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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

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.

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Inter university centre for astronomy and astrophysics pune india

  • 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

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……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

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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.)

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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.

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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

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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

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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

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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).

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  • 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

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  • 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

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Simulated drift (pitch and yaw directions) of ASTROSAT (data provided by ISRO Satellite Centre)

system parameters : satellite drift…..

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Errors in the estimation of Satellite pitch

system parameters : satellite drift…..

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  • 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

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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

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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

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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

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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

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  • 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

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  • 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

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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

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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

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  • 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

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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

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Before data corrections

After data corrections

system parameters : random errors…..

  • Random Errors : due to random fluctuations in pixel values

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  • 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

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>

>

~

  • 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…..

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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

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  • 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

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photometric properties : fake events due to 3-cross…..

  • Fake Event Detection due to 3-Cross algorithm

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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’

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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

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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

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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

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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)

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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.

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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

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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

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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

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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

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Thank you

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