Science Operations

Sensitivity

This page provides information necessary to plan MODS spectroscopic and imaging observations, reproducing and building on what is in the MODS1 Instrumental Sensitivities Document (2013 May 16) which was written before MODS2 came online. The sensitivities of MODS1 and MODS2 were nearly identical at commissioning however they, or rather the combined instrument+telescope throughput which is what is measured, have changed over time. The MODS1 zeropoints have changed by approximately -0.2 dex (a factor 1.6 in flux). The decline is seen in the imaging zeropoints as well. The cause is under investigation; a degradation of the coating of the SX adaptive secondary may partly account for the decline. The LBT-DX+MODS2 zeropoints have dropped by approximately 0.1 to 0 dex since it was commissioned in 2015. 

The grating zeropoints and signal-to-noise tracks in Figures 2.1-2.3, which indicate the SNR that may be reached for a given magnitude and exposure time, were updated based on zeropoints from Sep 2019. However, the grating efficiency curves shown in Figures 1 and 3, and the prism and imaging zeropoints in Tables 2 and 3, as also the imaging ETC, are all based on MODS1 Commissioning data taken in 2011.

On 12 January, 2021, the SNR tracks for grating modes (Figs 2.1-2.3) were once again updated. These use the same zeropoints (from Sep 2019) as the old tracks, but assume that the object trace is extracted over twice as many rows as earlier: 98% of the light, assuming a Gaussian PSF, falls on Nrows = 2*FWHM, while only 76% falls on Nrows = FWHM. The effect of this change is to increase the noise: both the sky background and the readnoise; and thus to decrease the faint-object sensitivity by ~0.4-0.5 mag.

During the observatory restart in September 2022 (20220925UT), the spectrophotometric standard star G191-B2B was observed in dual, blue and grating modes. Zeropoints based on these data are approximately 0.09-0.1 dex worse for MODS1 and about 0.03-0.04 dex better for MODS2 than those in Table 1. The zeropoints and tracks will be updated as soon as the data, at least in dual mode, for a few more stars are analyzed. Based on this binocular observation, the sensitivity of MODS2/DX is about twice that of MODS1/SX and, as this affects both the object (signal) and sky (noise), the MODS1 exposure would need to be twice as long as the MODS2 one to achieve the same SNR. [17/Oct/2022]

Spectroscopic Mode

The predicted counts per angstrom at a given wavelength, airmass and exposure time, may be calculated using the formula,

log Sλ = log Sλ ,0  + log Fλ  + log texp – 0.4  Kλ  X

where: 

log Sλ = log counts in ADU Å-1 at wavelength λ
log Sλ ,0 = Spectroscopic zero point in ADU Å-1at wavelength, see tables below.
Fλ = flux in units of erg/sec/cm2
texp = exposure time in seconds
Kλ = estimated extinction coefficient at wavelength λ
X = airmass at the time of the observation

To convert AB magnitudes to Fλ:

log Fλ = -0.9608 – 0.4 AB – 2 log λ

where: AB = Spectral AB magnitude and λ is the wavelength in Angstroms.

The spectroscopic zero points at selected wavelengths for the MODS red and blue grating and prism modes are listed in the tables 1 and 2 below. For a given source flux (Fλ), exposure time and airmass, these allow a 10-20% prediction of counts per angstrom, Sλ, which can be converted to counts per pixel when multiplied by the spectral pixel size in Å. The effect of atmospheric extinction is factored in by selecting a nominal airmass for the observation and applying an appropriate model for the atmospheric extinction (see below).  A caveat — predictions based on these zero points should be considered as for the best-case scenario, as there are various observational factors that can degrade the sensitivity achieved: slit losses, which depend on seeing among other factors; changes in sky brightness with time, telescope pointing or moon phase and distance from target; changes in transparency; and changes in the reflectivities of the telescope or instrument optics, are some examples.

Grating Mode

The efficiencies for the grating spectroscopy modes, based on MODS1 commissioning data, are plotted below. These efficiencies are for MODS1 plus the LBT SX primary and secondary mirrors, and are exclusive of the atmosphere.

Figure 1: MODS1+LBT SX airmass=0 efficiencies for direct and dual grating modes.

The spectroscopic zero points as a function of wavelength for the MODS1 grating modes, log Sλ ,0, are given in the table below.

The current sensitivity of MODS1+LBT-SX is lower than that of MODS2+LBT-DX. The instrument+telescope throughput has shown a steady decline since MODS1 commissioning in 2011. For this reason, updated zeropoints for MODS1 and zeropoints for MODS2 are provided in Table 1, based on measurements made in September 2019 which are consistent within ~12% (for MODS2, closer for MODS1)  with measurements made through the spring of 2020. Updates will be made as the numbers are refined. Updates will also be made to the zero points for the prism and imaging modes.

