# High-Transmission Neutron Optical Devices Utilizing Micro-Machined Structures

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Micro-Prism Fabrication

#### 2.2. Device Modelling

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

## Abbreviations

SANS | Small angle neutron scattering |

CRL | Compound refractive lens |

TARP | Triangular array refractive prism |

USANS | Ultra-small angle neutron scattering |

OD | Outer diameter |

ID | Inner diameter |

Ra | Roughness average |

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**Figure 1.**(

**a**) Micro-prisms before assembly into the TARP. Here, the angled faces of each prism can be seen tapering radially, and each prism has been segmented into equal pieces. These pieces are then assembled with the non-angled section at the base of each prism. A single prism element, expanded in (

**d**), is shown within a red box. (

**b**) Enlarged image of a single prism segment whose angled surfaces, indicated with black dashed lines, are machined to ${2}^{\circ}$. Labels indicate prism base width, peak width, and prism height. Note that these width dimensions are the cord length of segmented rings which form the base and apex of the prism. (

**c**) White light interferometry data showing the machined surface of the prism segment. Density plot colour shows surface height, where the flat base of the prisms is shown in red and the sloped face can be seen with varying colours. Surface imperfections can be observed which correspond to a surface finish of 20 nm roughness average (Ra). Points along the blue line were sampled to measure the angle of this surface. (

**d**) These points show an angle of $1.{999}^{\circ}\pm 0.{001}^{\circ}$. This angle matches the designed surface angle of ${2}^{\circ}$. The residual plot shown below indicates that within this region, the surface form is straight to within $\pm 0.1\mathsf{\mu}\mathrm{m}$.

**Figure 2.**(

**a**) Microscope image of assembled TARP device with peak locations labelled with red dots. Peaks are detected along each vertical slice of pixels. Peak locations along a single horizontal prism are fit to a line which is then used to determine prism spacing and alignment. (

**b**) The y-intercepts of each linear fit from (

**a**) are plotted and fit to a line. The slope of this line corresponds to the average spacing of the prism peaks. The y-intercept of this line indicates the position of the first prism peak relative to the top of the camera and therefore is not shown in this plot. (

**c**) Histogram of the slope of fit lines from (

**a**). This shows that prism alignment has a standard deviation of $\pm 0.{3}^{\circ}$.

**Figure 3.**(

**a**) Experimental apparatus used to measure beam deviation from the TARP. Small angle deviations are measured by utilizing a crystal applying Bragg diffraction to select a particular deviation angle caused by the sample. The neutron beam had a wavelength of $2.38\AA \pm 0.05\AA $, accounting for the reduction in wavelength at the sample due to Bragg refraction off the monochromator and the slit placed before the TARP device. The angles $\alpha $ and ${\theta}_{s}$ correspond to the analyzer angle and sample angles, respectively. (

**b**) Scaled schematic of TARP, where the red dashed box indicates the region which is magnified and shown with an exaggerated scale in (

**c**). The aspect ratio shown here (>14) is correct for the prototype TARP. (

**c**) Schematic of the TARP showing the arrangement and length scale of each prism. The neutron path and corresponding outgoing angle of the four possibilities modelled in Equations (1) to (4) are indicated as green lines. Imperfect prism apices are modelled as flat tops, shown here, with dashed lines indicating the ideal prism apex.

**Figure 4.**(

**a**) Ultra-small-angle neutron-scattering (USANS) results from the TARP where a false colour corresponds to the logarithm of counts. Scattering peaks have been fit to a Gaussian to extract the peak maximum. Red and pink lines correspond to first- and second-order theoretical scattering curves, respectively, fit to these peaks. Curves are calculated via Equations (1) to (4), accounting for the BT-5 wavelength distribution, and fit with a free-fit parameter for material index. Dashed lines show the $95\phantom{\rule{0.166667em}{0ex}}\%$ confidence interval of this fit. This fit returns a material index of $n=1-(1.95\pm 0.09)\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}{10}^{-6}$. The dashed yellow line indicates a sample angle of ${\theta}_{s}=-{1}^{\circ}$. (

**b**) Comparison of the TARP USANS measurements (blue) with Monte Carlo simulation (red) taken at $\theta =-{1}^{\circ}$. The shaded area in blue denotes the region where beam deviation is expected from the simulation of an ideal TARP, with perfect apices. Uncertainty on neutron counts is shown for a subset of analyzer measurement angles. Neutron ray deviations from USANS experiments with the TARP show qualitative agreement with simulations.

**Figure 5.**(

**a**) Quality-factor, ${Q}_{1}$, for a neutron prism, calculated using beam deviation and neutron transmission fraction, ${Q}_{1}=\mathsf{\Delta}\theta \phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}T$, as a function of prism angle. Here, it is clear that smaller prism angles provide a significant increase in prism quality-factor. Note that this plot is shown in logarithmic y-scale. Different materials are considered, and as black lines of different style (i.e., dotted, dashed). Prism angles utilized in other neutron prism experiments are shown in solid lines, with the TARP shown in black, the prisms of the Ref. [49] shown in red, and both prisms described in the Ref. [48] shown in dark and light blue. (

**b**) Schematic of prism orientation used in the TARP device, with both the prism angle $\beta $ and complementary angle, $\xi $, labelled. (

**c**) Schematic of prism orientation used in the Refs. [48,49] with prism angle, $\xi $, and neutron ray shown as a green arrow. (

**d**) Comparison of neutron deviation from prism orientations shown in (

**b**,

**c**) plotted in blue and black, respectively.

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## Share and Cite

**MDPI and ACS Style**

Kapahi, C.; Sarenac, D.; Bleuel, M.; Cory, D.G.; Heacock, B.; Henderson, M.E.; Huber, M.G.; Taminiau, I.; Pushin, D.
High-Transmission Neutron Optical Devices Utilizing Micro-Machined Structures. *Quantum Beam Sci.* **2023**, *7*, 10.
https://doi.org/10.3390/qubs7010010

**AMA Style**

Kapahi C, Sarenac D, Bleuel M, Cory DG, Heacock B, Henderson ME, Huber MG, Taminiau I, Pushin D.
High-Transmission Neutron Optical Devices Utilizing Micro-Machined Structures. *Quantum Beam Science*. 2023; 7(1):10.
https://doi.org/10.3390/qubs7010010

**Chicago/Turabian Style**

Kapahi, Connor, Dusan Sarenac, Markus Bleuel, David G. Cory, Benjamin Heacock, Melissa E. Henderson, Michael G. Huber, Ivar Taminiau, and Dmitry Pushin.
2023. "High-Transmission Neutron Optical Devices Utilizing Micro-Machined Structures" *Quantum Beam Science* 7, no. 1: 10.
https://doi.org/10.3390/qubs7010010