Limiting Uncertainty Relations in Laser-Based Measurements of Position and Velocity Due to Quantum Shot Noise

Fischer, Andreas

doi:10.3390/e21030264

Cited by 10 publications

(4 citation statements)

References 101 publications

(132 reference statements)

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Section: Micro-extrusion Strain Measurementmentioning

confidence: 99%

“…By using coherent (for DSP) and incoherent (for DIC) illumination complementarily, high-resolution speckle images and surface images were recorded between each of the consecutive forming steps along the forming path (Figure 17f). Locally resolved deformation and strain fields were calculated by means of a digital image/speckle correlation method [23,24], as shown in Figure 17f for the relative displacements in the extrusion direction y shift after a forming step with an average shift of 13 µm. Note the relative y-elongation of the micro sample after forming, which results in a positive strain in the extrusion direction.…”

Section: Micro-extrusion Strain Measurementmentioning

confidence: 99%

“…Figure23. Descriptors of the austenitizing peaks derived from DSC measurements of the GKZ and Q1 heat treatment conditions.…”

mentioning

confidence: 99%

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Descriptors for High Throughput in Structural Materials Development

et al. 2019

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The development of novel structural materials with increasing mechanical requirements is a very resource-intense process if conventional methods are used. While there are high-throughput methods for the development of functional materials, this is not the case for structural materials. Their mechanical properties are determined by their microstructure, so that increased sample volumes are needed. Furthermore, new short-time characterization techniques are required for individual samples which do not necessarily measure the desired material properties, but descriptors which can later be mapped on material properties. While universal micro-hardness testing is being commonly used, it is limited in its capability to measure sample volumes which contain a characteristic microstructure. We propose to use alternative and fast deformation techniques for spherical micro-samples in combination with classical characterization techniques such as XRD, DSC or micro magnetic methods, which deliver descriptors for the microstructural state.

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Section: Micro-extrusion Strain Measurementmentioning

confidence: 99%

Section: Micro-extrusion Strain Measurementmentioning

confidence: 99%

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Descriptors for High Throughput in Structural Materials Development

et al. 2019

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“…Laser speckle photography [12] transgresses these limitations and is already used for tensile tests [13] as well as an in-process measuring method for the induced deformation during machining [14,15]. Speckle photography is physically limited only by Heisenberg's uncertainty principle and the respective measurement uncertainty limit can be derived with the Cramér-Rao bound [16,17]. It has therefore the potential for precise small-scale measurements.…”

Section: Introductionmentioning

confidence: 99%

Uncertainty and Resolution of Speckle Photography on Micro Samples

et al. 2020

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The efficient development of new materials with defined properties requires fast methods of testing low volumes of material, such as a high-throughput investigation of spherical metallic micro samples with varying compositions and structuring treatments. A classical material testing method for macro samples, the tensile test cannot be employed for analyzing the mechanical properties of spherical samples with diameters below 1 mm since there are currently no methods for holding and stretching them. A combination between the incremental electrohydraulic extrusion as stress actuation unit and the speckle photography as strain measuring method is presented for obtaining the required mechanical characteristics. Positive longitudinal strain is generated at stepwise extrusion through < 1 mm wide forming channels using a liquid punch and the deformation is observed in situ after each forming step at the interface between the micro sample and a transparent window integrated into the forming die. The occurring local strain fields with a lateral extension down to 100 µm and high gradients require displacement measurements with high lateral resolution over a large range of local dislocations between 0.1 and > 10 µm. It is unknown, whether the speckle strain measuring method is able to provide the necessary low uncertainty for the required resolution in the whole measuring range. Therefore, theoretical and experimental investigations of the deformation measurability using the speckle correlation method are presented, showing that local displacements up to 10 µm can be measured with a spatial resolution between 3 and 10 µm depending on the displacement size. The dominant effect influencing the measurement uncertainty for displacements at this high spatial resolution is the speckle noise, resulting into measurement uncertainties of less than 100 nm. Hence, speckle photography is shown to be applicable for tensile test on micro samples.

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Fundamental flow measurement capabilities of optical Doppler and time-of-flight principles

Fischer

2021

Exp Fluids

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In order to understand the fundamental measurement capabilities of different flow velocity measurement principles based on Mie scattering, a fundamental equation of how to calculate the shot noise limit for a respective signal model is derived. The derivation is based on the well-known rules of uncertainty propagation and yields the Cramér–Rao bound without the necessity to calculate the Fisher information. The derived equation is next applied to compare the shot noise limit for Doppler and time-of-flight principles including laser Doppler anemometry (LDA), planar Doppler velocimetry (PDV), laser-two-focus velocimetry (L2F), particle tracking velocimetry (PTV) and particle image velocimetry (PIV). The comparison is performed for an identical mean laser power, while two cases are studied in detail: measuring on a single seeding particle as well as measuring on multiple seeding particles and averaging. LDA, L2F and PTV/PIV obey a similar shot noise limit. For the case of a measurement on multiple seeding particles, the minimal achievable measurement uncertainty is directly proportional to the absolute value of the measured velocity component and inversely proportional to the spatial resolution. The respective shot noise limit for PDV is almost independent of the measured flow velocity component and the spatial resolution. Since PDV is sensitive with respect to a different flow velocity component depending on the observation direction, a comparison with the other principles is only reasonable to a certain extent. However, all shot noise limits in case of measuring on multiple seeding particles show the expected inverse proportionality to the square root of the total number of detected photons and thus also to the square root of the measurement time. Considering a comparable spatiotemporal resolution, an identical mean light power and typical measurement configurations, the PDV shot noise limit is the largest. As a final result, it is derived that each measurement principle obeys an uncertainty principle between position and the respective component of the wave vector, which is in agreement with Heisenberg’s uncertainty principle. Therefore, a common basis is provided to assess the fundamental measurement capabilities of Doppler and time-of-flight measurement systems on the basis of what is possible within the quantum mechanical constraints. Graphic abstract

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Limiting Uncertainty Relations in Laser-Based Measurements of Position and Velocity Due to Quantum Shot Noise

Cited by 10 publications

References 101 publications

Descriptors for High Throughput in Structural Materials Development

Descriptors for High Throughput in Structural Materials Development

Uncertainty and Resolution of Speckle Photography on Micro Samples

Fundamental flow measurement capabilities of optical Doppler and time-of-flight principles

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