Showing papers on "Noise (electronics) published in 1988"
TL;DR: The first observation of stochastic resonance in an optical device, the bidirectional ring laser, is reported and the addition of injected noise can lead to an improved signal-to-noise ratio.
Abstract: We report the first observation of stochastic resonance in an optical device, the bidirectional ring laser. The experiment exploits a new technique to modulate periodically the asymmetry between the two counter-rotating lasing modes. The measurements verify that the addition of injected noise can lead to an improved signal-to-noise ratio (relative to that observed with no externally injected noise).
682 citations
TL;DR: It is shown that it may be made to further enhance the sensitivity within a narrow bandwidth, becoming tuned recycling, and the various sensitivity-bandwidth combinations, together with the tuning properties, are discussed.
Abstract: Laser interferometers may detect gravitational waves by sensing the strain in space produced by their passage. The resultant change in intensity of an interference fringe must be observable against a background noise due to the statistical fluctuations in the number of detected photons. Optimization of the detector sensitivity thus involves devising an optical system which both maximizes the signal and minimizes the noise. This is attempted in the various arrangements known collectively as light recycling. Here, the performance of these systems is quantitatively assessed. Standard or broadband recycling functions essentially by making efficient use of the available light, but it is shown that it may also be made to further enhance the sensitivity within a narrow bandwidth, becoming tuned recycling. This works, as do all the narrow-band variants, by arranging for both the laser light and a gravitational-wave-induced sideband to be resonant in the optical system. The original narrow-band system, resonant recycling, can also be made broadband; the various sensitivity-bandwidth combinations, together with the tuning properties of such a system, are discussed.
358 citations
01 Mar 1988
TL;DR: In this paper, a unified view of 1/f noise in semiconductors, semiconductor devices, and collision-free devices (like vacuum tubes) is presented from a unified point of view, using an extended version of the F.N. Hooge equation.
Abstract: 1/f noise in semiconductors, semiconductor devices, and collision-free devices (like vacuum tubes) is presented from a unified point of view, using an extended version of the F.N. Hooge equation (Physica, vol. 83b, p.9, 1976), which is generalized to all collision-dominated systems involving mobility, diffusion, and cross-section fluctuations. It also applies to collision-free processes involving vacuum tubes, Schottky barrier diodes operating in the thermionic mode, and in devices such as p-i-n diodes in which collision processes are not the determining factor. A generalized schematic is given for expressing the noise spectrum S/sub 1/(f) in the external circuit in terms of distributed noise sources of the nonuniform devices in terms of alpha /sub H/, so the latter can be determined from the former. It is then found that the Hooge parameter. alpha /sub H/ introduced by this equation can be used as a general measure of the noisiness of a system or device. Several cases in which the noise does not obey the quantum 1/f noise theory are discussed. Measurements on many different devices are examined, and an attempt is made to correlate measured values of the Hooge parameter with the values calculated from P.H. Handel's quantum theory of 1/f noise (1975, 1980). >
313 citations
TL;DR: It is shown that noise in the materialdensity images is negatively correlated and that this can be exploited for noise reduction in the two-basis material density images, and locally adaptive algorithms are presented.
Abstract: Dual-energy material density images obtained by prereconstruction-basis material decomposition techniques offer specific tissue information, but they exhibit relatively high pixel noise. It is shown that noise in the material density images is negatively correlated and that this can be exploited for noise reduction in the two-basis material density images. The algorithm minimizes noise-related differences between pixels and their local mean values, with the constraint that monoenergetic CT values, which can be calculated from the density images, remain unchanged. Applied to the material density images, a noise reduction by factors of 2 to 5 is achieved. While quantitative results for regions of interest remain unchanged, edge effects can occur in the processed images. To suppress these, locally adaptive algorithms are presented and discussed. Results are documented by both phantom measurements and clinical examples. >
224 citations
TL;DR: Detailed results on the form factors of two-dimensional systems undergoing phase-ordering processes, using both deterministic and stochastic cell dynamical systems are presented, and the robustness of the asymptotic form factors against quench depth, noise amplitude, etc is shown.
