{"id":182,"date":"2014-11-12T23:54:19","date_gmt":"2014-11-12T23:54:19","guid":{"rendered":"http:\/\/www.eaobservatory.org\/jcmt\/?page_id=182"},"modified":"2019-10-18T12:14:36","modified_gmt":"2019-10-18T22:14:36","slug":"time-and-sensitivity","status":"publish","type":"page","link":"https:\/\/www.eaobservatory.org\/jcmt\/instrumentation\/continuum\/scuba-2\/time-and-sensitivity\/","title":{"rendered":"SCUBA-2 Integration Time and Sensitivity"},"content":{"rendered":"<p style=\"text-align: justify\">The amount of elapsed time required to map a certain field size, to a certain depth, at a given atmospheric transmission is described in the equations below. For users who simply want a quick time estimate we advise using the ITC gui which is explained <a title=\"SCUBA-2 ITC gui\" href=\"http:\/\/www.eaobservatory.org\/jcmt\/instrumentation\/continuum\/scuba-2\/itc\/\">here<\/a>.<\/p>\n<p style=\"text-align: justify\"><div id=\"toc_container\" class=\"no_bullets\"><p class=\"toc_title\">Contents<\/p><ul class=\"toc_list\"><li><a href=\"#Elapsed_time\"><span class=\"toc_number toc_depth_1\">1<\/span> Elapsed time<\/a><\/li><li><a href=\"#Atmospheric_transmission\"><span class=\"toc_number toc_depth_1\">2<\/span> Atmospheric transmission<\/a><\/li><li><a href=\"#Sampling_factor_f\"><span class=\"toc_number toc_depth_1\">3<\/span> Sampling factor f<\/a><\/li><li><a href=\"#SCUBA-2_Confusion_limit\"><span class=\"toc_number toc_depth_1\">4<\/span> SCUBA-2 Confusion limit<\/a><\/li><li><a href=\"#Overheads\"><span class=\"toc_number toc_depth_1\">5<\/span> Overheads<\/a><\/li><\/ul><\/div>\n\n<h3><span id=\"Elapsed_time\">Elapsed time<\/span><\/h3>\n<p style=\"text-align: justify\">The elapsed telescope time (seconds) to map a given field size to a given 1-sigma depth (mJy) is described in the relations below.<\/p>\n<table style=\"height: 264px\" width=\"1068\">\n<tbody>\n<tr>\n<th style=\"text-align: center\">Mapping Mode<\/th>\n<th style=\"text-align: center\">Time elapsed 450 microns (s)<\/th>\n<th style=\"text-align: center\">Time elapsed 850 microns (s)<\/th>\n<\/tr>\n<tr>\n<td style=\"text-align: center\">Daisy<\/td>\n<td style=\"text-align: center\">\u00a0<img src=\"https:\/\/www.eaobservatory.org\/jcmt\/wp-content\/plugins\/youngwhans-simple-latex\/mathtex.cgi?\\frac{1}{f}\\bigg[\\bigg(\\frac{689}{T_{450}}-118\\bigg)\\frac{1}{\\sigma_{450}}\\bigg]^{2}\" style=\"vertical-align:middle; float:top;\" border=\"0px\" \/><\/td>\n<td style=\"text-align: center\"><img src=\"https:\/\/www.eaobservatory.org\/jcmt\/wp-content\/plugins\/youngwhans-simple-latex\/mathtex.cgi?\\frac{1}{f}\\bigg[\\bigg(\\frac{189}{T_{850}}-48\\bigg)\\frac{1}{\\sigma_{850}}\\bigg]^{2}\" style=\"vertical-align:middle; float:top;\" border=\"0px\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center\">900&#8243;<\/td>\n<td style=\"text-align: center\"><img src=\"https:\/\/www.eaobservatory.org\/jcmt\/wp-content\/plugins\/youngwhans-simple-latex\/mathtex.cgi?\\frac{1}{f}\\bigg[\\bigg(\\frac{1483}{T_{450}}-254\\bigg)\\frac{1}{\\sigma_{450}}\\bigg]^{2}\" style=\"vertical-align:middle; float:top;\" border=\"0px\" \/><\/td>\n<td style=\"text-align: center\"><img src=\"https:\/\/www.eaobservatory.org\/jcmt\/wp-content\/plugins\/youngwhans-simple-latex\/mathtex.cgi?\\frac{1}{f}\\bigg[\\bigg(\\frac{407}{T_{850}}-104\\bigg)\\frac{1}{\\sigma_{850}}\\bigg]^{2}\" style=\"vertical-align:middle; float:top;\" border=\"0px\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center\">1800&#8243;<\/td>\n<td style=\"text-align: center\"><img src=\"https:\/\/www.eaobservatory.org\/jcmt\/wp-content\/plugins\/youngwhans-simple-latex\/mathtex.cgi?\\frac{1}{f}\\bigg[\\bigg(\\frac{2904}{T_{450}}-497\\bigg)\\frac{1}{\\sigma_{450}}\\bigg]^{2}\" style=\"vertical-align:middle; float:top;\" border=\"0px\" \/><\/td>\n<td style=\"text-align: center\"><img src=\"https:\/\/www.eaobservatory.org\/jcmt\/wp-content\/plugins\/youngwhans-simple-latex\/mathtex.cgi?