Table1: MODS1+LBT-SX and MODS2+LBT-DX Grating Mode Spectroscopic Zero Points (based on 2019-2020 data and updated on 23 April 2020)

MODS1 Red Grating MODS2 Red grating MODS1 Blue Grating MODS2 Blue grating
λ(Å) Direct
logSλ,0
Dichroic
log Sλ ,0
Direct
logSλ,0
Dichroic
log Sλ ,0
λ(Å) Direct
logSλ,0
Dichroic
log Sλ ,0
Direct
logSλ,0
Dichroic
log Sλ ,0
5000 15.599 15.829  … 3200 15.158 15.109 15.428 15.348
5500 16.024 14.633 16.316  15.016 3500 15.469 15.444 15.730 15.690
6000 16.104 16.114 16.462  16.441 4000 15.806 15.773 16.011 15.961
6500 16.105 16.117 16.505  16.496 4500 15.888 15.873 16.065 16.041
7000 16.082 16.104 16.507  16.505 5000 15.887 15.888 16.036 16.024
7500 16.060 16.106 16.487  16.511 5500 15.861 15.842 15.986 15.945
8000 15.999 16.057 16.411  16.443 5800 15.824 14.559 15.952 14.593
8500 15.944 15.995 16.330  16.352 6000 15.780 15.898
9000 15.860 15.910 16.212  16.232 6450 15.677 15.796
9500 15.624 15.673 15.947  15.969
10000 15.516 15.337 15.777  15.556

Figures 2.1, 2.2 and 2.3, below, plot the sensitivity limits as a function of time for a given signal-to-noise ratio. These are based on measurements made with MODS1 and MODS2 in September 2019.

Figure 2.1:For signal-to-noise ratios, SNR= 5, 20 and 100 per 0.5 (blue) or 0.85 angstrom (red) pixel in a spectrum that has been extracted over the number of rows corresponding to the seeing FWHM, tracks of AB magnitude vs time are plotted for both blue (at g_sdss/4770 angstroms) and red (r_sdss/6300 angstroms) channels. These tracks use the MODS1 dual grating zeropoints tabulated here and have been calculated for a 1″ slit, seeing FWHM = 1″, airmass = 1 and dark (new moon, solid lines) and bright (10-d moon, dotted lines) skies. The blue and red shaded regions indicate the range of magnitudes predicted for sky brightnesses from new to 10-d moon. The slit loss calculation assumes a Gaussian PSF, so for a slit width equal to the seeing FWHM, 24 percent of the light is lost. For the sky contribution, the area is the number of pixels covered by the slit width times the FWHM. The dark(bright) sky brightnesses at g_sdss and r_sdss were assumed to be 22.3(20.7) and 21.3(20.6), respectively. These are interpolated from the KPNO sky brightnesses and agree well with published dark sky values for Mt. Graham (Taylor+2004,PASP,116,762 and Pedani 2009, PASP,121,778).

To do a “bye-eye interpolation” from this plot, recall that the SNR scales with the square root of the flux and of the exposure time, although for fainter objects whose flux is comparable to the sky brightness, SNR grows more slowly.

Caveat: The  predicted SNRs should be considered best-case scenarios, as there are various observational factors that can degrade the actual SNR you see in your data: transparency, slit loss, sky brightness which can change with time (in the red, for example) and with telescope pointing (looking at a low elevation target in the direction of a city, e.g.). Also the predictions are based on photon statistics and do not account for uncertainties introduced in the data processing (e.g. flat-fielding errors). At the red end of the optical, especially at z, where the sky is brighter that at r and the CCD quantum efficiency is dropping, the predicted SNRs will be worse.

Figure 2.2 The same as in Figure 2.1, but the red channel predictions are made at i (7500 angstroms) instead of at r. At i, the sky brightnesses have been assumed to be 20.7 mag/sq.arcsec (dark) and 20.2 mag/sq.arcsec (bright). Click on the image to view it at full scale.

Figure 2.3 The same as in Figure 2.1, but the red channel predictions are made at z (8950 angstroms) instead of at r. At z, the sky brightnesses have been assumed to be 19.0 mag/sq.arcsec (dark) and 18.7 mag/sq.arcsec (bright).

Prism Mode

The efficiency curves, exclusive of the atmosphere, for dual and direct prism modes are shown below:

Figure 3: MODS1+LBT SX airmass=0 efficiencies for direct and dual prism modes.

Spectroscopic zero points as a function of wavelength for the MODS1 prism modes are tabulated below:

Table 2: MODS1 Prism Mode Spectroscopic Zero Points

(based on MODS1 commissioning data taken in 2011)

Red Prism Blue Prism
log Sλ ,0 Pixel log Sλ ,0 Pixel
λ (Å) Direct Dichroic δ λ (Å) λ (Å) Direct Dichroic δ λ (Å)
5000 15.722 2.6 3600 15.663 15.640 3.4
5500 16.178 14.978 3.4 3850 15.886 15.858 4.4
6000 16.268 16.265 4.6 4030 15.978 15.927 5.1
6450 16.301 16.293 5.9 4500 16.121 16.096 7.1
7000 16.357 16.348 7.6 5000 16.162 16.138 9.8
7450 16.365 16.368 9.1 5500 16.172 16.112 12.7
8000 16.342 16.350 11.2 6000 16.143 15.478 15.8
8500 16.307 16.297 13.3 6450 16.082 18.5
8800 16.264 16.252 14.6 7000 15.964 21.8
9750 15.740 15.692 18.9
10000 15.396 15.333 20.1

The same formula for estimating counts per exposure time used for the grating mode apply to data in this table for the prism, but bear in mind that the size of spectral pixel is a strongly varying function of wavelength. Nominal pixel sizes are given in the final column for each side.