Abstract: We present detailed results on the form factors of two-dimensional systems undergoing phase-ordering processes, using both deterministic and stochastic cell dynamical systems. We show the robustness of the asymptotic form factors against quench depth, noise amplitude, etc. The effect of noise is essentially to delay the number of steps needed to reach the asymptotic behavior. In the case with a nonconserved order parameter, we demonstrate that the form factor obtained by T. Ohta, D. Jasnow, and K. Kawasaki [Phys. Rev. Lett. 49, 1223 (1982)] is asymptotically very accurate. We also present preliminary results for off-critical quenches.
197 citations
TL;DR: In this paper, the authors demonstrated 42% squeezing of 4.2-K thermal noise using a Josephson-parametric amplifier operated at 19.4 GHz with an excess noise of 0.28 K referred to the input port.
Abstract: We have demonstrated 42% squeezing of 4.2-K thermal noise using a Josephson-parametric amplifier operated at 19.4 GHz. The amplifier has been operated at 0.1 K with an excess noise of 0.28 K referred to the input port. This is less than the vacuum fluctuation noise h\ensuremath{
u}/2k=0.47 K at 19.4 GHz. The amplifier thus is less noise than a linear phase-insensitive amplifier such as a maser could in principle be.
171 citations
TL;DR: In this paper, it is demonstrated that near-threshold operation of a semiconductor laser exposed to moderate optical feedback may lead to low-frequency fluctuations and a kink is observed in the light-current characteristic.
Abstract: Near-threshold operation of a semiconductor laser exposed to moderate optical feedback may lead to low-frequency fluctuations. In the same region, a kink is observed in the light-current characteristic. Here it is demonstrated that these nonlinear phenomena are predicted by a noise driven multimode traveling-wave model. The dynamics of the low-frequency fluctuations are explained qualitatively in terms of bistability through an iterative description. >
163 citations
TL;DR: It is shown that for large signal-to-noise ratio, the asymptotic distribution of the phase is of the Tikhonov type and this framework is then used for the synthesis of differentially coherent receiver structures, one for M-ary phase-shift keying (MPSK) and the other for minimum-shiftkeying (MSK).
Abstract: Some results are presented regarding the asymptotic distribution of the phase of a vector perturbed by Gaussian noise. It is shown that for large signal-to-noise ratio, the asymptotic distribution of the phase is of the Tikhonov type. This framework is then used for the synthesis of differentially coherent receiver structures, one for M-ary phase-shift keying (MPSK) and the other for minimum-shift keying (MSK). The first structure bridges the performance gap between coherent and differentially coherent demodulation of MPSK. The MSK receiver uses matched filtering with differential demodulation. >
161 citations
TL;DR: Squeezed states of light are generated by the process of second-harmonic conversion within an optical cavity resonant at both fundamental and harmonic frequencies.
Abstract: Squeezed states of light are generated by the process of second-harmonic conversion within an optical cavity resonant at both fundamental and harmonic frequencies. Observations of squeezing are made by analyzing the spectral density of photocurrent fluctuations produced by the total field reflected from the nonlinear cavity. Reductions in photocurrent noise of 13% relative to the coherent-state or shot-noise level are achieved for frequency offsets near 4 MHz.
145 citations
TL;DR: It is shown that when the input to a sigma-delta modulator is a DC level that can be expressed as a rational number b/a, when normalized with respect to the quantizer step, the output bit string is periodic with a period that is multiple of the denominator a.
Abstract: It is shown that when the input to a sigma-delta modulator is a DC level that can be expressed as a rational number b/a, when normalized with respect to the quantizer step, the output bit string is periodic with a period that is multiple of the denominator a. On the basis of number theory, the structure of these cycles for single-loop modulators is determined and the noise contribution is computed. Around such levels the noise has two peaks, for which the maximum value and the width are proportional to the relative signal bandwidth and to the inverse of the period of the cycle, respectively. The effect of the limit cycles on the performance of the A/D and D/A converters using sigma-delta modulation is discussed. A comparison between single-loop and double-loop modulators from the point of view of this phenomena is made. >
128 citations
TL;DR: In this article, the effect of doping on the optical gain and the noise enhancement factor in a 100 A InGaAs/InP quantum well structure was studied. But the effect on the performance was not investigated.
Abstract: The maximum optical gain and the spontaneous noise enhancement factor in quantum well structures are expressed as extremely simple functions that are accurate over a wide range of carrier densities. These expressions are used to study the effect of doping on the optical gain and the noise enhancement factor in a 100 A InGaAs/InP quantum well structure. n-type doping is most effective in reducing the transparency excitation level (laser threshold) and the noise enhancement factor (amplifier noise figure), whereas p-type doping enables increased gain at a given excitation level.
