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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<!--
LOG of changes and updates:
- Version 1.0 (30 Apr 2019): Cloned the ExpTime calculator V1.4 and modified for different collecting areas for NRT
- Version 2.0 (17 May 2019): DMA used Marco Lam's graphical google chart work and modified to solve for Limiting Magnitude
- Version 3.0 (03 June 2019): DMA extended with a second plot with the Spectrograph options
Previous versions of the Exposure time calulutaor on which this was built were;
- Version 1.0 (19 Jun 2014): original code with guestimates for SPRAT, RISE and IO:I
- Version 1.1 ( 4 Jul 2014): reduced size of tables and tweaked text (CJD)
- Version 1.2 (20 Nov 2014): tweaked text (CJD)
- Version 1.3 (24 Apr 2015): Update IO:I H-band zeropoint (CJD)
- Version 1.4 (01 Oct 2015): Update to RINGO3 Zeropoint and Readnoise values (IAS via NRC)
** Make sure you update the version number (will be displayed) at the end of this doc **
-->
<html>
<title>The Liverpool Telescope Instruments : Limiting magnitude calculator for different telesope apertures</title>
<body>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap.min.css" integrity="sha384-1q8mTJOASx8j1Au+a5WDVnPi2lkFfwwEAa8hDDdjZlpLegxhjVME1fgjWPGmkzs7" crossorigin="anonymous">
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/css/bootstrap-theme.min.css" integrity="sha384-fLW2N01lMqjakBkx3l/M9EahuwpSfeNvV63J5ezn3uZzapT0u7EYsXMjQV+0En5r" crossorigin="anonymous">
<link rel="stylesheet" type="text/css" href="https://cdnjs.cloudflare.com/ajax/libs/bootstrap-slider/10.6.1/css/bootstrap-slider.min.css">
<link rel="stylesheet" type="text/css" href="https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min.css">
<script type="text/javascript" src="https://www.gstatic.com/charts/loader.js"></script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/jquery/2.2.4/jquery.min.js"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.3.6/js/bootstrap.min.js" integrity="sha384-0mSbJDEHialfmuBBQP6A4Qrprq5OVfW37PRR3j5ELqxss1yVqOtnepnHVP9aJ7xS" crossorigin="anonymous"></script>
<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/bootstrap-slider/10.6.1/bootstrap-slider.min.js"></script>
<style type="text/css">
td {padding:0 15px 0 15px;}
</style>
<center>
<br><br>
<p> Enter a comma seperated list of the telescope apertures (in metres) into the Apertures box</p>
<p style="width:600px"> NOTE: The calculation assumes that the collecting area of the telescope scales as the square of the aperture (i.e. that the ratio of primary mirror diameter to secondary mirror obscuration diameter is fixed). Further the pixel scale of an LT instrument on a larger telescope is assumed to be the same.</p>
<div id="curve_chart" style="width: 1000px; height: 600px"></div>
<!-- .......... INPUT DATA TABLE .......... -->
<table>
<tr>
<td id="pulldn">Instrument: </td>
<td>
<select name="instrument" id="instrum" onchange="calcimage();">
<option value="ioo"> IO:O</option>
<option value="ioi"> IO:I</option>
<option value="rise"> RISE</option>
<option value="ringo"> RINGO3</option>
</select>
</td>
<td id="pulldn"> Exposure Time (s):</td>
<td>
<input id="expt" data-slider-id='ex1Slider' type="text" data-slider-min="0" data-slider-max="1200" data-slider-step="30" data-slider-value="300" onchange="calcimage();"/>
</td>
</tr>
<tr>
<td id="pulldn">Binning: </td>
<td>
<select name="binning" id="binn" onchange="calcimage();">
<option value="two"> 2x2 </option>
<option value="one"> 1x1 </option>
<option value="rgbin"> RINGO3 (unbinned) </option>
</select>
</td>
<td id="pulldn"> SNR: </td>
<td>
