<p>Fourier integral microscopy (FIMic), or Fourier light-field microscopy, is the latest architecture of plenoptic (also known as light-field or integral) imagers. It has the highest demonstrated spatial resolution for integral microscopy and is equivalent to an array of micro-cameras that record full views of the scene. Thus, standard tomographic or triangulation algorithms can reconstruct the measurement volume at microscopic scales. By being compact, FIMic overcomes the physical space constraints of traditional multi-camera systems. It is demonstrated with molecular tagging velocimetry (MTV) in the near-wall region of a turbulent stagnation jet; this is the first volumetric implementation of MTV. The design rules for a FIMic system are reviewed in detail, as well as the calibration procedure. With a 0.28 numerical aperture microscope objective (10<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_4078_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">$\times$</EquationSource> <EquationSource Format="MATHML"><math> <mo>×</mo> </math></EquationSource> </InlineEquation>), the following resolutions are achieved: <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_4078_Article_IEq2.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">$7~\upmu \textrm{m}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>7</mn> <mspace width="3.33333pt" /> <mi mathvariant="normal">μ</mi> <mtext>m</mtext> </mrow> </math></EquationSource> </InlineEquation> laterally and <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_4078_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">$34~\upmu \textrm{m}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>34</mn> <mspace width="3.33333pt" /> <mi mathvariant="normal">μ</mi> <mtext>m</mtext> </mrow> </math></EquationSource> </InlineEquation> axially (wall-normal direction) over a <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_4078_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="TEX">$1700 ~\upmu \textrm{m}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1700</mn> <mspace width="3.33333pt" /> <mi mathvariant="normal">μ</mi> <mtext>m</mtext> </mrow> </math></EquationSource> </InlineEquation> field of view and <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_4078_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">$440~\upmu \textrm{m}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>440</mn> <mspace width="3.33333pt" /> <mi mathvariant="normal">μ</mi> <mtext>m</mtext> </mrow> </math></EquationSource> </InlineEquation> depth of field; however, the MTV signal can be recovered over a depth range of <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_4078_Article_IEq6.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="63" /> </InlineMediaObject> <EquationSource Format="TEX">$1500~\upmu \textrm{m}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1500</mn> <mspace width="3.33333pt" /> <mi mathvariant="normal">μ</mi> <mtext>m</mtext> </mrow> </math></EquationSource> </InlineEquation>. The 3D intensity field is reconstructed using Richardson–Lucy 3D deconvolution, which is commonly employed in microscopy. From the intensity field, a <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="348_2025_4078_Article_IEq7.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">$2\times 3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2</mn> <mo>×</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> array of MTV lines is interrogated, which, at first order, gives lateral displacements in wall-parallel slices. From the two velocity components, gradients are computed, and the wall-normal velocity component is integrated from the continuity equation. Finally, visualization of submillimeter 3D flow structures is demonstrated.</p>

Near-wall volumetric molecular tagging velocimetry with a Fourier integral microscope

期刊论文
发表日期：

2025年7月21日

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Peter D. Huck,
Mark J. Yamakaitis,
Charles Fort,
Philippe M. Bardet

摘要

Fourier integral microscopy (FIMic), or Fourier light-field microscopy, is the latest architecture of plenoptic (also known as light-field or integral) imagers. It has the highest demonstrated spatial resolution for integral microscopy and is equivalent to an array of micro-cameras that record full views of the scene. Thus, standard tomographic or triangulation algorithms can reconstruct the measurement volume at microscopic scales. By being compact, FIMic overcomes the physical space constraints of traditional multi-camera systems. It is demonstrated with molecular tagging velocimetry (MTV) in the near-wall region of a turbulent stagnation jet; this is the first volumetric implementation of MTV. The design rules for a FIMic system are reviewed in detail, as well as the calibration procedure. With a 0.28 numerical aperture microscope objective (10 $\times$ $\times$ ), the following resolutions are achieved: $7~\upmu \textrm{m}$ $7 μ m$ laterally and $34~\upmu \textrm{m}$ $34 μ m$ axially (wall-normal direction) over a $1700 ~\upmu \textrm{m}$ $1700 μ m$ field of view and $440~\upmu \textrm{m}$ $440 μ m$ depth of field; however, the MTV signal can be recovered over a depth range of $1500~\upmu \textrm{m}$ $1500 μ m$ . The 3D intensity field is reconstructed using Richardson–Lucy 3D deconvolution, which is commonly employed in microscopy. From the intensity field, a $2\times 3$ $2 \times 3$ array of MTV lines is interrogated, which, at first order, gives lateral displacements in wall-parallel slices. From the two velocity components, gradients are computed, and the wall-normal velocity component is integrated from the continuity equation. Finally, visualization of submillimeter 3D flow structures is demonstrated.