TL;DR: In this paper, a new class of random telegraph signal which exhibits anomalous behavior was observed in the drain current of submicrometer silicon metal-oxide-semiconductor field effect transistors.
Abstract: In the drain current of submicrometer silicon metal-oxide-semiconductor field-effect transistors, we have observed a new class of random telegraph signal which exhibits anomalous behavior. We discuss the various models that could account for these signals and suggest that they are due to individual Si/${\mathrm{SiO}}_{2}$ interface states which can exist in two or more charge-equivalent, metastable states. We describe one particular signal which is consistent with sequential two-electron capture involving a number of such metastable states at a single defect. We point out that these signals are a source of non-Gaussian noise.
TL;DR: In this article, a design technique for cryogenically cooled amplifiers is briefly discussed, and examples of realization of L-band, C-band and X-band amplifiers are described.
Abstract: Typical DC characteristics and X-band noise parameters are presented and qualitatively correlated wherever possible with other technological or experimental data. While certain general trends can be identified, further work is needed to explain a number of observed phenomena. A design technique for cryogenically cooled amplifiers is briefly discussed, and examples of realization of L-band, C-band, X-band, and K-band amplifiers are described. The noise temperature of amplifiers with HEMTs in input stages is usually less than half of that for all-FET realizations, setting new records of performance for cryogenically cooled, multistage amplifiers. >
TL;DR: In this paper, the Fourier transform method of fringe pattern analysis was investigated for increasing levels of signal-independent random additive noise and increasingly complicated phase functions and it was shown that the condition that the phase must be a slowly varying function compared to the variation introduced by the carrier frequency is a fairly flexible one.
01 Mar 1988-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this article, the relationship among the speed of response, the signal-to-noise ratio and the charge collection time in ionization chamber calorimeters is analyzed, and it is shown that a dominant limiting factor to the response is the charge transfer time from the electrodes to the amplifier determined by the electrode capacitance CD and the inductance of connections.
Abstract: Relations among the speed of response, the signal-to-noise ratio and the charge collection time in ionization chamber calorimeters are analyzed. A dominant limiting factor to the speed of response is the charge transfer time from the electrodes to the amplifier determined by the electrode capacitance CD and the inductance of connections Ls. The time parameter L s C D sol1 2 has to be at least an order of magnitude smaller than the required length of the overall calorimeter response. The charge collection time plays a secondary role in determining the speed of response, while together with the charge yield it affects the signal-to-noise ratio.
TL;DR: In this article, a 1/f noise model for diodes operating in the thermionic-emission mode under forward bias conditions has been developed, based on mobility and diffusivity fluctuations occurring in the space charge region and accounts for the current-limiting role of the metal-semiconductor interface.
Abstract: A 1/f noise model for diodes operating in the thermionic-emission mode under forward-bias conditions has been developed. The model is based on mobility and diffusivity fluctuations occurring in the space-charge region and accounts for the current-limiting role of the metal-semiconductor interface The bias dependence of the 1/f noise spectral density calculated from this model is in excellent agreement with the results of the authors' experiments but is at variance with the predictions of a model developed by T.G.M. Kleinpenning (1979). From the experimental data, a value of 4.2*10/sup -9/ for the Hooge parameter is derived. This value is in good agreement with theoretical calculation for electrons in silicon. >
TL;DR: In this paper, a planar array of hexagonal single-domain particles with long-range magnetostatic as well as possible nearest-neighbor exchange interactions is modeled as a close flying head with a small gap.
Abstract: Micromagnetic simulations of the recording of a single transition in thin-film metallic media are presented. The film is modeled as a planar array of hexagonal single-domain particles with long-range magnetostatic as well as possible nearest-neighbor exchange interactions. Magnetization configurations are determined by following the Landau-Lifshitz equations of motion with finite damping. The media parameters used here approximate Co films. The recording geometry resembles a close flying head with a small gap. Transition fluctuations, a source of transition noise, are also suited for both non-exchange-coupled and exchange-coupled media. It is shown that intergranular exchange coupling can significantly enhance transition noise and that films with well defined nonmagnetic grain boundaries exhibit better signal-to-noise ratios. >
TL;DR: In this article, temperature dependence of noise power spectra in a series of commercial p-channel MOSFETs is studied. And the experimental results were compared to first-principle calculations which showed that the noise was due to the capture and emission of carriers by oxide traps through thermal activation.
