File Name: shaped beadwork and beyond .zip
Focusing on geometric figures formed into three-dimensional beaded pieces, this gorgeous follow-up to her bestselling Diane Fitzgeralds Shaped Beadwork builds on Dianes earlier ideas with 40 stunning projects. In each chapter, Diane explores a different shape—from starry necklaces and heart pins to a Pirate Eyes Bracelet—and she goes in exciting new directions with imaginative and beautifully complex designs that play with patterns, crystals, and more. This means that when the Holy Spirit tells you to do something, do it.
Placing the MLA near the pupil plane of the microscope, instead of the image plane, can mitigate the artifacts and provide an efficient forward model, at the expense of field-of-view FOV.
Here, we demonstrate improved resolution across a large volume with Fourier DiffuserScope, which uses a diffuser in the pupil plane to encode 3D information, then computationally reconstructs the volume by solving a sparsity-constrained inverse problem.
Our diffuser consists of randomly placed microlenses with varying focal lengths; the random positions provide a larger FOV compared to a conventional MLA, and the diverse focal lengths improve the axial depth range. Our diffuser design outperforms the MLA used in LFM, providing more uniform resolution over a larger volume, both laterally and axially.
Volumetric fluorescence microscopy with video-rate capture is essential for understanding dynamic biological systems. Single-shot 3D imaging with a 2D sensor is possible by using a hardware encoding procedure followed by a computational decoding procedure.
The resulting 4D light field can be used for digital refocusing, perspective synthesis, or 3D reconstruction. However, using a 2D sensor to sample a 4D light field requires trading off angular and spatial sampling, resulting in poor resolution.
This is particularly undesirable in microscopy, where resolution is the key performance metric. The resolution of LFM can be improved without requiring multiple measurements [ 7 ] by taking a deconvolution approach to single-shot image reconstruction [ 8 , 9 ]. In this case, the captured 2D measurement is used to directly solve for the 3D object, without the intermediate step of calculating a 4D light field. The method makes an implicit assumption of no occlusions, which is valid for most fluorescence microscopy applications.
Deconvolution LFM can achieve significantly better nearly diffraction-limited resolution at some depth planes, but its performance degrades quickly with depth, even with wavefront coding [ 10 ].
Besides suffering from non-uniform resolution, deconvolution LFM incurs artifacts at the native focal plane and requires a computationally-intensive spatially-varying deconvolution procedure. These artifacts and the resolution loss can be mitigated by placing the MLA in an off-focus plane [ 11 — 13 ], but the spatial variance and resolution inhomogeneity remain. To solve some of these problems, an alternative configuration, termed Fourier light field microscopy FLFM , places the MLA at the Fourier pupil plane of the objective, with the sensor one microlens focal length away [ 14 — 17 ].
This effectively splits the 2D sensor into a grid of sub-images, with each microlens imaging the sample from a different perspective angle. FLFM achieves more uniform resolution near the native focal plane and has a spatially-invariant point spread function PSF for improved computational efficiency. However, the fundamental trade-off between spatial and angular sampling remains unless a camera array is used, greatly increasing cost and complexity [ 18 ].
The resolution is more homogeneous than LFM, but still degrades quickly with depth. The new architecture has several advantages: 1 By using microlenses with multiple focal lengths [ 19 — 22 ], the PSF will have sharp features at a wide range of depth planes, improving the axial depth range and resolution homogeneity.
Thus, we allow the microlens sub-images to overlap, then use compressed sensing algorithms [ 23 , 24 ] to reconstruct the 3D volume without trading off volumetric FOV and depth resolution. The resulting system achieves uniform resolution over a large volume, with imaging speed limited only by signal strength or camera frame rate.
Fourier DiffuserScope is a variant of our previous methods for diffuser-based imaging with different architectures [ 25 — 30 ]. Here, we provide the first theoretical framework for Fourier DiffuserScope design with given performance metrics e.
We demonstrate the advantages of both the random and multi-focal properties of our diffuser by comparing directly with FLFM and a random uni-focal design.
