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Abstract This work is concerned with optical imaging in strongly diffusive environments. We consider a typical setting in optical coherence tomography where a sample is probed by a collection of wavefields produced by a laser and propagating through a microscope. We operate in a scenario where the illuminations are in a speckle regime, namely fully randomized. This occurs when the light propagates deep in highly heterogeneous media. State-of-the-art coherent techniques are based on the ballistic part of the wavefield, that is the fraction of the wave that propagates freely and decays exponentially fast. In a speckle regime, the ballistic field is negligible compared to the scattered field, which precludes the use of coherent methods and different approaches are needed. We propose a new strategy based on blind source separation and total variation deconvolution to obtain images with diffraction-limited resolution. The source separation allows us to isolate the fields diffused by the different scatterers to be imaged, while the deconvolution exploits the speckle memory effect to estimate the relative position of these scatterers. Our method is validated with numerical simulations and is shown to be effective not only for imaging discrete scatterers, but also continuous objects. 

Third harmonic generation (THG) provides a valuable, label-free approach to imaging biological systems. To date, THG microscopy has been performed using point-scanning methods that rely on intensity measurements lacking phase information of the complex field. We report the first demonstration, to the best of our knowledge, of THG holographic microscopy and the reconstruction of the complex THG signal field with spatial synthetic aperture imaging. Phase distortions arising from measurement-to-measurement fluctuations and imaging components cause optical aberrations in the reconstructed THG field. We have developed an aberration-correction algorithm that estimates and corrects these phase distortions to reconstruct the spatial synthetic aperture THG field without optical aberrations. 

Using the structured illumination, single pixel detection imaging technique SPatIal Frequency modulation Imaging (SPIFI), we demonstrate a cascaded Wavelength Domain and Spatial Domain (WD-SD-SPIFI) system enabling real-time, in-line, second order dispersion compensation optimization for multiphoton imaging. Enhanced resolution is demonstrated by imaging a sub-diffractive 140 nm fluorescent nanodiamond with Two Photon Excitation Fluorescence (2PEF) to measure the Point Spread Function (PSF). With a 1034 nm pulsed laser through a Numerical Aperture (NA) of 0.5, a PSF Full Width at Half Max (FWHM) of 780 nm was measured with minimal post processing analysis that only requires Fast Fourier Transforms (FFTs). 

Second harmonic generation (SHG) microscopy is a valuable tool for optical microscopy. SHG microscopy is normally performed as a point scanning imaging method, which lacks phase information and is limited in spatial resolution by the spatial frequency support of the illumination optics. In addition, aberrations in the illumination are difficult to remove. We propose and demonstrate SHG holographic synthetic aperture holographic imaging in both the forward (transmission) and backward (epi) imaging geometries. By taking a set of holograms with varying incident angle plane wave illumination, the spatial frequency support is increased and the input and output pupil phase aberrations are estimated and corrected – producing diffraction limited SHG imaging that combines the spatial frequency support of the input and output optics. The phase correction algorithm is computationally efficient and robust and can be applied to any set of measured field imaging data. 

Spatial frequency modulation for imaging (SPIFI) has traditionally employed a time-varying spatial modulation of the excitation beam. Here, for the first time to our knowledge, we introduce single-shot SPIFI, where the spatial frequency modulation is imposed across the entire spatial bandwidth of the optical system simultaneously enabling single-shot operation. 

Spatialfrequency modulationimaging (SPIFI) is a structured illumination single pixel imaging technique that is most often achieved via a rotating modulation disk. This implementation produces line images with exposure times on the order of tens of milliseconds. Here, we present a new architecture for SPIFI using a polygonal scan mirror with the following advances: (1) reducing SPIFI line image exposure times by 2 orders of magnitude, (2) facet-to-facet measurement and correction for polygonal scan design, and (3) a new anamorphic magnification scheme that improves resolution for long working distance optics. 

A high-speed super-resolution computational imaging technique is introduced on the basis of classical and quantum correlation functions obtained from photon counts collected from quantum emitters illuminated by spatiotemporally structured illumination. The structured illumination is delocalized—allowing the selective excitation of separate groups of emitters as the modulation of the illumination light advances. A recorded set of photon counts contains rich quantum and classical information. By processing photon counts, multiple orders of Glauber correlation functions are extracted. Combinations of the normalized Glauber correlation functions convert photon counts into signals of increasing order that contain increasing spatial frequency information. However, the amount of information above the noise floor drops at higher correlation orders, causing a loss of accessible information in the finer spatial frequency content that is contained in the higher-order signals. We demonstrate an efficient and robust computational imaging algorithm to fuse the spatial frequencies from the low-spatial-frequency range that is available in the classical information with the spatial frequency content in the quantum signals. Because of the overlap of low spatial frequency information, the higher signal-to-noise ratio (SNR) information concentrated in the low spatial frequencies stabilizes the lower SNR at higher spatial frequencies in the higher-order quantum signals. Robust performance of this joint fusion of classical and quantum computational single-pixel imaging is demonstrated with marked increases in spatial frequency content, leading to super-resolution imaging, along with much better mean squared errors in the reconstructed images.