Dynamics of Neurons Controlling Movements of a Locust Hind Leg II. Flexor Tibiae Motor Neurons

1997 ◽  
Vol 77 (4) ◽  
pp. 1731-1746 ◽  
Author(s):  
Philip L. Newland ◽  
Yasuhiro Kondoh
Keyword(s):  
Motor Neuron ◽  
Motor Neurons ◽  
High Frequency ◽  
Cutoff Frequency ◽  
Second Order ◽  
Chordotonal Organ ◽  
Linear Component ◽  
Response Dynamics ◽  
First Order ◽  
Frequency Components

Newland, Philip L. and Yasuhiro Kondoh. Dynamics of neurons controlling movements of a locust hind leg. II. Flexor tibiae motor neurons. J. Neurophysiol. 77: 1731–1746, 1997. Imposed movements of a proprioceptor that monitors the relative position of the tibia about the femur, the femorotibial chordotonal organ (FeCO), evoke resistance reflexes in the motor neurons that control the movements of the tibia of the locust. The response dynamics of one pool of motor neurons, the flexor tibiae motor neurons, which are located in three groups (anterior, lateral, and posterior), have been analyzed by the Wiener kernel method. First- and second-order kernels that represent the linear and nonlinear responses, respectively, were computed by a cross-correlation between the intracellularly recorded synaptic responses in the motor neurons and the white noise stimulus applied to the FeCO, and were used to define the input-output characteristics of the motor neurons. The posterior fast, intermediate, and slow and the anterior fast and intermediate flexor tibiae motor neurons had biphasic first-order kernels with initial negative phases, indicating that they are velocity sensitive. The falling phases of the kernels had distinct shoulders, indicating that the responses of the motor neurons also had delayed low-pass components, i.e., position sensitivity. The anterior slow flexor motor neuron had a monophasic, low-passed, first-order kernel, indicating that it is position sensitive. The linear component of the motor neuron responses, predicted by convolving the first-order kernels with the stimulus signal, strongly resembled the actual response, whereas the second-order nonlinear component was small, particularly at >10 Hz. The power spectra of the fast motor neurons showed that they had the highest cutoff frequencies (at >8 Hz), whereas the slow flexor motor neurons had a gradual roll-off at 1 Hz. The intermediate flexor motor neuron had an intermediate cutoff frequency of ∼2–3 Hz. The linear responses of the flexor motor neurons could be decomposed into low- and high-frequency components. The high-frequency components (>10 Hz) were velocity dependent and linear, whereas the low-frequency components (<10 Hz) were position dependent and nonlinear. The nonlinearity was a signal compression (or half-wave rectification). The results show that although the flexor motor neurons receive many common inputs during FeCO stimulation, each individual has specific dynamic response properties. The responses of the motor neurons are fractionated so that a given individual within the pool will respond best to position, whereas others will respond better to velocity. Likewise, some motor neurons respond best at low frequencies, whereas others respond best at higher frequencies of stimulation.

Dynamics of Neurons Controlling Movements of a Locust Hind Leg III. Extensor Tibiae Motor Neurons

1997 ◽  
Vol 77 (6) ◽  
pp. 3297-3310 ◽  
Author(s):  
Philip L. Newland ◽  
Yasuhiro Kondoh
Keyword(s):  
White Noise ◽  
Motor Neurons ◽  
Cutoff Frequency ◽  
Second Order ◽  
Chordotonal Organ ◽  
Inhibitory Input ◽  
Pass Filter ◽  
Low Pass Filter ◽  
First Order ◽  
Synaptic Responses

