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TMT ETC Readme (under construction)

Here is the Readme page of TMT Exposure Time Calculator(ETC). Many functions of this ETC are basically under construction or improving. Please understand that the ETC have significant scope to continue to improve. If there are any questions and/or demands, contact mariko.kubo_at_nao.ac.jp (change _at_ to @).

Recent updates (2016/7/20)

  • Y-band and Narrow-band filters are added
  • QSO template is added

Future Improvements and additional Functions

  • Speed-up of calculation
  • User input interface of filter response function
  • User input interface of object spectra
  • Making simulated 2d image and spectrum of target object
  • Variety of supposed PSF

Calculation of signal to noise ratio
Signal to noise ratio per imaging frame (S/N1f) is basically calculated according to the following formula.

: Number of electrons generated by photons from a target object within extracted area (electrons/second).
: Number of electrons generated by background sources (electrons/second/pixel).
: Dark current of detector (electrons/second/pixel).
: Read out noise of detector (electrons/pixel in rms).
: Exposure time on source (second).
: Extract area to calculate S/N (pixel2).

and are calculated as follows.

: Flux density of target object (erg/s/cm2/μm)
: Filter band width (μm)
: Energy per photon (erg)
: Surface area of primary mirror (cm2)
: Total efficiency including both optics efficiency and instrumental quantum efficiency
: Light fraction within extract area
: Dimming factor associated with atmospheric absorption

: Surface brightness of background source (erg/s/cm2/μm/arcsecond2)
: Solid angle for 1 pixel (arcsecond2)

If multi frames are obtained, net of signal to noise ratio (S/N) is


: Number of imaging frames.
Sky transparency
Dimming by atmospheric absorption depends on air mass. Following parameters are adopted in TMT imaging ETC.
BandExtinction by atmosphere (mag/air mass)

Sky transparency used in TMT spectroscopic ETC is mainly from
Gemini observatory IR Transmission Spectra
The details are under construction.
Background sources
For ground telescopes, current version of TMT imaging ETC assumes optical and infrared sky background at Mt. Maunakea, based on sky data released by Gemini observatory.

Gemini observatory Optical Sky Background
Gemini observatory IR Sky Background

As reported above, the primary dependence of optical night sky brightness is on lunar condition (See also Sky Condition). For IR sky background the dependency on air mass is included but moonlight is not. Note that moonlight can be the dominant background source, especially in the J band when the moon is bright and especially when the target is close to the moon.

For space telescope, TMT imaging ETC assumes 4 blackbody background sources, consisting of Zodiacal Scattered Light(ZSL), Zodiacal Emission(ZE), Galactic Background Emission(GBE), and Cryogenic Space Telescope(CST). The general formula of surface brightness of blackbody component Nφis described as follows.


: Emissivity
: Wavelength in μm
: Temperature in Kelvin

Summary of adopted parameters for each component of space background (Allen's Astrophysical Quantities).
ZSL3 x 10-145800
ZE7.1 x 10-8275

Source Geometry
Point Source
Encircled region of point source is extracted to calculate signal-to-noise ratio in the imaging ETC. The aperture radius is user-specified factor x FWHM. This FWHM is referred from diffraction limited core if Adaptive Optics(AO) is selected in Point Spread Function or seeing size as in the non-AO case. See also Point Spread Function. For spectroscopic ETC, square region (slit width x spatial length) of point source is extracted.
Extended Source
Input size of extracted square region. Note that Point Spread Function is ignored if Extended Source is selected.

Target Brightness
Input total apparent magnitude for point source or surface brightness for extended source.
Basic information on filters used in TMT imaging ETC
Filter IDBand center (μm)Band width (μm)Vega flux density (erg/s/cm2/μm)Vega (AB mag)
U' 0.3751 0.0495 5.09 x 10-5 0.709
B 0.4448 0.1008 6.19 x 10-5 -0.111
V 0.5505 0.0827 3.60 x 10-5 -0.012
Rc 0.6588 0.1568 2.15 x 10-5 0.200
Ic 0.8060 0.1542 1.11 x 10-5 0.458
u' 0.3585 0.0556 3.6 x 10-5 0.931
g' 0.4858 0.1297 5.11 x 10-5 -0.086
r' 0.6290 0.1358 2.40 x 10-5 0.164
i' 0.7706 0.1547 1.28 x 10-5 0.401
z' 0.9222 0.1530 7.83 x 10-6 0.549
Y 1.003 0.1385 6.21 x 10-6 0.603
J 1.215 0.26 3.31 x 10-6 0.870
H 1.654 0.29 1.15 x 10-6 1.348
K 2.179 0.41 4.14 x 10-7 1.858
L 3.547 0.57 6.59 x 10-8 2.796
M 4.769 0.45 2.11 x 10-8 3.389
N 10.472 5.19 9.63 x 10-6 5.033
Q 20.130 7.8 7.18 x 10-5 6.433
NB515 0.516 0.0076 3.66 x 10-5 -0.033
NB973 0.9698 0.0115 1.14 x 10-5 0.537
NB1550 1.5487 0.0176 4.48 x 10-6 1.295

Filter response functions adopted in TMT spectroscopic ETC are as follows; U'-band of the Megaprime camera on CFHT; B,V,Rc,Ic-bands of the Suprime-Cam on Subaru Telescope ; g', r', i' and z'-bands of the SDSS; Y, NB515 and NB973-bands of the Hyper Suprime-Cam on Subaru Telescope;J, H, K, L, M, N, Q and NB1550 -bands of the MOIRCS on Subaru Telescope.

