of particles in a surface composed of random, irregular particles using equations of electromagnetic waves and materials with a complex index of refraction Some geometric properties of shadows are derived and used Good agreement is obtained between these results and measurements of polarized light from Mars, Mercury, and the moon, including the phenomenon of negative polarization at small phase angles Negative polarization is found to be caused by shade and shadows affecting the double-reflected rays Graphical results are provided for materials of varied real and complex indices of refraction The model can be used to calculate polarization and luminance of rough astronomical bodies and surfaces as a function of the viewing angle Calculated ratios of single-reflected, double-reflected, and randomly diffused light can be related to the surface structure and optical properties of the material

Abstract: The operation of tapered velocity couplers is analyzed from the point of view of mode conversion between local-normal modes. An approximate coupled mode representation of the local-normal modes is used with a step transition model to estimate analytically power transfer. This yields an upper limit for the maximum permissible variation in mode synchronism across the coupler to achieve satisfactory coupler operation. The analysis has also been used to demonstrate the importance of obtaining a large total change in mode synchronism to minimize coupler length.

Abstract: General equations are derived for the signal-to-noise ratio of a coherent (heterodyne) receiver in terms of the distribution functions of the signal and local oscillator fields and the size and shape of the detector. The optimum local oscillator field distribution is identical to the signal field distribution over the detector surface. The special case of an Airy function signal distribution and a uniform local oscillator distribution on a circular detector has an optimum detector radius 72% of the radius of the Airy disk, which gives a signal- to-noise ratio of 0.72 etaP(s)/hnuB(i.f.).

Abstract: Characterization of surface roughness has generally been limited to rms deviation from the mean and occasionally the autocorrelation length. By considering the surface to be a superposition of many sinusoidal gratings, the surface spectral density function (SDF) has been calculated from measurements of the light scattered out of a reflected He-Ne laser beam. By rotating the sample, the SDF can be found for anisotropic surfaces (such as machined surfaces). The SDF allows examination of roughness as a function of spatial frequency, which is important for many applications. Interferometric and scattering results are compared for a rough (350-Arms) machined surface, and finally a smooth (50-Arms) diamond machined surface is characterized.

Abstract: The cat's-eye retroreflector is a passive optical system consisting of a secondary mirror placed at the focal point of a primary lens. We analyze the cat's eye using the paraxial ray matrix approach. The position of the equivalent reflecting surface and the angular field of view of a realizable cat's eye are functions of the radius of curvature of the secondary mirror. The field of view is maximum for a secondary mirror with a concave radius of curvature equal to the focal length of the primary lens. We further derive the general dependence of retroreflection errors on misadjustment of the secondary mirror.

Abstract: The coupling of single-mode optical waveguides through the use of expanding and contracting tapers is examined theoretically. In particular, the problems of angular and transverse misalignments of an input and output taper are investigated along with the effects of the taper itself. A tradeoff is found to exist, that is, widening the guide by means of a taper leads to less critical coupling tolerances for transverse displacements, but tighter tolerances for angular misalignment. Similar considerations apply to large core singlemode fibers.

Abstract: Laser calorimetric or thermal rise techniques are useful for the determination of very low absorption coefficients in solids. A number of improvements in this technique are described of which the most important is a means of separating surface and bulk absorption. These techniques have been applied to study alkali halides in the ir but are applicable where laser sources of sufficient power are available.

Abstract: This paper is devoted to the results concerning NO, NO2, and HNO3 obtained during airborne experiments performed in June–July 1973 on Concorde 001. The altitude of flight was about 16 km. Results concerning NO are, within the accuracy of measurement, in agreement with results of a previous spectrometric balloonborne experiment conducted jointly by IASB and ONERA (14 May 1973). Nitric oxide is concentrated in stratospheric layers clearly above the flight altitude. Integrated amount of NO along the optical path is (4 ± 1.5) × 1016 mol cm−2 for a solar elevation varying from +2° above the horizontal plane to −1°. A value of 6 × 108 mol cm−3 may be given as an upper limit for the local concentration at the flight altitude. There is no significant difference in the integrated amount observed at sunset and sunrise. Measured value of NO2 local concentration at 15.5 km is (1.1 ± 0.2) × 109 mol cm−3, in sunset conditions. This value is not greatly modified between 15 km and 30 km. Measured value of HNO3 local concentration at 15.5 km is (1 ± 0.3) × 1010 mol cm−3. This value increases with altitude between 15 km and 20 km. The local concentration is maximum at 20 km. The measured value is (2 ± 1) × 1010 mol cm−3 at 20 km. It seems that local concentration decreases rapidly above 20 km.