Spatial Transfer Function Research Articles

Eye-Position Effects on the Visual Transfer Function

Light responses of neurons in several brain areas are affected by eye position (Andersen et al, 1990 Journal of Neuroscience10 1176 – 1196). To find out if eye position may influence contrast sensitivity, measurements were made of the spatial contrast modulation transfer function at two different eye positions: with the gaze directed straight ahead and horizontally deflected by 30 deg, respectively. Eleven gratings (1.05 – 36.8 cycles deg−1) were presented so that their retinal position was identical at both eye positions. The data obtained show a significant effect of eye position on contrast sensitivity in 4 subjects out of 8. We found a mean decrease in contrast sensitivity by 10.8% in the ‘deflected’ condition. The eye-position effect was pronounced at low (14.8%) and high (29.6%) frequencies, being insignificant at middle frequencies. The maximal sensitivity decrease observed was 62.1% at 25 cycles deg−1 in one subject. In 4 of the subjects, no significant eye-position effect was found. Thus a horizontal deflection of the gaze direction can narrow the visual transfer function in some observers and consequently impair perception of near-threshold objects dominated by high or low spatial frequencies. Further studies will show what may account for this phenomenon: the interaction of retinal and eye position signals and/or optical changes due to compression of the eye ball.

Tesla/volt calibration method for integrated planar SQUID gradiometers

A calibration method for integrated planar SQUID gradiometers is proposed based on a spatial Fourier technique and on the fact that each gradiometer design has its own theoretical spatial transfer function. The calibration consists in scanning the gradiometer over a known input field source and measuring the output voltage values. The measured transfer function is the result of the division of the Fourier transform of the output signal by the Fourier transform of the input signal. The calibration factor is obtained by fitting the measured transfer function with the theoretical one. The experimental procedure was simulated and calibration factors with imprecision of about 0.2% are expected in actual measurements.

Hot topic in architectural acoustcs: Auralization

High-speed computers and digital signal processing have brought us to the point where it is possible to hear a convincing simulation of the acoustic environment of an auditorium. A number of researchers around the world have contributed for years to this field and they have now assembled the major pieces of the puzzle to make this powerful tool, called ‘‘auralization,’’ work well enough to judge acoustic quality. One needs a computer model of the acoustic space including placement of sources and receivers, an appropriate source signal, a binaural spatial transfer function from free-field pressure to eardrum pressure, and a headset which has a known equalization function from the electrical signal to the wearer’s eardrum. A typical auralization session first runs the room computer model gathering sound ray arrival data at one receiver from a source. This receiver signal is then convolved with the binaural HRTF to produce a binaural electrical signal for the headset, which is equalized to achieve flat subjective response for a particular headset. The results are astonishing but positional accuracy in 3-D space is yet to be completely evaluated. Auralization provides an extra and independent layer of design security. Importantly, acoustic disasters can be avoided.

Dynamic holography in alkali metal vapour

Problems of dynamic hologram recording on resonant absorption lines of alkali metal vapour are discussed. Light beams and media parameters are determined that are necessary for hologram recording with usable efficiency. The effects of thermal atomic motion and the radiative transport of excitation influence on the spatial frequency transfer function of two-level media are investigated. Results of hologram recording in vapour of Rb (780.0 nm) and Cs (852.1 nm) using low-power CW-lasers are presented. Transmission holograms in the volume media and reflection holograms near the boundary of the resonant vapour and the dielectric are compared. For transmission holograms the advantage of collinear read-out when using pure vapour in comparison with a counterpropagating read-out is shown, and this makes it possible to achieve higher values of hologram efficiency over a wide range of atomic density. It is shown that reflection hologram recording is characterized by higher resolution, as compared with hologram recordings in the volume of extended media. Problems of metal vapour hologram usage for laser parameter control are discussed. The feasibility of holograms in Cs-vapour usage as a spectral-selective real-time feedback element in a semiconductor laser external cavity is shown.

Visual cortex neurons in monkey and cat: effect of contrast on the spatial and temporal phase transfer functions.

