We propose a high-precision method for measuring the orbital angular momentum (OAM) spectrum of ultra-broadband optical-vortex (OV) pulses from fork-like interferograms between OV pulses and a reference plane-wave pulse. It is based on spatial reconstruction of the electric fields of the pulses to be measured from the frequency-resolved interference pattern. Our method is demonstrated experimentally by obtaining the OAM spectra for different spectral components of the OV pulses, enabling us to characterize the frequency dispersion of the topological charge of the OAM spectrum by a simple experimental setup. Retrieval is carried out in quasi-real time, allowing us to investigate OAM spectra dynamically. Furthermore, we determine the relative phases (including the sign) of the topological-charge-resolved electric-field amplitudes, which are significant for evaluating OVs or OV pulses with arbitrarily superposed modes.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. m exp i , where m indicates the orbital angular momentum (OAM) per photon [2]. Here, m, the topological charge, can be any integer value, providing a new degree of freedom in phase control. The study of these unique properties of OVs has attracted enormous attention because of increasing applications in many fields, such as optical trapping [3,4] (especially, trapping for atom Bose-Einstein condensates [5,6]) or manipulation [7,8], optical telecommunications [9, 10], super-resolution microscopy [11][12][13], quantum information processing [14,15], nulling interferometry for extra-solar planet searches [16] and nonlinear spectroscopy [17,18].Since preceding research mainly concentrated on the spatial field distribution of OVs, for most cases temporally-continuous OVs have been used so far. In contrast, we have recently demonstrated the generation of ultra-broadband OV pulses [19] and few-cycle ultrashort OV pulses [20] for applications in ultra-broadband/ultrafast nonlinear spectroscopy and high-peak power field interactions with matter.The topological charge m describes the essential quantum character of OVs or OV pulses as well as their phase distribution. However, in many cases, these features have been so far investigated by observing fork-dislocation lines [21] or spiral patterns [22] in interferograms, dark lines using a cylindrical lens [23]/a tilted convex lens [24], or triangulardiffraction patterns [25]. Thus, while only the dominant topological charges have been determined, the purity or distribution of topological charge has not been discussed. Computergenerated holograms and spatial filtering has been utilized for obtaining OAM spectra mainly for continuous OVs rather than for dominant topological charge [14]. However, this is not suitable for ultra-broadband OV pulses because of inevitable angular dispersion from the diffraction effect of holograms on spatia...