test

<math xmlns="http://www.w3.org/1998/Math/MathML">
  <msub>
    <mi>r</mi>
    <mn>0</mn>
  </msub>
  <mo>=</mo>
  <msup>
    <mrow>
      <mo>[</mo>
      <mrow>
        <mn>0.423</mn>
        <msup>
          <mrow>
            <mo>(</mo>
            <mfrac>
              <mrow>
                <mn>2</mn>
                <mi>&#x03C0;<!-- π --></mi>
              </mrow>
              <mi>&#x03BB;<!-- λ --></mi>
            </mfrac>
            <mo>)</mo>
          </mrow>
          <mn>2</mn>
        </msup>
        <msubsup>
          <mo>&#x222B;<!-- ∫ --></mo>
          <mn>0</mn>
          <mi mathvariant="normal">&#x221E;<!-- ∞ --></mi>
        </msubsup>
        <msubsup>
          <mi>C</mi>
          <mi>N</mi>
          <mn>2</mn>
        </msubsup>
        <mo stretchy="false">(</mo>
        <mi>h</mi>
        <mo stretchy="false">)</mo>
        <mi>d</mi>
        <mi>h</mi>
      </mrow>
      <mo>]</mo>
    </mrow>
    <mrow class="MJX-TeXAtom-ORD">
      <mo>&#x2212;<!-- − --></mo>
      <mn>3</mn>
      <mrow class="MJX-TeXAtom-ORD">
        <mo>/</mo>
      </mrow>
      <mn>5</mn>
    </mrow>
  </msup>
  <mo>.</mo>
</math>

 

    • FRIED’S PARAMETER

 

    • The Fried’s parameter

r0

    •  is the typical size (diameter of a circular area for example) in which the perturbed wavefront is coherent i.e. the rms wavefront aberration due to the passage of a wavefront through the atmosphere is equal to 1 radian. It corresponds to the size of the equivalent telescope for an observation outside the earth’s atmosphere. The analytical expression of

r0

    •  normalized with respect to the zenith is:
𝑟0=[0.423(2𝜋𝜆)2∫0∞𝐶𝑁2(ℎ)𝑑ℎ]−3/5.
(7)
    • where

λ

    •  is the wavelength (

λ = 0.5 microns

    • ),

h

     the height above the ground.