Showing papers in "Applied Optics in 1971"

Weakly guiding fibers.

Abstract: Thin glass fibers imbedded into a glass cladding of slightly lower refractive index represent a promising medium for optical communication. This article presents simple formulas and functions for the fiber parameters as a help for practical design work. It considers the propagation constant, mode delay, the cladding field depth, and the power distribution in the fiber cross section. Plots vs frequency of these parameters are given for 70 modes

Light waves in thin films and integrated optics.

Abstract: Integrated optics is a far-reaching attempt to apply thin-film technology to optical circuits and devices, and, by using methods of integrated circuitry, to achieve a better and more economical optical system. The specific topics discussed here are physics of light waves in thin films, materials and losses involved, methods of couplings light beam into and out of a thin film, and nonlinear interactions in waveguide structures. The purpose of this paper is to review in some detail the important development of this new and fascinating field, and to caution the reader that the technology involved is difficult because of the smallness and perfection demanded by thin-film optical devices.

Theory of Transparency of the Eye

Abstract: The present work relates the turbidity of the eye to microscopic spatial fluctuations in its index of refraction. Such fluctuations are indicated in electron microscope photographs. By examining the superposition of phases of waves scattered from each point in the medium, we provide a mathematical demonstration of the Bragg reflection principle which we have recently used in the interpretation of experimental investigations: namely, that the scattering of light is produced only by those fluctuations whose fourier components have a wavelength equal to or larger than one half the wavelength of light in the medium. This consideration is applied first to the scattering of light from collagen fibers in the normal cornea. We demonstrate physically and quantitatively that a limited correlation in the position of near neighbor collagen fibers leads to corneal transparency. Next, the theory is extended to predict the turbidity of swollen, pathologic corneas, wherein the normal distribution of collagen fibers is disturbed by the presence of numerous lakes-regions where collagen is absent. A quantitative expression for the turbidity of the swollen cornea is given in terms of the size and density of such lakes. Finally, the theory is applied to the case of the cataractous lens. We assume that the cataracts are produced by aggregation of the normal lens proteins into an albuminoid fraction and provide a formula for the lens turbidity in terms of the molecular weight and index of refraction of the individual albuminoid macromolecules. We provide a crude estimate of the mean albuminoid molecular weight required for lens opacity.

Estimation of the coupling matrix elements for one-electron transfer systems.

Abstract: Correlation coupling matrix elements for one electron transfer and ion-ion recombinations in Landau-Zener calculations

Multiple scattering calculations for technology.

Abstract: A many-flux (discrete ordinate) radiative transfer calculation procedure is described with the goal of making the mathematics easy to learn and use. The major approximation is the neglect of polarization. Emission within the scattering medium is not included, and the formulas are restricted to a scattering medium bounded by parallel planes. The boundary conditions allow for a variety of kinds of illumination, and the surface reflection coefficients at the boundaries of the scattering medium are accurately determined. A comparison is made with the two-flux (Kubelka-Munk) and four-flux calculation methods, and this leads to empirical expressions for the scattering and absorption coefficients in these simple theories, which make them give nearly the same results as exact theories. These empirical expressions provide a very simple method for estimating the absolute reflectance and transmittance of turbid media and greatly increase the utility of the two-flux and four-flux calculation methods. The two-flux equations give excellent results provided the absorption is small compared to scattering and the optical thickness is greater than 5. A comparison with experimental data taken with collimated illumination shows that the four-flux equations give good results at any optical thickness even if the absorption is strong.

Propagation of a Finite Optical Beam in an Inhomogeneous Medium

Abstract: The first part of this paper is devoted to extending the Huygens-Fresnel principle to a medium that exhibits a spatial (but not temporal) variation in index of refraction. Utilizing a reciprocity theorem for a monochromatic disturbance in a weakly inhomogeneous medium, it is shown that the secondary wavefront will be determined by the envelope of spherical wavelets from the primary wavefront, as in the vacuum problem, but that each wavelet is now determined by the propagation of a spherical wave in the refractive medium. In the second part, the above development is applied to the case in which the index of refraction is a random variable; a further application of the reciprocity theorem results in a formula for the mean intensity distribution from a finite aperture in terms of the complex disturbance in the aperture and the modulation transfer function (MTF) for a spherical wave in the medium. The results are applicable for an arbitrary complex disturbance in the transmitting aperture in both the Fresnel and Fraunhofer regions of the aperture. Using a Kolmogorov spectrum for the index of refraction fluctuations and a second-order expression for the MTF, the formula is used to calculate the mean intensity distribution for a plane wave diffracting from a circular aperture and to give approximate expressions for the beam spreading at various ranges.