Newland, Philip L. and Yasuhiro Kondoh. Dynamics of neurons controlling movements of a locust hind leg. III. Extensor tibiae motor neurons. J. Neurophysiol. 77: 3297–3310, 1997. Imposed movements of the apodeme of the femoral chordotonal organ (FeCO) of the locust hind leg elicit resistance reflexes in extensor and flexor tibiae motor neurons. The synaptic responses of the fast and slow extensor tibiae motor neurons (FETi and SETi, respectively) and the spike responses of SETi were analyzed with the use of the Wiener kernel white noise method to determine their response properties. The first-order Wiener kernels computed from soma recordings were essentially monophasic, or low passed, indicating that the motor neurons were primarily sensitive to the position of the tibia about the femorotibial joint. The responses of both extensor motor neurons had large nonlinear components. The second-order kernels of the synaptic responses of FETi and SETi had large on-diagonal peaks with two small off-diagonal valleys. That of SETi had an additional elongated valley on the diagonal, which was accompanied by two off-diagonal depolarizing peaks at a cutoff frequency of 58 Hz. These second-order components represent a half-wave rectification of the position-sensitive depolarizing response in FETi and SETi, and a delayed inhibitory input to SETi, indicating that both motor neurons were directionally sensitive. Model predictions of the responses of the motor neurons showed that the first-order (linear) characterization poorly predicted the actual responses of FETi and SETi to FeCO stimulation, whereas the addition of the second-order (nonlinear) term markedly improved the performance of the model. Simultaneous recordings from the soma and a neuropilar process of FETi showed that its synaptic responses to FeCO stimulation were phase delayed by about −30° at 20 Hz, and reduced in amplitude by 30–40% when recorded in the soma. Similar configurations of the first and second-order kernels indicated that the primary process of FETi acted as a low-pass filter. Cross-correlation between a white noise stimulus and a unitized spike discharge of SETi again produced well-defined first- and second-order kernels that showed that the SETi spike response was also dependent on positional inputs. An elongated negative valley on the diagonal, characteristic of the second-order kernel of the synaptic response in SETi, was absent in the kernel from the spike component, suggesting that information is lost in the spike production process. The functional significance of these results is discussed in relation to the behavior of the locust.

Neural computation of motion in the fly visual system: quadratic nonlinearity of responses induced by picrotoxin in the HS and CH cells

1995 ◽  
Vol 74 (6) ◽  
pp. 2665-2684 ◽  
Author(s):  
Y. Kondoh ◽  
Y. Hasegawa ◽  
J. Okuma ◽  
F. Takahashi
Keyword(s):  
Mean Square Error ◽  
Order Term ◽  
Mirror Image ◽  
Second Order ◽  
The Other ◽  
Linear Component ◽  
Mean Square ◽  
Nonlinear Component ◽  
First Order ◽  
Order Kernel

1. A computational model accounting for motion detection in the fly was examined by comparing responses in motion-sensitive horizontal system (HS) and centrifugal horizontal (CH) cells in the fly's lobula plate with a computer simulation implemented on a motion detector of the correlation type, the Reichardt detector. First-order (linear) and second-order (quadratic nonlinear) Wiener kernels from intracellularly recorded responses to moving patterns were computed by cross correlating with the time-dependent position of the stimulus, and were used to characterize response to motion in those cells. 2. When the fly was stimulated with moving vertical stripes with a spatial wavelength of 5-40 degrees, the HS and CH cells showed basically a biphasic first-order kernel, having an initial depolarization that was followed by hyperpolarization. The linear model matched well with the actual response, with a mean square error of 27% at best, indicating that the linear component comprises a major part of responses in these cells. The second-order nonlinearity was insignificant. When stimulated at a spatial wavelength of 2.5 degrees, the first-order kernel showed a significant decrease in amplitude, and was initially hyperpolarized; the second-order kernel was, on the other hand, well defined, having two hyperpolarizing valleys on the diagonal with two off-diagonal peaks. 3. The blockage of inhibitory interactions in the visual system by application of 10-4 M picrotoxin, however, evoked a nonlinear response that could be decomposed into the sum of the first-order (linear) and second-order (quadratic nonlinear) terms with a mean square error of 30-50%. The first-order term, comprising 10-20% of the picrotoxin-evoked response, is characterized by a differentiating first-order kernel. It thus codes the velocity of motion. The second-order term, comprising 30-40% of the response, is defined by a second-order kernel with two depolarizing peaks on the diagonal and two off-diagonal hyperpolarizing valleys, suggesting that the nonlinear component represents the power of motion. 4. Responses in the Reichardt detector, consisting of two mirror-image subunits with spatiotemporal low-pass filters followed by a multiplication stage, were computer simulated and then analyzed by the Wiener kernel method. The simulated responses were linearly related to the pattern velocity (with a mean square error of 13% for the linear model) and matched well with the observed responses in the HS and CH cells. After the multiplication stage, the linear component comprised 15-25% and the quadratic nonlinear component comprised 60-70% of the simulated response, which was similar to the picrotoxin-induced response in the HS cells. The quadratic nonlinear components were balanced between the right and left sides, and could be eliminated completely by their contralateral counterpart via a subtraction process. On the other hand, the linear component on one side was the mirror image of that on the other side, as expected from the kernel configurations. 5. These results suggest that responses to motion in the HS and CH cells depend on the multiplication process in which both the velocity and power components of motion are computed, and that a putative subtraction process selectively eliminates the nonlinear components but amplifies the linear component. The nonlinear component is directionally insensitive because of its quadratic non-linearity. Therefore the subtraction process allows the subsequent cells integrating motion (such as the HS cells) to tune the direction of motion more sharply.