The responses of simple cells (recorded from within the striate visual cortex) were measured as a function of the contrast and the frequency of sine-wave grating patterns in order to explore the effect of contrast on the spatial and temporal phase transfer functions and on the spatiotemporal receptive field. In general, as the contrast increased, the phase of the response advanced by approximately 45 ms (approximately one-quarter of a cycle for frequencies near 5 Hz), although the exact value varied from cell to cell. The dynamics of this phase-advance were similar to the dynamics of the amplitude: the amplitude and the phase increased in an accelerating fashion at lower contrasts and then saturated at higher contrasts. Further, the gain for both the amplitude and the phase appeared to be governed by the magnitude of the contrast rather than the magnitude of the response. For the spatial phase transfer function, variations in contrast had little or no systematic effect; all of the phase responses clustered around a single straight line, with a common slope and intercept. This implies that the phase-advance was not due to a change in the spatial properties of the neuron; it also implies that the phase-advance was not systematically related to the magnitude of the response amplitude. On the other hand, for the temporal phase transfer function, the phase responses fell on five straight lines, related to the five steps in contrast. As the contrast increased, the phase responses advanced such that both the slope and the intercept were affected. This implies that the phase-advance was a result of contrast-induced changes in both the response latency and the shape/symmetry of the temporal receptive field.

磁界とその信号源に関する空間伝達関数について

Spatial transfer functions were derived from the Fourier transforms of Biot-Savart's law to relate magnetic fields to their sources. Although the functions naturally have 3-D forms, the authors derived their 1-D forms in order to investigate their frequency characteristics. Some of them have band-pass and others low-pass filter characteristics. In the preparation of a multichannel system, a proper spatial arrangement of the sensors can be determined by considering their frequency characteristics.

Infrared projector optical design considerations

The optical considerations that need to be addressed during the design of IR projectors intended for application within real-time hardware-in-the-loop simulation systems are examined. Attention is paid to the form of the spatial frequency transfer function and, thereby, to the factors that affect the spatial resolution within the composite optical system defined by the IR projector and the imaging unit under test, with particular emphasis on the sampling effects (aliasing) that need to be avoided.

Transient acoustic pressure radiated from a finite duct

The time-dependent pressure radiated from a finite, rigid, circular duct of constant cross section is determined for the specified motion (velocity or acceleration) of a piston source within the duct. The modal composition of the internal field variables is represented as an eigenfunction expansion over the duct cross section, and a time- and space-dependent Green’s function is used to develop a generalized boundary condition which describes the effect of the external surroundings at the duct exit. Solution of this boundary value problem results in a duct transfer function which is then cascaded with the spatial transfer function connecting the duct exit port and a selected external field point. In this paper, inversion to the time domain is accomplished via the FFT algorithm. Numerical examples demonstrating the calculation of the external time-dependent pressure are presented based upon the specification of a gated sinewave piston acceleration over an assumed piston spatial profile. Confirming the theoretical analysis, the numerical results show that the time-dependent pressure for the cross modes develops its peak value off-axis and is always zero on-axis, while the plane wave mode always peaks precisely on-axis.

Responses of cat horizontal cells to sinusoidal gratings

The spatiotemporal properties of cat horizontal (H-) cells were studied by recording the intracellular responses in the optically intact, in vivo, eye to sinusoidal gratings at a photopic mean illumination level. In order to investigate the linearity of spatial summation a “null test” was performed in which the responses to contrast reversal gratings were measured at different positions of the grating relative to the receptive field. Spatial and temporal transfer functions were measured using drifting sinusoidal gratings of variable spatial and temporal frequencies. The amplitudes of cat H-cell responses to contrast reversal gratings modulated with a square wave time-course showed a sinusoidal dependence on spatial phase. When zero crossings of the grating were lined up with the receptive field center, as defined by the maximum of the measured line weighting function, contrast reversal produced no response modulation. This result did not depend on the spatial frequency of the grating or the temporal frequency of contrast modulation over substantial ranges. The response waveform was found not to depend on the spatial phase of the grating. The spatial transfer function of cat H-cells has low-pass characteristics with a cut-off frequency in the range of about 0.4–1.5 c/deg. The shape of the spatial transfer function was roughly the same for temporal frequencies ranging from 3 to 10 Hz. The temporal transfer function exhibited band-pass characteristics with a maximum response amplitude at 3–6 Hz. The amplitude fall-off for low and high temporal frequencies was independent of the spatial frequency of the grating. The results obtained with sine gratings were found not to agree with the receptive field profiles measured with narrow slits flashed at different positions in the receptive field.

Microstructure characterization by angle-resolved scatter and comparison to measurements made by other techniques

The theory and measurement of angle-resolved scatter are described. Values of rms roughness that were obtained by using this technique to characterize four different materials are compared with values that were obtained by using a total integrated scatter measuring instrument, an optical profiler, and a mechanical profiler. The spatial frequency bandwidths and modulation transfer functions of the four instruments are different, and results are described in light of these differences.

