Two-photon excitation fluorescence microscopy with a high depth of field using an axicon

In conventional two-photon excitation fluorescence microscopy, the numerical aperture of the objective determines the lateral resolution and the depth of field. In some situations, as with functional imaging of dynamic events distributed in live biological tissue, an improved temporal resolution is needed; as a consequence, it is imperative to use optics with a high depth of field to simultaneously image objects at different axial positions. With a conventional microscope objective, increasing the depth of field is achieved at the expense of lateral resolution. To overcome this limitation, we have incorporated an axicon in a two-photon excitation fluorescence microscopy system; measurements have shown that an axicon provides a depth of field in excess of a millimeter, while the lateral resolution is maintained at the micrometer scale. Thus axicon-based two-photon microscopy has been shown to yield a high-resolution projection image of a sample with a single 2D scan of the laser beam while maintaining the improved tissue penetration typical of two-photon microscopy.     

Demonstration of a Fresnel axicon

We design and manufacture a Fresnel axicon (fraxicon) that generates a quasi-diffraction-free/Bessel beam with a large depth of field. The novel optical element is characterized with both coherent and incoherent light, and its behavior is compared with that of a classical axicon. While the fraxicon exhibits a strong interference pattern in the on-axis intensity distribution, it can be smoothed out when using broadband light, partial spatial coherence light, or by period randomization. As inexpensive, compact/lightweight, and low-absorption elements, fraxicons may find applications in imaging, illumination, and situations where low absorption and dispersion are important.     

Influences of twist phenomenon of partially coherent field with uniform-intensity diffractive axicons

The effects of twist phenomenon (beam rotation) of a partially coherent field are studied on the operation of two classes of uniform-intensity diffractive axicons. A general theory of axicon image formation is developed, discussed, and examined. We show that the intensity of the diffracted field is a multiple Bessel field, and only the energy of the zero-order Bessel field diffracts along the propagation axes. We also show that, at any twist strength in all correlation levels, the images can be evaluated by using the stationary-phase method. The three-dimensional stationary-phase formula of axicon images is derived. Such formula may be used in fast image evaluation, for designing diffractive axicons that perform a uniform axial intensity in a twisted partially coherent field.     

Multispectral imaging axicons

Large-aperture linear diffractive axicons are optical devices providing achromatic nondiffracting beams with an extended depth of focus when illuminated by white light sources. Annular apertures introduce chromatic foci separation, making chromatic imaging possible despite important radiometric losses. Recently, a new type of diffractive axicon has been introduced, by multiplexing concentric annular axicons with appropriate sizes and periods, called a multiple annular linear diffractive axicon (MALDA). This new family of conical optics combines multiple annular axicons in different ways to optimize color foci recombination, separation, or interleaving. We present different types of MALDA, give an experimental illustration of the use of these devices, and describe the manufacturing issues related to their fabrication to provide color imaging systems with long focal depths and good diffraction efficiency. Application to multispectral image analysis is discussed.     

Point-spread function synthesis in scanning holographic microscopy

Scanning holographic microscopy is a two-pupil synthesis method allowing the capture of single-sideband in-line holograms of noncoherent (e.g., fluorescent) three-dimensional specimens in a single two-dimensional scan. The flexibility offered by the two-pupil method in synthesizing unusual point-spread functions is discussed. We illustrate and compare three examples of holographic recording, using computer simulations. The first example is the classical hologram in which each object point is encoded as a spherical wave. The second example uses pupils with spherical phase distributions having opposite curvatures, leading to reconstructed images with a resolution limit that is half that of the objective. In the third example, axicon pupils are used to obtain axially sectioned images.     

Multiple annular linear diffractive axicons

We propose a chromatic analysis of multiple annular linear diffractive axicons. Large aperture axicons are optical devices providing achromatic nondiffracting beams, with an extended depth of focus, when illuminated by a white light source, due to chromatic foci superimposition. Annular apertures introduce chromatic foci separation, and because chromatic aberrations result in focal segment axial shifts, polychromatic imaging properties are partially lost. We investigate here various design parameters that can be used to achieve color splitting, filtering, and combining using these properties. In order to improve the low-power efficiency of a single annular axicon, we suggest a spatial multiplexing of concentric annular axicons with different sizes and periods we call multiple annular aperture diffractive axicons (MALDAs). These are chosen to maintain focal depths while enabling color imaging with sufficient diffraction efficiency. Illustrations are given for binary phase diffractive axicons, considering technical aspects such as grating design wavelength and phase dependence due to the grating thickness.     

