1. Inter-University Centre for Astronomy and Astrophysics Pune, India. 30 th June 2009 Imaging Characteristics of Ultra-Violet Imaging Telescope (UVIT) through Numerical Simulations by Mudit K. Srivastava Publications of the Astronomical Society of the Pacific (PASP), 2009, 121, 621-633 Mudit K. Srivastava, Swapnil M. Prabhudesai & Shyam N. Tandon 1 / 41

2. Purpose and Plan of the Talk System Parameters for UVIT Imaging Photometric Properties of UVIT images : Origin and Effects Angular Resolution of UVIT images Introduction UV Imaging in Astronomy Imaging with UVIT : Photon Counting Detectors UVIT Data frames : Simulations Satellite drift and correction Detector parameters and thresholds Image reconstruction Related errors Non-linearity / Distortion Simulated point sources Extended sky sources (based on archival data) Summary 2 / 41

3. Introduction Ultra-Violet Imaging in Astronomy Studies of hot stars (over 10,000 K) Many strong and important transitions occur in UV: H, D, H2, He, C, N, O, Mg, Si, S, Fe Tracer of star formation activities in Galaxies http://www.astro.virginia.edu/~rwo/ Images have to be “Sharp and Accurate” ……and a lot more, through the studies of UV Images Photometry (measurement of photon flux in the images) BUT 3 / 41

4. Introduction….. “Quality” of the Images Instruments, Detectors and Methods Detector Telescope Object in the Sky Recorded image on the detector How to quantify image quality ? Resolution  Point Spread function (PSF) (Optical design, detectors, hardware etc.) Blurred and pixelated Photometric Accuracy  Calibration (Response of optics and detectors, Source, background etc.) 4 / 41

5. Introduction….. Ultra-Violet Imaging Telescope (UVIT) Two Ritchey-Chretien Telescopes : ~ 38 cm Diameter FOV ~ 0.5 square degree Simultaneous Observations in : FUV (1300-1800 Angstrom); NUV (1800- 3000 Angstrom); Visible (3200-5300 Angstrom) Designed with Spatial Resolution ~ 1.5 arc-seconds FWHM Micro Channel Plate (MCP) based intensified CMOS Photon Counting Detectors. 5 / 41

6. Introduction….. Imaging with UVIT : Photon Counting Detectors UV Photon Photo-electron Bunch of Photo-electrons Optical Glow Detector Photo-Cathode MCP Stack Phosphor Screen Fibre Taper C-MOS image sensor Photon-Event Footprint on the C-MOS 512 X 512 CMOS Pixels 1 pixel ~ 3 X 3 square arc-sec Photon-event footprint ~ 5 X 5 Pixels Frame acquisition Rate ~ 30 fr/s UVIT Point Source UV Photons 6 / 41

7. Introduction….. UVIT Data Frames So, the job is, Determine Photons position in data frames Reconstruct the Image Detector Telescope UV Photons UVIT data frame`s’ containing events footprints Object in the Sky BUT “Satellite Drift ” (All the data frames are drifted w.r.t. each other ) Satellite drift is to be corrected before image reconstruction 7 / 41

8. Introduction….. UVIT Data Simulations : Process Detector Telescope UV Photons Image from GALEX database Input Output Simulated UVIT data frames 1. Generate Photon’s positions in a UVIT data frame from input image using Poisson Statistics 2. Apply Satellite Drift and PSF of the Optics and Detector, to the incoming photon’s position on the detector. 3. Convert Photons positions in to event footprints and Record UVIT data frames of 512 X 512 pixels containing photon events footprints. 8 / 41

9. Introduction….. UVIT Data Simulations : Parameters PSF due to optics and detectors : 2-D Gaussian (sigma = 0.7 arc-sec) CMOS pixel scale : 3 arc-sec/pixel Photon-event footprint : 5 X 5 CMOS pixels Photon-event profile on CMOS : 2-D Gaussian (sigma = 0.7 CMOS pixels) 1 Photon Event corresponds to “some” Digital Units/counts (DU) on CMOS Number of DU per photon events : Gaussian distr. (Average = 1500 DU and sigma = 300 DU) Events footprints are recorded against laboratory dark frames (512 X 512 pixels). 9 / 41

