  With the emergence of super-resolution lenses such as superlens and
hyperlens, coupled with advancements in metamaterials, the diffraction limit of
approximately half wavelength is no longer unbreakable. However, superlenses
are easily affected by weak intrinsic losses and hyperlenses cannot achieve
perfect imaging, significantly constraining their practical utility. To address
these challenges, here we propose a perfect hyperlens based on the
transformation optics. Importantly, perfect hyperlens is capable of
self-focusing in geometrical optics while supporting propagating waves with
exceptionally large wavenumbers, which endows it with key advantages such as
ultra-high resolution, no aberration and strong robustness. Furthermore, we
demonstrate the hyperbolic focusing performance in naturally in-plane
hyperbolic polaritons of {\alpha}-MoO3 films numerically, which can be achieved
by gradient thickness. The results greatly innovate the design principles of
traditional imaging lens, providing many potentially significant applications
for super-resolution real-time imaging, lithography, and sensing.