Point Spread Function
Input seeing size (FWHM) in milli-arcsecond and select AO availability and strehl ratio. Note that this section is ignored if extended source is selected in Source Geometry.
Adaptive Optics
As in the instrument+AO case, PSF is approximated by double 2d-gaussian profile as below.

: Flux ratio of diffraction core corrected by AO system to total flux.
: Flux ratio of uncorrected (seeing-limited) halo to total flux.
: Spatial broadening of AO-corrected core,
which is calculated by using a formula of diffraction limit . is observed wavelength and is diameter of primary mirror.
: Spatial broadening of uncorrected halo. This is equal to seeing/2.35.

and are calculated from user-specified strehl ratio as follows.

Here strehl is defined as the peak ratio of double-gaussian PSF to completely AO-corrected diffraction limited core (i.e., all photons are corrected in diffraction core without halo component). Note that user-specified seeing size must be larger than diffraction limited core.

Seeing limited PSF
If "without AO" is selected, single 2d-gaussian PSF is assumed written as bellow.

The integration between aperture radius r = 0 and R is

Aperture radii of 1.0, 2.0, and 3.0 in FWHM (FWHM ~ 2.35σ) correspond to aperture losses of 6.3, 1.6e-3, and 1.6e-9% in the imaging ETC.

Sky Condition
Observatory Site
Current version of TMT imaging ETC assumes optical and infrared sky background at Mt. Maunakea. Note that blackbody background is included instead of sky emission if 6.5 m space telescope is selected. See Background sources in Calculation of signal to noise ratio for details.
Air mass
The intensity of sky emission depends on air mass mainly for IR. Current version of TMT imaging ETC does not include the optical dependency of sky background on air mass. Sky transparency also depends on air mass. See Calculation of signal to noise ratio for details.
Lunar Phase Angle and Angular distance between moon and target
Lunar phase angle is the angle between the light from the sun incident onto the moon and the light reflected from the moon. The phase angle varies from 0 to 180 degree. The value of 0 and 180 degree correspond to full and new moon, respectively. The primary dependence of optical night sky brightness is on lunar phase, and secondarily on moon - target distance, as reported by Gemini Optical Sky Background page. On the other hand, IR sky background depends little on the moon especially for H, K-band and longer wavelength. Note that the lunar effect on the sky background is taken into account only for optical wavelength range in TMT ETC.

The change of optical sky brightness caused by the moonlight is based on Krisciunas, K. & Schaefer, B. E. 1991, PASP 103, 1033. The colour of the sky actually changes with lunar phase (See Gemini Optical Sky Background). For now, the sky color dependence on lunar phase is not included in the ETC.

System Configuration
Telescope Diameter
Select telescope size. Dominant noise sources are different between ground and space.

8, 30, 39 m (Ground)
Sky background, detector readout noise, and dark current are supposed as noise sources.

6.5 m (Space)
Zodiacal scattered light, zodiacal emission, galactic background emission, cryogenic space telescope, detector readout noise, and dark current are supposed as noise sources.
Pixel scale
Please input pixel scale of detector in milli-arcsecond/pixel.
Full width at half maximum (FWHM) of PSF in milli-arcsecond. Please input a value on demand, e.g., seeing limited condition and full performance of adaptive optics. Note that this input is ignored if extended source is selected in Source Geometry.
Read out noise
Read out noise in electrons/pixel in rms. The results differ so little if sky background limited condition is considered.
Dark current
Dark current in electrons/sec/pixel. The results differ so little as long as sky background limited condition is considered.
Total efficiency
Input total efficiency. This includes whole optics (telescope, instrument, and adaptive optics) efficiency and instrumental quantum efficiency, except for sky absorption. Since photons gathered by primary mirror decline through the optical path of whole telescope and instrument system, only photons reached to detector can generate electrons. For instance, if 100 photons incident at the telescope entrance finally generate 20 electrons on the detector, total efficiency is 0.2.

Output Format
Calculate Exp time
Not available. Under construction.
Calculate S/N
Input exposure time per frame and number of imaging frames. Please take care of saturation level by user own. ETC will calculate S/N under input condition as well as S/N as a function of total exposure time and aperture size (under construction).

Target Spectral Energy Distribution
Specify the rest-frame spectral energy distribution of target object. Templates of stellar spectra are based on A.J. Pickles, PASP 110, 863, 1998. Model spectra of galaxies are from GALAXEV, which is a library of evolutionary stellar population synthesis models by Bruzual & Charlot (2003). The QSO template is the combination of a mean quasar spectrum between 350 and 3000 Å from the HST/FOS Composite Quasar Spectrum and Type 1 QSO template between 3000 Å and 1000 μm from the SWIRE Template Liberary.Additional emission or absorption line feature is also available if the box is checked. Extinction laws are referred from analytical formula by Li et al. 2008, ApJ 686, 1046L. The absorption by Lyα and Lyβ forest is based on the lognormal optical depth distribution proposed by Becker et al. 2007, ApJ 662, 72 at redshift higher than 1.7. At the redshift lower than 1.7, the Lyα and Lyβ forest is not taken into account. Note that the spectral broadening based on spectral resolution specified in System Configuration is ignored if the input resolution is higher than that of input line width or template spectra (R=500 for stars and Δλ=3Å for galaxies) without user-specified line feature.

Input redshift of target object. If redshift is equal to 0.0 and "Absolute magnitude" in Scale Flux Density is selected, 10 pc is used as radial distance of target object.

Scale Flux Density
Input parameters to scale the SED specified in Target Spectral Energy Distribution.

Exposure Time
Specify exposure time for each frame and the number of frames. For instance, input 600 second x 4 frames in the case of ABBA nodding spectroscopy with 600 second exposure for each frame.