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Inter-University Centre for Astronomy and Astrophysics Pune, India.

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. 30 th June 2009.

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Inter-University Centre for Astronomy and Astrophysics Pune, India.

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  1. 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 30th June 2009 Inter-University Centre for Astronomy and Astrophysics Pune, India. 1 / 41

  2. 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) Purpose and Plan of the Talk • Introduction • System Parameters for UVIT Imaging • Photometric Properties of UVIT images : Origin and Effects • Angular Resolution of UVIT images • Summary 2 / 41

  3. ……and a lot more, through the studies of UV Images http://www.astro.virginia.edu/~rwo/ Photometry (measurement of photon flux in the images) 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 Images have to be “Sharp and Accurate” BUT 3 / 41

  4. Instruments, Detectors and Methods • “Quality” of the Images Blurred and pixelated Telescope Detector • Resolution  Point Spread function (PSF) • (Optical design, detectors, hardware etc.) Object in the Sky Recorded image on the detector Introduction….. • How to quantify image quality ? • 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. Photo-Cathode UV Photon UVIT Photo-electron • 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 MCP Stack UV Photons Phosphor Screen Bunch of Photo-electrons Point Source Fibre Taper Optical Glow C-MOS image sensor Photon-Event Footprint on the C-MOS Introduction….. • Imaging with UVIT : Photon Counting Detectors Detector 6 / 41

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

  8. Input Output Telescope UV Photons Detector Image from GALEX database Simulated UVIT data frames Introduction….. • UVIT Data Simulations : Process 3. Convert Photons positions in to event footprints andRecord UVIT data frames of 512 X 512 pixels containing photon events footprints. 2. Apply Satellite Drift and PSF of the Optics and Detector, to the incoming photon’s position on the detector. 1. Generate Photon’s positions in a UVIT data frame from input image using Poisson Statistics 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. Satellite Drift : Estimation • UVIT would drift with Satellite ~ 0.2 arc-sec/second • Simultaneous Observations in Visible UVIT : Optical Layout for Near UV and Visible channels System Parameters for UVIT Imaging 10 / 41

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

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

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

  15. 3-Cross Algorithm 3-Square Algorithm 5-Square Algorithm • Criteria to detect photon events : 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 system parameters : centroid algorithms….. • Centroid Finding Algorithms : Energy Thresholds • Background : Minimum of 4 corner pixels in 5 X 5 shape 15 / 41

  16. Xc=[I-11 * (-1) +I01 * (0) +I11 * (1) +I-10 * (-1) +I00 * (0) +I10* (1) +I-1-1 * (-1) + I0-1* (0) +I1-1* (1)] _____________________________ Itotal (0,1) (1,1) (-1,1) (0,0) (1,0) (-1,0) Itotal =Sum of allIij 3-Square Algorithm (0,-1) (1,-1) (-1,-1) (Xc, Yc) would be estimated much better than a CMOS pixel resolution • Similar equation for Yc system parameters : event centroid….. • Calculation of Event Centroid : Centre of Gravity Method 16 / 41

  17. Overlapping photon-events footprints in a UVIT data frame system parameters : double events….. • Double/Multiple Events : Rejection Threshold • Due to overlap of two of more photon events • Results in missing photons and/or wrong value of calculated event centroids. • 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 17 / 41

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

  19. 1-D Example Footprint Intensity • If Photon falls in the centre I-2 =I+2 & I-1=I+1 -2 -1 0 1 2 1-D pixels • Xc = 0 system parameters : systematic bias….. • Origin of ‘Grid pattern’ : Algorithm Shape Xc=I0 * (0) +I-2 * (-2) +I-1 * (-1) +I+2 * (+2) +I+1* (+1) _____________________ Itotal 19 / 41

  20. If Photon falls on –ve Side I-2 >I+2 & I-1>I+1 -2 -1 0 1 2 • Xc -ve system parameters : systematic bias….. • Origin of ‘Grid pattern’ : Algorithm Shape • 1-D Example Footprint Intensity Xc=I0 * (0) +I-2 * (-2) +I-1 * (-1) +I+2 * (+2) +I+1* (+1) _____________________ Itotal 1-D pixels 20 / 41

  21. Xc=I0 * (0) +I-2 * (-2) +I-1 * (-1) +I+2 * (+2) +I+1* (+1) _____________________ Itotal • And as, I-2 >I+2  A –ve contribution is not being considered -2 -1 0 1 2 system parameters : systematic bias….. • But if profile falls outside the algorithm shape: 3-Square Footprint Intensity • Xcwill be “shifted” on +ve side  Towards Centre 1-D pixels 21 / 41

  22. Xc=I0 * (0) +I-2 * (-2) +I-1 * (-1) +I+2 * (+2) +I+1* (+1) _____________________ Itotal • And if, I-2 <I+2  A +ve contribution is not being considered -2 -1 0 1 2 system parameters : systematic bias….. • But if profile falls outside the algorithm shape: 3-Square Footprint Intensity • Xcwill be “shifted” on -ve side  Towards Centre 1-D pixels 22 / 41

  23. 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 system parameters : systematic bias….. • Grid pattern : Centroids near the corners/edges would be drifted inside the pixel by 3-square / 3-cross algorithm • Grid pattern would NOT be present in 5-square algorithm 23 / 41

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

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

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

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

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

  29. Flat Response is desired over pixel face Low values of energy thresholds But Lead to Fake Event Detection 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 29 / 41

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

  31. Overlapping photon-events footprints in a UVIT data frame photometric properties : non-linearity.... • Photometric non-linearity in the reconstructed images : Double Events • 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 • Non-linearity is expected due to ‘Photon Statistics’ 31 / 41

  32. Probability of getting ‘x’ photons in unit time from a source with average ‘μ’ photons/unit time • Poisson Statistics : photometric properties : non-linearity.... • 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. For 3-Square Algorithm : Cen. Pxl Thrs. = 150 DU; Total Energy Thrs = 450 DU Rejection Threshold = 500 DU Rejection Threshold = 40 DU photometric properties : non-linearity.... • Ratio Map = Final Reconstructed Image / True Image • 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. Rejection Threshold = 40 DU Rejection Threshold = 500 DU True Image Recons. Image Ratio photometric properties : non-linearity.... • Simulation of a Galaxy (based on GALEX far UV data) 35 / 41

  36. Correction for Photometric Distortion….. ???? 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. 36 / 41

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

  38. angular resolution.... • A 2-D Gaussian fit to the PSF  Sigma of 0.7 arc-sec • PSF is dominated by optics + detectors • No significant effects of centroiding errors or errors in drift correction • PSF is independent of ‘Centroid Algorithms’ and Rejection Threshold • 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. summary.... • 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 • 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

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