<input id="snr" data-slider-id='ex1Slider' type="text" data-slider-min="1" data-slider-max="100" data-slider-step="1" data-slider-value="50" onchange="calcimage();"/>
</td>
</tr>
<tr>
<td id="pulldn">Filter: </td>
<td>
<select name="filter" id="filt" onchange="calcimage();">
<option value="fsu"> SDSS-U (AB system) </option>
<option value="fbb"> Bessell-B (Vega) </option>
<option value="fbv"> Bessell-V (Vega) </option>
<option value="fsg"> SDSS-G (AB system) </option>
<option value="fsr"> SDSS-R (AB system) </option>
<option value="fsi"> SDSS-I (AB system) </option>
<option value="fsz"> SDSS-Z (AB system) </option>
<!--<option value="fjj"> J (IO:I) </option>-->
<option value="fhh"> H (Vega) </option>
<option value="frise"> RISE V+R </option>
<option value="frise720"> RISE 720nm </option>
<option value="fringr"> RINGO3 Red 'd' </option>
<option value="fringg"> RINGO3 Green 'f' </option>
<option value="fringb"> RINGO3 Blue 'e' </option>
</select>
</td>
<td>Sky Brightness: </td>
<td>
<input id="sky" data-slider-id='ex1Slider' type="text" data-slider-min="0" data-slider-max="10" data-slider-step="0.5" data-slider-value="2" onchange="calcimage();"/>
</td>
</tr>
<tr>
<td></td>
<td></td>
<td id="pulldn">Apertures (m):</td>
<td>
<input id="apers" value="2.0,3.5,4.2" onchange="calcimage();">
</td>
</table>
<br><br>
<div id="spcurve_chart" style="width: 1000px; height: 600px"></div>
<table>
<tr>
<td id="pulldn">Instrument: </td>
<td>
<select name="spectrometer" id="spinstrum" onchange="calcspec();">
<option value="frodo"> FRODOspec</option>
<option value="sprat"> SPRAT</option>
</select>
</td>
<td id="pulldn"> Exposure Time (s):</td>
<td>
<input id="spexpt" data-slider-id='ex1Slider' type="text" data-slider-min="0" data-slider-max="1200" data-slider-step="30" data-slider-value="300" onchange="calcspec();"/>
</td>
</tr>
<tr>
<td id="pulldn">Slit: </td>
<td>
<select name="slitwidth" id="spslit" onchange="calcspec();">
<option value="ifu"> IFU fibre bundle </option>
<option value="spratslit"> SPRAT 2 arcsec slit </option>
</select>
</td>
<td id="pulldn"> SNR: </td>
<td>
<input id="spsnr" data-slider-id='ex1Slider' type="text" data-slider-min="1" data-slider-max="100" data-slider-step="1" data-slider-value="50" onchange="calcspec();"/>
</td>
</tr>
<tr>
<td id="pulldn">Spectrometer arm: </td>
<td>
<select name="specarm" id="sparm" onchange="calcspec();">
<option value="frredarmv"> FRODOspec Red arm (VPH) </option>
<option value="frbluarmv"> FRODOspec Blue arm (VPH) </option>
<option value="frredarm"> FRODOspec Red arm (low res) </option>
<option value="frbluarm"> FRODOspec Blue arm (low res) </option>
<option value="spredarm"> SPRAT Red region </option>
<option value="spbluarm"> SPRAT Blue region </option>
</select>
</td>
<td>Sky Brightness: </td>
<td>
<input id="spsky" data-slider-id='ex1Slider' type="text" data-slider-min="0" data-slider-max="10" data-slider-step="0.5" data-slider-value="2" onchange="calcspec();"/>
</td>
</tr>
<tr>
<td><td>
<td id="pulldn">Apertures (m):</td>
<td>
<input id="spapers" value="2.0,3.5,4.2" onchange="calcspec();">
</td>
</tr>
</table>
<br><br><br>
<p> <i>(Version 3.0 - May 2019, Marco Lam and Doug Arnold)</i> </p>
</center>
<!-- ......................................................................... -->
<!-- ... The rest of this file is JavaScript code within the <script> tags ... -->
<!-- ......................................................................... -->
<script>
/*
* This script defines the calculate() function called by the event handlers
* in HTML above. The function reads values from
<input> elements or
<select>
* pull-down options, calculates exposure times, then displays the results
* in
<span> elements.
