A review of snapshot multidimensional optical imaging: Measuring photon tags in parallel
Multidimensional optical imaging has seen remarkable growth in the past decade. Rather than measuring only the two-dimensional spatial distribution of light, as in conventional photography, multidimensional optical imaging captures light in up to nine dimensions, providing unprecedented information about incident photons' spatial coordinates, emittance angles, wavelength, time, and polarization. Multidimensional optical imaging can be accomplished either by scanning or parallel acquisition.
... ared with scanning-based imagers, parallel acquisitionalso dubbed snapshot imaging-has a prominent advantage in maximizing optical throughput, particularly when measuring a datacube of high dimensions. Here, we first categorize snapshot multidimensional imagers based on their acquisition and image reconstruction strategies, then highlight the snapshot advantage in the context of optical throughput, and finally we discuss their state-of-the-art implementations and applications. Aperture-division describes an acquisition strategy that splits the system's aperture, followed by dispersing or filtering the resultant sub-pupils in other domains, such as wavelength and polarization. Optical-path-division refers to an acquisition strategy that splits the system's optical path and directs photons with different characteristics in different directions. Frequency-domain-division refers to an acquisition strategy that multiplexes photons with different characteristics in the spatial or spectral domain, followed by splitting the resultant signals in the corresponding frequency domains. Direct image reconstruction is a reconstruction strategy that directly applies linear operators, e.g., the inverse Fourier transformation or the wavelet transformation, to the captured data to recover a multidimensional datacube. Iterative image reconstruction is a reconstruction strategy that iteratively calculates a multidimensional datacube while minimizing an object function. The reconstruction process normally starts with an initial estimate of the datacube, computes the corresponding measurement data, compares it with the actual measurement, and makes suitable adjustments to the datacube. Compared with direct image reconstruction, the computational cost of iterative image reconstruction is generally higher. The snapshot advantage in multidimensional imaging Akin to the Jacquinot advantage in Fourier transform spectrometry , snapshot multidimensional imaging has a much higher optical throughput than its scanning-based counterparts. This throughput improvement due to parallel acquisition has been referred to as the snapshot advantage  and has been considered as an important criterion to evaluate the performance of a multidimensional imager. Before proceeding to detailed discussions, we first define the optical throughput of a multidimensional optical imaging system as the ratio of the photons measured at an FPA to the incident photons collected by the entrance pupil of the system and within a unit time interval (i.e., a single camera exposure). For easy comparison, we also assume that the incident photons have an equal distribution across all characteristic bins.