Die Ortsfrequenzgrenze und das Auflösungsvermögen des visuellen Systems der Taube

The spatial contrast transfer function of the visual system of the pigeon was determined by recording from the optic tectum evoked potentials or extracellular unit activity in response to a pattern stimulus contrast transfer function, determined as a "response function", describes the relationship between the contrast in the pattern--which consisted of vertically oriented stripes of sinusoidally varying luminance--and the amplitude of the response at various spatial frequencies (c/deg). The transfer function yields an estimate of the high frequency limit, which in turn is a measure of visual resolving power. Action potentials were recorded extracellularly using glass microelectrodes; for evoked potentials, stainless steel electrodes were used. Recordings were made from the stratum griseum et fibrosum superficiale of the optic tectum. The highest spatial frequency detectable in a visual system is limited by various factors, including the diffraction of light at the pupil and the anatomical spacing of the photoreceptors. The pupil factor can be controlled in experiments in a suitable way. In this paper, the electrophysiologically determined high-frequency limit was compared with the theoretical resolution limit imposed by the photoreceptor mosaic. The experimental results show that the visual system of the pigeon has a high-frequency limit at a spatial frequency of 15.5 c/deg, corresponding to a visual acuity of 1.9 min of arc. The attempt to relate visual acuity in the pigeon to the anatomical spacing of the photoreceptors shows that the Nyquist frequency of the photoreceptor mosaic, the theoretical upper bound of the spatial resolution, agrees with measurement.

A spatio-temporal Fourier-transform approach to acousto-optic interaction of light beams with cw and pulsed ultrasonic waves

We use a spatio-temporal Fourier-transform approach and a perturbation technique to analyze acousto-optic interaction between an input optical beam of arbitrary profile and pulsed ultrasound. We write the sound field as a superposition of a time- harmonic constant-amplitude wave and a modulated pulse. While the scattering of the input light beam by the former component can be effectively handled using a spatial Fourier-transform technique, the additional contribution can be analyzed using a spatio- temporal Fourier-transform approach. Numerical results, calculated using the equivalent spatial and spatio-temporal transfer functions, are shown for the case of Bragg diffraction.

A Transfer Function Description of Sheet Metal Forming for Process Control

Three-dimensional forming of sheet metal parts is typically accomplished using one or two shaped tools (dies) that impart the necessary complex curvature and induce sufficient in-plane strain for part strength and shape stability. This research proposes a method of applying closed-loop process control concepts to sheet forming in a manner that automatically converges upon the appropriate tooling design. The problem of controlling complex deformation is reduced to a system identification problem where the die-part transformation is developed as a spatial frequency domain transfer function. This transfer function is simply the ratio of the measured change in spatial frequency content of the part and the die. It is then shown that such a transfer function can be used to implement closed-loop process control via rapid die redesign. Axisymmetric forming experiments are presented that establish the appropriateness of the linear transfer function description (via a test of superposition) and demonstrate the convergence properties of the proposed control method.

A Taylor synthesis for principal solution patterns of multiplicative antenna systems

A multiplicative (cross-correlation) receiving antenna system with a linear aperture can have a power pattern P/sub 0/(u) (the so-called principal-solution power pattern) whose spatial frequency transfer function (SFTF) is uniform over the entire spatial frequency (SF) bandwidth. A modified principal solution system which retains the uniform SFTF except for smooth transitions at the ends of the SF passband is described. The transitions are due to a change in the original pattern P/sub 0/(u), which suffers from high sidelobes, to a Taylor (1955) synthesis pattern P/sub T/(u) which involves a slowly varying envelope pattern. All of the slowly varying envelope sidelobes of P/sub T/(u) are set at the same appropriate low level, e.g. -30 dB. The aperture weighting distributions are free of singularities, unlike those for P/sub 0/(u), and can be sampled to provide the current weightings for a linear multiplicative array.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Scanning laser vibrometer system for structural intensity measurements

The steady‐state real‐time velocity response at successive locations on a beam are measured with a laser vibrometer and stored in a computer. The scanning system associated with the vibrometer consists of precision linear translation stages to control a lens/mirror combination. The laser beam is scanned along the length of the beam and the flexural vibration of a sinusoidally driven beam is measured at several locations. The amplitude and phase data are recorded at each location as well as a signal proportional to and in phase with the driving force. Knowing the distance between measurement locations, the recorded data are used to compute any of the following: spatial derivatives, transfer functions, and intensity.

