Aperture Transmission Research Articles

Transmission Apertures (T-Stops) for Taking Lenses

The geometrically defined relative apertures, f-stops, engraved on objective lenses, are quite imprecise as measurements of the amounts of light actually transmitted, especially for zoom lenses with their many glass-air interfaces. This can lead to errors in exposure as a consequence of reflection, absorption and other light losses within the objective. The problems and the needs for the standardization of true transmission stops are discussed. A photometric measuring method in accordance with the German standard draft DIN 19 010, sheet 2 (photoelectric exposure meters, automatic exposure adjustment in photographic cameras) is presented for discussion.

Hexamine electro-optic light modulators

Although hexamine exhibits a low electro-optic coefficient, large strain-free crystals offer practical devices for both DC and high frequency modulation at reduced operating voltages. A modulator with a light aperture of f/10 has a half-wave voltage of 4.5 kV and shows an extinction ratio of 2000:1. In a multipass mode the voltage can be reduced to less than 100 V but with a consequent loss of angular aperture and light transmission. Precautions taken during modulator construction in order to preserve crystal isotropy included the selection of gold leaf as electrode material and flexible mounts to support the section.

Focused Laser Irradiance Fluctuations in a Turbulent Medium

A standard diagrammatic technique is used to obtain an integral representation for the fourth moment of the field of irradiance in a random weakly inhomogeneous medium. For the case of an incident focused coherent wave, it is shown that the spectral and correlation properties of the random field of intensity depend in an essential manner upon the magnitude of the phase structure function, computed on the transmitter aperture size. The region of large values of this parameter is of particular concern, where an analytical expression for the correlation function of intensity fluctuations is derived, and saturation of the magnitude of the normalized variance of intensity fluctuations is investigated.

Experimental effects of finite transmitter apertures on scintillations*

The use of large transmitter apertures has been theoretically predicted to result in a substantial reduction of laser-beam scintillations under certain conditions. Experiments have been conducted on transmitter-aperture effects through turbulence, including photographic studies for qualitative interpretation, and measurements of log-amplitude variance, covariance, probability distributions, and the spectra of scintillations. It was found that the predicted reduction imposes strict requirements on transmitter optical adjustments, and will not be realized in the presence of significant beam wander. In the case of either transmitter misadjustment or strong turbulence, the beam at the receiver plane consists of a proliferation of transmitter-diffraction-scale patches, with large attendant scintillations. The theory suggests a novel means of reducing scintillations arising from a thin layer of turbulence at the tropopause in earth-to-space systems. Comparisons of the beam-wave analyses with results from a recent theory of reciprocity suggest a limited range of validity for the analytical predictions.

Focused Irradiance Fluctuations Beyond a Layer of Turbulent Atmosphere

The spectral and correlation properties of intensity fluctuations of irradiance of a focused transmitter, beyond a layer of rubulent atmosphere, are studied. Of particular concern is the range of large values of the phase structure function, computed on the transmitter aperture size, where saturation of fluctuations is predicted. The analysis is based on the phase-screen approximation.

Maximum Power Transmission Between Two Reflector Antennas in the Fresnel Zone

Power transfer between two ellipsoidal reflector antennas with common focal points and dual-mode feeds has been investigated. Assuming a circularly symmetric feed pattern, the H-plane pattern of an open-end circular waveguide excited by the TE 11 mode, the maximum transmission coefficient between reflector apertures is found to be within 0.5 percent of the value computed for transmission between two circular apertures with optimum illumination described by the generalized prolate spheroidal function. Transmission loss between two reflector antennas versus illumination taper is computed for various values of the parameter [p = (ka 1 a 2 )/R]. The minimum transmission loss is obtained as a compromise between feed spill-over and aperture transmission efficiency. In view of the inconvenience of building different ellipsoidal reflectors for different antenna spacings in order to achieve maximum power transfer, we examine the feasibility of using a defocused ellipsoid to simulate ellipsoids of different focal lengths. The deviation of the aperture phase distribution of a defocused ellipsoid from a required spherical phase front is approximately given by an explicit expression. A simple upper bound of the transmission loss due to small phase deviation is obtained for a given maximum phase deviation.

