PACS Instrument Model and Performance Prediction

1. PACS Instrument Model andPerformance Prediction A. Poglitsch Instrument Performance Prediction

2. PACS Instrument Model • Purpose of instrument model: provide best guess of in-orbit performance based on existing knowledge of the instrument and its subunits and the satellite • Incomplete knowledge about FM subunit / instrument / system performance • Some knowledge of QM instrument performance, but with degraded subunit and OGSE performance • Instrument model is a “living document” that has been maintained since the early design phases of PACS and updated whenever new test results became available • Parameters lacking experimental values have been assigned calculated or estimated values • PACS instrument model is not a deliverable document (but has been used regularly as a reference for preparation and evaluation of tests and their results) Instrument Performance Prediction

3. Spectrometer Model Model strategy • Determine the background power reaching an individual detector (pixel) and determine the NEP of an individual detector under this background (photon noise + detector/readout noise) • Determine the coupling of an astronomical (point) source to the detector array • Telescope PSF • Vignetting / diffraction in instrument • Transmission of optical elements (mirrors, filters, grating) • Detector (quantum) efficiency • Effective number of pixels (spatial/spectral) needed for optimum source/line extraction and resulting total noise and fraction of detected source flux • Combine above results to calculate “raw” noise referred to sky • Add overheads created by need for background subtraction (AOT-dependent) Instrument Performance Prediction

4. Detector Performance • Relative spectral response within modules • Relative photometric response within modules • Absolute photometric peak responsivity (moduleaverage) Instrument Performance Prediction

5. noise bias [mV] bias [mV] HS Detector Performance Model 4.7x10-15 W 2.9x10-15 W signal Circles: measured noise Dashed line: CRE noise Squares: CRE noise subtr. Solid lines: combined model Dotted lines: background noise • Observed noise consistent with photon noise + CRE noise (input-equivalent current noise density) • Peak QE=0.26; QE(l) follows directly from rel. spectral responsivity • Average CRE noise 3.7x10-16 A/√Hz, average peak responsivity 45 A/W Instrument Performance Prediction

6. LS Detector Model • No reliable measurement of peak QE available; assumed to be the same as for HS detectors (by design) • Quite limited consequence for system performance – CRE noise and responsivity dominate (see below) • CRE noise same as for HS detector • Average peak responsivity 10…12 A/W Instrument Performance Prediction

7. Spectrometer Model: Background Basics (Calculated for groups/ elements along optical train from telescope to detector) AW: etendue of optical train (conserved by optics, except for detector light cones) n: optical frequency d: detected optical bandwidth (around given frequency) T: temperature of emitter em: emissivity of emitter t: transmission of all optics between respective emitter and detector h: detector quantum efficiency Instrument Performance Prediction

8. Spectrometer Model: Background Etendue throughout optical train, for all contributions from outside of the 5K environment [deviations are lumped into effective emissivities] AWcold := 4 AW correcting for the effective cone acceptance angle seeing the 5K optics Instrument Performance Prediction

9. Spectrometer Model: Background/Straylight Temperatures and Emissivities • PACS-external contributions dominant Instrument Performance Prediction

10. Spectrometer Model: Background/Straylight Transmission to Detector and Bandwidth • Bandwidth same for all background contributions except 5K post-grating (which is negligible) • Effective transmission for background contributions varies slightly (pupil aperture sizes etc.) Telescope backgroundtransmission Background optical bandwidth/pixel [Hz] Wavelength [µm] Wavelength [µm] Instrument Performance Prediction

11. Spectrometer Model: Transmission Breakdown • Filter transmission based on RT FTS measurements of FM filters • Dichroic will be replaced before ILT Filter transmission Calculated grating efficiency Wavelength [µm] Wavelength [µm] Instrument Performance Prediction

12. Spectrometer Model: Transmission Breakdown • Slicer efficiency: vignetting of diffraction side lobes by optics • Additional transmission factors • Lyot stop efficiency: 0.9(diffraction by field stop plus telescope/instrument alignment tolerances) • Mirror train: 0.85(dissipation, scattering) Calculated slicer efficiency Wavelength [µm] Instrument Performance Prediction

13. Spectrometer Model: Additional Optical Efficiencies Relevant for Source Coupling • Telescope efficiency: fraction of power received from point source measured in central peak of PSF • Pixel efficiency: inverse number of pixels (spatial/spectral) needed to retrieve power of unresolved spectral line in central peak of PSF Estimated telescope main beamefficiency (diffraction + WFE) Calculated pixel efficiency Wavelength [µm] Wavelength [µm] Instrument Performance Prediction

14. Background Power and BLIP Noise per Pixel • HS detector QE based on measurement (peak QE + relative spectral responsivity) • LS detector QE based on assumed, same peak QE + relative spectral responsivity measurement QE Background power [W] BLIP NEP [W/√Hz] Wavelength [µm] Wavelength [µm] Wavelength [µm] Instrument Performance Prediction

15. BLIP Noise vs. Readout Noise • BLIPNEP converted to electrical noise (solid lines) • Readout noise (dashed line) • BLIPNEP (and, therefore, QE) significant/dominant noise source in “red” band (1st order, HS) • BLIPNEP (and, therefore, QE) not dominant noise source – readout noise and responsivity relevant NEI [A/√Hz] = NEP [W/√Hz] x responsivity [A/W] NEI [A/√Hz] Wavelength [µm] Instrument Performance Prediction

16. Total Noise at Detector and Coupling to Sky Coupling correction Total NEP [W/√Hz] Wavelength [µm] Wavelength [µm] • Total NEP at detector: BLIP NEP and electrical readout-noise equivalent power • Coupling correction: inverse of all optical efficiencies; factor 2 forbackground subtraction; chopper duty-cycle of ≥0.8 Instrument Performance Prediction