*/
// TIP: variables declared as "var" are Global variables. However,
// variables declared inside a function as "var" are local to the function.
google.charts.load('current', {'packages':['corechart']});
google.charts.setOnLoadCallback(calcimage);
google.charts.setOnLoadCallback(calcspec);
var slider1 = new Slider("#expt", {
formatter: function(value) {
return value;
}
});
var slider2 = new Slider("#snr", {
formatter: function(value) {
return value;
}
});
var slider3 = new Slider("#sky", {
formatter: function(value) {
return value;
}
});
var slider4 = new Slider("#spexpt", {
formatter: function(value) {
return value;
}
});
var slider5 = new Slider("#spsnr", {
formatter: function(value) {
return value;
}
});
var slider6 = new Slider("#spsky", {
formatter: function(value) {
return value;
}
});
function calcimage() {
var chart = new google.visualization.LineChart(document.getElementById('curve_chart'));
// Look up (Define?) the input elements in the document for IMAGING
var instrum = document.getElementById("instrum").value;
var binn = document.getElementById("binn").value;
var filt = document.getElementById("filt").value;
var expt = +document.getElementById("expt").value;
var snr = +document.getElementById("snr").value;
var sky = +document.getElementById("sky").value;
var apers = document.getElementById("apers").value;
// FIRST PULL-DOWN ***
// Look-up tables of variables - INSTRUMENT CHARACTERISTICS
if (instrum == "ioo") {
var pixscale = 0.15;
var darkcurrent = 0;
var readnoise = 10;
} else if (instrum == "ioi") {
var pixscale = 0.18;
var darkcurrent = 0;
var readnoise = 17;
} else if (instrum == "rise") {
var pixscale = 0.54;
var darkcurrent = 0;
var readnoise = 10;
} else { // ringo3
var pixscale = 0.48;
var darkcurrent = 0;
var readnoise = 17; // Updated by IAS via NRC October 2015
};
// SECOND PULL-DOWN ***
// Look-up tables of variables -BINNING
if (binn == "two") {
var bin = 2;
} else {
var bin = 1;
};
// THIRD PULL-DOWN ***
// Look-up tables of variables - ZERO POINTS & SKY (inst and filter specific)
// NB. ZPs should correspond to 1 electron/second (i.e. corrected for GAIN)
// The RINGO3 values assume GAIN = 1, and therefore become increasingly
// inaccurate at exposure times >3 sec.
// For skybrightness data see:
// http://www.ing.iac.es/Astronomy/observing/conditions/skybr/skybr.html
// ...
if (filt == "fsu") { // IO:O sdss_u
var zp = 22.17; // 21.30 from old ETC, modified by CMC in Jan 2016 using Helen Jermak's post-recoating factors (29 June 2015 email)
var skybr = 21.0; // Skybr values are similar to ING
var skyoff = 1.5; // measurements on their web-site
} else if (filt == "fbb") { // IO:O bessell_b
var zp = 24.90; // 24.10 from old ETC, modified with HJ's factor
var skybr = 22.3;
var skyoff = 1.5;
} else if (filt == "fbv") { // IO:O bessell_v
var zp = 24.96; // 24.20 from old ETC, modified with HJ's factor
var skybr = 21.4;
var skyoff = 1.5;
} else if (filt == "fsg") { // IO:O sdss_g
var zp = 25.14; // 24.40 from old ETC, modified with HJ's factor
var skybr = 21.7;
var skyoff = 1.0;
} else if (filt == "fsr") { // IO:O sdss_r
var zp = 25.39; // 24.60 from old ETC, modified with HJ's factor
var skybr = 20.4;
var skyoff = 1.0;
} else if (filt == "fsi") { // IO:O sdss_i
var zp = 25.06; // 24.40 from old ETC, modified with HJ's factor
var skybr = 19.3;
var skyoff = 1.0;
} else if (filt == "fsz") { // IO:O sdss_z
var zp = 24.52; // 24.0 from old ETC, modified with HJ's factor
var skybr = 18.3;
var skyoff = 0.5;
} else if (filt == "fjj") { // IO:I J-band
var zp = 24.50; // 24.0 from IO:I webpage (pre-commissioning, so RMB estimate?). In Jan 2016 CMC added 0.5 after 2015 recoating.
