We present the results of our recent experimental and numerical studies on femtosecond pulse spectrotemporal imaging in a similariton-induced temporal lens aimed to designing a femtosecond optical oscilloscope [1]. We have studied nonlinear and dispersive peculiarities of modern high-tech materials, such as photonic crystal fibers, hollow-core fibers etc, to use them in the scheme, and to provide compactness and reliability of the device. The use of hollow-core fibers, as a dispersive medium instead of a pair of prisms or gratings, is of special importance for constructing the industrial tool. Additionally, we are experimenting on the method of dispersive Fourier transformation, using the effect of chromo-modal dispersion in multimode fibers [2], to provide real-time performance of the device.