We use the system to record 3D videos of a freely-moving C. Besides variations of LFM, our work is related to other methods for single-shot 3D fluorescence microscopy. Multifocal microscopy methods simultaneously capture multiple in-focus images at different depths. This can be done by using beamsplitters and multiple cameras conjugate to different depth planes [ 31 ]; however, the resulting system is expensive and bulky.
To acquire multiple depths with a single sensor, a distorted phase grating can be inserted in the pupil plane to project different axial layers onto different sub-images on the sensor [ 32 — 34 ]. A similar result can be achieved with superimposed Fresnel lenses [ 35 ] or a diffractive metalens [ 36 ]. For more than a few depth planes, multiplexed volume holography is a good option due to its low cross-talk [ 37 ]. PSF engineering for point localization refers to methods that use a coded mask in Fourier space, like our system, but with the image captured in image real space.
This results in a depth-dependant PSF e. Because our Fourier DiffuserScope places both the phase mask and the sensor near the Fourier plane, we have a much larger PSF in which the energy is distributed into more features, so that the cross-correlation of laterally and axially shifted PSFs is lower than that of engineered PSFs.
As a result, the design matrix of our random diffuser has nearly orthogonal columns, which is better suited to reconstruct a 3D volume from an undersampled 2D measurement, according to compressed sensing theory [ 44 ].
Lensless mask-based imaging , which uses a coded aperture for lens-free 2D [ 45 ] or 3D [ 46 ] imaging, first emerged in X-ray and gamma-ray systems [ 47 , 48 ] for 2D imaging in situations where lenses are difficult to implement.
Amplitude coded masks are straightforward to design and easy to fabricate, but come with the inherent issue of blocking a lot of light, which leads to low signal-to-noise ratio SNR in the acquisition and noise amplification during reconstruction.
Phase masks are more difficult to fabricate but have much better light efficiency [ 49 ]. Diffuser-based microscopy describes several different architectures that emerged from our original DiffuserCam [ 25 ], which is a lensless phase-mask-based imager that uses a diffuser for encoding 3D information.
We have demonstrated 2D [ 28 , 50 ], 3D [ 25 , 27 , 29 , 30 ], and 4D light field imaging [ 26 ], flat [ 29 ] and miniature microscopy [ 30 ]. However, the resulting PSFs had substantial background light, which amplifies noise during deconvolution. Here, we use a designed diffuser made of randomly-located microlenses to focus light into high-contrast random multi-focal spots, providing good SNR across a large depth range, while maintaining the randomness of the PSF.
Our Fourier DiffuserScope consists of a diffuser a phase mask with randomly-located multi-focal microlenses in the Fourier plane of a microscope objective, with the sensor placed after, spaced by the average focal length of the diffuser Fig.
Because the actual Fourier plane of the objective is physically inaccessible, we insert a relay system to image its pupil plane onto the diffuser. For each point emitter in the object space, the diffuser will produce a unique multi-spot PSF on the sensor. As compared to Gaussian diffusers or highly-scattered speckle patterns, our diffuser PSF concentrates light onto fewer pixels in order to improve SNR, while also ensuring that different points come into focus at different depths.
Because our PSF is distributed and different for each point location within the 3D space, it is possible to reconstruct the whole volume from a single measurement with compressed sensing algorithms. A diffuser or microlens array is placed in the Fourier plane of the objective relayed by a 4 f system and a sensor is placed one microlens focal length after. From a single 2D sensor measurement, together with a previously calibrated point spread function PSF stack, 3D objects can be reconstructed by solving a sparsity-constrained inverse problem.
Our RMM design provides a non-periodic PSF with different spots coming into focus at different planes, enabling 3D reconstructions with full FOV and high resolution across a wider depth range. Note that the PSF images bottom right are shown with a gamma correction of 0. To model the image formation process, we divide the 3D volume into 2D slices, where each slice corresponds to a single depth plane.
Neighboring slices are separated axially by less than half the axial resolution. Our experimental system is designed to ensure that the system PSF the sensor measurement resulting from a single point source for each depth can be modeled as shift-invariant. Thus, the measurement contribution from each 2D plane is the convolution between the object slice at that depth and the PSF at that depth.
The PSFs for different depths have different sizes and different microlenses come into focus, such that each depth has a unique PSF. The forward model in Eq. Because we solve for 3D from a single 2D measurement without reducing the number of lateral pixels in the reconstruction, the inverse problem is under-determined.
