Correction of wave-front retrieval errors caused by the imperfect collimation of reference beam in phase-shifting interferometry

In phase-shifting interferometry (PSI) the standard wave retrieval formulae are usually derived based on the condition of a plane reference beam normal to the recording plane. In practice, however, the reference wave may be a spherical wave of large radius or even have a slight inclination at the same time due to the imperfect collimation and coaxality of the optical system, and this fact will introduce phase distortion for the reconstructed object wave-front. A simple digital processing algorithm without any additional measurements is proposed to determine the unknown parameters of the spherical reference wave and then correct the object wave errors reconstructed with standard wave retrieval formulae. The effectiveness of this method is verified by a series of computer simulations, and its limitation is also discussed.     

Applications of DNP-NMR for the measurement of heteronuclear T1 relaxation times

Measurement of heteronuclear spin-lattice relaxation times is hampered by both low natural abundance and low detection sensitivity. Combined with typically long relaxation times, this results in extended acquisition times which often renders the experiment impractical. Recently a variant of dynamic nuclear polarisation has been demonstrated in which enhanced nuclear spin polarisation, generated in the cryo-solid state, is transferred to the liquid state for detection. Combining this approach with small flip angle pulse trains, similar to the FLASH-T(1) imaging sequence, allows the rapid determination of spin-lattice relaxation times. In this paper we explore this method and its application to the measurement of T(1) for both carbon-13 and nitrogen-15 at natural abundance. The effects of RF inhomogeneity and the influence of proton decoupling in the context of this experiment are also investigated.     

Measurement of relaxation times by phase-modulated ultrashort light pulses

In the measurement of relaxation times of nonlinear response of media by means of ultrashort light pulses the resolution time is determined by the pulse duration. Here we show that using phase-modulated pulses the resolution can be as high as the coherence time $\text{τ}{}_{\mathrm{c}}\text{≈}\text{1}\text{Δν}$ (Δν is the width of pulse spectrum in Hz) which is less than the pulse duration.     

Bayesian estimation of relaxation times T(1) in MR images of irradiated Fricke-agarose gels

The authors present a novel method for processing T(1)-weighted images acquired with Inversion-Recovery (IR) sequence. The method, developed within the Bayesian framework, takes into account a priori knowledge about the spatial regularity of the parameters to be estimated. Inference is drawn by means of Markov Chains Monte Carlo algorithms. The method has been applied to the processing of IR images from irradiated Fricke-agarose gels, proposed in the past as relative dosimeter to verify radiotherapeutic treatment planning systems. Comparison with results obtained from a standard approach shows that signal-to noise ratio (SNR) is strongly enhanced when the estimation of the longitudinal relaxation rate (R1) is performed with the newly proposed statistical approach. Furthermore, the method allows the use of more complex models of the signal. Finally, an appreciable reduction of total acquisition time can be obtained due to the possibility of using a reduced number of images. The method can also be applied to T(1) mapping of other systems.     

Methodology for the measurement and analysis of relaxation times in proton imaging

Measurements of proton T1 and T2 were performed on GdCl3 solutions (20 less than T2 less than 500 msec, 90 less than T1 less than 1000 msec) on large-bore NMR imaging systems operating at 1.0T and 1.5T. CPMG multi-echo (ME), multiple saturation recovery (MSR) and modified fast inversion recovery (MFIR) pulse sequences as well as a sequence that combines and interleaves T1 and T2 weighted data acquisition (which we call "multiple saturation-recovery multiple-echo" (MSRME) were used. The relaxation data are compared to those obtained on a small bore NMR spectrometer operated at 1.5T. T1 and T2 values for the solutions were found to be the same within 10% for the two fields. Reproducibility of measurements of T1, T2 and the unnormalized spin density of the solutions was better than 5%. Systematic errors, amenable to correction through calibration, are noted in the imager T1 and T2 values. T1 and T2 values for some typical neural tissues at 1.5T and body tissue at 1.0T for human volunteers were obtained and are tabulated.     

Two-exponential analysis of spin-spin proton relaxation times in MR imaging using surface coils

Proton relaxation time measurements were performed on a standard whole body MR imager operating at 1.5 T using a conventional surface coil of the manufacturer. A combined CP/CPMG multiecho, multislice sequence was used for the T1 and T2 relaxation time measurements. Two repetition times of 2000 ms (30 echoes) and 600 ms (2 echoes) with 180 degrees-pulse intervals of 2 tau = 22 ms were interleaved in this sequence. A two-exponential T2 analysis of each pixel of the spin-echo images was computed in a case of an acoustic neurinoma. The two-exponential images show a "short" component (T2S) due to white and gray matter and a "long" component (T2S) due to the cerebrospinal fluid. In the fatty tissue two components with T2S = 35 +/- 3 ms and T2L = 164 +/- 7 ms were measured. Comparing with Gd-DTPA imaging the relaxation time images show a clear differentiation of vital tumor tissue and cerebrospinal fluid.     

Design of self-refocused pulses under short relaxation times

The effect of using self-refocused RF pulses of comparable duration to relaxation times is studied in detail using numerical simulation. Transverse magnetization decay caused by short T2 and longitudinal component distortion due to short T1 are consistent with other studies. In order to design new pulses to combat short T1 and T2 the relaxation terms are directly inserted into the Bloch equations. These equations are inverted by searching the RF solution space using simulated annealing global optimization technique. A new T2-decay efficient excitation pulse is created (SDETR: single delayed excursion T2 resistive) which is also energy efficient. Inversion pulses which improve the inverted magnetization profile and achieve better suppression of the remaining transverse magnetization are also created even when both T1 and T2 are short. This is achieved, however, on the expense of a more complex B1 shape of larger energy content.     