Signal-to-Noise Relationships for Coaxial Systems that Heterodyne Backscatter from the Atmosphere.

Abstract: This paper analyzes the signal-to-noise ratio for a coaxial laser system that heterodynes the signal backscattered from the atmospheric aerosol. The laser radiation, which is assumed to have a wavefront with a gaussian amplitude distribution, is transmitted into the atmosphere through a telescope. Radiation is collected by the same telescope and directed onto a detector where it is mixed with a local oscillator beam originating from the same laser source. The signal-to-noise ratio at the output of the detector is calculated under shot noise limited conditions. The calculation is general and applies for both near and far fields and for focused and unfocused systems. Three specific cases are considered. These are a pulsed system, a cw system illuminating an infinite target, and a cw system illuminating a target of finite extent.

Dispersion in Weakly Guiding Fibers

Abstract: Optical signals transmitted through cladded glass fibers are subject to delay distortion because of (1) dispersion in the material, (2) dispersion caused by the waveguide characteristic, and (3) delay differences between modes. We isolate these effects and evaluate their significance for cases of practical interest. These concern fibers in which the refractive index of the cladding is only slightly lower than that of the core.

Volume Hologram Formation in Photopolymer Materials

Abstract: Holograms have been constructed in photopolymer materials which give bright, low-noise images. These holograms are of the volume type and have no surface variations in all but a few special cases. They are constructed in virtually real time and in situ, requiring no processing. Materials sensitive to both uv and blue-green radiation have been used. In this paper, the mechanism of hologram formation is examined. Experimental results on sensitivity, spatial frequency response, particle scattering noise, and nonlinearities are discussed. A few holographic applications of the material are presented.

Testing aspherics using two-wavelength holography.

Abstract: It is shown that both single exposure and double exposure two-wavelength holography provide a good method of using visible light to obtain an interferogram identical to what would be obtained if a longer nonvisible wavelength were used. Both techniques provide for the real-time adjustment of defocus and tilt in the final interferogram. When both hologram exposures are made simultaneously, the sensitivity to air turbulence is essentially the same as if the longer nonvisible wavelength were used. Results are shown for testing both lenses and mirrors at equivalent wavelengths at 6.45 μ, 9.47 μ, 14.20 μ, 20.22 μ, and 28.50 μ obtained by using an argon laser for the visible light source.

Computer Generated Holograms for Testing Optical Elements

Abstract: The application of computer generated holograms to the interferometric testing of aspheric optical elements has been investigated, and it has been shown that they provide a convenient and practical method of producing an aspheric reference wavefront.

Ultrahigh speed photography of picosecond light pulses and echoes.

Abstract: Three new results have been obtained with a recently developed camera of 10-psec framing time: (1) The effect of the finite speed of light in photographing relativistic objects is experimentally demonstrated, by photographing a dumbbell-like entity formed by two packets of light. In contrast to material objects, which, theory predicts, should appear rotated, the light dumbbell appears sheared. (2) Photographs of the mode-locked Nd: glass laser radiation show numerous subsidiary pulses accompanying the main ultrashort pulses in the train. The latter have durations ranging from 7 psec to 15 psec. (3) The technique of gated picture ranging, previously used with nanosecond pulses, is extended to the picosecond range where a resolution of 1 cm is demonstrated. Some potentially useful applications are proposed.

Optical second harmonic generation in biological systems.

Abstract: A Q-switched ruby laser was used to irradiate excised biological tissues. An isolated narrow band emission line was observed at 347 nm on irradiation of collagenous tissues. Temporal pulses at 347 nm were narrower than the laser pulses at 694 nm. Reduced crystalline glutathione yielded narrow band emission at 347 nm that was similar to that for the collagenous tissues. The observed narrow band emission at 347 nm is thought to be due to optical second harmonic generation.

Bidirectional scattering characteristics of healthy green soybean and corn leaves in vivo.

