Some experiments in partially coherent imaging and modulation transfer function evaluation

A relatively simple and inexpensive scanning optical system is described as a versatile tool for the demonstration and analysis of a variety of optical imaging properties. Some examples of partially coherent imaging and modulation transfer function (MTF) evaluation are presented.     

Detection of temporal gaps in bandlimited noise: effects of variations in bandwidth and signal-to-masker ratio

Thresholds were measured for the detection of a temporal gap in a bandlimited noise signal presented in a continuous wideband masker, using an adaptive forced-choice procedure. In experiment I the ratio of signal spectrum level to masker spectrum level (the SMR) was fixed at 10 dB and gap thresholds were measured as a function of signal bandwidth at three center frequencies: 0.4, 1.0, and 6.5 kHz. Performance improved with increasing bandwidth and increasing center frequency. For a subset of conditions, gap threshold was also measured as bandwidth was varied keeping the upper cutoff frequency of the signal constant. In this case the variation of gap threshold with bandwidth was more gradual, suggesting that subjects detect the gap using primarily the highest frequency region available in the signal. At low center frequencies, however, subjects may have a limited ability to combine information in different frequency regions. In experiment II gap thresholds were measured as a function of SMR for several signal bandwidths at each of three center frequencies: 0.5, 1.0, and 6.5 kHz. Gap thresholds improved with increasing SMR, but the improvement was minimal for SMRs greater than 12-15 dB. The results are used to evaluate the relative importance of factors influencing gap threshold.     

Detection of silent temporal gaps in sinusoidal markers

Gap detection thresholds were measured by forced-choice procedure for conditions where the duration of a silent gap was varied adaptively between pairs of sinusoidal markers of the same or different frequency. Frequencies of the first sinusoid in a pair of markers ranged from F1 = 500 to 4000 Hz. Second-sinusoid marker frequencies F2 included F1 = F2, and usually frequencies 2%, 5%, 24%, and 50% higher than F1. In preliminary studies the role of presentation level (E/N0) on gap detection was considered. Preliminary data revealed confounding extraneous factors arising from gating transients and from overall stimulus (i.e., markers + gap) and/or masker duration cues. In the main experiments, the contributions of these extraneous cues were evaluated with experimental designs aimed at identifying and minimizing the confounding roles of these cues in gap detection. For conditions where extraneous gating transient cues were minimized (by presenting the sinusoidal markers in a continuous noise masker with random onset phase for the second sinusoid in every pair of markers) and overall stimulus duration cues were diminished (by randomizing the duration of each marker independently), gap detection thresholds increased from 5 to 90 ms as the frequency separation between F1 and F2 was increased by half an octave. When the gap detection thresholds were treated as filter attenuation values by normalizing and converting the data into decibels, the data were closely fit by the roex filter model. On average, the listeners' performances were modeled well by a constant-percentage (7%) bandwidth filter centered on F1.     

The effects of frequency region and level on the temporal modulation transfer function

Temporal modulation transfer functions (TMTFs) were measured using narrow-band AM and QFM noises with upper spectral edges from 0.6 to 4.8 kHz, and spectrum levels of 10 and 40 dB SPL. The cutoff frequency of the TMTF increases as the upper spectral edge is increased up to 4.8 kHz at low levels, and is constant at higher levels. Sensitivity increases with bandwidth if frequency region is constant. In a second experiment, these results were compared to predictions of a model incorporating peripheral and central limitations to modulation detection. To obtain an estimate of peripheral filtering, frequency selectivity was measured using the notched-noise method, with probe frequencies and levels chosen to parallel those in the first experiment. The TMTF data were then predicted using the model. Predicted cutoff frequencies as a function of the upper spectral edge of the test stimulus were lower than but parallel to those of the subjects at the lower stimulus level. The model predicted only a slight increase in cutoff frequency with level, and thus predicted an increase in cutoff frequency with frequency region at the higher level as well, in contrast to the measured data. These results suggest that there are peripheral and central limitations to temporal resolution, but the psychoacoustically derived auditory filter may be only an indirect measure of peripheral filtering, and/or a more complex model may be needed.     

The detection of temporal gaps as a function of frequency region and absolute noise bandwidth.

