Frequency Domain Phase Research Articles

Near-infrared phase cancellation instrument for fast and accurate localization of fluorescent heterogeneity

Near-infrared (NIR) diffuse optical imaging has become a promising method for noninvasive in vivo detection of breast cancer with intrinsic chromophores. Recent developments in molecular specific targeting fluorescent contrast agents offer high tumor to normal tissue contrast, and are capable of selectively labeling various precancer/cancer signatures, thus enhancing both the sensitivity and specificity of cancer detection. To detect a subsurface tumor labeled by fluorescent contrast agents, we have developed a phase cancellation imaging system for fast localization of fluorescent object embedded several centimeters deep inside the turbid media. The instrument is a frequency domain (50 MHz) phase modulation system with dual out-of-phase sources. The excitation wavelength is 780 nm and the fluorescence photons are collected through an 830±10 nm band-pass filter. Localization of fluorescent objects inside the scattering media is accurate using a phase cancellation device. The localization error for a 5 mm diameter sphere filled with 1 nanomole fluorescent dye and 3 cm deep inside the turbid media is about 2 mm. The accuracy of the localization suggests that this system could be helpful in guiding clinical fine-needle biopsy, and would benefit the early detection of breast tumors.

Wavelet depulsing of ultrasound echo sequences

Methods and associated apparatuses for imaging a target. An echo sequence image of the target is acquired (10) and a log spectrum of at least a portion of the echo sequence image is computed. A point spread function is estimated (14) by one of two methods. According to the first method, a low-resolution wavelet projection of the echo sequence log spectrum (22) is used as an estimate of the log spectrum of the point-spread function. According to the second method, an outlier-resistant wavelet transform of the echo sequence log spectrum is effected (44), followed by soft-thresholding (46) and an inverse wavelet transform (48). Under both methods, a frequency domain phase of the point spread function also is estimated. The relevant portion of the echo sequence image is deconvolved using the estimated point spread function.

History and development of frequency domain methods in experimental modal analysis

The paper presents the most important key dates of the history and the development of the Frequency Domain Methods in Experimental Modal Analysis. First, the mathematical foundations are discussed, then the Phase Resonance Method is presented, and finally the different algorithms of Frequency Domain Phase Separation Methods are considered. They start with the SDOF Methods followed by the MDOF Methods in the form of Forced Response Modal Methods and FRF Modal and Polynomial Methods, completed by the recent developments and trends of Frequency Domain Modal Identification Methods.

Complete pulse characterization: measurements of linear and nonlinear properties

We present a frequency-domain phase measurement technique coupled with a numerical chirp processing of the recorded sonogram to realise a pulse characterisation. Applications to the propagation of ultrashort pulses in linear and nonlinear media are investigated. Calibration of the experimental setup is performed using spectral interferometry technique. Results on linear dispersion glass and Kerr effect in vitreous samples are presented.

Feedback-controlled femtosecond pulse shaping

We describe the experimental implementation of feedback-optimized femtosecond laser pulse shaping. A frequency-domain phase shaper is combined with different pulse characterization methods and appropriate optimization algorithms to compensate for any phase deviation. In particular, bandwidth-limited, amplified laser pulses are achieved by maximizing the second-harmonic generation (SHG) of the shaped laser pulses with the aid of an evolutionary algorithm. Real-time measurement of the absolute phases is achieved with spectral interferometry where the reference pulse is characterized by FROG, the so-called TADPOLE method. Using the complete electric field as feedback, arbitrary laser pulse shapes can be optimally generated in two different ways. First, a local convergence algorithm can be used to apply reliable and accurate spectral chirps. Second, an evolutionary algorithm can be employed to reach specific temporal profiles.

Major World Equity Market Interdependence a Decade After the 1987 Crash: Evidence From Cross Spectral Analysis

Several studies have focused on the pre‐ post‐October 1987 crash. Results indicate that major market equity correlations rose during the crash period. Cross spectral analysis is applied to six of the G‐7 markets to determine whether frequency domain correlations have increased post‐crash relative to the pre‐crash period. The results indicate that correlations have increased for most of the markets studied. Most striking are the increased post‐crash correlations among the three European markets, in light of the European Union. Additional evidence shows mixed results regarding frequency domain phase leads among the markets.

Noise robust one-dimensional blind deconvolution of medical ultrasound images

Recently, several blind cepstral deconvolution methods for medical ultrasound images were compared experimentally. The results indicated that the generalized cepstrum or the complex cepstrum with phase unwrapping give the blind homomorphic deconvolution algorithms with the best performance. However, the frequency domain phase unwrapping for pulse estimation, which is an essential part of both methods, is sensitive to the sensor noise when the values of the spectrum are small due to the randomness of the tissue response. The noise introduces abrupt changes in the phase. The phase degradation due to the noise causes variable spatial and gray scale resolution in image sequences following deconvolution. This paper introduces a noise robust Bayesian phase unwrapping method using a noncausal Markov random chain model. The prior regularizing term accounts for the noise and smoothes the phase. The phase unwrapping is formulated as a least mean square optimization problem. The optimization is done noniteratively by solving a difference equation using the cosine transform. The resulting improvement in radial and lateral blind deconvolution is demonstrated on six short ultrasound image sequences recorded in vitro or in vivo.