Theory of Cavity-Mode-Mixing Effects in Internally Scanned Lasers

An analysis of cavity-mode-mixing effects is given for a variety of cavity geometries and coupling parameters in the presence of a continuous transverse aperture velocity. The paper represents an extension of the previous work by Fox and Li, and Boyd and Gordon to include the effects of time-dependent changes in the transverse aperture location. The average beam profile in the scanning reference frame is calculated through a continuous reexpansion of the optical field in terms of the set of self-reproducing modes characteristic of the same cavity under static transverse boundary conditions. Results are specifically given for square aperture, plane-parallel, concentric, and confocal geometry for light, plane polarized orthogonally to the scan velocity. The effects of a random variation in the mirror-transmission coefficient are calculated, and it is shown that these effects are largely averaged out in the scanning process. Cavities of the type considered earlier by Pole and Myer and by Beiser are specifically considered. A method of evaluating different real systems with the present calculations is discussed; it is shown that a "push-pull"-type scanning laser should have an inherent scan velocity roughly twice that for the single-ended scanning laser geometry previously considered for the same degree of beam degradation and other cavity parameters. A method is developed for the derivation of self-reproducing confocal modes which arise with stationary, continuously varying aperture transmission functions. The method is specifically applied to a confocal Gaussian gain aperture and to a nonsymmetric confocal gain aperture. It is shown that the odd-symmetry mode of the Gaussian gain aperture dominates over the even-symmetry mode at low-gain coefficients, in opposition to the normal diffraction-limited rectangular-transmission-aperture case. An extension of the scanning problem is given to include the transverse displacement of a continuous gain aperture; it is shown formally that the solution of the continuous-aperture problem goes continuously over to the rectangular-aperture results at low values of the gain. The method is specifically applied to a hypothetical scanning laser employing swept Gaussian and nonsymmetric gain apertures.

Application of Optical Scintillation Measurements to Turbulence Diagnostics*

The irradiance fluctuations of beams which propagate through a turbulent medium can be used to infer the spatial spectrum of the turbulent scatterers. The propagation of Goubau-type beam waves in a random medium is used to show that amplitude fluctuations depend upon the transmitter aperture size, observation distance, and wavelength. Most of the results are presented in terms of a parameter, αL, which is inversely proportional to the Fresnel number, πW02/Lλ. A Monte Carlo numerical procedure is used to obtain the normalized mean-square log-amplitude fluctuation as a function of the inverse Fresnel number for various magnitudes of the turbulence inner scale. The applicability of these procedures to measured turbulence spectra is also discussed.

Experimental Investigation of Thermally Scanned Fabry-Perot Interferometry

A thermally scanned Fabry-Perot interferometer in the flat-flat resonator configuration has been constructed. It is extremely easy to use, and, in addition, provides large values of finesse (>60), high transmission, and large usable apertures. Experimental data analyzing the characteristics of the device are presented. Use of the interferometer for the spectral analysis of several physical processes involving very high optical resolution is demonstrated.

Log-Amplitude Fluctuations of Laser Beam in a Turbulent Atmosphere

In this paper, the Rytov approximation is used to calculate the log-amplitude fluctuations of a laser beam in an atmosphere whose statistics are assumed to be homogeneous and isotropic and to obey the Kolmogorov law. Asymptotic expressions are obtained for the variance of the log amplitude in the near field of the transmitter aperture. It is found that the variance is not homogeneous across the beam cross section. Near the center of the beam, the variance is somewhat smaller than that of an infinite plane wave; it increases toward the edge of the beam to a value which is greater than that of an infinite plane wave. The increase is most pronounced in the near field of the inner scale l0 of the turbulence when the transmitter aperture size is comparable to l0.

Time-Average Surface-Reflected Energy Received from a Collimated Beam of Radiant Energy Normally Incident on the Ocean Surface*

The geometrical-optics solution for the time-average surface-reflected energy received from a collimated beam of radiant energy normally incident on a rough ocean surface is developed. The received power is expressed as a function of the transmitter power, the height of the receiver aperture above the surface, the areas of the receiver and transmitter apertures, the distance between them, and the wind velocity and direction.

Effects of the Atmosphere on Laser Beam Propagation

An experimental study of horizontal laser beam propagation over paths up to 145 km long was made in which beam diameter and shape, intensity fluctuations, and optical phase distortion were measured. It was found that (1) received beam diameter decreases (on-axis power density increases) with increasing transmitter aperture to a limit reached at an aperture of about 11 cm, (2) beam diameter varies as the 1.2 power of path length, (3) the amplitude of intensity fluctuations decreases with increasing receiver aperture and is nearly independent of path length for paths longer than 0.55 km, (4) the fluctuation spectrum shows a decrease in spectral power with increasing frequency, this negative slope becoming steeper with increasing receiver aperture and remaining constant with path length, and (5) rms fluctuation in phase path length was observed to be 0.25 micro over a 48.8-m path. In addition, it is shown that geometrical optics based on the effects of large scale atmospheric irregularities does not adequately account for signal intensity fluctuations. These results may be helpful in predicting the capability of specific communications systems and in understanding better the nature of atmospheric turbulence.