Segmental giant: evidence for a driver neuron interposed between command and motor neurons in the crayfish escape system

1982 ◽  
Vol 47 (5) ◽  
pp. 761-781 ◽  
Author(s):  
A. Roberts ◽  
F. B. Krasne ◽  
G. Hagiwara ◽  
J. J. Wine ◽  
A. P. Kramer
Keyword(s):  
Motor Neuron ◽  
Motor Neurons ◽  
High Frequency ◽  
Functional Significance ◽  
Escape Behavior ◽  
Dendritic Branch ◽  
Command Neurons ◽  
Firing Threshold ◽  
Conventional Tests ◽  
Bilateral Pair

1. The giant command neurons for tailflip escape behavior in crayfish have been thought to excite the nongiant fast flexor (tailflip producing) motor neurons (FFs) via monosynaptic connections. We show here that excitation of FFs instead occurs via a bilateral pair of segmental giant neurons (SGs) interposed between the command axons and FFs in each segment. 2. Anatomically, the SGs appear to make numerous contacts with ipsilateral command axons and FFs and fewer contacts contralaterally. In contrast, the command axons have only sparse direct connections to the FFs. An SG has an axon in the ipsilateral first ganglionic root and may be a modified swimmeret motor neuron. 3. Each SG is depolarized well beyond threshold by the firing of an ipsilateral command axon and is depolarized to near threshold by the firing of a contralateral command axon. The synapses between command axons and SGs are electrical and probably rectifying. 4. Each FF is excited to a level near firing threshold by the SG ipsilateral to its axon and is excited weakly by the contralateral SG. The synapses between SGs and FFs are electrical and nonrectifying. 5. Variations in excitatory postsynaptic potentials (EPSPs) recorded in FFs during prolonged, high-frequency firing of the command axons can be accounted for by refractoriness of SG spikes, as opposed to refractoriness of dendritic branch spikes as had previously been delivered. 6. These findings illustrate the limitations of conventional tests for monosynapticity. 7. The functional significance of having driver neurons interposed between command neurons and motor neurons is discussed.

scholarly journals Functional Analysis of the Sensory Motor Pathway of Resistance Reflex in Crayfish. I. Multisensory Coding and Motor Neuron Monosynaptic Responses

1997 ◽  
Vol 78 (6) ◽  
pp. 3133-3143 ◽  
Author(s):  
Didier Le Ray ◽  
François Clarac ◽  
Daniel Cattaert
Keyword(s):  
Functional Analysis ◽  
Motor Neuron ◽  
Motor Neurons ◽  
Reflex Response ◽  
Chordotonal Organ ◽  
Upward Movement ◽  
Intracellular Recordings ◽  
Motor Pathway ◽  
Sensory Motor

Le Ray, Didier, François Clarac, and Daniel Cattaert. Functional analysis of the sensory motor pathway of resistance reflex in crayfish. I. Multisensory coding and motor neuron monosynaptic responses. J. Neurophysiol. 78: 3133–3143, 1997. An in vitro preparation of the fifth thoracic ganglion of the crayfish was used to study in detail the negative feedback loop involved in the control of passive movements of the leg. Release-sensitive primary afferents of from the coxo-basipodite chordotonal organ (CBCO), a proprioceptor whose strand is released by upward movement of the leg, monosynaptically connect to depressor motor neurons (Dep MNs). Extracellular identification of sensory units from the CBCO neurogram allowed us to determine the global coding of a sine-wave movement, imposed from the most released position of the CBCO strand. Intracellular recordings from sensory terminals (CBTs) and ramp movement stimulations applied to the CBCO strand allowed us to characterize two groups of release-sensitive CBCO fibers. The first group, divided into two subgroups (phasic and phaso-tonic), is characterized by discontinuous firing patterns: phasic CBTs fired exclusively during release movements; phaso-tonic CBTs displayed both a phasic firing and a tonic discharge during the more released plateaus. The second group was continuously firing whatever the movement, with higher frequencies during the release phase of the movement stimulation. All CBTs displayed a marked sensitivity for release movements while only the phaso-tonic ones showed a clear sensitivity to maintained positions. Surprisingly, no pure tonic sensory fibers were encountered. Systematic intracellular recordings from all resistant Dep MNs, performed in high divalent cation saline, allowed us to describe two shapes of monosynaptic resistance reflex responses. A phasic response was characterized by bursts of excitatory postsynaptic potentials (EPSPs) occurring exclusively during CBCO strand release movements. A phaso-tonic response was characterized by a progressive depolarization occurring all along the release phase of the stimulation: during maintained released positions, the amplitude of the sustained depolarization was position dependent; in addition, each release movement produced a phasic burst of EPSPs in the MN. The parallel study of the Dep MN properties failed to point out any correlation between the type of reflex response recorded from the MN and the MN intrinsic properties, which would indicate that the type of MN response is entirely determined by the afferent messages it receives.