\\frac{1}{f}\\bigg[\\bigg(\\frac{795}{T_{850}}-203\\bigg)\\frac{1}{\\sigma_{850}}\\bigg]^{2}\" style=\"vertical-align:middle; float:top;\" border=\"0px\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center\">3600&#8243;<\/td>\n<td style=\"text-align: center\"><img src=\"https:\/\/www.eaobservatory.org\/jcmt\/wp-content\/plugins\/youngwhans-simple-latex\/mathtex.cgi?\\frac{1}{f}\\bigg[\\bigg(\\frac{6317}{T_{450}}-1082\\bigg)\\frac{1}{\\sigma_{450}}\\bigg]^{2}\" style=\"vertical-align:middle; float:top;\" border=\"0px\" \/><\/td>\n<td style=\"text-align: center\"><img src=\"https:\/\/www.eaobservatory.org\/jcmt\/wp-content\/plugins\/youngwhans-simple-latex\/mathtex.cgi?\\frac{1}{f}\\bigg[\\bigg(\\frac{1675}{T_{850}}-428\\bigg)\\frac{1}{\\sigma_{850}}\\bigg]^{2}\" style=\"vertical-align:middle; float:top;\" border=\"0px\" \/><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center\">7200&#8243;<\/td>\n<td style=\"text-align: center\"><img src=\"https:\/\/www.eaobservatory.org\/jcmt\/wp-content\/plugins\/youngwhans-simple-latex\/mathtex.cgi?\\frac{1}{f}\\bigg[\\bigg(\\frac{12837}{T_{450}}-2200\\bigg)\\frac{1}{\\sigma_{450}}\\bigg]^{2}\" style=\"vertical-align:middle; float:top;\" border=\"0px\" \/><\/td>\n<td style=\"text-align: center\"><img src=\"https:\/\/www.eaobservatory.org\/jcmt\/wp-content\/plugins\/youngwhans-simple-latex\/mathtex.cgi?\\frac{1}{f}\\bigg[\\bigg(\\frac{3354}{T_{850}}-857\\bigg)\\frac{1}{\\sigma_{850}}\\bigg]^{2}\" style=\"vertical-align:middle; float:top;\" border=\"0px\" \/><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p style=\"text-align: justify\">The 450 and 850 transmission factors (\u03a4<sub>450<\/sub>, \u03a4<sub>850<\/sub>) and the sampling factor (<b><i>f<\/i><\/b>) in the above equations are described below:<\/p>\n<h3><span id=\"Atmospheric_transmission\">Atmospheric transmission<\/span><\/h3>\n<p style=\"text-align: justify\">For a given air mass (AM) and\u00a0opacity (classically defined at 225GHz, \u03c4<sub>225GHz<\/sub>), the transmission can be calculated using the following relations:<\/p>\n<p style=\"text-align: center\"><img src=\"https:\/\/www.eaobservatory.org\/jcmt\/wp-content\/plugins\/youngwhans-simple-latex\/mathtex.cgi?T_{450}=exp(-AM\\times26(\\tau_{225GHz}-0.01196))\" style=\"vertical-align:middle; float:top;\" border=\"0px\" \/><\/p>\n<p style=\"text-align: center\"><img src=\"https:\/\/www.eaobservatory.org\/jcmt\/wp-content\/plugins\/youngwhans-simple-latex\/mathtex.cgi?T_{850}=exp(-AM\\times4.6(\\tau_{225GHz}-0.00435))\" style=\"vertical-align:middle; float:top;\" border=\"0px\" \/><\/p>\n<p>The opacity (\u03c4<sub>225GHz<\/sub>) ranges for various weather Grades are given below:<\/p>\n<ul>\n<li>Grade 1: Less than 0.83mm PWV. \u00a0(\u03c4<sub>225GHz<\/sub> &lt; 0.05)<\/li>\n<li>Grade 2: 0.83 \u2013 1.58 mm PWV. \u00a0(0.05 &lt;\u00a0\u03c4<sub>225GHz<\/sub> &lt; 0.08)<\/li>\n<li>Grade 3: 1.58 \u2013 2.58 mm PWV. \u00a0(0.08 &lt;\u00a0\u03c4<sub>225GHz<\/sub> &lt; 0.012)<\/li>\n<li>Grade 4: 2.58 \u2013 4.58 mm PWV. \u00a0(0.12 &lt;\u00a0\u03c4<sub>225GHz<\/sub> &lt; 0.2)<\/li>\n<li>Grade 5: More than 4.58 mm PWV. \u00a0(\u03c4<sub>225GHz<\/sub> &gt; 0.2)<\/li>\n<\/ul>\n<p style=\"text-align: justify\">For a source at a given declination (\u03b4, measured in degrees), a representative air mass near transit can be derived using:<\/p>\n<p style=\"text-align: center\"><img src=\"https:\/\/www.eaobservatory.org\/jcmt\/wp-content\/plugins\/youngwhans-simple-latex\/mathtex.cgi?AM=\\frac{1}{0.9cos\\big[\\frac{\\pi}{180}(\\delta-19.823)\\big]}\" style=\"vertical-align:middle; float:top;\" border=\"0px\" \/><\/p>\n<h3><span id=\"Sampling_factor_f\">Sampling factor <b><i>f<\/i><\/b><\/span><\/h3>\n<p>Elapsed times are derived using the basic reduction parameters in SMURF and use default map pixels of 2&#8243; and 4&#8243; at 450 and 850 