Measurement of the Transmission Loss of a Finite-Depth Aperture

To provide experimental verification of an approximate solution for the diffraction of sound waves by a circular aperture in a plane rigid wall of finite thickness, a series of experiments was conducted on the transmission of reverberant sound through steel pipes inserted individually into a thick wall between two reverberation chambers. The usually recommended methods of evaluating the transmission loss proved inadequate because long, narrow apertures have sharp resonant peaks. By electronically averaging and equalizing the outputs of four microphones in each chamber and using a slowly sweeping sine wave with a small super-imposed warble, it was possible to record continuous plots of the aperture transmission loss with high resolution of frequency and amplitude. Experimental accuracy of 1 dB was possible over most of the frequency range of 300–12 000 cps, diverging to 2 dB at the frequency extremes, and for apertures with sharp resonances, diverging to about 4 dB at the peaks. The accuracy was limited by reading the “average” of the recorded fluctuating sound level, which was most difficult at resonant peaks. For larger-diameter apertures, which gave data relatively uninfluenced by flanking sound, the agreement with theoretical results was within 1 dB over most of the frequency range.

The Optical Coupling of a Scintillation Chamber to an Image-Intensifying Tube

Several methods for coupling a fiber scintillation chamber to an image intensifying tube will be considered. A high-speed lens has been designed to image the ends of a curved fiber bundle on the curved cathode of an image intensifying tube. The lens covers a five-inch field at one-to-one magnification, and at a speed of f/1.5. The details of this lens design and its expected performance will be discussed. The results of a series of experiments on plastic scintillating fibers have been used to determine that the internal reflectivity is 0.993 and absorption constant is 0.015 cm-1 in the fiber. The data have then been used to compute the optical properties of fibers appropriate to a scintillation chamber system. Certain other optical properties of the components were estimated so that three possible optical coupling schemes could be compared in detail. They are; 1) the lens alone, 2) a glass fiber bundle alone, and 3) a combination of the lens and a glass fiber bundle. The lens alone is about half as efficient as either of the other two methods. The numerical aperture and probable transmission properties of each system will be outlined.

Diffraction by Apertures

The diffraction of plane electromagnetic waves by apertures in a plane screen which is infinitesimally thin and perfectly conducting is studied both theoretically and experimentally. The theoretical analysis employs a dyadic Green's function to develop vector formulas for the scattered fields, and from these formulas integral equations are obtained for the aperture distributions. The vector representation makes possible a compact demonstration of the electromagnetic form of Babinet's principle by means of which one may extend the aperture analysis to complementary disks. The integral equations are then used to construct a variational principle for the aperture transmission coefficient. Detailed analysis and numerical computations are carried out for two configurations. For the circular aperture a first-order vector trial function with frequency dependent coefficients is chosen for the aperture distribution. The approximate transmission coefficient is found to agree closely with the exact value in the region 2πa/λ≤3. For elliptical apertures a zeroth-order approximation is evaluated using a one-component trial function. Numerical results are given for minor-to-major axis ratios of ½ and ⅓. Transmission coefficient measurements were carried out in the 24 000 megacycle band (λ=1.25 cm) using an image plane technique. The apparatus was first calibrated with the exact solution of the circular aperture. The approximate results calculated for elliptical apertures are then seen to be in good agreement with the measurements over the accessible range.

The diffraction of a plane wave through a grating

The problem of diffraction and scattering of a normally incident plane wave of sound by an infinite plane grating consisting of infinitely thin, coplanar, equally spaced (b apart) strips with parallel edges is solved. The potentials on the two sides of the screen are written as Fourier expansions in terms of the velocity in the aperture, and an integral equation for this velocity is determined. An impedance parameter Z Z whose real part is the transmission coefficient, is defined, and it is shown that the real and imaginary parts of the reciprocal of this parameter may both be specified by variational expressions, which are absolute minima for the solution to the aforementioned integral equation. An alternative formulation, in terms of the pressure discontinuity across the screen, is given, leading to an integral equation and to variational expressions for the real and imaginary parts of ( 1 − Z ) − 1 {\left ( {1 - Z} \right )^{ - 1}} A solution to the integral equation is given which reduces the problem to the solution of an infinite number of simultaneous equations. It is shown that solving only one of these equations gives a solution which is essentially a solution to Laplace’s equation, while if N N equations are solved the terms neglected are of the order N − 1 [ ( 1 − 4 b 2 / N 2 λ 2 ) − 1 / 2 − 1 ] {N^{ - 1}}\left [ {{{\left ( {1 - 4{b^2}/{N^2}{\lambda ^2}} \right )}^{ - 1/2}} - 1} \right ] or less, where λ \lambda is the wave length. The solution is extended to the case of a vertically polarized electromagnetic incident wave by direct analogy and to the case of a horizontally polarized electromagnetic wave by a transformation which is a special case of Babinet’s principle. The integral equations for an aperture of finite thickness are set up, and an approximate solution including only first order terms in thickness/wavelength is given. Results are given in the form of curves for the transmission coefficient vs. aperture opening for several ratios of grating spacing to wave length less than unity. For the special case of a half open grating the transmission coefficient is plotted out to that value of spacing/wavelength at which the results agree with Kirchhoff’s theory.