Plane wave analysis of coherent holographic image reconstruction by phase transfer (CHIRPT)

Design and analysis of polygonal mirror-based scan engines for improved spatial frequency modulation imaging

Spatial frequency modulation imaging (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.

Fisher information and the Cramér-Rao lower bound in single-pixel localization microscopy with spatiotemporally modulated illumination

Single-pixel imaging, the concept that an image can be captured via a single-pixel detector, is a cost-effective yet powerful technique to reduce data acquisition duration without sacrificing image resolution when properly structured illumination patterns are introduced. Normally, the image reconstruction process is subject to the diffraction limit. Here, we study the possibility of exploiting the information contained in the illumination patterns to enable a form of single-pixel localization microscopy (SPLM) for super-resolution. This concept is inspired by coherent holographic image reconstruction by phase transfer (CHIRPT) microscopy. CHIRPT microscopy is a single-pixel imaging technique that uses structured illumination that is spatiotemporally modulated (STM) so that a unique temporal modulation pattern is imparted to each point within a large illumination volume. The fluorescent light emitted by molecules contains the same temporal modulations as the illumination patterns at the locations of the molecules. By recording a portion of the total emitted fluorescent power, the signal may be numerically processed to form an image. Unique temporal modulation patterns that excite fluorescent probes at each point can also be used to localize individual molecules by matching their particular temporal light emission patterns to the measured temporal signal. This paper evaluates the feasibility of SPLM with STM illuminations used in and inspired by CHIRPT microscopy via the information content its data carry about the emitter location(s). More specifically, we provide the mathematical formalism of Fisher information (FI) and the Cramér-Rao lower bound (CRLB) associated with the location parameters of the emitter(s). The FI and CRLB are then numerically evaluated under different experimental assumptions to assess the effects of experimental parameters on localization precision. Last, we compare the single-pixel CRLB to that from camera-based single-molecule localization microscopy in the localization of a single emitter. We show that SPLM has several distinguishing characteristics that provide certain advantages, such as relatively constant CRLB over a very large illumination volume and improved CRLB for 3D localization due to the information coupling introduced by simultaneous modulations of the transverse axes.

Single-pixel fluorescent diffraction tomography

Optical diffraction tomography (ODT) is an indispensable tool for studying objects in three dimensions. Until now, ODT has been limited to coherent light because spatial phase information is required to solve the inverse scattering problem. We introduce a method that enables ODT to be applied to imaging incoherent contrast mechanisms such as fluorescent emission. Our strategy mimics the coherent scattering process with two spatially coherent illumination beams. The interferometric illumination pattern encodes spatial phase in temporal variations of the fluorescent emission, thereby allowing incoherent fluorescent emission to mimic the behavior of coherent illumination. The temporal variations permit recovery of the spatial distribution of fluorescent emission with an inverse scattering model. Simulations and experiments demonstrate isotropic resolution in the 3D reconstruction of a fluorescent object.

Spatial frequency modulated imaging in coherent anti-Stokes Raman microscopy

For sparse samples or in the presence of ambient light, the signal-to-noise ratio (SNR) performance of single-point-scanning coherent anti-Stokes Raman scattering (CARS) images is not optimized. As an improvement, we propose replacing the conventional CARS focus-point illumination with a periodically structured focus line while continuing to collect the transmitted CARS intensity on a single detector. The object information along the illuminated line is obtained by numerically processing the CARS signal recorded for various periods of the structured focus line. We demonstrate experimentally the feasibility of this spatial frequency modulated imaging (SPIFI) in CARS (SPIFI-CARS) and SHG (SPIFI-SHG) and identify situations where its SNR is better than that of the single-point-scanning approach.

Fourier computed tomographic imaging of two dimensional fluorescent objects

We introduce a new form of tomographic imaging that is particularly advantageous for a new class of super-resolution optical imaging methods. Our tomographic method, Fourier Computed Tomography (FCT), operates in a conjugate domain relative to conventional computed tomography techniques. FCT is the first optical tomography method that records complex projections of the object spatial frequency distribution. From these spatial frequency projections, the spatial slice theorem is derived, which is used to build a tomographic imaging reconstruction algorithm. FCT enables enhancement of spatial frequency support along a single spatial direction to be isotropic in the entire transverse spatial frequency domain.