17. Point source continuum sensitivity per spectral resolution element [Jy] (5s, 1h) Point source line sensitivity [W/m2] (5s, 1h) Wavelength [µm] Wavelength [µm] Predicted Sensitivity • Calculated for (off-array) chopping • Wavelength switching could have advantage (spectral line always within instantaneous coverage) or disadvantage (off-line switching and likely need for off-position observation) Instrument Performance Prediction

18. Operation/Performance under p+ Irradiation Simulated chopped observation with one ramp/chopper plateau. For each bias value, 5 ramp lengths tested: 1s, 1/2 s, 1/4 s, 1/8s, 1/16 s. The detector was in its high responsivity plateau, ~2 hours after the last curing. NEP as a function of detector/readout setting Instrument model value,based on lab measurementswithout irradiation • With optimum bias setting (lower than in lab!) and ramp length / chopping parameters, NEP close to lab values possible in space • Curing may be necessary only after solar flare, or once per day (self- curing under telescope IR background sufficient) Instrument Performance Prediction

19. Spectral Resolving Power • Simple calculation, requiring some fine tuning • Pixel sampling • Exact grating illumination(physical optics) Resolving power Wavelength [µm] Instrument Performance Prediction

20. Main Limitations of Spectrometer Model • No “systematics”/ higher-order effects and their implications for AOTs considered • no real instrument simulator • No end-to-end test of instrument in representative high-energy radiation environment • Limited feed-back from QM ILT • Serious uncertainty about detector responsivity makes evaluation of instrument optical efficiency difficult • Defocus, low transmission and high/inhomogeneous window emissivity have hampered PSF determination • Lack of laser source (or adequate gas cell) – no unresolved, strong lines available Instrument Performance Prediction

21. Photometer Model Model strategy • Determine the background power reaching an individual detector (pixel) and determine the NEP of an individual detector under this background (photon noise + detector/readout noise) • Determine the coupling of an astronomical (point) source to the detector array • Telescope PSF • Vignetting / diffraction in instrument • Transmission of optical elements (mirrors, filters) • Detector (quantum) efficiency • Effective number of pixels needed for optimum source extraction and resulting total noise and fraction of detected source flux • Combine above results to calculate “raw” noise referred to sky • Add overheads created by need for background subtraction (AOT-dependent) Instrument Performance Prediction

22. Bolometer Performance • Pixel yield ~98% • NEP “blue” ~1.7...2 x nominal • Small variation with BG power • But 1/f noise • Best NEP only for fast modulation (chopping/ scanning) • NEP “red” slightly higher NEP vs.backgroundpower “blue” BFP Instrument Performance Prediction

23. Photometer Model: Background Basics (Calculated for groups/ elements along optical train from telescope to detector) Crude approximation for largebandwidth of photometer! (But it doesn’t matter.) AW: etendue of optical train (conserved by optics, except for detector light cones) n: optical frequency d: detected optical bandwidth (around given frequency) T: temperature of emitter em: emissivity of emitter t: transmission of all optics between respective emitter and detector h: detector quantum efficiency Instrument Performance Prediction

24. Photometer Model: Background Etendue “Red” Photometer: 6.4”□ pixels“Blue” Photometer: 3.2”□ pixels throughout optical train, for all contributions from outside of the 5K environment [deviations are lumped into effective emissivities] AWcold := 10 AW correcting for the effective detector/baffle acceptance cone seeing the 5K optics Instrument Performance Prediction

25. Photometer Model: Background/Straylight Temperatures and Emissivities • PACS-external contributions dominant Instrument Performance Prediction

26. Photometer Model: Background/Straylight Transmission to Detector and Bandwidth • Bandwidth same for all background contributions except 5K post-grating (which is negligible) • Filter transmission based on RT FTS measurements of FM filters • Dichroic will be replaced before ILT Instrument Performance Prediction

27. Photometer Background Power andNoise per Pixel • QE assumed to be 0.8 (from bolometer absorber structure reflectivity measurement) for BLIPNEP • Realisation of “measured NEP” requires modulation near 3 Hz (1/f noise) Instrument Performance Prediction

28. Photometer Model: Additional Optical Efficiencies Relevant for Source Coupling • Telescope efficiency: fraction of power received from point source measured in central peak of PSF • Pixel efficiency: inverse number of pixels needed to retrieve power in central peak of PSF Instrument Performance Prediction

29. Total Coupling to Sky • Coupling correction • inverse of all optical efficiencies • factor 2 for background subtraction • chopper duty-cycleof ≥0.8 Instrument Performance Prediction

30. 5 off-position chopping 4 3 on-array chopping/line scanning [mJy] (point source; 5s/1h) 2 1 0 50 100 150 200 wavelength [µm] Predicted Sensitivity • Point source sensitivity equivalent to mapping speed of ~10’ x 10’ in 1 day Photometric Bands filter transmission wavelength [µm] Instrument Performance Prediction

31. Main Limitations of Photometer Model • No “systematics”/ higher-order effects and their implications for AOTs considered • no real instrument simulator • Origin of 1/f noise not clear • Is it driven thermally? • Will operation in PACS cryostat be representative for in-orbit Herschel cryostat thermal (in)stability? • Limited feed-back from QM ILT • Serious uncertainty about detector responsivity makes evaluation of instrument optical efficiency difficult • Defocus, low transmission and high/inhomogeneous window emissivity have hampered PSF determination Instrument Performance Prediction