Structured illumination enhances the resolution of a standard microscope by encoding the high spatial frequencies of an object's image into lower spatial frequencies through the use of a carefully selected pattern. In essence, it modifies the optical transfer function (OTF), which is the Fourier Transform of the point spread function (PSF), to increase sensitivity to high spatial frequencies. In [G. Noetinger et al, Arxiv 2306.14631 (2023)], the authors introduce a novel technique that further leverages time by incorporating a temporal periodic modulation, specifically through the use of a rotating mask, to encode multiple transfer functions within the temporal domain. This methodology is exemplified using a confocal microscope setup. At each scanning position, a temporal periodic signal is captured, enabling the construction of multiple images of the same object. The image carried by each harmonic is a convolution of the object with a phase vortex of topological charge, similar to the outcome when using a vortex phase plate as an illumination. This enables the collection of chosen high spatial frequencies from the sample, thereby enhancing the spatial resolution of the confocal microscope.

The resolution of a confocal microscope is governed by how various spatial frequencies are transmitted through the optical system to the detector, a process that is influenced by the shape of the objective's pupil. Spatial frequencies higher than [2NA/\lambda\] are filtered out, but not all spatial frequencies are collected with the same efficiency; the maximum gain is achieved for low spatial frequencies. This results in an unfavorable signal-to-noise ratio for sharp details (high spatial frequencies). The idea in [G. Noetinger et al, Arxiv 2306.14631 (2023)] s to take advantage of temporal degrees of freedom to reconstruct multiple images of the same object with different PSFs that selectively gather images with varying relative gains for the different spatial frequencies.

The principle is depicted in Fig. 1, where, using a rotating mask, the authors obtain a periodic set of temporally varying images. Similar to a confocal microscope, the object plane is scanned using piezoelectric actuators, and the backscattered signal is measured with a photodiode. The distinction lies in sending a full sequence of the rotating mask. Consequently, for each position, a time-varying signal is obtained instead of just retaining a single value. Once the complete spatiotemporal image is acquired, a temporal Fourier transform can be performed.

The authors demonstrate that by selecting the complex profile corresponding to each harmonic of the modulated signal, the convolution of the object with different PSFs is obtained.

**Figure 1.** Schematic view of the experimental process.

Each PSF corresponds to a phase vortex with varying topological charge, or orbital angular momentum (see Fig. 2). To obtain an accurate image from each harmonic, we have to invert the PSFs. This is approximately equivalent to convolving each harmonic image with a phase vortex of opposite topological charge.