Lens axicons in oblique illumination

Lens axicons, i.e., lenses or lens systems designed to work like axicons, can be a simple and inexpensive way of generating the characteristic axicon focal line. In the design of most lens axicons, only on-axis properties have been considered. We present the design of a lens axicon with improved off-axis characteristics. It is constructed from a singlet lens but with a double-pass feature that allows for a line of uniform width and a stop positioned to minimize aberrations. We perform off-axis analysis and experiments for this system and for another lens axicon, one designed for its on-axis characteristics. We conclude that the off-axis performance of the double-pass axicon is better than both that of an ordinary cone axicon and that of the other lens axicon.     

Systematic design of an anastigmatic lens axicon

We present an analytical method for systematic optical design of a double-pass axicon that shows almost no astigmatism in oblique illumination compared to a conventional linear axicon. The anastigmatic axicon is a singlet lens with nearly concentric spherical surfaces applied in double pass, making it possible to form a long narrow focal line of uniform width. The front and the back surfaces have reflective coatings in the central and annular zones, respectively, to provide the double pass. Our design method finds the radii of curvatures and axial thickness of the lens for a given angle between the exiting rays and the optical axis. It also finds the optimal position of the reflecting zones for minimal vignetting. This method is based on ray tracing of the real rays at the marginal heights of the aperture and therefore is superior to any paraxial method. We illustrate the efficiency of the method by designing a test axicon with optical parameters used for a prototype axicon, which was manufactured and experimentally tested. We compare the optical characteristics of our test axicon with those of the experimental prototype.     

A study of synthetic-aperture imaging with virtual source elements in B-mode ultrasound imaging systems

We propose an all point transmit and receive focusing method based on transmit synthetic focusing combined with receive dynamic focusing in a linear array transducer. In the method, on transmit, a virtual source element is assumed to be located at the transmit focal depth of conventional B-mode imaging systems, and transmit synthetic focusing is used in two half planes, one before and the other after the transmit focal depth, using the RF data of each scanline, together with all other relevant RF scanline data previously stored. The proposed new method uses the same data acquisition scheme as the conventional focusing method while maintaining the same frame rate via high-speed signal processing, but it is not suitable for imaging moving objects. It improves upon the lateral resolution and sidelobe level at all imaging depths. Also, it increases the transmit power and image signal-to-noise ratio (SNR), due to transmit field synthesis, and extends the image penetration depth as well. Evaluations with simulation and experimental data show much improvement in resolution and SNR at all imaging depths.     

Detection of ultrawide-band ultrasound pulses in optoacoustic tomography

A laser optoacoustic imaging system (LOIS) uses time-resolved detection of laser-induced pressure profiles in tissue in order to reconstruct images of the tissue based on distribution of acoustic sources. Laser illumination with short pulses generates distribution of acoustic sources that accurately replicates the distribution of absorbed optical energy. The complex spatial profile of heterogeneous distribution of acoustic sources can be represented in the frequency domain by a wide spectrum of ultrasound ranging from tens of kilohertz to tens of megahertz. Therefore, LOIS requires a unique acoustic detector operating simultaneously within a wide range of ultrasonic frequencies. Physical principles of an array of ultrawide-band ultrasonic transducers used in LOIS designed for imaging tumors in the depth of tissue are described. The performance characteristics of the transducer array were modeled and compared with experiments performed in gel phantoms resembling optical and acoustic properties of human tissue with small tumors. The amplitude and the spectrum of laser-induced ultrasound pulses were measured in order to determine the transducer sensitivity and the level of thermal noises within the entire ultrasonic band of detection. Spatial resolution of optoacoustic images obtained with an array of piezoelectric transducers and its transient directivity pattern within the field of view are described. The detector design considerations essential for obtaining high-quality optoacoustic images are presented.     