Accurate Measurements of the Zero-Dispersion Wavelength in Optical Fibers.

We have developed a frequency-domain phase shift system for measuring the zero-dispersion wavelength and the dispersion slope of single-mode optical fibers. A differential phase shift method and nonlinear four-wave mixing technique were also investigated. The frequency-domain phase shift method is used to produce Standard Reference Materials that have their zero-dispersion wavelengths characterized with an expanded uncertainty (k = 2) of ± 0.060 nm.

Distance distributions from the tyrosyl to disulfide residues in the oxytocin and [Arg8]-vasopressin measured using frequency-domain fluorescence resonance energy transfer.

We have examined the fluorescence intensity decays of oxytocin and [Arg8]-vasopressin resulting from the single tyrosyl residue in each peptide, and the intensity decay of the Asu1,6-analogues in which the disulfide bridge is substituted by a CH2-CH2 bridge. Viscosity-dependent steady state and intensity decay measurements indicated that fluorescence resonance energy transfer (FRET) from tyrosyl phenol to the disulfide bridge is responsible for the decrease in fluorescence relative to the Asu-analogues. The frequency-domain phase and modulation data for the tyrosyl donor were interpreted in terms of fluorescence resonance energy transfer (FRET) to the weakly absorbing disulfide bridge and a distribution of donor-to-acceptor distances. Energy transfer efficiencies were determined from both time-resolved and steady-state measurements. Fitting the frequency-domain phase and modulation data to a Gaussian distance distribution indicated that the average inter-chromophoric distance (Rav) is similar in both compounds, Rav = 7.94 A for oxytocin and Rav = 8.00 A for vasopressin. However, the width of the distance distribution is narrower for vasopression (hw = 2.80 A) than for oxytocin (hw = 3.58 A), which is consistent with restriction of the tyrosine phenol motion due to its stacking wih the Phe3 side chain of vasopressin. Finally, the recovered distance distribution functions are compared with histograms describing the distance between the chromophores during the course of long, in vacuo, molecular dynamics runs using the computer program CHARMm and the QUANTA 3.0 parameters.

Subpicosecond pulse amplification in semiconductor laser amplifiers: theory and experiment

We present a phenomenological model of subpicosecond pulse evolution in semiconductor laser amplifiers, which includes carrier heating effect, gain dispersion, gain saturation, and three kinds of self-phase modulations (SPM). The results obtained from this model are applied to and found to agree very well with experimental measurements of spectral distortions and time-resolved gain on a semiconductor laser amplifier with 460-fs and 2-ps input pulses. The device parameters that are used to match the experimental results are within a reasonable range, either suggested by previous experiments or by published calculations, The results show that the evolution of the pulses and their spectra is sensitively dependent on the input pulse shape and on a variety of time domain and frequency domain amplitude and phase shaping effects. Matching the theory to the experimental data suggests that among the possible causes of the carrier heating two-photon absorption (TPA) is the most important. This effect of TPA needs to be included to properly account for the observed dependence of the carrier heating gain reduction on the pulse length. By examining separately the contribution of the corresponding terms, we also prove the importance of SPM due to the carrier heating and to the instantaneous nonlinear index in shaping the output spectrum. We compare our model with Agrawal's theory, which is valid for pulses of tens of picosecond duration, and find large differences for subpicosecond pulses. For 2-ps pulses, on the other hand, the differences are fewer and less dramatic. The good agreement of the new model with experiments will now allow diagnostics and predictions of pulse evolution in semiconductor optical amplifiers from the picosecond to the subpicosecond range.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Frequency domain phase measurement of ultrashort light pulses. Effect of noise

We study the effect of fluctuations of the input pulse on our method of phase measurement of ultrashort light pulses in the frequency domain. We show that the method is nearly insensitive to fluctuations in the input pulse. An estimate is given for the second order correction that results. In our derivation we employ Glauber's P representation, so that our result holds for all classical states and those quantum ones that have P representation. Some results that we obtain are not restricted to our particular case, but are still applicable to other correlation measurements.

