Theory of diffraction effects in spatial frequency-modulated imaging

Wavelength domain spatial frequency modulation imaging: enabling fiber optic delivery and detection

Spatial frequency modulation imaging (SPIFI) provides a simple architecture for modulating an extended illumination source that is compatible with single pixel imaging. We demonstrate wavelength domain SPIFI (WD-SPIFI) by encoding time-varying spatial frequencies in the spectral domain that can produce enhanced resolution images, like its spatial domain counterpart, spatial domain (SD) SPIFI. However, contrary to SD-SPIFI, WD-SPIFI enables remote delivery by single mode fiber, which can be attractive for applications where free-space imaging is not practical. Finally, we demonstrate a cascaded system incorporating WD-SPIFI in-line with SD-SPIFI enabling single pixel 2D imaging without any beam or sample scanning.

Single-shot spatial frequency modulation for imaging

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.

Understanding and correcting wavenumber error in interference pattern structured illumination imaging

The impacts of uncertainty in mirror movements in mechanically scanned interference pattern structured illumination imaging (IPSII) are discussed. It is shown that uncertainty in IPSII mirror movements causes errors in both the phase and amplitude of the Fourier transform of the resulting imaging. Finally, we demonstrate that iterative phase retrieval algorithms can improve the quality of IPSII images by correcting the phase errors caused by mirror movement uncertainties.

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.

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.

Compressive Raman imaging with spatial frequency modulated illumination

We report a line scanning imaging modality of compressive Raman technology with spatial frequency modulated illumination using a single pixel detector. We demonstrate the imaging and classification of three different chemical species at line scan rates of 40 Hz.

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.

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.

Simultaneous spatial frequency modulation imaging and micromachining with a femtosecond laser

A Ti:Al2O3 chirped-pulse amplification system is used to simultaneously image and machine. By combining simultaneous spatial and temporal focusing (SSTF) with spatial frequency modulation for imaging (SPIFI), we are able to decouple the imaging and cutting beams to attain a resolution and a field-of-view that is independent of the cutting beam, while maintaining single-element detection. This setup allows for real-time feedback with the potential for simultaneous nonlinear imaging and imaging through scattering media. The novel SSTF machining platform uses refractive optics that, in general, are prohibitive for energetic, amplified pulses that might otherwise compromise the integrity of the focus as a result of nonlinear effects.

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

Fluorescent imaging plays a critical role in a myriad of scientific endeavors, particularly in the biological sciences. Three-dimensional imaging of fluorescent intensity often requires serial data acquisition, that is, voxel-by-voxel collection of fluorescent light emitted throughout the specimen with a nonimaging single-element detector. While nonimaging fluorescence detection offers some measure of scattering robustness, the rate at which dynamic specimens can be imaged is severely limited. Other fluorescent imaging techniques utilize imaging detection to enhance collection rates. A notable example is light-sheet fluorescence microscopy, also known as selective-plane illumination microscopy, which illuminates a large region within the specimen and collects emitted fluorescent light at an angle either perpendicular or oblique to the illumination light sheet. Unfortunately, scattering of the emitted fluorescent light can cause blurring of the collected images in highly turbid biological media. We recently introduced an imaging technique called coherent holographic image reconstruction by phase transfer (CHIRPT) that combines light-sheet-like illumination with nonimaging fluorescent light detection. By combining the speed of light-sheet illumination with the scattering robustness of nonimaging detection, CHIRPT is poised to have a dramatic impact on biological imaging, particularly for in vivo preparations. Here we present the mathematical formalism for CHIRPT imaging under spatially coherent illumination and present experimental data that verifies the theoretical model.

Two-dimensional single-pixel imaging by cascaded orthogonal line spatial modulation

Two-dimensional (2D) images are taken using a single-pixel detector by temporally multiplexing spatial frequency projections from orthogonal, time varying spatial line modulation gratings. Unique temporal frequencies are applied to each point in 2D space, applying a continuous spread of frequencies to one dimension, and an offset frequency applied to each line in the orthogonal dimension. The object contrast information can then be recovered from the electronic spectrum of the single pixel, and through simple processing be reformed into a spatial image.

Two-dimensional spatial-frequency-modulated imaging through parallel acquisition of line images

This Letter demonstrates a two-dimensional imaging technique that uses a line scan camera to resolve one spatial dimension and temporal modulation to resolve the perpendicular dimension. A temporal intensity modulation, which increases linearly in frequency along one direction is applied to an illumination beam. The modulated light distribution is imaged onto an object then onto a line scan camera oriented perpendicularly to the direction of the modulation sweep. A line diffuser is placed shortly before the line scan camera and diffuses light along the direction of modulation so that each pixel collects all modulation frequencies.