Abstract: Bidirectional reflection and transmission distribution functions are measured for healthy green soybean and corn leaves in vivo, for nineteen narrow wavelength bands from 375 nm to 1000 nm. Off-normal incidence reflection distribution functions show considerable specular contributions at wavelengths of strong absorption, while transmission distribution functions show a near-lambertian shape for all wavelengths employed. An empirical m-layer leaf model affords a reasonable qualitative understanding of these scattering distributions.

Quenching of Infrared Chemiluminescence. 1: The Rates of De-Excitation of CO (4 ≤ v ≤ 13) by He, CO, NO, N 2 , O 2 , OCS, N 2 O, and CO 2

Abstract: Infrared chemiluminescence has been observed from vibrationally excited CO, formed in the reaction, O + CS → CO + S. The quenching of the CO overtone spectrum has been studied as a function of the concentration of each of a number of added gases. A steady-state treatment is developed which allows rates to be determined for the de-excitation of individual vibrational levels of CO (4 ≤ v ≤ 13) by He, CO (v = 0), NO, N2, O2, OCS, N2O, and CO2. The experimental results are compared with theoretically predicted rates. Finally, the importance of the results for interpreting the behavior of CO vibrational lasers is considered.

Improvement in the OTF of a Defocused Optical System Through the Use of Shaded Apertures.

Abstract: To improve the imaging properties of a defocused optical system, the use of shaded apertures is studied theoretically and experimentally. The study is based on the optical transfer function (OTF). The two shaded apertures studied are the type in which the amplitude transmittance decreases gradually from the center of the pupil toward its rim, T(A), and the type in which the amplitude transmittance decreases from its rim toward the center, T(B). For comparison, the effects achieved with a clear aperture, T(C), are included. The results of the calculations show that near focus the OTF for T(A) has higher values in the low frequency region than has either T(B) or T(c). When the system is defocused, the shaded aperture of the type T(A) yields an improved defocused image that is faithful to the outline of the object. The quality of the defocused image obtained with T(B) is worsened. When the OTF is used as a means for judging the quality of the defocused image, the two necessary conditions on the functions appear to be that the OTF (1) must be a monotonically decreasing function and (2) must be nonnegative. These conditions are confirmed by experiment. Since the transmittance variation of the shaded apertures is achieved by absorption, the effects due to the resultant decreases in light level are also considered.

Shearing interferometer using the grating as the beam splitter.

Abstract: The theoretical interpretation of the shearing interferometer based on the moire method using the fourier image of the grating is described. To obtain a pattern with good contrast, the observing plane must coincide with the normal fourier image plane of the grating or with the reversed fourier image plane. The information obtained by this method is the first partial derivative and under certain conditions the second partial derivative of the distortion from the reference wavefront, which is planar or spherical. Applications to measurement of the phase gradient and lens aberration are shown.

Time-lapse interferometry and contouring using television systems.

Abstract: A novel approach to time-lapse interferometry and contouring is introduced that uses television rather than photographic techniques. A first interferogram is stored on a video storage device such as a magnetic disk. After a change in the stress of the object, a second interferogram is electronically compared to the stored pattern to form a signal representative of the fringe pattern caused by the deformation. This signal may be directly displayed on a cathode-ray tube or employed by some automatic inspection device.

Scanning laser microscope for biological investigations.

Abstract: The theory and design of a special purpose scanning laser microscope are described. This microscope, particularly suited for biological investigations, is intended for the observation of objects embedded within transparent or translucent bodies, such as nerve cells in an intact brain. Some photographs made with a prototype are shown.

Geometrical optics in thin film light guides

Abstract: We consider thin film light guides consisting of a transparent film of high refractive index deposited on a substrate of lower index. The propagation of light in such a two-dimensional transmission medium can be described within the limits of geometrical optics by an effective index of refraction N. Its value depends on the film thickness. Therefore, a light beam in the thin film guide is refracted or totally reflected at a step of film thickness. We discuss these phenomena (Snell’s law) and demonstrate them experimentally, using ZnS films on glass as guides. As applications, we show a thin film prism and thin film lenses for guided light beams. By properly choosing the film thicknesses at both sides of the step, one can obtain an unusually large positive or negative wavelength dispersion of the refraction or, if desired, achromatic refraction.

Photon-noise-limited laser transducer for gravitational antenna.

