Rafael Piestun

Three-dimensional single-molecule fluorescence imaging beyond the diffraction limit using a double-helix point spread function

We demonstrate single-molecule fluorescence imaging beyond the optical diffraction limit in 3 dimensions with a wide-field microscope that exhibits a double-helix point spread function (DH-PSF). The DH-PSF design features high and uniform Fisher information and has 2 dominant lobes in the image plane whose angular orientation rotates with the axial (z) position of the emitter. Single fluorescent molecules in a thick polymer sample are localized in single 500-ms acquisitions with 10- to 20-nm precision over a large depth of field (2 μm) by finding the center of the 2 DH-PSF lobes. By using a photoactivatable fluorophore, repeated imaging of sparse subsets with a DH-PSF microscope provides superresolution imaging of high concentrations of molecules in all 3 dimensions. The combination of optical PSF design and digital postprocessing with photoactivatable fluorophores opens up avenues for improving 3D imaging resolution beyond the Rayleigh diffraction limit.

High-speed scattering medium characterization with application to focusing light through turbid media

We introduce a phase-control holographic technique to characterize scattering media with the purpose of focusing light through it. The system generates computer-generated holograms implemented via a deformable mirror device (DMD) based on micro-electro-mechanical technology. The DMD can be updated at high data rates, enabling high speed wavefront measurements using the transmission matrix method. The transmission matrix of a scattering material determines the hologram required for focusing through the scatterer. We demonstrate this technique measuring a transmission matrix with 256 input modes and a single output mode in 33.8 ms and creating a focus with a signal to background ratio of 160. We also demonstrate focusing through a temporally dynamic, strongly scattering sample with short speckle decorrelation times.

Three dimensional tracking of fluorescent microparticles using a photon-limited double-helix response system

We demonstrate three-dimensional tracking of fluorescent microparticles, with a computational optical system whose point spread function (PSF) has been engineered to have two twisting lobes along the optical axis, generating a three-dimensional (3D) double-helix (DH) PSF. An information theoretical comparison in photon limited systems shows that the DH-PSF delivers higher Fisher information for 3D localization than the standard PSF. Hence, DH-PSF systems provide better position estimation accuracy. Experiments demonstrate average position estimation accuracies under 14nm and 37nm in the transverse and axial dimensions respectively. The system determines the 3D position of multiple particles with a single image and tracks them over time while providing their velocities.

Depth from diffracted rotation

The accuracy of depth estimation based on defocus effects has been essentially limited by the depth of field of the imaging system. We show that depth estimation can be improved significantly relative to classical methods by exploiting three-dimensional diffraction effects. We formulate the problem by using information theory analysis and present, to the best of our knowledge, a new paradigm for depth estimation based on spatially rotating point-spread functions (PSFs). Such PSFs are fundamentally more sensitive to defocus thanks to their first-order axial variation. Our system acquires a frame by using a rotating PSF and jointly processes it with an image acquired by using a standard PSF to recover depth information. Analytical, numerical, and experimental evidence suggest that the approach is suitable for applications such as microscopy and machine vision.

Genetic algorithm optimization for focusing through turbid media in noisy environments

We introduce genetic algorithms (GA) for wavefront control to focus light through highly scattering media. We theoretically and experimentally compare GAs to existing phase control algorithms and show that GAs are particularly advantageous in low signal-to-noise environments.

Electromagnetic degrees of freedom of an optical system

We present a rigorous electromagnetic formalism for defining, evaluating, and optimizing the degrees of freedom of an optical system. The analysis is valid for the delivery of information with electromagnetic waves under arbitrary boundary conditions communicating between domains in three-dimensional space. We show that, although in principle there is an infinity of degrees of freedom, the effective number is finite owing to the presence of noise. This is in agreement with the restricted classical theories that showed this property for specific optical systems and within the scalar and paraxial approximations. We further show that the best transmitting and receiving functions are the solutions of well-defined eigenvalue equations. The present approach is useful for understanding and designing modern optical systems for which the previous approaches are not applicable, as well as for application in inverse and synthesis problems.

WAVE FIELDS IN THREE DIMENSIONS : ANALYSIS AND SYNTHESIS

Distributions of wave fields in three-dimensional domains are analyzed, synthesized, and generated experimentally. Fundamental limits are discussed and sampling conditions are derived for their generation, with use of a single diffractive element. A general design procedure, based on optimization algorithms, is developed and implemented. Experimental results show that special three-dimensional light distributions can be achieved with low-information-content elements in on-axis configurations.

High-efficiency rotating point spread functions

Rotating point spread functions (PSFs) present invariant features that continuously rotate with defocus and are important in diverse applications such as computational imaging and atom/particle trapping. However, their transfer function efficiency is typically very low. We generate highly efficient rotating PSFs by tailoring the range of invariant rotation to the specific application. The PSF design involves an optimization procedure that applies constraints in the Gauss-Laguerre modal plane, the spatial domain, and the Fourier domain. We observed over thirty times improvement in transfer function efficiency. Experiments with a phase-only spatial light modulator demonstrate the potential of high-efficiency rotating PSFs.

Propagation-invariant wave fields with finite energy

Propagation invariance is extended in the paraxial regime, leading to a generalized self-imaging effect. These wave fields are characterized by a finite number of transverse self-images that appear, in general, at different orientations and scales. They possess finite energy and thus can be accurately generated. Necessary and sufficient conditions are derived, and they are appropriately represented in the Gauss-Laguerre modal plane. Relations with the following phenomena are investigated: classical self-imaging, rotating beams, eigen-Fourier functions, and the recently introduced generalized propagation-invariant wave fields. In the paraxial regime they are all included within the generalized self-imaging effect that is presented. In this context we show an important relation between paraxial Bessel beams and Gauss-Laguerre beams.

Total external reflection from metamaterials with ultralow refractive index

Metamaterials composed of metal-dielectric nanostructures are engineered to have an effective refractive index less than unity at optical wavelengths. The effect of total external reflection is demonstrated when light from vacuum is incident onto these materials at an angle exceeding the critical angle defined by Snell’s law. Novel approaches are discussed to derive the effective index of refraction from the reflection and refraction properties of finite slabs. The effect of losses and dispersion are analyzed in the visible range of frequencies by consideration of the measured properties of silver. The differences among ultralow refractive-index metamaterials, photonic bandgap materials, and metals are discussed. Remarkably, a bandgap is not required to obtain total external reflection.