Mean- and Low-Frequency Wave Forces on Semisubmersibles

1982 ◽  
Vol 22 (04) ◽  
pp. 563-572
Author(s):  
J.A. Pinkster
Keyword(s):  
Low Frequency ◽  
Second Order ◽  
Irregular Waves ◽  
Wave Forces ◽  
Frequency Wave ◽  
First Order ◽  
Wave Drift ◽  
Frequency Components ◽  
Wave Drift Forces ◽  
Drift Forces

Abstract Mean- and low-frequency wave drift forces on moored structures are important with respect to low-frequency motions and peak mooring loads. This paper addresses prediction of these forces on semisubmersible-type structures by use of computations based on three-dimensional (3D) potential theory. The discussion includes a computational method based on direct integration of pressure on the wetted part of the hull of arbitrarily shaped structures. Results of computations of horizontal drift forces on a six-column semisubmersible are compared with model tests in regular and irregular waves. The mean vertical drift forces on a submerged horizontal cylinder obtained from model tests also are compared with results of computations. On the basis of these comparisons, we conclude that wave drift forces on semisubmersible-type structures in conditions of waves without current can be predicted with reasonable accuracy by means of computations based on potential theory. Introduction Stationary vessels floating or submerged in irregular waves are subjected to large first-order wave forces and moments that are linearly proportional to the wave height and that contain the same frequencies as the waves. They also are subjected to small second-order mean- and low- frequency wave forces and moments that are proportional to the square of the wave height. Frequencies of second-order low-frequency components are associated with the frequencies of wave groups occurring in irregular waves.First-order wave forces and moments cause the well-known first-order motions with wave frequencies. First-order wave forces and motions have been investigated for several decades. As a result of these investigations, methods have been developed to predict these forces and moments with reasonable accuracy for many different vessel shapes.For semisubmersibles, which consist of a number of relatively slender elements such as columns, floaters, and bracings, computation methods have been developed to determine the hydrodynamic loads on those elements without accounting for interaction effects between the elements. For the first-order wave loads and motion problem, these computations give accurate results.This paper deals with the mean- and low-frequency second-order wave forces acting on stationary vessels in regular and irregular waves in general and presents a method to predict these forces on the basis of computations.The importance of mean- and low-frequency wave drift forces, from the point of view of motion behavior and mooring loads on vessels moored at point of view of motion behavior and mooring loads on vessels moored at sea, has been recognized only within the last few years. Verhagen and Van Sluijs, Hsu and Blenkarn, and Remery and Hermans showed that the low-frequency components of wave drift forces in irregular waves-even though relatively small in magnitude-can excite large-amplitude low- frequency horizontal motions in moored structures. It was shown for irregular waves that the drift forces contain components with frequencies coinciding with the natural frequencies of the horizontal motions of moored vessels. Combined with minimal damping of low-frequency horizontal motions of moored structures, this leads to large-amplitude resonant behavior of the motions (Fig. 1). Remery and Hermans established that low-frequency components in drift forces are associated with the frequencies of wave groups present in an irregular wave train.The vertical components of the second-order forces sometimes are called suction forces. SPEJ p. 563