Abstract: Detailed measurements of the temperature dependence of noise power spectra in a series of commercial p-channel MOSFETs are presented It was found that both the magnitude and the functional form of the voltage noise power spectral density varied greatly in the range between 60 and 260 K The experimental results were compared to first-principle calculations which showed that the noise was due to the capture and emission of carriers by oxide traps through thermal activation The process caused fluctuations in both the density and the surface mobility of the channel carriers through the modulation of the surface potential and the scattering rate respectively
TL;DR: It is found that the interference noise plays a dominant role in determining the operating margin of the DRAM and that a novel process or a cell array architecture for minimizing the interferencenovelity is indispensable in 16-MbDRAM and beyond.
Abstract: A kind of data-line (DL) interference noise in a scaled DRAM cell array is found and studied through analysis. The dynamic behavior of cell arrays due to sense-amplifier operation is derived analytically. Analysis shows that the amount of interference noise is more than three times larger than expected from simple data-line coupling. A novel experimental technique for precise noise determination is developed to verify the analysis. Analytical results are in good agreement with the experimental data. It is found that the interference noise plays a dominant role in determining the operating margin of the DRAM and that a novel process or a cell array architecture for minimizing the interference noise is indispensable in 16-Mb DRAM and beyond. >
Patent•
NEC1
TL;DR: A carrier-to-noise detector comprises an A/D converter which samples an output of the demodulator of a digital transmission system at a symbol clock rate and converts it to a digital signal having positive and negative values as mentioned in this paper.
Abstract: A carrier-to-noise detector comprises an A/D converter (1) which samples an output of the demodulator of a digital transmission system at a symbol clock rate and converting it to a digital signal having positive and negative values. An absolute value converting circuit (2) converts the output of A/D converter into an absolute value which is averaged by a first averaging circuit (3) over a period sufficient to suppress short term variations and then squared by a first squaring circuit (4) to give an output representing the carrier component. The output of A/D converter is, on the other hand, squared by a second squaring circuit (5) and averaged by a second averaging circuit (6) to suppress short term variations to give an output representing a total of the carrier and noise components. The carrier component in the output of the second averaging circuit 6 is subtracted by a subtractor (7). A ratio between the outputs of the first squaring circuit (4) and subtracting circuit (7) is derived by a divider (8) as a representation of a carrier-to-noise ratio.
TL;DR: An analysis of pre- and postoperative voices of six patients with benign laryngeal disease showed that the N/S ratio for vowel /u/ in running speech consistently improved after surgery for all subjects, in agreement with their successful therapeutic results.
Abstract: A method of pitch‐synchronous acoustic analysis of hoarseness requiring a voice sample of only four fundamental periods is presented. This method calculates a noise‐to‐signal (N/S) ratio, which indicates the depth of valleys between harmonic peaks in the power spectrum. The spectrum is calculated pitch synchronously from a Fourier transform of the signal, windowed through a continuously variable Hanning window spanning exactly four fundamental periods. A two‐stage procedure is used to determine the exact duration of the four fundamental periods. An initial estimate is obtained using autocorrelation in the time domain. A more precise estimate is obtained in the frequency domain by minimizing the errors between the preliminary calculated power spectrum and the predicted spectrum spread of a windowed harmonic signal. Analysis of synthesized voices showed that the N/S ratio is sensitive to additive noise, jitter, and shimmer, and is insensitive to slow (8 Hz) modulation in fundamental frequency and amplitude. An analysis of pre‐ and postoperative voices of six patients with benign laryngeal disease showed that the N/S ratio for vowel /u/ in running speech consistently improved after surgery for all subjects, in agreement with their successful therapeutic results.
TL;DR: In this paper, the effect of fiber dispersion on the performance of lightwave systems is analyzed for the case where multimode semiconductor lasers operating near the zero-dispersion wavelength of the singlemode fiber are used as sources.
