Constant amplitude broadband refocusing pulses from numerical optimization

Abstract

Broadband refocusing pulses for high-field NMR can be constructed with broadband 90× pulses from numerical optimization of Bloch simulations concatenated with their time and phase reversed transformations. This work describes the search for minimal duration 18-kHz modulation frequency constant amplitude refocusing pulses made in this manner for bandwidths of 40, 60 and 80 kHz. Variants optimized at multiple frequencies and with sine squared amplitude truncation also are described. The resulting pulses are expected to have immediate application especially for (13)C refocusing in multidimensional experiments.

Exploring the limits of broadband 90° and 180° universal rotation pulses

“…The extension of the study to limited rf Cho and Pines [26], Emsley and Bodenhausen [32], Shaka and Pines [27]. 180°UR pulses were from (d): Brown [37], Anand et al [15], Tycko et al [24], Geen and Freeman [30], Emsley and Bodenhausen [32], Shaka and Pines [27], Odedra and Wimperis [38], Borneman et al [9]. Additional pulses from Refs.…”

“…Next to PP excitation and inversion pulses, UR 90°and 180°refocusing pulses are the most important pulse sequence elements in modern NMR spectroscopy. So far, many broadband 90°and 180°UR pulses [1,2,9,14,[24][25][26][27][29][30][31][32][33][34][35][36][37][38][39] have been developed. However, a systematic assessment of the physical boundaries for the two classes of pulses has not been available.…”

“…The GRAPE algorithm derived from optimal control principles has previously been applied to optimize unitary operators [6][7][8][9][10][11][12][13][14]. In particular, specific 180°UR pulses for CPMG-type experiments [9,37] and general high resolution applications [14] as well as slice-selective broadband 180 UR pulses [10] were derived recently using this type of algorithm. GRAPE-derived and constructed UR pulses have already been applied in a variety of experiments [20,45,[64][65][66][67][68].…”

“…Although UR pulse design is generally considered to be more difficult than optimizing PP pulses, traditional pulse design methods have yielded a number of composite or shaped UR pulses in the last decades [1,2,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]. More recently, a principle has been derived which allows the construction of a UR pulse with flip angle a based on PP pulses with effective flip angle a=2 starting with initial magnetization along the y-axis [3].…”

SORDOR Pulses: Expansion of the Böhlen-Bodenhausen Scheme for Low-Power Broadband Magnetic Resonance

“…, regardless, only universal rotation (UR) pulses can be used as full replacements of conventional, bandwidth-limited, hard pulses. UR pulses, however, are especially demanding regarding both rf-amplitude and rf-energy (Tycko et al, 1985a, b;Cho and Pines, 1987;Shaka and Pines, 1987;Levitt, 1988;Garwood and Ke, 1991;Wimperis, 1991Wimperis, , 1994Emsley and Bodenhausen, 1992;Henkelman, 1992, 1995;Abramovich and Vega, 1993;Luy et al, 2005;Brown, 2011;Anand et al, 2012;Kobzar et al, 2012;Moore et al, 2012;Odedra and Wimperis, 2012;Skinner et al, 2012;Altenhof et al, 2019).…”