Mechanically scanned interference pattern structured illumination imaging

We present a fully lensless single pixel imaging technique using mechanically scanned interference patterns. The method uses only simple, flat optics; no lenses, curved mirrors, or acousto-optics are used in pattern formation or detection. The resolution is limited by the numerical aperture of the angular access to the object, with a fundamental limit of a quarter wavelength and no fundamental limit on working distance. While it is slower than some similar techniques, the lack of a lens objective and simplification of the required optics could make it more applicable in difficult wavelength regimes such as UV or X-ray.

Fluorescent coherent diffractive imaging with accelerating light sheets

Fluorescence microscopy is a powerful method for producing high fidelity images with high spatial resolution, particularly in the biological sciences. We recently introduced coherent holographic image reconstruction by phase transfer (CHIRPT), a single-pixel imaging method that significantly improves the depth of field in fluorescence microscopy and enables holographic refocusing of fluorescent light. Here we demonstrate that by installing a confocal slit conjugate to the illuminating light sheets used in CHIRPT, out-of-focus light is rejected, thus improving lateral spatial resolution and rejecting noise from out-of-focus fluorescent light. Confocal CHIRPT is demonstrated and fully modeled. Finally, we explore the use of beam shaping and point-spread-function engineering to enable holographic single-lens light-sheet microscopy with single-pixel detection.

Interferometric spatial frequency modulation imaging

Interferometric spatial frequency modulation for imaging (I-SPIFI) is demonstrated for the first time, to our knowledge. Significantly, this imaging modality can be seamlessly combined with nonlinear SPIFI imaging and operates through single-element detection, making it compatible for use in scattering specimens. Imaging dynamic processes with submicrometer axial resolution through long working distance optics is shown, and high contrast images compared to traditional wide-field microscopy images. Finally, enhanced lateral resolution is achieved in I-SPIFI. To our knowledge, this is the first single platform that enables multimodal linear and nonlinear imaging, with enhanced resolution, all of which can be performed simultaneously.

Three-dimensional single-pixel imaging of incoherent light with spatiotemporally modulated illumination

We derive analytic expressions for the three-dimensional coherent transfer function (CTF) and coherent spread function (CSF) for coherent holographic image reconstruction by phase transfer (CHIRPT) microscopy with monochromatic and broadband illumination sources. The 3D CSF and CTF were used to simulate CHIRPT images, and the results show excellent agreement with experimental data. Finally, we show that the formalism presented here for computing the CSF/CTF pair in CHIRPT microscopy can be readily extended to other forms of single-pixel imaging, such as spatial-frequency-modulated imaging.

Fabrication and characterization of modulation masks for multimodal spatial frequency modulated microscopy

Spatial frequency modulated imaging (SPIFI) is a powerful imaging method that when used in conjunction with multiphoton contrast mechanisms has the potential to improve the spatial and temporal scales that can be explored within a single nonlinear optical microscope platform. Here we demonstrate, for the first time to our knowledge, that it is possible to fabricate inexpensive masks using femtosecond laser micromachining that can be readily deployed within the multiphoton microscope architecture to transform the system from a traditional point-scanning system to SPIFI and gain the inherent advantages that follow.

General theoretical treatment of spectral modulation light-labeling spectroscopy

We theoretically derive the analytic relationship between experimental parameters and the measured incident (or illumination) optical power spectrum for a new form of spectroscopy, entitled light labeling spectroscopy. The light labeling signals are shown to arise from the interference between fields diffracted from a grating with time varying ruling density. A Gaussian model is used to illustrate the bounds of the method for recovering power spectra without artificial spectral apodization. Finally, several example systems are tabulated to give numerical insight into the possible system performances across a range of wavelength regions.

Superresolved multiphoton microscopy with spatial frequency-modulated imaging

Superresolved far-field microscopy has emerged as a powerful tool for investigating the structure of objects with resolution well below the diffraction limit of light. Nearly all superresolution imaging techniques reported to date rely on real energy states of fluorescent molecules to circumvent the diffraction limit, preventing superresolved imaging with contrast mechanisms that occur via virtual energy states, including harmonic generation (HG). We report a superresolution technique based on spatial frequency-modulated imaging (SPIFI) that permits superresolved nonlinear microscopy with any contrast mechanism and with single-pixel detection. We show multimodal superresolved images with two-photon excited fluorescence (TPEF) and second-harmonic generation (SHG) from biological and inorganic media. Multiphoton SPIFI (MP-SPIFI) provides spatial resolution up to 2η below the diffraction limit, where η is the highest power of the nonlinear intensity response. MP-SPIFI can be used to provide enhanced resolution in optically thin media and may provide a solution for superresolved imaging deep in scattering media.