In digital holographic particle image velocimetry, the particle image depth-of-focus and the inaccuracy of the measured particle position along the optical axis are relatively large in comparison to the characteristic transverse dimension of the reconstructed particle images. This is the result of a low optical numerical aperture (NA), which is limited by the relatively large pixel size of the CCD camera. Additionally, the anisotropic light scattering behaviour of the seeding particles further reduces the effective numerical aperture of the optical system and substantially increases the particle image depth-of-focus. Introducing an appropriate Fourier filter can significantly suppress this additional reduction of the NA. Experimental results illustrate that an improved Fourier filter reduces the particle image depth-of-focus. For the system described in this paper, this improvement is nearly a factor of 5. Using the improved Fourier filter comes with an acceptable reduction of the hologram intensity, so an extended exposure time is needed to maintain the exposure level.
In this paper, we describe measurements of a three-dimensional (3D) flow in a T-shaped micromixer by means of digital holographic microscopy. Imaging tracer particles in a microscopic flow with conventional microscopy is accompanied by a small depth-of-field, which hinders true volumetric flow measurements. In holographic microscopy, the depth of the measurement domain does not have this limitation because any desired image plane can be reconstructed after recording. Our digital holographic microscope (DHM) consists of a conventional in-line recording system with an added magnifying optical element. The measured flow velocity and the calculated vorticity illustrate four streamwise vortices in the micromixer outflow channel. Because the investigated flow is stationary and strongly 3D, the DHM performance (i.e. accuracy and resolution) can be precisely investigated. The obtained Dynamic spatial range and Dynamic velocity range are larger than 20 and 30, respectively. High-speed multipleframe measurements illustrate the capability to simultaneously track about 80 particles in a volumetric measurement domain.
A theoretical analysis describing the dependence of the signal-tonoise ratio (SNR) on the number of pixels and the number of particles is presented for in-line digital particle holography. The validity of the theory is verified by means of numerical simulation. Based on the theory we present a practical performance benchmark for digital holographic systems. Using this benchmark we improve the performance of an experimental holographic system by a factor three. We demonstrate that the ability to quantitatively analyze the system performance allows for a more systematic way of designing, optimizing, and comparing digital holographic systems.
In a typical digital holographic PIV recording set-up, the reference beam and the object beam propagate towards the recording device along parallel axes. Consequently, in a reconstructed volume, the real image of the recorded particle field and the speckle pattern that originates from the virtual image of the recorded particle field overlap. If the recorded particle field experiences a longitudinal displacement between two recordings and if the two reconstructed complex-amplitude fields are analysed with a 3D correlation analysis, two separate peaks appear in the resulting correlation-coefficient volume. The two peaks are located at opposite longitudinal positions. One peak is related to the displacement of the real image and the other peak is related to the displacement of the speckle pattern that originates from the virtual image. Because both peaks have a comparable height, a sign ambiguity appears in the longitudinal component of the measured particle field displacement. Additionally, the measured longitudinal particle field displacement suffers from a bias error. The sign ambiguity and the bias error can be suppressed by applying a threshold operation to the reconstructed amplitude. The sign ambiguity, characterized by , is suppressed by more than a factor of 60. The dimensionless bias error is reduced by a factor of 5.
Currently, three MAPPER multi-electron beam lithography tools are operational. Two are located at customers, TSMC and LETI, and one is located at MAPPER. The tools at TSMC and LETI are used for process development. These tools each have 110 parallel electron beams and have demonstrated sub-30 nm half pitch resolution in chemically amplified resists [5].One important step towards the high volume tool is the capability to stitch the exposure of one electron beam to the next. The pre-alpha tool at MAPPER has been upgraded with an interferometer to enable exposures with a scanning stage and demonstrate first beam-to-beam stitching. A scan of 200 micrometers has been used to create a stitch area of 50 x 3 microns. The stitch error over all stitches was found to be below 25 nm.The electron beam position stability during the 10 seconds required for beam-to-beam stitching showed a contribution to the stitch error of 2.3 nm. The beam separation measurement, used to correct the static error, adds about 2.2 nm and the stage stability and linearity adds another 5 nm in the scan (interferometer) direction. In the perpendicular direction the stage instability gives the largest contribution to the stitch error (15 nm) due to the use of capacitive sensors.Overall, the electron beam stability and the beam position correction method work correctly and with sufficient accuracy for the high volume tool, 'Matrix'. The wafer stage for the Matrix system will incorporate full interferometer control to attain the needed positioning accuracy and stability.
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