Heterogeneity and central modulation of feedback reflexes in crayfish motor pool

1992 ◽  
Vol 67 (3) ◽  
pp. 648-663 ◽  
Author(s):  
P. Skorupski ◽  
B. M. Rawat ◽  
B. M. Bush
Keyword(s):  
Motor Activity ◽  
Motor Neuron ◽  
Motor Neurons ◽  
Positive Feedback ◽  
Active State ◽  
Reflex Response ◽  
Chordotonal Organ ◽  
Dependent Manner ◽  
Reflex Effect ◽  
State Dependent

1. Movement of the crayfish thoracocoxal leg joint is monitored by a muscle receptor organ (TCMRO) and a chordotonal organ (TCCO). Both receptors span the joint in parallel but signal opposite directions of leg movement. The TCMRO is innervated by afferents responsive to lengthening, which corresponds to leg remotion, whereas TCCO afferents are responsive to shortening of the chordotonal strand, which corresponds to leg promotion. 2. When both receptors are stimulated in parallel, in an otherwise isolated preparation, reflex responses of coxal promoter and remotor motor neurons occur on both stretch and release. By comparison with experiments where one or the other of these receptors is stimulated selectively, we conclude that reflexes evoked by stretch of the two receptors are due to the TCMRO and reflexes evoked by release are due to the TCCO. 3. Reflexes mediated by these receptors are both state dependent and phase dependent. In preparations that produce patterns of reciprocal motor activity in promotor and remotor motor neurons (the active state), the reflex effect depends on the phase of this centrally generated activity. In preparations that are quiescent, or that produce only tonic motor output (the inactive state), the reflex effect is stable, corresponding to a typical resistance (negative feedback) reflex for both directions of receptor movement. 4. In the active state, coxal promotor motor neurons are both excited and inhibited in a phase-dependent manner by stretching the TCMRO. A subgroup of promotor motor neurons is excited by shortening the TCCO. One subgroup of the antagonistic coxal remotor motor neurons receives phase-dependent excitation from stretch of the TCMRO, whereas a second subgroup receives phase-dependent excitation from shortening the TCCO. 5. There are, therefore, at least two ways in which reflex effects can be modulated. At the level of a single motor neuron, the reflex response can vary in gain, and in some cases in sign, in a manner depending on centrally generated motor activity. In addition, at the level of a pool of synergistic motor neurons, the reflex effect is not uniform; instead, different subgroups of motor neurons display different reflex effects, so that the relative levels of excitability of different motor neuron reflex subgroups can also determine the net reflex effect. 6. Excitation of promotor motor neurons by TCCO shortening and of remotor motor neurons by TCMRO lengthening are positive feedback reflexes. The subgroups of motor neurons in which positive feedback reflexes can be evoked in both promotor and remotor pools are termed group 1.(ABSTRACT TRUNCATED AT 400 WORDS)

scholarly journals Evidence for second-order singleton suppression based on probabilistic expectations

2018 ◽  
Author(s):  
Bo Yeong Won ◽  
Mary Kosoyan ◽  
Joy Geng
Keyword(s):  
High Frequency ◽  
Repetition Priming ◽  
Search Display ◽  
Second Order ◽  
Color Singleton ◽  
Probe Display ◽  
Multiple Objects ◽  
Frequency Condition ◽  
First Order ◽  
Singleton Distractor

Decades of research in attention have shown that salient distractors (e.g., a color singleton) tend to capture attention. However, in most studies, singleton distractors are just as likely to be present as absent. We therefore have little knowledge of how probabilistic expectations of the salient distractor's occurrence and features affect suppression. In three experiments, we explored this question by manipulating the frequency of a singleton distractor and the variability of its color within a search display. We found that increased expectations regarding the occurrence of the singleton distractor eliminated the singleton RT cost and reduced the number of first saccades to the singleton. In contrast, expectations regarding variability in the singleton color did not affect singleton capture. This was surprising and suggests the ability to suppress second order salience over and above that of first order features. We next inserted the probe display that included a to-be-reported letter inside each shape between search trials to measure if attention went to multiple objects. The letter in the singleton location was reported less often in the high frequency condition, suggesting proactive suppression of expected singleton. Additionally, we found that trial-to-trial repetitions of a singleton (irrespective of its color and location) facilitated performance (i.e., singleton repetition priming), but repetitions of its specific color or location did not. Together our findings demonstrate that attentional capture by a color singleton distractor is attenuated by probabilistic expectations of its occurrence, but not of its color and location.

