## 1 Introduction  
Two-photon ionization (2 PI), or multi-photon ionization more generally, has consistently been receiving a great deal of attention for decades (see e.g., [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11]). Also these processes have been used in a variety of applications in laser optics and spectroscopy. It is well known that the two-photon photoelectron angular distributions (PAD) are directly related to the relative amplitudes and the relative phase between different partial waves [8; 12; 13; 14; 15; 16]. However, these earlier works dealt with the laser pulses in the optical range whose pulse width is very long in comparison with the modern standard of femtosecond laser technology. The advent of extreme ultraviolet (EUV) [17; 18] and X-ray [19; 20] free-electron lasers (FELs) as well as intense ultrashort high-harmonic sources has led to renewed interest in two-photon processes in the EUV to X-ray regimes (see, e.g., [21; 22; 23; 24; 25; 26; 27; 28]). Photoelectron angular distribution is nowadays extensively studied by the velocity map imaging technique (see e.g., [29; 30]). These new light sources have also enabled two-photon ionization (2 PI) of species with a deep ionization potential such as He [31; 32; 33; 34; 35] and \(\rm N_{2}\)[36]. Single-color two-photon single ionization of a helium atom, apart from a hydrogen atom, may be one of the simplest two-photon processes. For theoretical study, see, for example, the work by [PERSON] _et al._[37], [PERSON] and [PERSON] [38], and references cited therein. On the experimental side, [PERSON] _et al._[32] were the first to observe this process and used it for an autocorrelation measurement of high-order harmonic pulses, and [PERSON] _et al._[35] recently used it for an autocorrelation measurement of the EUV FEL pulses provided by the SPring-8 Compact SASE Source (SCSS) test accelerator [18]. The absolute two-photon ionization cross sections of He were measured using an intense high harmonic source [31] as well as the SCSS test accelerator [39]. [PERSON] _et al._[40] recently investigated two- and three-photon ionization of He at the SCSS test accelerator by photoelectron spectroscopy using a magnetic bottle spectrometer. Though not single-color, the PAD from multi-color above-threshold ionization of He has recently been reported [41; 42]. Two-photon single ionization of H and He produces a continuum electron wave packet, which is a superposition of \(s\) and \(d\) partial waves. The photoelectron angular distribution provides information about the ratio of amplitudes for the \(s\) and \(d\) partial waves and their relative phase. Extracting a phase shift difference from the PAD that is observed from a photoexcited state is a well-established method. For example, [PERSON] _et al._[29] excited the ground state helium atom to the \(1 snp\) Rydberg states by high-order harmonics and measured the PAD emitted from these excited states using IR and UV lasers as ionizing pulses. A similar experiment was also performed by [PERSON] _et al._[43] using synchrotron radiation for the excitation and a laboratory laser for the ionization. Both these experiments confirmed that the relative phase extracted from measured PADs resulting from sequential two-color excitation and ionization agrees well with the theoretically predicted scattering phase shift difference. We have recently studied the PAD from two-photon single ionization of He by femtosecond (fs) EUV pulses theoretically [44]. In the case of resonance-enhanced 2 PI, the resonant ionization path via resonant levels and the nonresonant path via nonresonant intermediate levels coexist [2]. We have shown [44] that a feature peculiar to the few fs regime is the competition between the two paths, leading to a relative phase \(\delta\) between \(s\) and \(d\) that is distinct from the value expected from the correspondingscattering phase shifts, which is otherwise intrinsic to the target atom or molecule.