  Complex field imaging, which captures both the amplitude and phase
information of input optical fields or objects, can offer rich structural
insights into samples, such as their absorption and refractive index
distributions. However, conventional image sensors are intensity-based and
inherently lack the capability to directly measure the phase distribution of a
field. This limitation can be overcome using interferometric or holographic
methods, often supplemented by iterative phase retrieval algorithms, leading to
a considerable increase in hardware complexity and computational demand. Here,
we present a complex field imager design that enables snapshot imaging of both
the amplitude and quantitative phase information of input fields using an
intensity-based sensor array without any digital processing. Our design
utilizes successive deep learning-optimized diffractive surfaces that are
structured to collectively modulate the input complex field, forming two
independent imaging channels that perform amplitude-to-amplitude and
phase-to-intensity transformations between the input and output planes within a
compact optical design, axially spanning ~100 wavelengths. The intensity
distributions of the output fields at these two channels on the sensor plane
directly correspond to the amplitude and quantitative phase profiles of the
input complex field, eliminating the need for any digital image reconstruction
algorithms. We experimentally validated the efficacy of our complex field
diffractive imager designs through 3D-printed prototypes operating at the
terahertz spectrum, with the output amplitude and phase channel images closely
aligning with our numerical simulations. We envision that this complex field
imager will have various applications in security, biomedical imaging, sensing
and material science, among others.