var skybr = 16.6; // from ING sky brightness page, in mag per sqr arcsec
var skyoff = 0.0; // skyoff assumes moon has no affect on J-band sky
} else if (filt == "fhh") { // IO:I H-band
var zp = 24.00; // 23.5 updated after commissioning; corrected for gain (CJD). CMC added 0.5 after 2015 recoating.
var skybr = 12.5; // from ING sky brightness page, in mag per sqr arcsec
var skyoff = 0.0; // skyoff assumes moon has no affect on H-band sky
} else if (filt == "frise") { // rise V+R
var zp = 25.20; // In Jan 2016 CMC added 0.7 to original value of 24.50 following 2015 recoating
var skybr = 20.4; // ... same as sdss-r above
var skyoff = 1.0; // ... same as sdss-r above
} else if (filt == "frise720") { // rise 720
var zp = 23.40; //
var skybr = 19.3; // ... same as sdss-i above
var skyoff = 1.0; // ... same as sdss-i above
} else if (filt == "fringr") { // ringo3 (red 'd') - assume like I
var zp = 21; // Updated by IAS via NRC October 2015
var skybr = 19.3; // ... same as sdss-i above
var skyoff = 1.0; // ... same as sdss-i above
} else if (filt == "fringg") { // ringo3 (green 'f') - assume like R
var zp = 21.8; // Updated by IAS via NRC October 2015
var skybr = 20.4; // ... same as sdss-r above
var skyoff = 1.0; // ... same as sdss-r above
} else { // ringo3 (blue 'e') - assume like B
var zp = 23; // Updated by IAS via NRC October 2015
var skybr = 22.3; // ... same as bessel B above
var skyoff = 1.5; // ... same as bessel B above
};
// *************************************************************************
// ****
// **** Check the select-option combinations are valid
// ****
//IO:O
if (instrum == "ioo" && binn == "rgbin") {
alert("Incorrect Instrument-Binning Combination!");
}
if (instrum == "ioo" && filt == "fjj") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioo" && filt == "fhh") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioo" && (filt == "frise" || filt == "frise720") ) {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioo" && filt == "fringr") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioo" && filt == "fringg") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioo" && filt == "fringb") {
alert("Incorrect Instrument-Filter Combination!");
}
//IO:I
if (instrum == "ioi" && binn == "rgbin") {
alert("Incorrect Instrument-Binning Combination!");
}
if (instrum == "ioi" && filt == "fsu") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioi" && filt == "fbb") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioi" && filt == "fbv") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioi" && filt == "fsg") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioi" && filt == "fsr") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioi" && filt == "fsi") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioi" && filt == "fsz") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioi" && (filt == "frise" || filt == "frise720") ) {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioi" && filt == "fringr") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioi" && filt == "fringg") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ioi" && filt == "fringb") {
alert("Incorrect Instrument-Filter Combination!");
}
//RISE
if (instrum == "rise" && binn == "rgbin") {
alert("Incorrect Instrument-Binning Combination!");
}
if (instrum == "rise"){
if ( !(filt == "frise" || filt == "frise720") ) {
alert("Incorrect Instrument-Filter Combination!");
}
}
//RINGO3
if (instrum == "ringo" && binn == "one") {
alert("Incorrect Instrument-Binning Combination!");
}
if (instrum == "ringo" && binn == "two") {
alert("Incorrect Instrument-Binning Combination!");
}
if (instrum == "ringo" && filt == "fsu") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ringo" && filt == "fbb") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ringo" && filt == "fbv") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ringo" && filt == "fsg") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ringo" && filt == "fsr") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ringo" && filt == "fsi") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ringo" && filt == "fsz") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ringo" && filt == "fjj") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ringo" && filt == "fhh") {
alert("Incorrect Instrument-Filter Combination!");
}
if (instrum == "ringo" && (filt == "frise" || filt == "frise720") ) {
alert("Incorrect Instrument-Filter Combination!");
}
// Could display in table the ZP to be used - commented out below
// document.getElementById("zpused").innerHTML = zp.toFixed(2);
// *************************************************************************
// ****
// **** SETUP OUTPUT VALUES
// ****
var data = new google.visualization.DataTable();
data.addColumn('number', 'Seeing Value');
const aperSizes = apers.split(",").map(Number);
console.log(aperSizes)
aperSizes.forEach(function(aper){
data.addColumn('number', aper.toFixed(1) + 'm Aperture');
});
//}
// ****
// **** MAIN CALCULATION (Imaging)
// ****
// POINT sources
// Calculate the number of counts per second from a source for the LT, across a range of seeing values,
// and calculate the limiting magnitude based on a ZP change for different telescop e appertures.