Abstract: The effect of fiber dispersion on the performance of lightwave systems is analyzed for the case where multimode semiconductor lasers operating near the zero-dispersion wavelength of the single-mode fiber are used as sources. Both the intersymbol interference and the mode-partition noise are considered in the discussion of dispersion-induced power penalties. The theory is in agreement with an experiment in which the bit error rate is measured for lasers at various bit rates. The tolerable limits on the deviation of the laser wavelength from the zero-dispersion wavelength are obtained for a 1.3- mu m system operating at 1.7 Gb/s. Monte Carlo simulations are used to predict the effect of mode-partition noise on the performance of such high-speed lightwave communication systems. >
20 Apr 1988
TL;DR: In this paper, the spectral averaging technique was used to measure the harmonic distortion and noise floor of an analog/digital (A/D) digitizing subsystem, and the noise floor was derived for an ideal B-bit A/D converter in closed form.
Abstract: The author proposes to use spectral averaging techniques to measure the harmonic distortion and noise floor of an analog/digital (A/D) digitizing subsystem. The noise floor of an ideal B-bit A/D converter is derived in closed form. It is shown that this noise floor is a function of the A/D resolution B, the record length N, and the equivalent noise bandwidth E/sub B/ of the window function used in the discrete-Fourier-transform (DFT) computation. For an example, the noise floor is given for the case in which the magnitude square of the spectrum is averaged. Both experimental and simulation results are presented and it is shown that they are in good agreement with the theoretical results. >
TL;DR: In this paper, the concentration of silicon-silicon dioxide interface traps with energies down to within 20 meV of the majority-carrier band edge was determined using 1/f noise measurements.
Abstract: The concentration of silicon-silicon dioxide interface traps with energies down to within 20 meV of the majority-carrier band edge was determined using 1/f noise measurements. p-type diffused resistors of four-probe geometry were fabricated in a metal-oxide-silicon structure. Flicker noise measurements were performed on these devices at cryogenic temperatures of 20 to 280 K. Using A. L. McWhorter's (1957) 1/f noise model and the calculated position of the Fermi level with respect to the valence band edge at each temperature, the density of interface traps was calculated at energy levels corresponding to the position of the Fermi level at that temperature. This technique is proposed as an alternate method to measure the oxide trap and slow interface-state densities with energies close to the band edges. >
TL;DR: In this paper, a microcalorimeter was proposed to measure the energy released in the absorption of a single photon by sensing the rise in temperature of a small absorbing structure, which can in principle be made as low as 1 eV.
Abstract: Thermal detectors for X-ray spectroscopy combining high spectral resolution and quantum efficiency have been developed. These microcalorimeters measure the energy released in the absorption of a single photon by sensing the rise in temperature of a small absorbing structure. The ultimate energy resolution of such a device is limited by the thermodynamic power fluctuations in the thermal link between the calorimeter and isothermal bath and can in principle be made as low as 1 eV. The performance of a real device is degraded due to noise contributions such as excess 1/f noise in the thermistor and incomplete conversion of energy into phonons. The authors report some recent advances in thermometry, X-ray absorption and thermalization, fabrication techniques, and detector optimization in the presence of noise. These improvements have resulted in a device with a spectral resolution of 17 eV FWHM, measured at 6 keV. >
TL;DR: The fact that receptor coupling and synaptic convergence can, under some circumstances, improve the signal: noise ratio in bipolar cells suggests a principle of retinal design that may compete with the requirements of high spatial resolution.
Abstract: Electrical coupling of vertebrate photoreceptors is well known to improve the signal:noise ratio in the photoreceptor layer for large-area stimuli. For example, if N photoreceptors are perfectly coupled to each other, the signal:noise ratio is improved for stimuli illuminating more than a number M = $\surd $ N of the receptors but is made worse for small-area stimuli illuminating less than M of the N receptors. Using the model of Lamb & Simon (J. Physiol., Lond. 263, 257 (1976)), which treats the photoreceptor layer as a square array of cells, each coupled through a resistive gap junction to the four cells around it, we show that the signal:noise ratio for small-area stimuli is much greater than would be expected from a model in which receptors are assumed to be perfectly coupled. Contrary to predictions made assuming perfect coupling, receptor coupling should not prevent rods from detecting single photons, but whether the single photon signal can be detected at the bipolar cell level depends on how signals are read out of the receptor layer. The signal:noise ratio in bipolar cells postsynaptic to the photoreceptor layer is determined partly by synaptic convergence and nonlinearity in synaptic transmission from receptors. If the synaptic gain decreases with light-induced receptor hyperpolarization, as is found experimentally, then receptor coupling can improve the postsynaptic signal:noise ratio for stimuli illuminating only one receptor, even though coupling decreases the presynaptic signal:noise ratio for such stimuli. Moreover, increasing the number of coupled receptors projecting to a bipolar cell can improve the signal:noise ratio for localized stimuli if the synapse is sufficiently nonlinear (although, for the degree of nonlinearity seen in lower vertebrates, synaptic convergence makes the ratio worse for the single photon event). The fact that receptor coupling and synaptic convergence can, under some circumstances, improve the signal:noise ratio in bipolar cells suggests a principle of retinal design that may compete with the requirements of high spatial resolution.