Fourier-domain digital holographic optical coherence imaging of living tissue

Digital holographic optical coherence imaging is a full-frame coherence-gated imaging approach that uses a CCD camera to record and reconstruct digital holograms from living tissue. Recording digital holograms at the optical Fourier plane has advantages for diffuse targets compared with Fresnel off-axis digital holography. A digital hologram captured at the Fourier plane requires only a 2D fast Fourier transform for numerical reconstruction. We have applied this technique for the depth-resolved imaging of rat osteogenic tumor multicellular spheroids and acquired cross-section images of the anterior segment and the retinal region of a mouse eye. A penetration depth of 1.4 mm for the tumor spheroids was achieved.     

Extended depth of field with the optimal ‘0, π’ binary phase pupil mask

A ‘0, π’ phase pupil mask was developed to extend the depth of the field of a circularly symmetric optical imaging system. A global search algorithm was used to seek an optimal pupil mask which provides the largest spatial frequency band in a certain desired contrast value. The modulation transfer function curves and the normalized point spread function figures of the imaging system with the optimal mask were analyzed. The results show that the imaging system has a high resolution in a long frequency band and can obtain clear images without any post-processing. The experimental results also demonstrate that the depth of field of the imaging system is extended sixfold successfully.     

Chemical imaging with a confocal scanning Fourier-transform-Raman microscope

Traditional approaches in confocal microscopy have focused on techniques to generate volumetric intensity or phase images of an object. In these different imaging modes the scattered optical-field properties depend on local refractive index and absorption, properties not unique to a given material. We report here on a confocal microscope that uses Raman scattered light to generate volumetric chemical images of a material. We designed and built a prototype instrument, called a confocal scanning laser Raman microscope, that combines a confocal scanning laser microscope with a Fourier-transform-Raman spectrometer. The high depth and lateral spatial resolution of the confocal optics design define a volume element from which the Raman scattered light is collected, and the spectrometer analyzes its spectral content. The sample is scanned through the microscope probe volume, and a chemical image isgenerated based on the content of the Raman spectrum extracted from each scan position in the sample. The results inclu e instrument characterization measurements and examples of confocal chemical imaging.     

Phase plate to extend the depth of field of incoherent hybrid imaging systems

A hybrid imaging system combines a modified optical imaging system and a digital postprocessing step. We describe a spatial-domain method for designing a pupil phase plate to extend the depth of field of an incoherent hybrid imaging system with a rectangular aperture. We use this method to obtain a pupil phase plate to extend the depth of field, which we refer to as a logarithmic phase plate. Introducing a logarithmic phase plate at the exit pupil of a simulated diffraction-limited system and digitally processing the detector's output extend the depth of field by an order of magnitude more than the Hopkins defocus criterion. We also examine the effect of using a charge-coupled device optical detector, instead of an ideal optical detector, on the extension of the depth of field. Finally, we compare the performance of the logarithmic phase plate with that of a cubic phase plate in extending the depth of field of a hybrid imaging system with a rectangular aperture.     

Lateral Migration Radiography

Lateral migration radiography (LMR) is a new form of Compton backscatter imaging (CBI) that utilizes both multiple-scatter and single-scatter photons. The LMR imaging modality uses two pairs of detectors. Each set has a detector that is uncollimated to predominantly image single-scatter photons and the other collimated to image predominantly multiple-scattered photons. This allows generation of two separate images, one containing primarily surface features and the other containing primarily subsurface features. These two images make LMR useful for imaging and identifying objects to a depth of several X-ray photon mean free paths even in the presence of unknown surface clutter or surface imperfections. The principles of LMR are demonstrated through Monte Carlo simulation of the photon transport. The Monte Carlo simulation results are verified with experimental measurements from an LMR system used for landmine detection. The presented research demonstrates the methodology for designing an LMR system, identifies methods for restoring and enhancing LMR images, and lays the foundation for the development of other applications of LMR, including, for example, the nondestructive examination of welds, castings, and composites.     

Simple and rigorous analytical expression of the propagating field behind an axicon illuminated by an azimuthally polarized beam

A simple and rigorous analytical expression of the propagating field behind an axicon illuminated by an azimuthally polarized beam has been deduced by use of the vector interference theory. This analytical expression can easily be used to calculate accurately the propagation field distribution of azimuthally polarized beams throughout the whole space behind an axicon with any size base angle, not just restricted inside the geometric focal region as does the Fresnel diffraction integral. The numerical results show that the pattern of the beam produced by the azimuthally polarized Gaussian beam that passes through an axicon is a multiring, almost-equal-intensity, and propagation-invariant interference beam in the geometric focal region. The number of bright rings increases with the propagation distance, reaching its maximum at half of the geometric focal length and then decreasing. The intensity of bright rings gradually decreases with the propagation distance in the geometric focal region. However, in the far-field (noninterference) region, only one single-ring pattern is produced and the dark spot size expands rapidly with propagation distance.     