// Step through seeing (nested loop)
// - seeing is 0.5 when i=0; step by 0.1 arcsec so seeing is 3.0 when i=25
// Output values stored in a 1-D variable (2D a pain to code)
var skymag = skybr - (skyoff * sky) ; // calculate the skymag
// skyoff takes into account 1 mag change in
// V doesn't equal 1 mag change in u or r.
var see = 0.5; // base seeing
for (var i = 0; i <= 25; i++) {
var seeing = see + (i / 10); // stepping through seeing (in arcsec)
var dataLine = [seeing]
var areaofdisk = (seeing * 2 * seeing * 2); // area in arcsec
var numberofpixels = areaofdisk / (pixscale * pixscale * bin * bin); // area in pixels
aperSizes.forEach(function(aper){ // For each aperture size
instZp = zp -2.5*Math.log10((2*2)/(aper*aper))
var skyphotons = Math.pow(10.0,((instZp - skymag)/2.5)) * areaofdisk; // within aperture
// - must multiply by areaofdisk since skymag
// in mag/arcsec2
var a = expt * expt;
var b = -snr * snr * expt;
var c = -snr * snr * ((skyphotons * expt) + (darkcurrent * expt * numberofpixels) + (readnoise * readnoise * numberofpixels));
var starphotonsa = (-b + Math.sqrt(b*b - 4*a*c))/(2*a); // solve quadratic equation (+ve)
var starphotonsb = (-b - Math.sqrt(b*b - 4*a*c))/(2*a); // solve quadratic equation (-ve)
var starphotons = Math.max(starphotonsa, starphotonsb); // Select highest value.
// Calculate the inst zeropoint offset (this should be out of the loop for improved performance!)
limMag = -2.5 * Math.log10(starphotons) + instZp; // Calculate the limiting magnitude
dataLine.push(limMag); // Add to list
});
data.addRow(dataLine);
}
// *************************************************************************
var options = {
title: 'Limiting Magnitude Calculator - Imaging',
curveType: 'function',
legend: { position: 'right' },
hAxis: {
title: "Seeing / arcsec",
viewWindow: {
min: 0.5,
max: 3
}
},
vAxis: {
title: "Limiting Magnitude",
viewWindow: {
min: 14,
max: 24,
}
}
};
chart.draw(data, options);
}
function calcspec() {
var spchart = new google.visualization.LineChart(document.getElementById('spcurve_chart'));
// Look up (Define?) the input elements in the document for IMAGING
var spinstrum = document.getElementById("spinstrum").value;
var spslit = document.getElementById("spslit").value;
var sparm = document.getElementById("sparm").value;
var spexpt = document.getElementById("spexpt").value;
var spsnr = document.getElementById("spsnr").value;
var spsky = document.getElementById("spsky").value;
var spapers = document.getElementById("spapers").value;
// FIRST PULL-DOWN ***
// Look-up tables of variables - INSTRUMENT CHARACTERISTICS
if (spinstrum == "frodo") { // FRODO
var sppixscale = 0.82; // spatial pixel scale (arcsec)
var spdarkcurrent = 0; // ??
var spreadnoise = 10; // from website
} else { // sprat
var sppixscale = 0.48; // spatial pixel scale (arcsec)
var spdarkcurrent = 0; // ??
var spreadnoise = 9; // from SPIE 2014 paper.