Temporal gap detection was measured as a function of absolute signal bandwidth at a low-, a mid-, and a high-frequency region in six listeners with normal hearing sensitivity. Gap detection threshold decreased monotonically with increasing stimulus bandwidth at each of the three frequency regions. Given conditions of equivalent absolute bandwidth, gap detection thresholds were not significantly different for upper cutoff frequencies ranging from 600 to 4400 Hz. A second experiment investigated gap detection thresholds at two pressure-spectrum levels, conditions typically resulting in substantially different estimates of frequency selectivity. Estimates of frequency selectivity were collected at the two levels using a notched-noise masker technique. The gap threshold-signal bandwidth functions were almost identical at pressure-spectrum levels of 70 dB and 40 dB for the two subjects in experiment II, while estimates of frequency selectivity showed poorer frequency selectivity at the 70-dB level than at 40 dB. Data from both experiments indicated that gap detection in bandlimited noise was inversely related to signal bandwidth and that gap detection did not vary significantly with changes in signal frequency over the range of 600 to 4400 Hz. Over the range of frequencies investigated, the results indicated no clear relation between gap detection for noise stimuli and peripheral auditory filtering.     

Second-order temporal modulation transfer functions

Detection thresholds were measured for a sinusoidal modulation applied to the modulation depth of a sinusoidally amplitude-modulated (SAM) white noise carrier as a function of the frequency of the modulation applied to the modulation depth (referred to as f'm). The SAM noise acted therefore as a "carrier" stimulus of frequency fm, and sinusoidal modulation of the SAM-noise modulation depth generated two additional components in the modulation spectrum: fm-f'm and fm+f'm. The tracking variable was the modulation depth of the sinusoidal variation applied to the "carrier" modulation depth. The resulting "second-order" temporal modulation transfer functions (TMTFs) measured on four listeners for "carrier" modulation frequencies fm of 16, 64, and 256 Hz display a low-pass segment followed by a plateau. This indicates that sensitivity to fluctuations in the strength of amplitude modulation is best for fluctuation rates f'm below about 2-4 Hz when using broadband noise carriers. Measurements of masked modulation detection thresholds for the lower and upper modulation sideband suggest that this capacity is possibly related to the detection of a beat in the sound's temporal envelope. The results appear qualitatively consistent with the predictions of an envelope detector model consisting of a low-pass filtering stage followed by a decision stage. Unlike listeners' performance, a modulation filterbank model using Q values > or = 2 should predict that second-order modulation detection thresholds should decrease at high values of f'm due to the spectral resolution of the modulation sidebands (in the modulation domain). This suggests that, if such modulation filters do exist, their selectivity is poor. In the latter case, the Q value of modulation filters would have to be less than 2. This estimate of modulation filter selectivity is consistent with the results of a previous study using a modulation-masking paradigm [S. D. Ewert and T. Dau, J. Acoust. Soc. Am. 108, 1181-1196 (2000)].     

Dynamic modulation transfer function: a method to characterize the temporal performance of liquid-crystal displays

A method to measure the dynamic modulation transfer function (DMTF) of a liquid-crystal display (LCD) is proposed to characterize its performance when rendering motion images. The method includes a measurement system to capture the temporal luminance variation of a LCD while using a well-designed input data sequence and a simulation model based on smooth pursuit eye tracking and temporal light integration at the human retina. It predicts the perceived performance of a moving sine wave pattern on a LCD and subsequently calculates the DMTF. With this approach, several technologies to reduce motion blur were evaluated and discussed.     

Detection of temporal gaps in sinusoids by normally hearing and hearing-impaired subjects