microns, respectively. A change to this default pixel size is taken into account by the sampling factor (<b><i>f<\/i><\/b>) when estimating the elapsed time. The sampling factor f is simply defined as:<\/p>\n<p style=\"text-align: center\">\u00a0<b><i>f<\/i><\/b>\u00a0= ( pixel size requested \/ default pixel size )<sup>2<\/sup><\/p>\n<p>At 450 and 850 this becomes:<\/p>\n<p style=\"text-align: center\"><b><i>f<\/i><\/b><sub>450<\/sub> = ( pixel size requested \/ 2 )<sup>2\u00a0 <\/sup>and <b><i>f<\/i><\/b><sub>850<\/sub> = ( pixel size requested \/ 4 )<sup>2<\/sup><\/p>\n<p style=\"text-align: justify\"><span style=\"text-decoration: underline\">For Point-source detections<\/span> the S\/N can be dramatically improved by applying a matched-beam filter which utilizes the full flux in the beam rather than just the peak value at the position of a source. This will shorten required observing times to reach a certain S\/N typically by factors of <b><i>f<\/i> =<\/b> 8 (450\u03bcm) and <b><i>f<\/i> = <\/b>5 (850\u03bcm).<\/p>\n<h3 style=\"text-align: justify\"><span id=\"SCUBA-2_Confusion_limit\">SCUBA-2 Confusion limit<\/span><\/h3>\n<p>The confusion limit depends on a number of factors including Galactic cirrus emission, the extra galactic background as well as the beam size. While dependent on assumptions and location the derived values are close to<\/p>\n<ul>\n<li style=\"text-align: justify\">850 microns = 0.7 mJy\/beam<\/li>\n<li style=\"text-align: justify\">450 microns = 0.5 mJy\/beam<\/li>\n<\/ul>\n<p>The sensitivity of a SCUBA-2 blank field will be limited by a un-reduceable noise level of this order.<br \/>\nThe implies that going below a detection limit of ~ 2 mJy in a blank field will give a high risk of false detections. See for instance Chen et.al Ap.J. 762, 81 (2011) &#8220;<a href=\"https:\/\/ui.adsabs.harvard.edu\/abs\/2013ApJ...762...81C\/abstract\">Faint Submillimeter Galaxy Counts at 450 micron<\/a>&#8221;. The situation is better for detection of a source at a known position. The lower probability that a random peak coincide with your know source increases the chance it is a real detection. However, the confusion limit still needs to be taken into account when estimating the position and flux error.<\/p>\n<h3><span id=\"Overheads\">Overheads<\/span><\/h3>\n<p style=\"text-align: justify\">The SCUBA-2 ITC currently takes into account the 90 seconds required for set ups and fast flats<\/p>\n<p style=\"text-align: justify\">If you are calculating an integration time for a proposal it should be noted that there is no need to provide an overhead estimate for calibrations (pointing, focus, flux). The time used for calibration is absorbed by the observatory.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The amount of elapsed time required to map a certain field size, to a certain depth, at a given atmospheric transmission is described in the equations below. For users who simply want a quick time estimate we advise using the ITC gui which is explained here. Elapsed time The elapsed\u2026 <a class=\"continue-reading-link\" href=\"https:\/\/www.eaobservatory.org\/jcmt\/instrumentation\/continuum\/scuba-2\/time-and-sensitivity\/\">Continue reading<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"parent":176,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/pages\/182"}],"collection":[{"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/comments?post=182"}],"version-history":[{"count":84,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/pages\/182\/revisions"}],"predecessor-version":[{"id":10294,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/pages\/182\/revisions\/10294"}],"up":[{"embeddable":true,"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/pages\/176"}],"wp:attachment":[{"href":"https:\/\/www.eaobservatory.org\/jcmt\/wp-json\/wp\/v2\/media?parent=182"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}