};
// SECOND PULL-DOWN ***
// Look-up tables of variables - SLIT width (arcsec)
if (spslit == "spratslit") {
var slitwd = 2; // SPRAT slit ESTIMATE
} else {
var slitwd = 10; // FRODO field-of-view
};
// THIRD PULL-DOWN ***
// Look-up tables of other variables (all instrument and arm specific)
// * spzp should be ZP corresponding to 1 electron/second/Angstrom
// * spskybr (Sky brightness) in mag/sqr arcsec
// ...
if (sparm == "frredarmv") { // **** FRODO Red VPH @ 7000 (R-band)
var spzp = 16.0; // FRODO zeropoint at 7000 (from website) = 15.30. In Jan 2016 CMC added 0.7 following 2015 recoating.
var spskybr = 20.8; // sky brightness in mag/arcsec^2
var spskyoff = 1.0; // Used when calculating bright sky; +2 mag,+4 mag,etc.
var spres = 5300; // spectral resolution, lambda/delta-lambda
var wvpixscale = 0.8; // spectral pixel scale, in Angstrom
var refwav = 7000; // reference wavelength for calculation, in Angstrom
} else if (sparm == "frbluarmv") { // **** FRODO Blue VPH @ 4500 (B-band)
var spzp = 14.5; // FRODO zeropoint at 4500 (from website) = 14.50. In Jan 2016 CMC added 0.7 following 2015 recoating.
var spskybr = 22.8; // Bessell B-band
var spskyoff = 1.5; // Bessell B-band
var spres = 5500;
var wvpixscale = 0.35;
var refwav = 4500;
} else if (sparm == "frredarm") { // **** FRODO Red @ 7000
var spzp = 15.60; // FRODO zeropoint at 7000 (from website) = 14.90. In Jan 2016 CMC added 0.7 following 2015 recoating.
var spskybr = 20.8; // R band
var spskyoff = 1.0; // R band
var spres = 2200;
var wvpixscale = 1.9;
var refwav = 7000;
} else if (sparm == "frbluarm") { // **** FRODO Blue @ 4500
var spzp = 14.70; // FRODO zeropoint at 4500 (from website) = 14.20. In Jan 2016 CMC added 0.7 following 2015 recoating.
var spskybr = 22.8; // Bessell B-band
var spskyoff = 1.5; // Bessell B-band
var spres = 2600;
var wvpixscale = 0.60;
var refwav = 4500;
} else if (sparm == "spredarm") { // **** SPRAT Red @ 7000
var spzp = 17.7; // Estimate giving results similar to SPIE paper = 17.0. In Jan 2016 CMC added 0.7 following 2015 recoating.
var spskybr = 20.8; // r band (Originally had 24.6 here. Not sure why. C Benn measures 21.8 in V. 20.8 in R is a reasonable guess.)
var spskyoff = 1.0; // r band
var spres = 350; // Estimate from SPIE paper
var wvpixscale = 9.0; // GUESSED!!!
var refwav = 7000;
} else { // **** SPRAT blue @ 4500
var spzp = 17.2; // Estimate giving results similar to SPIE paper = 16.5. In Jan 2016 CMC added 0.7 following 2015 recoating.
var spskybr = 22.8; // Bessell B-band (Originally had 24.6 here. Not sure why. C Benn measures 21.8 in V. 22.8 in B is a reasonable guess.)
var spskyoff = 1.5; // Bessell B-band
var spres = 350; // Estimate from SPIE paper
var wvpixscale = 3.0; // GUESSED!!!
var refwav = 4500;
};
// *************************************************************************
// ****
// **** Check the select-option combinations are valid
// ****
//FRODO
if (spinstrum == "frodo" && spslit == "spratslit") {
alert("Incorrect Instrument-Slit Combination!");
}
if (spinstrum == "frodo" && sparm == "spbluarm") {
alert("Incorrect Instrument-Arm Combination!");
}
if (spinstrum == "frodo" && sparm == "spredarm") {
alert("Incorrect Instrument-Arm Combination!");
}
//SPRAT
if (spinstrum == "sprat" && spslit == "ifu") {
alert("Incorrect Instrument-Slit Combination!");
}
if (spinstrum == "sprat" && sparm == "frredarmv") {
alert("Incorrect Instrument-Arm Combination!");
}
if (spinstrum == "sprat" && sparm == "frbluarmv") {
alert("Incorrect Instrument-Arm Combination!");
}
if (spinstrum == "sprat" && sparm == "frredarm") {
alert("Incorrect Instrument-Arm Combination!");
}
if (spinstrum == "sprat" && sparm == "frbluarm") {
alert("Incorrect Instrument-Arm Combination!");
}
// *************************************************************************
// ****
// **** MAIN CALCULATION (Spectroscopy)
// ****
// As for imaging, calculate exposure times based on a range of seeing
// and sky brightness values.