TL;DR: An analysis of the effect of noise introduced by the transduction process on the minimum detectable signal (MDS) of piezoresistive and capacitive pressure sensors has been performed as mentioned in this paper.
Abstract: An analysis of the effect of noise introduced by the transduction process on the minimum detectable signal (MDS) of piezoresistive and capacitive pressure sensors has been performed. MDS is first introduced as an appropriate figure of merit for comparing different sensor transduction schemes. Analyses are then performed to determine the minimum MDS theoretically achievable for a broad range of generic transducer circuits. The results of the analyses indicate that noise in the transduction process is not a limiting factor in the performance of properly designed integrated silicon sensors. >
TL;DR: In this paper, the observed 1/f noise in the light output power S/sub p/ of four different types of heterostructure lasers is explained in terms of spatially uncorrelated gain fluctuations and spontaneous emission fluctuations.
Abstract: The observed 1/f noise in the light-output power S/sub p/ of four different types of heterostructure lasers is explained in terms of spatially uncorrelated gain fluctuations and spontaneous emission fluctuations. Two possible noise sources are suggested: fluctuations in the absorption coefficient and fluctuations in the number of free carriers. Both models are in agreement with the experimental results obtained from index-guided and gain-guided diodes at wavelengths of 1.3 and 0.8 mu m. The dependence S/sub p/ varies as P/sup m/ has been observed with P the average light-output power and m=3/2 under spontaneous emission, a small transition region with m=5/2, m=4 in the superradiation region, and 0 >
21 Dec 1988
TL;DR: In this article, Fano-noise-limited test data is presented for two different CCD types and a CCD derived estimate of the Fano factor is determined by evaluating ultra low-modulation images (less than 1 electron peak-to-peak) it is shown that the CCD's global CTE is now superior to its read noise floor.
Abstract: Recent developments of scientific CCDs have produced sensors that achieve ultra low read noise performance (less than 2 electrons rms) and near perfect charge transfer efficiency (09999996) without the addition of a fat-zero This progress has now made it possible to achieve Fano-noise-limited performance in the soft X-ray where the detector's energy resolution is primarily limited by the statistical variation in the charge generated by the interacting X-ray photon In this paper, Fano-noise-limited test data is presented for two different CCD types and a CCD derived estimate of the Fano factor is determined By evaluating ultra low-modulation images (less than 1 electron peak-to-peak) it is shown that the CCD's global CTE is now superior to its read noise floor To capitalize on this capability CCD manufacturers are now focusing their attention on reducing the noise floor below the 1 electron level thereby matching the sensor's CTE performance This improvement, if accomplished, will push Fano-noise-limited performance for the CCD into the extreme ultra-violet
IBM1
TL;DR: In this paper, the tunneling tip is vibrated parallel to the sample surface at a frequency f0, above that of the feedback response frequency, and two signals are obtained simultaneously: the conventional topography and a differential image corresponding to the amplitude of current modulation at f0.
Abstract: Noise stemming from mechanical vibration, electronic noise, or low frequency (1/f power spectrum) inherent in the tunneling process, often limits the resolution, speed, or range of application of scanning tunneling microscopy (STM). We demonstrate a technique for minimizing the effect of these noise sources on the STM image. In our method, the tunneling tip is vibrated parallel to the sample surface at a frequency f0, above that of the feedback response frequency. Two signals are obtained simultaneously: the conventional topography, and a differential image corresponding to the amplitude of current modulation at f0. The resultant ac signal can be simply related to the normal STM topographic image, with significant improvement in the signal‐to‐noise ratio.