Visual cortical receptive fields in monkey and cat: Spatial and temporal phase transfer function

The response amplitude of simple cortical cells to spatiotemporal sine-wave patterns has been thoroughly documented in both cat and monkey. However, comparable measurements of response phase are not available even though phase measurements are essential for estimating the complete transfer function of a cell, and thus its spatiotemporal receptive field. This report describes a simple procedure for measuring both the amplitude and the phase transfer functions of striate cells. This technique was applied to 15 monkey and 27 cat simple cells. The spatiotemporal phase response functions were found to be adequately described by linear equations in four parameters. Both the amplitude and phase responses were found to satisfy several strong constraints implied by the class of linear quadrature models proposed recently in theories of biological motion sensitivity. Because the data satisfied these constraints, it was possible to determine four important receptive field properties from the phase data: the spatial symmetry, the temporal symmetry, the response latency, and the spatial position. The receptive fields were found to have a wide range of spatial symmetries, but a more narrow range of temporal symmetries. Spatiotemporal receptive fields reconstructed from complete transfer functions are used to illustrate some of the differences between direction selective and nondirection selective cells. Finally, the effects of linear and nonlinear mechanisms on amplitude, phase, and direction selective responses are considered.

Temporal Persistence of Spatial Patterns of Soil Water Content in the Tilled Layer Under a Corn Crop

AbstractThe temporal persistence of the spatial pattern of soil water storage (0∼0.2 m) under a corn (Zea mays L.) canopy during drying and recharge periods were examined using spatial coherency analysis and transfer function theory. The corn crop caused both drying and recharge to occur at very specific scales, equal to the crop row spacing. The calculated transfer function, or time varying spectrum showed the scale at which the change in the spatial pattern was occurring and quantified the increase or decrease in variance at that scale. The spatial pattern of the drying coefficients, a measure of the relative drying rate, also varied systematically with significantly higher drying rates in the row area developing as the growing season progressed. The increase in relative drying rate in the row area caused the spatial pattern of drying to change at a scale equal to the crop row spacing. The calculated transfer function of the drying coefficients over the growing season indicated a steady increase in variance at that same scale, while the variance at other scales did not change significantly. An equation is developed relating the transfer function of soil water content in space to the spectrum of the process causing the change in the spatial domain.

Center-surround, orientation, and directional properties of turtle retinal horizontal cells.

The spatial transfer functions (STF) of L-type horizontal cells (HC) in turtle retina were measured using drifting sine wave grafting stimuli. Two classes of STF were identified: low-pass and band-pass. A low-pass STF corresponds to a linespread function (LSF) having an excitatory center that attenuates monotonically with distance; a band-pass STF corresponds to a LSF with an excitatory center and an inhibitory surround. Two models of the surround inhibitory mechanism, based on retinal outer plexiform layer (OPL) anatomy, are tested experimentally: surround mediated lateral inhibition and surround modulated self-inhibition. In both types, sign inverting pathways are based on GABA feedback synapses, and sign conserving pathways are based on excitatory synapses and gap junctions. Temperature variation was used to modify synaptic properties and study their effect on STF. The low frequency limb of band-pass STF was most sensitive to temperature changes; its slope increased with decreasing temperature. Synaptic properties were also manipulated pharmacologically. Cutoff frequency of low-pass STF decreased from 0.5 to 0.4 cpmm during exogenous GABA. Picrotoxin (PTX) increases upper cutoff frequency and decreases low frequency limb slope in band-pass STF. Band-pass STF of a ganglion cell (GC) has higher upper and lower cutoff frequencies than a HC in the same retinal region, which corresponds to strong spatial convergence from HC to GC. Orientation sensitivity and directional selectivity were found in some HC. Differences between major and minor response axes in orientation sensitive HC were small, ca. 2 dB; orientation differences in directionally selective HC were also small (ca. 1-2 dB) but directional asymmetry was large (ca. 10-12 dB).

Spatial Fourier transform method for evaluating SQUID gradiometers

A simple method of measuring the spatial transfer function of a gradiometer, consisting of a flux transformer coupled to a SQUID, is presented and it is compared with theoretical predictions. Based, on this approach, a new method of reporting a gradiometer’s performance is proposed; the rejection factor is expressed in decibels obtained directly from the transfer function plot.

Coherent Transfer Function Of A Hololens/Parabolic Optical Fiber System

A new integral equation is presented and solved by a matrix method based on iterative procedures to obtain information about the transmission and reflection of light (scalar field) in inhomogeneous media. The method, which may be applied to a wide category of arbitrary x,y,z-varying refractive index profiles, is used to study the holographic lens/ SELFOC optical fiber coupling system. The properties of the spatial transfer function for invariant linear systems are used.