// Step through seeing and sky brightness.
// - seeing is 1.0 when si=1; step by 0.5 arcsec so seeing is 4.0 when si=7
// - sky brightness is Dark when sj=0; step by 1 mag so sky is dark+10 when sj=10
// Output values stored in a 1-D variable
var spdata = new google.visualization.DataTable();
spdata.addColumn('number', 'Seeing Value');
const spaperSizes = spapers.split(",").map(Number)//[2, 2.5, 3.0, 4.0];
//console.log(spaperSizes[0]);
spaperSizes.forEach(function(spaper){
spdata.addColumn('number', spaper.toFixed(1) + 'm Aperture');
});
var spskymag = spskybr - (spskyoff * spsky); //
var spsee = 0.5; // same as imaging - base seeing
for (var si = 0; si <= 25; si++) {
var spseeing = spsee + (si / 10) ; // same as for imaging - step through seeing in arcsec
var spdataLine = [spseeing] // Create the list for the dataline with seeing value
var spatialarcs = (slitwd * spseeing * 2) ; // area on sky, in arcsec
var spatialarea = (slitwd * spseeing * 2) / (sppixscale * sppixscale) ; // area on sky, in pixels
var specpixsc = (refwav) / (spres * wvpixscale) ; // spec resolution, in pixels
var spnumberofpixels = spatialarea * specpixsc ; // number of pixels per spat/spect resln element
spaperSizes.forEach(function(spaper){ // For each aperture size
spinstZp = spzp -2.5*Math.log10((2*2)/(spaper*spaper))
// NOTE: spzp is ZP (in mags) that gives 1 photon/sec/Angstrom
var spskyphotons = (Math.pow(10.0,((spinstZp - spskymag)/2.5)) * (refwav/spres) * spatialarcs);
// spstarphotons and spskyphotons should be in units of photons per spatial/spectral
// resolution element (really electrons/res elem):
// - multiplying by (refwav/spres) convert from "per Angstrom" to "per res element"
// - multiplying by spatialarcs corrects spskyphotons for the "per arcsec"
var spa = spexpt * spexpt;
var spb = -spsnr * spsnr * spexpt;
var spc = -spsnr * spsnr * ((spskyphotons * spexpt) + (spdarkcurrent * spexpt * spnumberofpixels) + (spreadnoise * spreadnoise * spnumberofpixels));
var spstarphotonsa = (-spb + Math.sqrt(spb*spb - 4*spa*spc))/(2*spa); // solve quadratic equation (+ve)
var spstarphotonsb = (-spb - Math.sqrt(spb*spb - 4*spa*spc))/(2*spa); // solve quadratic equation (-ve)
var spstarphotons = Math.max(spstarphotonsa, spstarphotonsb);
// Calculate the inst zeropoint offset (this should be out of the loop for improved performance!)
var splimMag = -2.5 * Math.log10(spstarphotons / (refwav/spres)) + spinstZp; // Calculate the limiting magnitude
spdataLine.push(splimMag); // Add to list
});
spdata.addRow(spdataLine);
}
var spoptions = {
title: 'Limiting Magnitude Calculator - Spectroscopy',
curveType: 'function',
legend: { position: 'right' },
hAxis: {
title: "Seeing / arcsec",
viewWindow: {
min: 0.5,
max: 3
}
},
vAxis: {
title: "Limiting Magnitude",
viewWindow: {
min: 8,
max: 20,
}
}
};
spchart.draw(spdata, spoptions);
}
</script>
</body>
</html>