The choice of optimal parameters for measurement of spin-lattice relaxation times. IV. Effects of nonideal pulses

Optimum pulse spacing times are determined for measurements of spin-lattice relaxation times, T,, when the radiofrequency pulses deviate from their ideal values of 90 and 180°. The performance of the fast inversion-recovery technique in the presence and absence of separate estimates of the values of the effective flip angles resulting from nonideal rf pulses are compared, using as the criterion the total experimental time required to achieve a specified precision in the estimate of T1. The important assumptions made are (1) that the cosine of the effective flip angles are either unknown or can be estimated in a separate experiment, (2) that M(∞) and T₁ are unknown, and (3) that an interval of uncertainty is known for the value of T₁.     

On the measurement of multi-component T2 relaxation in cartilage by MR spectroscopy and imaging

The multicomponent T₂ relaxation in bovine nasal cartilage (BNC) was investigated by nuclear magnetic resonance spectroscopy using the Carr-Purcell-Meiboom-Gill (CPMG) sequence and microscopic magnetic resonance imaging (μMRI) method using a CPMG-SE imaging sequence. All experimental data were analyzed by the non-negative least square (NNLS) procedure. Only one T₂ component was found in BNC by both experimental methods (about 113 and 170 ms before and after being enzymatically digested by trypsin). Several experimental and specimen-related factors were investigated in this study, and it was found that some of them could produce artificial multi-component T₂, including the use of the standard MSME imaging sequence at certain imaging gradients.     

Correction for random errors in infrared integral-intensity measurement

The effects of random errors in relation to working conditions are examined for various integral absorption functions. It is shown that the mean transmission ¯T should lie in the range 0.3 to 0.7 as regards minimization of the random errors in the integral quantities; this corresponds to transmission at band peaks T_M of about 0.10. Optimum conditions are also deduced for extrapolated measurements and for structureless bands. Integral intensities can be measured to much higher precision if the optimal conditions are used.     

Changes of relaxation times T1 and T2 in rat tissues after biopsy and fixation

NMR spectroscopical measurements of relaxation times were conducted on muscle, intestine, fatty tissue and cerebral cortex and white matter of the rat at various time intervals following removal of the tissue. It appeared that most tissues can be stored at 4 degrees C up to 24 hours without noticeable effects on NMR relaxation parameters. Exceptions are the T2 of muscle and the T1 and T2 of intestine, which tended to change in the first hour after biopsy. Relaxation parameters change considerably after fixation of the tissues. Therefore the effects of fixation have to be taken into account when carrying out NMR measurements on fixed tissues.     

The choice of optimal parameters for measurement of spin-lattice relaxation times. III. Mathematical preliminaries for nonideal pulses

An earlier analysis for the optimization of T₁ measurements is extended to allow for an initially unknown effective flip angle. In contrast to other studies which rely on simulation, this and the following paper deal with a case in which the signal-to-noise ratio is sufficiently great so that a linear least-squares analysis is possible. In practice this is a minor restriction. The equations that allow for optimization are derived and discussed. The least-squares analysis not only allows an a priori optimization of T₁ measurements but also provides an a posteriori confidence interval for the T₁ estimate. Detailed results that follow from the formalism of this paper are presented and discussed in a companion paper.     

An MR imaging method for simultaneous measurement of gaseous diffusion constant and longitudinal relaxation time

A magnetic resonance imaging method for simultaneous and accurate determination of gaseous diffusion constant and longitudinal relaxation time is presented. The method is based on direct observation of diffusive motion. Initially, a slice-selective saturation of helium-3 (3He) spins was performed on a 3He/O2 phantom (9 atm/2 atm). A time-delay interval was introduced after saturation, allowing spins to diffuse in and out of the labeled slice. Following the delay interval a one-dimensional (1-D) projection image of the phantom was acquired. A series of 21 images was collected, each subsequent image having been acquired with an increased delay interval. Gradual spreading of the slice boundaries due to diffusion was thus observed. The projection profiles were fit to a solution of the Bloch equation corrected for diffusive motion. The fitting procedure yielded a value of D3He = 0.1562+/-0.0013 cm2/s, in good agreement with a measurement obtained with a modified version of the standard pulsed-field gradient technique. The method also enabled us to accurately measure the longitudinal relaxation of 3He spins by fitting the change of the total area under the projection profiles to an exponential. A value of T1 = 1.67 s (2 T field) was recorded, in excellent agreement with an inversion recovery measurement.     

Rapid and accurate measurement of transverse relaxation times using a single shot multi-echo echo-planar imaging sequence

Methods for making rapid and accurate measurements and maps of the transverse relaxation time from a single free induction decay (FID) are proposed. The methods use a multi-echo sequence in combination with B1 insensitive (hyperbolic secant or BIREF2b) refocusing pulses and rapid echo-planar imaging techniques. The results were calibrated against a single spin echo echo-planar imaging sequence using a phantom containing a range of CuSO4 concentrations. The mean percentage absolute difference between the multi-echo and single-echo results was 3% for the multi-echo sequence using the hyperbolic secant refocusing pulse, and 7% for the multi-echo sequence using the BIREF2b refocusing pulse, compared to 13% for a multi-echo sequence using a nonselective sinc refocusing pulse. The use of the sequences in vivo has been demonstrated in studies of gastric function, i.e., the measurement of gastric dilution and monitoring of formation of a raft of alginate polysaccharide within the stomach.     

In vivo measurements of T1 relaxation times of 31P-metabolites in human skeletal muscle

The T1 relaxation times were estimated for 31P-metabolites in human skeletal muscle. Five healthy volunteers were examined in a 1.5 Tesla wholebody imaging system using an inversion recovery pulse sequence. The calculated T1 relaxation times ranged from 5.517 sec for phosphocreatine to 3.603 sec for -ATP.