ETC verification

The “ETC Requirements Specification”, VIS-SPE-4MOST-47110-1740-0001 document describes how the ETC works and which TOAD data should be used (e.g. average fibre area, effective telescope area, etc.). This document lists some tests designed to check intermediate steps as well as the final product (S/N curve) of the ETCs. This test report will be only partially comprehensible without a close read of the specification..

The comparison data were obtained from TOAD. TOAD models the 4MOST instrument extensively and as accurately as possible at this stage of the development. TOAD is therefore considered to be closest to reality. The version of the TOAD validation data, used in all tests, can be found in the Gitlab repository.

Note

In some spectrograph arms, typically green/red, in the bottom panels one sees large P-Cygni-like residuals coming from emission or absorption lines. These residuals can get much higher than our limit of 5%. They are due to the difference in the resolution of the input spectra/transmission curves and the difference in the interpolation techniques. E.g. TOAD sky emission and transmission spectra have 650,000 resolution elements. 4FS has 100,000. Therefore, these spikes in the residual are of no consequence and do not influence the results or conclusions.

The selected wavelengths of the tests are:

spectrograph	arm	Bin #25	Bin #2950	Bin #5400
lrs	blue	370.81 nm	462.61 nm	536.19 nm
lrs	green	524.86 nm	623.36 nm	701.94 nm
lrs	red	692.15 nm	821.58 nm	924.95 nm
hrs	blue	392.80 nm	414.96 nm	431.82 nm
hrs	green	516.27 nm	545.69 nm	568.15 nm
hrs	red	610.32 nm	645.32 nm	672.01 nm

These pixels are indicated as stars in the verification plots.

Test #1: Coupling to fibre flux

Testing if the coupling from total to fibre flux is correctly done. Compares the number of electrons per pixel for each spectrograph without sky. Full line is TOAD (reference), dashed line is 4FS ETC. None of the selected pixels (indicated as stars) has a higher than indicated tolerance.

The success condition of test 1 has been fulfilled, and 4FS is consistent with TOAD.

Settings:

• target_airmass: 1.2

• seeing: 0.8 arcsec

• dit: 20 min

• ndit: 1

• template: white

• magnitude: 16 mag

• mag_system: ab

• tolerance: 5%

The test includes variations of:

• spectrograph (hrs, lrs)

• target seeing (0.45 arcsec, 0.89 arcsec, 1.34 arcsec, 1.78 arcsec, 2.23 arcsec)

• target_shape (point, flat)

Test #2: Re-binning and instrument convolving

Here we test if the projection of emission lines on the instrument pixel borders is correct. The plots below show the output spectra for lines with varying center and line width. The test is about the FWHM and the recovered flux of each line, which is within 5% (original requirement is 10%).

Settings:

• target_airmass: 1.2

• seeing: 0.8 arcsec

• dit: 20 min

• ndit: 1

• template: line

• target_shape: point

• tolerance: 7%

The test includes variations of:

• spectrograph (hrs, lrs)

• line_fwhm_scaling (0.7, 3.0)

• line_offset (0.2 pix, 0.0 pix, 0.5 pix)

Test #3: SNR scaling with exposure time

Testing if the SNR per pixel scales correctly with exposure time and with NDIT. This compares a point source. Compares the SNR per pixel for each spectrograph without sky flux for different exposure times. Full line is TOAD (reference), dashed line is 4FS ETC. None of the selected pixels (indicated as stars) has a higher than indicated tolerance. The SNR of the long exposure time is within 1% of √2 times the SNR of the short exposure time.

Settings:

• seeing: 0.8 arcsec

• template: white

• target_airmass: 1.2

• target seeing: 0.89 arcsec

• magnitude: 12 mag

• mag_system: ab

• target_shape: point

• tolerance: 5%

The test includes variations of:

• spectrograph (hrs, lrs)

• dit (10 min, 20 min)

• ndit (1, 2)

Test #4: Sky brightness

Testing the sky brightness. Assume a sky fibre observation, no target flux. Full line is TOAD (reference), dashed line is 4FS ETC. None of the selected pixels (indicated as stars) has a higher than indicated tolerance.

Settings:

• target_airmass: 1.2

• seeing: 0.8 arcsec

• dit: 20 min

• ndit: 1

• tolerance: 7%

The test includes variations of:

• spectrograph (hrs, lrs)

• sky_brightness (dark, gray, bright, superbright)

Test #5/7: “Real” spectra and end-to-end performance

These tests are performed with “real” spectra. First, the resulting spectra are compared with TOAD. Full line is TOAD (reference), dashed line is 4FS ETC (test #5). None of the selected pixels (indicated as stars) has a higher than indicated tolerance.

Then, the SNR calculated by TOAD is converted into “Rules” and “Rulesets” files, which are used by the ETC to calculate the exposure time. The exposure time for the given SNR is recalculated by the ETC and compared with the original time (20 min) (test #7). The calculated exposure time together with its deviation is shown in the plot. It is always within the required tolerance.

The wavelength ranges for the rules are:

spectrograph	arm	wavelength range
hrs	blue	413.0 … 415.0 nm
hrs	green	551.0 … 553.0 nm
hrs	red	641.0 … 643.0 nm
lrs	blue	413.0 … 415.0 nm
lrs	green	551.0 … 553.0 nm
lrs	red	725.0 … 727.0 nm

Settings:

• target_airmass: 1.2

• seeing: 0.8 arcsec

• target_shape: point

• target seeing: 0.89 arcsec

• filter: Generic_Johnson.V

• dit: 20 min

• ndit: 1

• tolerance: 7%

The test includes variations of:

• spectrograph (hrs, lrs)

• sky_brightness (dark, gray, bright)

• template (Pickles_A0V, Kinney_starb1)

• magnitude (16 mag, 21 mag, 23 mag)

• mag_system (ab, vega)

Test #8: Extended source and airmass

These tests are performed with “real” spectra in different target shapes, magnitudes, seeings, airmasses and sky brightnesses. First, the resulting spectra are compared with TOAD. Full line is TOAD (reference), dashed line is 4FS ETC. None of the selected pixels (indicated as stars) has a higher than indicated tolerance.

Then, the SNR calculated by TOAD is converted into “Rules” and “Rulesets” files, which are used by the ETC to calculate the exposure time. The exposure time for the given SNR is recalculated by the ETC and compared with the original time (20 min). The calculated exposure time together with its deviation is shown in the plot. It is always within the required tolerance.

The wavelength ranges for the rules are:

spectrograph	arm	wavelength range
hrs	blue	413.0 … 415.0 nm
hrs	green	551.0 … 553.0 nm
hrs	red	641.0 … 643.0 nm
lrs	blue	413.0 … 415.0 nm
lrs	green	551.0 … 553.0 nm
lrs	red	725.0 … 727.0 nm

Settings:

• seeing: 0.8 arcsec

• mag_system: ab

• filter: Generic_Johnson.V

• dit: 20 min

• ndit: 1

• tolerance: 7%

The test includes variations of:

• spectrograph (hrs, lrs)

• target_airmass (1.2, 1.8, 1.0, 1.3)

• target seeing (0.88 arcsec, 1.13 arcsec, 0.82 arcsec, 0.91 arcsec)

• sky_brightness (gray, bright, dark)

• template (Pickles_A0V, Kinney_starb1)

• magnitude (16 mag, 21 mag, 23 mag)

• target_shape (point, sersic, flat)

• sersic_index (-1.0, 0.56, 1.0, 4.12)

• sersic_reff (-1.0 arcsec, 0.523 arcsec, 1.0 arcsec, 2.14 arcsec)