Abstract: We have constructed and tested a laser interferometer transducer for a long, wideband, laser-linked gravitational radiation antenna. Photon-noise-limited performance was achieved using 80 microW from a single mode Spectra-Physics 119 laser in a modified Michelson interferometer on a vibration isolation table in a quiet room. A piezoelectric driver on one of the interferometer mirrors was used to generate subangstrom (3 x 10(-14)-m) vibrations of known amplitude. The measured displacement sensitivity of the system in the kilohertz region was 1.3 x 10(-14)m/Hz(1/2), which compares well with the calculated photon noise limit of 1.06 x 10(-14) m/Hz(1/2). This is the smallest vibrational displacement measured directly with a laser to date.

Moiré Contour-Sum Contour-Difference, and Vibration Analysis of Arbitrary Objects

Abstract: A grid is projected onto an object and focused into a viewing camera which is offset from the angle of illumination. When the image is superimposed by double exposure or by filtering with the image of another object, contour-difference moire fringes appear. By the use of two offset projectors, measurements of contour sums or contour doubling may be accomplished. The properties, limitations, sensitivity, and procedures are analyzed and discussed. The method lends itself to image enhancement and is extended to the study of vibration analysis in real time. In the latter application, time-average moire fringes appear according to the zeroth-order Bessel function, which contains the modal amplitude function in its argument.

Formation of Vibrationally Excited OH by the Reaction H + O(3).

Abstract: Vibrationally excited hydroxyl formation by atomic hydrogen reaction with ozone, using Fourier transform spectroscopy

Optimum design and depth resolution of lens-sheet and projection-type three-dimensional displays.

Abstract: The primary purpose of this paper is to propose a comprehensive optimum-design theory of lenticular-sheet three-dimensional pictures. The proposed theory features the use of depth resolution of a 3-D image as the measure of the 3-D picture quality. The optimum parameters in the picture taking process, the optimum lens pitch and the depth-resolution limitation, are discussed. The obtained results are also applicable to a specific type of integral photography and to the projection-type 3-D display including projection-type holography. It is found that the optimum pitch of the lens sheet or the lens-type direction selective screen ranges between 0.1 mm and 0.5 mm in most cases, whereas it ranges between 0.2 mm and 1 mm for the triple-mirror screen.

Refractive index, dispersion, and birefringence of silicon carbide polytypes.

Abstract: The refractive index of each of the four common silicon carbide polytypes has been measured over the visible range. The data were analyzed in an attempt to relate the birefringence to the relative hexagonal character of the polytype. A general relationship exists, namely, that the birefringence increases with increasing hexagonal character of the polytype. This relationship is not sufficiently precise to use for the identification of polytypes.

Computer-based analysis of hologram imagery and aberrations. I. Hologram types and their nonchromatic aberrations.

Abstract: Numerical values are shown for the aberrations that are present in holograms which may be constructed and reconstructed from a plane wave or point source. This study centers on four types of hologram geometries: in-line, off-axis, near-image plane, and lensless-fourier transform. The aberrations illustrated in this paper have been caused by a spatial deviation of the reconstruction beam from the location where either an ideal aberration free virtual or real image is reconstructed. In addition to the above analysis of aberrations a close parallelism between the bending characteristics of lenses and the construction geometry of holograms is noted. This analogy between lenses and holograms illustrates the flexibility with which the aberrations of a hologram may be modified by changes in the recording geometry.

Spot dancing of the laser beam propagated through the turbulent atmosphere.

Abstract: The problem of spot dancing of the laser beam has attracted theoretical and experimental attention in recent years as one of the important problems in an optical communication system through the atmosphere. An analysis of this problem is made by using the Kolmogorov structure function of the refractive index and geometrical optics. Laser propagation experiments are carried out over 480-m and 1380-m paths. The standard deviations of spot dancing are measured by two methods, and the magnitudes of the structure constant Cn(2) are measured at the same time. The theoretical value of the spot dancing shows a satisfactory agreement with the experimental value. In addition, measurements of the fluctuations of spot dancing reveal that the power spectra show an inverse frequency characteristic over the frequency range of about 0.03-10 Hz.

Determination of Refractive Index and Film Thickness from Interference Fringes

Abstract: Simple equations are given for determining both refractive index and film thickness from a measurement of interference fringe separation where the question of phase change and the order of the fringes can be disregarded. The equations are quite general, since they apply to fringe maxima or minima for either transmission or reflection and can be used for free-standing films or films on substarates of higher refractive index. Advantages of recording fringes via reflection rather than transmission are discussed. A unique attachment for commercial spectrophotometers for making measurements over a wide range of angles of incidence is described.