Image coding for three-dimensional range-gated imaging

In the present paper we discuss the method of image coding by multiple exposure of range-gated images. This method enlarges the depth mapping range of range-gated imaging systems exponentially with the number of utilized images. We developed a theoretical model to give a precise prediction of the number of permutations that can be used for image coding. For what we believe is the first time, we realized an image coding sequence for three range-gated images to enlarge the depth mapping range by a factor of 12. We demonstrate three-dimensional imaging in a range of 460 to 1000 m using a laser pulse width of 300 ns. Because of the impact of noise, a critical linking error occurs during the encoding of the intensity images. It is possible to reduce this error by the application of effective noise reduction strategies and the use of a threshold value to the tolerance drift of intensity levels.     

Lateral Migration Radiography

Abstract

Lateral migration radiography (LMR) is a new form of Compton backscatter imaging (CBI) that utilizes both multiple-scatter and single-scatter photons. The LMR imaging modality uses two pairs of detectors. Each set has a detector that is uncollimated to predominantly image single-scatter photons and the other collimated to image predominantly multiple-scattered photons. This allows generation of two separate images, one containing primarily surface features and the other containing primarily subsurface features. These two images make LMR useful for imaging and identifying objects to a depth of several X-ray photon mean free paths even in the presence of unknown surface clutter or surface imperfections.

The principles of LMR are demonstrated through Monte Carlo simulation of the photon transport. The Monte Carlo simulation results are verified with experimental measurements from an LMR system used for landmine detection. The presented research demonstrates the methodology for designing an LMR system, identifies methods for restoring and enhancing LMR images, and lays the foundation for the development of other applications of LMR, including, for example, the nondestructive examination of welds, castings, and composites.     

Attenuated total reflection-Fourier transform infrared imaging of large areas using inverted prism crystals and combining imaging and mapping

Attenuated total reflection-Fourier transform infrared (ATR-FT-IR) imaging is a very useful tool for capturing chemical images of various materials due to the simple sample preparation and the ability to measure wet samples or samples in an aqueous environment. However, the size of the array detector used for image acquisition is often limited and there is usually a trade off between spatial resolution and the field of view (FOV). The combination of mapping and imaging can be used to acquire images with a larger FOV without sacrificing spatial resolution. Previous attempts have demonstrated this using an infrared microscope and a Germanium hemispherical ATR crystal to achieve images of up to 2.5 mm x 2.5 mm but with varying spatial resolution and depth of penetration across the imaged area. In this paper, we demonstrate a combination of mapping and imaging with a different approach using an external optics housing for large ATR accessories and inverted ATR prisms to achieve ATR-FT-IR images with a large FOV and reasonable spatial resolution. The results have shown that a FOV of 10 mm x 14 mm can be obtained with a spatial resolution of approximately 40-60 microm when using an accessory that gives no magnification. A FOV of 1.3 mm x 1.3 mm can be obtained with spatial resolution of approximately 15-20 microm when using a diamond ATR imaging accessory with 4x magnification. No significant change in image quality such as spatial resolution or depth of penetration has been observed across the whole FOV with this method and the measurement time was approximately 15 minutes for an image consisting of 16 image tiles.     

Self-referenced interferometry for the characterization of axicon lens quality

A simple interferometer for the characterization of axicon lenses is presented. The phase cone acquired by a wave propagating through an axicon, when interfered with a collinear reference wave, produces a nearly cylindrically symmetric self-referenced interference pattern from which the distortions of the axicon surface may be readily obtained. Comparison with two-dimensional off-axis interferometry is used to validate the self-referenced technique. The measurements are based on retrieval of the accrued spatial phase distribution from interference fringes with on- and off-axis reference beams and are found to be equivalent. We use the ellipticity of the phase maps to qualify axicon lenses, which are expected to exhibit radial symmetry and engage the self-referential capability of the on-axis method to derive deviation maps that characterize the surface quality of the axicons.