scholarly journals A MODIFIED LEARNING ALGORITHM INCORPORATING ADDITIONAL FUNCTIONAL CONSTRAINTS INTO NEURAL NETWORKS

2006 ◽  
Vol 20 (02) ◽  
pp. 129-142 ◽  
Author(s):  
FEI HAN ◽  
XU-QIN LI ◽  
MICHAEL R. LYU ◽  
TAT-MING LOK
Keyword(s):  
High Frequency ◽  
Learning Algorithm ◽  
Neural Activation ◽  
Functional Constraints ◽  
Generalization Performance ◽  
First Order ◽  
Efficiency And Effectiveness ◽  
Frequency Components ◽  
The Cost ◽  
Derivatives Of

In this paper, a modified learning algorithm to obtain better generalization performance is proposed. The cost terms of this new algorithm are selected based on the second-order derivatives of the neural activation at the hidden layers and the first-order derivatives of the neural activation at the output layer. It can be guaranteed that in the course of training, the additional cost terms for this algorithm can penalize both the input-to-output mapping sensitivity and the high frequency components to obtain better generalization performance. Finally, theoretical justifications and simulation results are given to verify the efficiency and effectiveness of the proposed learning algorithm.

Nonspiking and Spiking Proprioceptors in the Crab: White Noise Analysis of Spiking CB-Chordotonal Organ Afferents

2003 ◽  
Vol 89 (4) ◽  
pp. 1815-1825 ◽  
Author(s):  
E. Rolland Gamble ◽  
Ralph A. DiCaprio
Keyword(s):  
White Noise ◽  
Information Transfer ◽  
Noise Analysis ◽  
Second Order ◽  
Chordotonal Organ ◽  
White Noise Analysis ◽  
Response Component ◽  
First Order ◽  
Wiener Kernels ◽  
Order Kernel

The proprioceptors that signal the position and movement of the first two joints of crustacean legs provide an excellent system for comparison of spiking and nonspiking (graded) information transfer and processing in a simple motor system. The position, velocity, and acceleration of the first two joints of the crab leg are monitored by both nonspiking and spiking proprioceptors. The nonspiking thoracic-coxal muscle receptor organ (TCMRO) spans the TC joint, while the coxo-basal (CB) joint is monitored by the spiking CB chordotonal organ (CBCTO) and by nonspiking afferents arising from levator and depressor elastic strands. The response characteristics and nonlinear models of the input-output relationship for CB chordotonal afferents were determined using white noise analysis (Wiener kernel) methods. The first- and second-order Wiener kernels for each of the four response classes of CB chordotonal afferents (position, position-velocity, velocity, and acceleration) were calculated and the gain function for each receptor determined by taking the Fourier transform of the first-order kernel. In all cases, there was a good correspondence between the response of an afferent to deterministic stimulation (trapezoidal movement) and the best-fitting linear transfer function calculated from the first-order kernel. All afferents also had a nonlinear response component and second-order Wiener kernels were calculated for afferents of each response type. Models of afferent responses based on the first- and second-order kernels were able to predict the response of the afferents with an average accuracy of 86%.

Simulations of high-resolution images of amorphous silicon films

1986 ◽  
Vol 44 ◽  
pp. 544-545
Author(s):  
G. Y. Fan ◽  
J. M. Cowley
Keyword(s):  
Electron Microscope ◽  
High Frequency ◽  
Fourier Transformation ◽  
Amorphous Materials ◽  
Low Frequency ◽  
Chromatic Aberration ◽  
Structure Information ◽  
Frequency Components ◽  
High Resolution Images ◽  
Spatial Frequency Spectrum

It is well known that the structure information on the specimen is not always faithfully transferred through the electron microscope. Firstly, the spatial frequency spectrum is modulated by the transfer function (TF) at the focal plane. Secondly, the spectrum suffers high frequency cut-off by the aperture (or effectively damping terms such as chromatic aberration). While these do not have essential effect on imaging crystal periodicity as long as the low order Bragg spots are inside the aperture, although the contrast may be reversed, they may change the appearance of images of amorphous materials completely. Because the spectrum of amorphous materials is continuous, modulation of it emphasizes some components while weakening others. Especially the cut-off of high frequency components, which contribute to amorphous image just as strongly as low frequency components can have a fundamental effect. This can be illustrated through computer simulation. Imaging of a whitenoise object with an electron microscope without TF limitation gives Fig. 1a, which is obtained by Fourier transformation of a constant amplitude combined with random phases generated by computer.

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