Externally Dispersed Interferometry

<body> <div id="PageDiv"> <table border=0 cellspacing=0 cellpadding=0 width=736> <colgroup> <col width=18> <col width=555> <col width=12> <col width=150> <col width=1> </colgroup> <tr valign=top> <td height=19 colspan=4></td> <td height=19></td> </tr> <tr valign=top> <td height=105 rowspan=3></td> <td height=105 rowspan=3><p class="style6"><span class="Treb10" lang="en">Abstract</span><span class="style8" lang="en"><br></span><span class="style12" lang="en">Externally Dispersed Interferometry</span><span class="style7" lang="en"><br></span><span class="style28" lang="en">Lawrence Livermore Nat. Lab.    &    Space Sciences Lab. UC Berkeley</span></p> <p class="f-lp"><span class="style13" lang="en">Principal investigators </span><span class="style7" lang="en"><br></span><span class="style30" lang="en">David Erskine & Jerry Edelstein</span></p> </td> <td height=90 colspan=2></td> <td height=90></td> </tr> <tr valign=top> <td height=12></td> <td height=12><p class="style32 f-fp f-lp" lang="en">Feb 2005</p> </td> <td height=12></td> </tr> <tr valign=top> <td height=3 colspan=2></td> <td height=3></td> </tr> <tr class="f-sp"> <td><img src="Resources/_clear.gif" border=0 width=18 height=1 alt="" style="float:left"></td> <td><img src="Resources/_clear.gif" border=0 width=555 height=1 alt="" style="float:left"></td> <td><img src="Resources/_clear.gif" border=0 width=12 height=1 alt="" style="float:left"></td> <td><img src="Resources/_clear.gif" border=0 width=150 height=1 alt="" style="float:left"></td> <td height=11><img src="Resources/_clear.gif" border=0 width=1 height=1 alt="" style="float:left"></td> </tr> </table> <table border=0 cellspacing=0 cellpadding=0 width=460> <colgroup> <col width=18> <col width=441> <col width=1> </colgroup> <tr valign=top> <td height=132></td> <td height=132><img src="Resources/planet-star-anim2.gif" border=0 width=435 height=127 alt="" style="float:left"></td> <td height=132></td> </tr> <tr class="f-sp"> <td><img src="Resources/_clear.gif" border=0 width=18 height=1 alt="" style="float:left"></td> <td><img src="Resources/_clear.gif" border=0 width=441 height=1 alt="" style="float:left"></td> <td height=15><img src="Resources/_clear.gif" border=0 width=1 height=1 alt="" style="float:left"></td> </tr> </table> <table border=0 cellspacing=0 cellpadding=0 width=696> <colgroup> <col width=11> <col width=684> <col width=1> </colgroup> <tr valign=top> <td height=87></td> <td height=87 bgcolor="#cccccc"><p class="style5" lang="en">For the Doppler planet search, <br> and for boosting the performance/size <br>of high resolution spectrographs</p> </td> <td height=87></td> </tr> <tr class="f-sp"> <td><img src="Resources/_clear.gif" border=0 width=11 height=1 alt="" style="float:left"></td> <td><img src="Resources/_clear.gif" border=0 width=684 height=1 alt="" style="float:left"></td> <td height=6><img src="Resources/_clear.gif" border=0 width=1 height=1 alt="" style="float:left"></td> </tr> </table> <table border=0 cellspacing=0 cellpadding=0 width=696> <colgroup> <col width=8> <col width=687> <col width=1> </colgroup> <tr valign=top> <td height=721></td> <td height=721> <table border=1 cellspacing=3 cellpadding=0> <tr> <td width=679 height=713 valign=top><p class="style16"><span class="style35" lang="en">A method for boosting the performance of grating and prism spectrographs, by inserting a small optical device (fixed delay interferometer) in series with the beam, and processing the data to extract so-formed moire patterns</span></p> <p class="style16"><span class="Treb12" lang="en">This is a method of</span><span class="style36" lang="en"> </span><span class="style10" lang="en"><br></span><span class="style69" lang="en">• Performing precision stellar Doppler radial velocimetry with inexpensive and compact low resolution spectrographs</span></p> <p class="style16"><span class="style69" lang="en">• Performing high resolution spectroscopy over a wide simultaneous bandwidth at good photon signal to noise ratio, with compact and inexpensive dispersive spectrographs</span></p> <p class="style24" lang="en">• Retrofitting, in a reversible manner like an inserted "filter", an existing spectrograph to increase its resolution and robustness</p> <hr><p class="style16"><span class="ArialBlack12" lang="en">How it measures Doppler shifts</span><span class="style38" lang="en"><br></span><span class="Treb12" lang="en">The interferometer has two unequal arms so there is a relative delay between the two paths of light. If a whole number of wavelengths fits in the delay, then there is constructive interference and the light passes out the main output perfectly. If there is an odd number of half wavelengths, then there is destructive interference and the light passes totally out the complementary output and zero out the main output. (The intensities of the two outputs summed together is constant, independent of wavelength.) Thus for each output, the transmission function is sinusoidal versus wavelength (actually, vs wavenumber which is 1/wavelength).</span></p> <p class="style16"><span class="Treb12" lang="en">When this transmission pattern is dispersed by the spectrograph it creates a periodic grid. This grid multiplies the input stellar spectrum. A consequence is that beats are formed between features and the grid, for the features that have similar size as the grid. These beats are also called moire patterns.</span></p> <p class="style16"><span class="Treb12" lang="en">When the exoplanet pulls the star it creates a Doppler shift in the spectrum vs wavelength. In a conventional device this wavelength shift is attempted to be measured directly-- but this is difficult because it is a small shift easily confused with irregularities in the spectrograph. </span></p> <p class="style16"><span class="Treb12" lang="en">In the EDI the wavelength shift creates a phase shift in the moire pattern. (Usually we arrange for the interferometer phase to vary vertically so that a moire phase shift is a vertical shift.) In most caes, this phase shift can be more easily measured than the wavelength shift because the moire patterns are broader than the features that created them, and less susceptible to instrument distortions. You can confirm this by looking at this animation from far away and you can easily see the moire pattern move up and down even though you may not be able to see the slight sideways motion of the underlying spectrum.</span></p> <p class="style16"><span class="ArialBlack12" lang="en">How it measures high resolution spectra</span><span class="style71" lang="en"><br></span><span class="Treb12" lang="en">The moire patterns represent originally high spatial frequency information (that is, narrow features in the spectrum) beaten down to low spatial frequencies (broad moire patterns). These broad patterns are more easily measured by small inexpensive and light efficient spectrographs. This is also called a heterodyning process and is represent by a simple shift in spatial frequency, if the data is plotted vs spatial frequency (a Fourier transformation easily does this). This optical heterodyning process can be reversed numerically during data analysis to recover high spatial frequencies that would ordinarily not be resolved by the spectrograph.</span></p> <p class="style16"><span class="Treb12" lang="en">The ordinary spectrum is recovered from the data simply by adding all the channels vertically so that the moire patterns cancel. Hence the original spectrograph capabilities are retained. 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