A two-alternative forced-choice task was used to measure psychometric functions for the detection of temporal gaps in a 1-kHz, 400-ms sinusoidal signal. The signal always started and finished at a positive-going zero crossing, and the gap duration was varied from 0.5 to 6.0 ms in 0.5-ms steps. The signal level was 80 dB SPL, and a spectrally shaped noise was used to mask splatter associated with the abrupt onset and offset of the signal. Two subjects with normal hearing, two subjects with unilateral cochlear hearing loss, and two subjects with bilateral cochlear hearing loss were tested. The impaired ears had confirmed reductions in frequency selectivity at 1 kHz. For the normal ears, the psychometric functions were nonmonotonic, showing minima for gap durations corresponding to integer multiples of the signal period (n ms, where n is a positive integer) and maxima for durations corresponding to (n - 0.5) ms. For the impaired ears, the psychometric functions showed only small (nonsignificant) nonmonotonicities. Performance overall was slightly worse for the impaired than for the normal ears. The main features of the results could be accounted for using a model consisting of a bandpass filter (the auditory filter), a square-law device, and a sliding temporal integrator. Consistent with the data, the model demonstrates that, although a broader auditory filter has a faster transient response, this does not necessarily lead to improved performance in a gap detection task. The model also indicates that gap thresholds do not provide a direct measure of temporal resolution, since they depend at least partly on intensity resolution.     

Temporal gaps in noise and sinusoids

The ability of human observers to detect partially filled or completely silent intervals (gaps) was measured using a variety of different waveforms. The slopes of the psychometric functions for gap detection using broadband noise are dependent upon the amount of noise remaining during the gap. For completely silent intervals, the psychometric function covers a range of only 2 ms, but the psychometric functions for partially filled intervals are less steep. The detection of gaps in narrow-band noise (surrounded by complementary band-reject maskers) is strongly influenced by the signal-to-noise ratio. The signal bandwidth and center frequency also influence detectability. Gap detection improved as signal bandwidth increased, and detection improved when signal bands containing gaps were centered at higher frequencies. Detection of gaps in single components of a 21-component, equal-amplitude complex also showed lower thresholds as the frequency of the component containing the gap increased. Increasing the number of components in the complex that contained the gap improved the detectability of the gap, more so when the gaps were all presented at the same time (synchronous condition). Uncertainty about the temporal position of the gap within the observation interval made the gap more difficult to detect. This temporal uncertainty effect occurred for gaps in broadband noise, in narrow-band noise, and in sinusoidal waveforms.     

Level-dependent changes in detection of temporal gaps in noise markers by adults with normal and impaired hearing

Compression in the basilar-membrane input-output response flattens the temporal envelope of a fluctuating signal when more gain is applied to lower level than higher level temporal components. As a result, level-dependent changes in gap detection for signals with different depths of envelope fluctuation and for subjects with normal and impaired hearing may reveal effects of compression. To test these assumptions, gap detection with and without a broadband noise was measured with 1,?000-Hz-wide (flatter) and 50-Hz-wide (fluctuating) noise markers as a function of marker level. As marker level increased, background level also increased, maintaining a fixed acoustic signal-to-noise ratio (SNR) to minimize sensation-level effects on gap detection. Significant level-dependent changes in gap detection were observed, consistent with effects of cochlear compression. For the flatter marker, gap detection that declines with increases in level up to mid levels and improves with further increases in level may be explained by an effective flattening of the temporal envelope at mid levels, where compression effects are expected to be strongest. A flatter effective temporal envelope corresponds to a reduced effective SNR. The effects of a reduction in compression (resulting in larger effective SNRs) may contribute to better-than-normal gap detection observed for some hearing-impaired listeners.     

The modulation transfer function in the hologram copying process

The concept of MTF is introduced to analyze and describe consistently the hologram copying process, considering the original hologram as a volume hologram. The effect of the copying condition on the quality of the replica is expressed quantitatively in terms of the MTF. It turns out that holograms can be copied most successfully when the copying beam is oriented parallel to the original reference beam. The theoretical prediction is experimentally confirmed.     

Apparent transfer function for partially coherent optical information processing

In this paper, the general formulations of the apparent transfer function for the partially coherent optical processor will be derived. Although these formulas show that the apparent transfer function is dependent upon the degree of spatial and temporal coherence, there is actually more variability in the spatial coherence. We note that the obtained formulas may also be used as a criterion in the selection of source size and spectral bandwidth of an incoherent light source. Thus a specific optical information processing operation can be carried out with an incoherent source.     