Figure 3: For signal-to-noise ratios, SNR= 5, 20 and 100 per pixel in a prism spectrum that has been extracted over the number of rows corresponding to the seeing FWHM, tracks of AB magnitude vs time are plotted for both blue (at g_sdss/4770 angstroms) and red (r_sdss/6300 angstroms) channels.  These tracks use the MODS1 dual prism zeropoints tabulated here and have been calculated for a 1″ slit, seeing FWHM = 1″, airmass = 1 and dark (new moon, solid lines) and bright (10-d moon, dotted lines) skies. With the prisms, the number of angstroms per pixel increases with wavelength, from ~3 angstroms/pix to ~20 angstroms/pix (see Table 2 above), so while the zeropoints for the prism and grating are similar, the predicted SNR per pixel is greater for the prism than for the grating, all other input parameters being equal. The blue and red shaded regions indicate the range of magnitudes predicted for sky brightnesses from new to 10-d moon. The slit loss calculation assumes a Gaussian PSF, so for a slit width equal to the seeing FWHM, 24 percent of the light is lost. For the sky contribution, the area is the number of pixels covered by the slit width times the FWHM. The dark(bright) sky brightnesses at g_sdss and r_sdss were assumed to be 22.3(20.7) and 21.3(20.6), respectively. These are interpolated from the KPNO sky brightnesses and agree well with published dark sky values for Mt. Graham (Taylor+2004,PASP,116,762 and Pedani 2009, PASP,121,778).
To do a “bye-eye interpolation” from this plot, recall that the SNR scales with the square root of the flux and of the exposure time, although for fainter objects whose flux is comparable to the sky brightness, SNR grows more slowly. Caveat: The  predicted SNRs should be considered best-case scenarios, as there are various observational factors that can degrade the actual SNR you see in your data: transparency, slit loss, sky brightness which can change with time (in the red, for example) and with telescope pointing (looking at a low elevation target in the direction of a city, e.g.). Also the predictions are based on photon statistics and do not account for uncertainties introduced in the data processing (e.g. flat-fielding errors). At the red end of the optical, especially at z, where the sky is brighter that at r and the CCD quantum efficiency is dropping, the predicted SNRs will be worse. 

Imaging Mode

Estimates of the imaging sensitivity of MODS are based on measurements of secondary photometric standard stars in the SDSS AB magnitude system (Clem, VandenBerg, and Stetson (2008)).  By manipulation of the photometric conversion formula,

m= mf,0 – 2.5 log Sf + 2.5 log texp – Kf X

the predicted integrated counts in ADU in a filter given its SDSS AB magnitude in the filter band is given by:

log Sf = log Sf,0  –  0.4mf  +  log texp  – 0.4 K f X

where: 

log Sf = log counts in ADU for filter f
log Sf,0 = ADU zero point (counts for mf=0.0mag in 1 second) listed in the table below.
mf = SDSS magnitude in filter f in AB units
mf,0 = photometric zero point magnitude in filter f in AB units listed in the table below.
texp = exposure time in seconds
Kf = estimated extinction coefficient for filter f
X = airmass at the time of the observation

Table 3: MODS ugriz Photometry ADU Zero Points and Zero Point Magnitudes

(based on MODS1 commissioning data taken in 2011)
 

 Filter  mf,0 (mag)  Kf  log Sf,0
 SDSS u  25.68±0.12  0.47  10.25
 SDSS g  27.38±0.03  0.17  10.94
 SDSS r  27.24±0.03  0.10  10.90
 SDSS i 27.21±0.04  0.05  10.91
 SDSSz  26.41±0.04  0.03  10.58


A good rule of thumb is:
The peak pixel will saturate on an r = 15th mag in 30 sec in 0.6 arcsec seeing.

 

Model LBT Atmospheric Extinction

Table 4: LBT Model Extinction Curve

 λ (Å)  Kλ
 3200  0.866
 3500  0.511
 4000  0.311
 4500  0.207
 5000  0.153
 5500  0.128
 6000  0.113
 6450  0.088
 6500  0.085
 7000  0.063
 7500  0.053
 8000  0.044
 8210  0.043
 8260  0.042
 8370  0.041
 8708  0.026
 10256  0.020

The coefficients in this model LBT extinction curve do not include strong telluric absorption features, so this correction should be done with caution if using it to predict signal in a given exposure time at wavelengths in proximity to strong telluric features.