Digitization of electrocardiograms by desktop optical scanner

The fidelity of a semiautomated technique for converting paper electrocardiogram (ECG) tracings to digital form by optical scanning was examined. Sample tracings from one nonmechanical and three mechanical ECG writers (recorders) were used. The optically scanned signals were compared with the digitized version (402 Hz, 12-bit precision) of the original analog signals using time- and frequency-domain correlation coefficients and root mean square error. A total of 261 QRS complexes and 207 RR intervals were examined in 21 leads acquired from 8 patients. When data were low-pass filtered at 25 Hz, the correlation coefficients for the 261 QRS complexes were 0.997 +/- 0.005 (mean +/- SD) for the time domain data, 0.992 +/- 0.010 for the complex frequency domain (amplitude and phase) data, and 0.998 +/- 0.002 for the power spectrum. The corresponding correlations for the 207 RR intervals were 0.993 +/- 0.008, 0.992 +/- 0.008, and 0.993 +/- 0.009. The RMS errors, normalized for signal amplitude, were 2.62 +/- 1.28 (percent +/- SD) for QRS complexes and 1.82 +/- 0.87 for RR intervals. The correlations for the mechanical ECG recorder tracings were the same or better than those of the nonmechanical recorder, and the RMS errors were generally smaller. When data were low-pass filtered at 105 Hz, the correlation coefficients ranged from 0.984 to 0.996 for the QRS complexes and 0.982 to 0.988 for RR intervals. Root mean square errors were 4.54 +/- 2.03 and 2.38 +/- 1.14, respectively. For purposes of arrhythmia analysis by QRS classification, digitization of ECG signals by optical scanning appears equivalent to acquisition via standard analog-to-digital conversion.

On frequency-domain and time-domain phase unwrapping

Time-domain phase unwrapping of analytic or complex functions of time is an unavoidable operation when processing such signals within an FM-modeling framework or when attempting to establish the instantaneous frequency of such signals. With the help of an alternate derivation of his equations, Tribolet's frequency-domain phase unwrapping algorithm is easily rewritten for time-domain application. The time derivative of the argument of the signal, a quantity needed in these modified equations, is developed and furthermore recognized to be proportional to the instantaneous frequency of the signal.

Measurement of RF signal generator phase noise using a one-generator delay-line method

A technique is described which utilizes a single generator and a delay line for the measurement of frequency-domain phase noise (£<(f)) in synthesized signal generators. Terms are defined and equations developed for theory and calculations of normalized phase-noise sideband power in a 1-Hz bandwidth offset 20 kHz from signal frequencies of interest. The system described covers the range from 0.45 to 2000 MHz. The function and contribution of each component in the measurement system is presented. Advantages of this method are discussed and a brief error analysis is given.

Two-dimensional IIR filter design with magnitude and phase error criteria

Two-dimensional IIR filters are designed using an error criterion consisting of the weighted sum of magnitude, phase, and stability errors, thereby extending the spectral factorization-based method to complex approximation. The weights are adjusted to effectively constrain stability while minimizing a weighted sum of frequency domain magnitude and phase errors. We use a derivative-free variant of the Marquardt optimization algorithm augmented by a one-dimensional search. We present examples of approximation of both linear and nonlinear phase ideal transfer functions, and conduct comparisons across a range of numerator and denominator orders, from FIR to all-pole, while keeping the total number of coefficients approximately constant. We find that the designed IIR filters offer better magnitude response in the case of linear phase ideal functions, even considering coefficient reflection symmetry, but of course, the FIR filter has the better (zero) phase error. When the ideal transfer function has nonlinear phase, and hence no coefficient reflection symmetry, we find that the designed IIR filter can perform better than the FIR filter with regard to both magnitude and phase error, when magnitude error is weighted more heavily than phase error.

Harmonic Analysis of SAW Transducers

The excitation function of an interdigital transducer (IDT) is determined by measuring the discrete impulse response, taking into account the first seven harmonics of the frequency domain. Using a time segregation method, all non-SAW time-domain components are suppressed. A single transducer is isolated by a method of autodeconvolution that utilizes a theoreticalIy derived phase function. The resulting excitation function provides experimental insight into the operation of IDT electrodes and compares well with the theoretical response of Smith and Pedler. The basic analysis technique can be used for other configurations, once the frequency-domain phase response of one transducer is known.

Time-Domain Configuration of Certain Narrow Frequency-Bandwidth Pulses

In mode-locked laser studies and other applications, it is desirable to derive relationships giving the time-domain length and the properties of the waveform under the envelope for pulses presenting narrow spectral widths, without performing inverse-Fourier-transform calculations. The method presented is based on an approximate expression for the transform of a sinusoid with variable frequency, and leads to simple rules for pulse-length evaluation from the frequency-domain phase function. If the phase function has no inflection points, the length is approximately equal to the range covered by the slope of the phase function, and the actual waveform sweeps monotonically in frequency. When inflection points occur, the pulse comprises several superimposed envelopes, each modulating a monotonically swept sinusoid. The effect of dispersive filters is also analyzed. Illustrative examples are discussed numerically.