We solve it by using a compressed sensing algorithm that leverages the multiplexed nature of our measurements and assumes the sample is sparse in some domain. To separate out the effects of randomness and multi-focal, we also compare to random uni-focal microlenses RUM. The MLA Fig. Assigning different focal lengths to each of the microlenses, as with our RMM Fig. This trades SNR near the native focal plane for an increased depth range due to spreading high-frequency information across the whole volume.
In this section, we derive the relationship between diffuser design and system performance in terms of lateral resolution, axial resolution, FOV and depth range. All three designs have the same size and number of microlenses, but the locations and focal-length distributions are different.
The minimum and maximum focal lengths are designed to focus at the closest and furthest depth planes within the volume-of-interest. The system schematic and parameter definitions are shown in Fig. System performance analysis. The axial resolution is determined by the minimum resolvable separation on the sensor. Table 1. Parameter definitions for the optical system. In Fourier configuration, each microlens forms a perspective view of the object. Consider the middle microlens in Fig.
Other bundles of light from the same point source will reach other microlenses, focusing to separate spots on the sensor. To achieve the diffraction-limited resolution derived above, the sensor pixel spacing must be small enough to Nyquist sample the pattern after taking into account magnification. To derive the off-focus resolution in our setup, we first calculate the defocus distance of the intermediate image for an off-focus point source the green dot in object space in Fig.
Thus, the subset of microlenses that are in focus at each depth will have spots with size matching the in-focus diffraction-limited lateral resolution derived in the previous section.
Hence, the lateral resolution does not degrade with depth within the volume-of-interest. When the object moves beyond the designed range, the lateral resolution will degrade linearly with defocus distance. A detailed analysis on the depth range is in Sec.
We define the axial resolution as the minimum axial distance between two point emitters that can be resolved in the reconstruction. The off-axis microlenses have disparity, such that point sources from different depths are imaged to different lateral locations on the sensor; two points will be resolved if their images are separated by at least the diffraction-limited lateral resolution after magnification.
We analyze the limits for the outermost microlens, which has the largest disparity angle. In Fig. Note that the slope of the defocused axial resolution as a function of depth is proportional to that of defocused lateral resolution. We analyze the in-focus FOV for each of the three microlens designs, and assume that the FOV throughout the volume will be approximately the same as that at the native focal plane.
When a point in the scene moves laterally by an amount that shifts the PSF by an integer number of pitches, the shifted PSF is nearly the same as the unshifted one; this creates ambiguities that cause the deconvolution to fail. To avoid this problem, a field stop is inserted to guarantee that the PSF shifts by less than one period over the FOV [ 15 , 16 ].
This is based on ideal optics; in reality, aberrations can break the shift-invariance of the PSF in the peripheral FOV so that the final reconstruction has a smaller FOV or reduced resolution near the edges.
In practice, we determine the FOV for by calculating the similarity between on-axis and off-axis PSFs, described in more detail in Sec.
Finished pieces resemble peyote stitch with their staggered rows, but the construction of brick stitch allows far more control over the shape of the piece. Step up your brick stitch game with increases and decreases, and follow fun patterns to create animal, flower or geometric components that make eye-catching jewelry pieces. Color in your own pattern with our free blank brick stitch grid! See project tutorials and beading patterns using the brick stitch or variations of this basic bead weaving stitch to create jewelry. All you really need to bead weave are some seed beads, a needle and thread.
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Published Written in English. Port Authority, labour relations and attempts at decasualization in the Port of London to Speech of Mr. She takes her designs to the next level with crystals, patterning, and a variety of fascinating new three-dimensional shapes. Shaped Beadwork and Beyond Take three-dimensional shapes for jewelry to a new level: more than 40 projects based on triangles, squares, pentagons and hexagons. Diane Fitzgerald's Shaped Beadwork.
Shaped Beadwork Beyond: Dimensional Jewelry in Peyote Stitch [PDF] DONWLOAD LAST PAGE!!!! DETAIL Diane Fitzgerald is the world's.
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The ability of metallic nanostructures to confine light at the sub-wavelength scale enables new perspectives and opportunities in the field of nanotechnology.
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