  Nonlinear interferometry with entangled photons allows for characterizing a
sample without detecting the photons interacting with it. This method enables
highly sensitive optical sensing in the wavelength regions where efficient
detectors are still under development. Recently, nonlinear interferometry has
been applied to interferometric measurement techniques with broadband light
sources, such as Fourier-transform infrared spectroscopy and infrared optical
coherence tomography. However, they were demonstrated with photon pairs
produced through spontaneous parametric down-conversion (SPDC) at a low
parametric gain, where the average number of photons per mode is much smaller
than one. The regime of high-gain SPDC offers several important advantages,
such as the amplification of light after its interaction with the sample and a
large number of photons per mode at the interferometer output. In this study,
we demonstrate broadband spectroscopy and high-resolution optical coherence
tomography with undetected photons generated via high-gain SPDC in an
aperiodically poled lithium niobate crystal. To prove the principle, we
demonstrate reflective Fourier-transform near-infrared spectroscopy with a
spectral bandwidth of 17 THz and optical coherence tomography with an axial
resolution of 11 {\mu}m.
