# A Review of Super-Resolution Imaging through Optical High-Order Interference [Invited]
## 7 Super-Resolution via Dynamic Phase Control  
In 2017, [PERSON] and [PERSON] designed a dynamic phase screen to replace the imaging lens, and achieved direct n-photon imaging [42] as shown in Figure 10I. It has been shown that synchronous-position multi-photon interference plays a key role in the scheme, leading to super-resolution imaging for the object with the resolution reaching the HL. Importantly, the designed phase screen can be easily implemented with a commercial spatial light modulator [27], indicating the developed Heisenberg-resolution imaging is achievable with current well-developed technology. The phase screen is of specially designed dynamic phase structure, i.e., each point on the phase screen is loaded with a different complex amplitude that is a superposition of n correlated dynamic phase modes together with a lens-type static phase mode as detailed in Ref [42]. In the two-photon interference case, it was found that the synchronous-position two-photon interference pattern is mainly caused by the two-photon paths with the pair of photons transmitting through the same point of the phase screen as illustrated in Figure 10 II. Therefore, the linear dynamic phase screen is of similar functionality as the conceptual nonlinear n-photon transmitting screen discussed by [PERSON] et al. [31], leading to the HL two-photon imaging. To realize the proposed n-photon Heisenberg-resolution imaging, the object should be illuminated by an entangled n-photon source or a scanning focused beam as shown in Figure 10 III,IV, corresponding to coherent and incoherent Heisenberg-resolution imaging, respectively. Recently, [PERSON] et al. have experimentally realized the Heisenberg-resolution imaging with scanning focused-beam illumination [43]. In the experiment, the dynamic phase screen was realized by  
Figure 9: **(a)**: Schematic of the super-resolution imaging scheme by encoding the image of an object onto the optical centroid measurement state (OCM). The spatial information of the object is first encoded onto the pump light (\(\sum_{0}^{\prime}\)), and a lens \(L_{1}\) is used to project the pump light onto its focal plane, where parametric down conversion process transfers the Fourier information of the object into the two-photon amplitude of the generated entangled light. By employing an additional Fourier transform with lens \(L_{2}\), the OCM state of the object is built, i.e., subwavelength far-field interference of the Fourier image of the object. **(b)**: HL super-resolution image realized through the OCM state of a triple-slit object with entangled light at 810 nm. The super-resolution effect is demonstrated by comparing with the conventional intensity images at wavelengths 810 nm and 405 nm. The figure is reproduced with permissions from Ref. [41] of OSA. using a reflection-type phase-only spatial light modulator (see Figure 11I). Both the laser and the pseudothermal light were introduced for illumination, and the synchronous-position two-photon correlation was measured by using a CCD camera. Both the PSF and the spatial resolution of the Heisenberg-resolution imaging system were characterized. The results with laser light are shown in Figure 11 II, which demonstrate the HL super-resolved spatial resolution of the imaging system. Figure 11: **(I)**: Schematic of experimental setup for realizing Heisenberg-resolution imaging with scanning focused-beam illumination. The phase-controlled screen (PCS) is realized by a phase-only spatial light modulator. The objects to be imaged are shown in the inset, indicated by the red arrows; **(II)**: The HL super-resolution images (red circles) for different objects. The super-resolution effect is demonstrated by comparing with the conventional intensity images (blue circles). Please note that the object with a RN = 5.0 is with slit separation beyond the SQL. The figure is reproduced with permissions from Ref. [43] of OSA. Figure 10: **(I)**: Schematic of the super-resolution imaging scheme with a phase-controlled screen (PCS).