10. System Parameters for UVIT Imaging Simultaneous Observations in Visible UVIT : Optical Layout for Near UV and Visible channels  Satellite Drift : Estimation UVIT would drift with Satellite ~ 0.2 arc-sec/second 10 / 41

11. system parameters : satellite drift….. Process to estimate satellite drift Select some points sources in FOV in Visible Use Integrating mode of photon counting detector. Take very short exposure images (~1s) Compare successive image and generate time series of the drift Use this time series during reconstruction of the UV images. Simulations : To estimate “error” in satellite drift determination Took star field from Hubble/ESO catalog Simulated observations through visible channel Used “Simulated Satellite drift” as an input Took first 10 sec image as a reference Recovered drift parameters by comparing 1 sec images with the reference image 11 / 41

12. system parameters : satellite drift….. Simulated drift (pitch and yaw directions) of ASTROSAT (data provided by ISRO Satellite Centre) 12 / 41

13. system parameters : satellite drift….. Errors in the estimation of Satellite pitch 13 / 41

14. system parameters : image recons…..  Image-Reconstruction Event Detection and Centroid Estimation A section of UVIT data frame Scan the data frame Identify event candidates Calculate (??) event centroid Steps are : Centroid-Algorithms 14 / 41

15. system parameters : centroid algorithms….. Centroid Finding Algorithms : Energy Thresholds 5-Square Algorithm 3-Square Algorithm 3-Cross Algorithm 1. Central pixel should be singular maximum within algorithm shape 2. Central Pixel Value > Central Pixel Energy Threshold 3. Total Event Energy > Total Energy Threshold Criteria to detect photon events : B ackground : Minimum of 4 corner pixels in 5 X 5 shape 15 / 41

16. system parameters : event centroid….. Calculation of Event Centroid : Centre of Gravity Method Xc = [ I -11 * (-1) + I 01 * (0) + I 11 * (1) + I -10 * (-1) + I 00 * (0) + I 10 * (1) + I -1-1 * (-1) + I 0-1 * (0) + I 1-1 * (1) ] _____________________________ I total I total = Sum of all I ij Similar equation for Yc 3-Square Algorithm (0,0) (0,1) (0,-1) (-1,0) (-1,1) (-1,-1) (1,0) (1,1) (1,-1) (Xc, Yc) would be estimated much better than a CMOS pixel resolution 16 / 41

17. system parameters : double events….. Double/Multiple Events : Rejection Threshold Overlapping photon-events footprints in a UVIT data frame Corner Difference = [ Maximum of the 4 Corner pixels – Minimum of the 4 Corner pixels ] in 5 X 5 pixel shape around central pixel If Corner Difference > Rejection Threshold  Double Photon Event Due to overlap of two of more photon events Results in missing photons and/or wrong value of calculated event centroids. 17 / 41

18. system parameters : centroid errors….. Systematic Bias : due to algorithms itself Random Errors : due to random fluctuations, dark frames etc.  Errors in Centroid estimation Grid Frequency : 1 CMOS pixel Centroid data are to be corrected for this bias Reconstructed image by 3-square algorithm : Showing systematic bias  Grid pattern / Modulation pattern / Fixed pattern Noise 18 / 41

19. system parameters : systematic bias….. Origin of ‘Grid pattern’ : Algorithm Shape 1-D Example 1-D pixels Footprint Intensity 012-2 Xc = I 0 * (0) + I -2 * (-2) + I -1 * (-1) + I +2 * (+2) + I +1 * (+1) _____________________ I total I -2 = I +2 & I -1 = I +1 If Photon falls in the centre Xc = 0 19 / 41

20. system parameters : systematic bias….. Origin of ‘Grid pattern’ : Algorithm Shape 1-D pixels Footprint Intensity 012-2 1-D Example Xc = I 0 * (0) + I -2 * (-2) + I -1 * (-1) + I +2 * (+2) + I +1 * (+1) _____________________ I total I -2 > I +2 & I -1 > I +1 If Photon falls on –ve Side Xc  -ve 20 / 41