Analysis of noise barrier overlap gaps

Sound propagation through the gap produced by two parallel vertical barriers with overlapped ends is formulated for traffic noise sources. The analysis identifies both source and receiver regions according to the mechanisms that influence noise propagation in the vicinity of an overlap gap. A method to account for the contributions from the various source regions for a given receiver location is described. The derived method can be implemented using various equations for sound propagation. The results of using equations approved by the United States Federal Highway Administration for traffic noise propagation are given. Uncalibrated predictions are compared with field measurements for up to 30 receiver positions from each of four overlap gaps. The relative importance of contributions from reflected rays to the noise levels at receiver positions is given. The analysis confirms the initial hypothesis that a commonly used strategy of overlapping barriers by an amount equal to two or three times the overlap width is useful for controlling line-of-sight propagation but ignores the substantial effect of reflections.     

Two-dimension optical low frequency de-emphasis of the modulation transfer function

Optical configurations providing low spatial frequency de-emphasis for incoherently illuminated two-dimensional objects, based on non-interacting two-pupils systems are analyzed. Design of optical pupils providing the necessary band-pass characteristics in all spatial directions is presented together with experimental results testing the procedure.     

Monaural and interaural temporal modulation transfer functions measured with 5-kHz carriers

Temporal modulation transfer functions (TMTFs) were measured for detection of monaural sinusoidal amplitude modulation and dynamically varying interaural level differences for a single set of listeners. For the interaural TMTFs, thresholds are the modulation depths at which listeners can just discriminate interaural envelope-phase differences of 0 and 180 degrees. A 5-kHz pure tone and narrowband noises, 30- and 300-Hz wide centered at 5 kHz, were used as carriers. In the interaural conditions, the noise carriers were either diotic or interaurally uncorrelated. The interaural TMTFs with tonal and diotic noise carriers exhibited a low-pass characteristic but the cutoff frequencies changed nonmonotonically with increasing bandwidth. The interaural TMTFs for the tonal carrier began rolling off approximately a half-octave lower than the tonal monaural TMTF (approximately 80 Hz vs approximately 120 Hz). Monaural TMTFs obtained with noise carriers showed effects attributable to masking of the signal modulation by intrinsic fluctuations of the carrier. In the interaural task with dichotic noise carriers, similar masking due to the interaural carrier fluctuations was observed. Although the mechanisms responsible for differences between the monaural and interaural TMTFs are unknown, the lower binaural TMTF cutoff frequency suggests that binaural processing exhibits greater temporal limitation than monaural processing.     

TDICCD调制传递函数检测及评价方法研究

MTF是评价TDICCD成像质量的重要参数 ,基于对影响TDICCD成像质量诸多因素的考虑 ,提出TDICCD的MTF检测及评价方法 ,并对这种方法进行了理论分析 ,理论分析与实验结果相吻合。在检测过程中 ,采用局部视场扫描测量方法 ,测量 96级TDICCD的MTF。     

Wave numbers of partially filled rectangular waveguide

An approximate method is proposed for determination of the wave numbers of a partially filled rec angular waveguide. The method employs the eigenvalues and parameters of Mathieu equations. The natural H-and E-waves of a partially filled rectangular waveguide are expressed in terms of Mathieu functions. Numerical results of waven number studies are presented and interpreted graphically.     

Eigenfunctions of a partially filled rectangular waveguide

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 12, pp. 1385–1390, December, 1990.     

Device for measurement of the modulation transfer function of photographic materials

This paper introduces a device for measurement of the modulation transfer function of photographic materials. The device is a realization of the method based on the incoherent imaging of a rectangular parallel wave grating with continuously varying spatial frequency in space to the photographic material under test by means of an auxiliary photographic objective of known properties. The theory of that method is shortly introduced, the principle of measurement is explained, the realized device is described and evaluated and some results of measurement are shown.     

Average modulation transfer function of line-array fiber-optic image bundles

The image quality evaluation in fiber-optic image bundles was addressed by the modulation transfer function(MTF).With the definition of the contrast transfer function(CTF),the MTF model of line-array fiber-optic image bundles was established and analyzed numerically.The average MTF was carefully evaluated by considering the influence of phase match on the MTF between input pattern and fiber-optic image bundles.In this paper,the average MTF is mean arithmetical value on the MTFs of eight different phases.The results show that,for certain fiber diameter and spatial frequency,the relationship between the core diameter and the average MTF is inverse proportion; for certain fiber cladding thickness,the relationship between the core diameter and the average MTF is also inverse proportion.And at Nyquist frequency,the MTF value is near 0.5.