21. system parameters : systematic bias….. But if profile falls outside the algorithm shape: 3-Square 1-D pixels Footprint Intensity 012-2 I -2 > I +2  A –ve contribution is not being considered And as, Xc will be “shifted” on +ve side  Towards Centre Xc = I 0 * (0) + I -2 * (-2) + I -1 * (-1) + I +2 * (+2) + I +1 * (+1) _____________________ I total 21 / 41

22. system parameters : systematic bias….. But if profile falls outside the algorithm shape: 3-Square 1-D pixels Footprint Intensity 012-2 I -2 < I +2  A +ve contribution is not being considered And if, Xc will be “shifted” on -ve side  Towards Centre Xc = I 0 * (0) + I -2 * (-2) + I -1 * (-1) + I +2 * (+2) + I +1 * (+1) _____________________ I total 22 / 41

23. system parameters : systematic bias….. Grid pattern would NOT be present in 5-square algorithm Grid pattern : Centroids near the corners/edges would be drifted inside the pixel by 3-square / 3-cross algorithm To remove grid pattern : Take flat field data Event’s “actual” centroids would be distributed uniform over the pixel Calculate centroids using algorithms Compare the distribution of “actual” and “calculated” centroids Generate a correction table for “calculated Vs actual” centroids 23 / 41

24. system parameters : systematic bias….. Algorithms to correct systematic bias N (y) 0.0 0.5 Pixel Boundary 1.0 Actual Histogram N (x) 0.0 0.5 Pixel Boundary 1.0 Calculated Histogram P(x).dx = P(y).dy  y = f (x) Calculated Centroid x Actual Centroid y 0.00 0.00 …. … 0.10 0.12 …… …… 0.50 0.50 …. …. 0.90 0.88 …. …. 24 / 41

25. system parameters : random errors….. Random Errors : due to random fluctuations in pixel values Before data corrections After data corrections 25 / 41

26. Photometric Properties of Reconstructed Images  Photometric Variations due to Energy Thresholds Too high values of ‘energy-thresholds’ Genuine Events would be lost Too low values of ‘energy-thresholds’ Fake Events would be counted Also due to Photon’s position over the pixel face Photon falls in the centre Photon falls at a corner 26 / 41

27. Photon falls in the centre Photon falls at a corner photometric properties : pixel face….. Centre Pixel Energy > Total Event Energy in 3-square / 3-cross > Total Event Energy in 5-square ~ Events falling in the centre are more probable to detect, compare to those falling near a corner/edge 27 / 41

28. photometric properties : pixel face….. Given the energy thresholds ; ‘Non-uniformity’ exists over the pixel face. Rejection Fraction For 3-Square Algorithm Cen. Pxl Thres. : 150 DU (low) Total Pxl. Thres. : 250 DU (low) Minimum rejections and non-uniformity Cen. Pxl Thres. : 150 DU (low) Total Pxl. Thres. : 1050 DU (high) non-uniformity visible Cen. Pxl Thres. : 450 DU (high) Total Pxl. Thres. : 650 DU (moderate) Significant non-uniformity 28 / 41

29. photometric properties : pixel face….. 5-Square Algorithm : Least sensitive to Total Energy Threshold 3-Cross Algorithm : Most sensitive to Total Energy Threshold Central Pixel Energy Threshold : All the algorithms would be affected in the same way Flat Response is desired over pixel face Low values of energy thresholds But Lead to Fake Event Detection 29 / 41

30. photometric properties : fake events due to 3-cross…..  Fake Event Detection due to 3-Cross algorithm 30 / 41

31. photometric properties : non-linearity....  Photometric non-linearity in the reconstructed images : Double Events Non-linearity is expected due to ‘Photon Statistics’ Overlapping photon-events footprints in a UVIT data frame Corner Difference = [ Maximum of the 4 Corner pixels – Minimum of the 4 Corner pixels ] in 5 X 5 pixel shape around central pixel If Corner Difference > Rejection Threshold  Double Photon Event 31 / 41

32. photometric properties : non-linearity.... Poisson Statistics : Probability of getting ‘x’ photons in unit time from a source with average ‘μ’ photons/unit time For ‘average 1 photon / frame’ For ‘average 2 photons / frame P (0) = 36.8 % P (1) = 36.8 % P (>= 2) = 24.4 % P (0) = 13.5 % P (1) = 27.0 % P (>= 2) = 59.5 % Simulations : To estimate the effects of double events over photometric non-linearity in the reconstructed image Simulated Points Sources : 25 photons/sec (~0.8 photons / frame) Sky Background : 0.004 photons / sec / arc-sec^2 Integration time : 3000 sec, with 30 frames / sec Without the effects of Optics 32 / 41

33. photometric properties : non-linearity.... Ratio Map = Final Reconstructed Image / True Image For 3-Square Algorithm : Cen. Pxl Thrs. = 150 DU; Total Energy Thrs = 450 DU Rejection Threshold = 40 DU Rejection Threshold = 500 DU Significant reduction in the photometry of surrounding background : photometric distortion Extent of the region : depends on rejection threshold 33 / 41

34. photometric properties : non-linearity.... But why background photons are lost ??? Sky Background is too low : 0.004 photons / sec / arc-sec^2 No question of double events due to sky background It is the strong source that is causing ‘photometric distortion’ in the background Due to overlap of a source photon with a background photon Probability (1 source + 1 background photons in a frame) = 57% Probability (1 source + 1 source photons in a frame) = 20% More complex situation in actual extended astronomical sources : Galaxies 34 / 41

35. photometric properties : non-linearity.... Simulation of a Galaxy (based on GALEX far UV data) Rejection Threshold = 40 DU Rejection Threshold = 500 DU True Image Recons. ImageRatio 35 / 41

36. photometric properties : non-linearity.... Input GALEX image ~ 0.05 photons / sec / arc-sec^2 Still significant distortion is observed Reason : It is the count rate within algorithm shape that matters For 3-Square ~ 3 X 3 CMOS pixels ~ 0.13 photons / frame A number of ‘Star forming Galaxies’ are expected to show such distortion. Correction for Photometric Distortion….. ???? 36 / 41

37. Simulations : Using ‘Hubble ACS B band image’ Input Image Reconstructed Image Angular Resolution of the Reconstructed Images Structures ~ 3 arc-sec scales can easily be identified 37 / 41

38. angular resolution.... PSF is dominated by optics + detectors A 2-D Gaussian fit to the PSF  Sigma of 0.7 arc-sec PSF is independent of ‘Centroid Algorithms’ and Rejection Threshold No significant effects of centroiding errors or errors in drift correction Double photon events could change the profile of the PSF Photon count rate ~ 2 counts / frame  sigma < 0.5 arc-sec 38 / 41

39. Summary Aim of Imaging in Astronomy is to produce, Shape Images : Angular Resolution Correct Images : Photometric Accuracy Two major factors in UVIT Imaging Photon Counting Detectors : Data frames Satellite Drift : To be removed from data frames Satellite drift can be tracked during the observations through simultaneous observations of point sources in visible channel  Time Series data of drift Drift can be recovered with accuracy ~ 0.15 arc-sec 39 / 41

40. Images are to be reconstructed from the photon-event centroid data in data frames (with resolution better than 1 CMOS pixel) Centroid Algorithms : 5-Square, 3-Square and 3-Cross Two Energy Thresholds : Total, Central Pixel Double photon event : Rejection Threshold summary.... Systematic Bias (in form of a grid pattern) is to be removed from centroid data by 3-square / 3-cross algorithms. Improper Values of energy thresholds could lead to ‘non- uniformity of event detection’ over the face of the pixel. Double photon events could give rise to ‘photometric distortion’ in the reconstructed Images. Angular resolution : dominated by performance of the optics + detectors 40 / 41

41. Thank you 41 / 41