Inter-University Centre for Astronomy and Astrophysics

Pune, India.

30th 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

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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)

Summary2 / 41

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

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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

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

Introduction…..

Imaging with UVIT : Photon Counting Detectors

UV Photon

Photo-electron

Bunch ofPhoto-electrons

Optical Glow

Detector

Photo-Cathode

MCP Stack

Phosphor Screen

Fibre Taper

C-MOS imagesensor

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

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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

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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.

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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). 9 / 41

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

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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

system parameters : satellite drift…..

Simulated drift (pitch and yaw directions) of

ASTROSAT (data provided by ISRO Satellite Centre)

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system parameters : satellite drift…..

Errors in the estimation of Satellite pitch

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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

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system parameters : centroid algorithms…..

Centroid Finding Algorithms : Energy Thresholds

5-Square Algorithm

3-Square Algorithm3-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 :

Background : Minimum of 4 corner pixels in 5 X 5 shape 15 / 41

system parameters : event centroid…..

Calculation of Event Centroid : Centre of Gravity Method

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

Itotal = Sum of all Iij

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 resolution16 / 41

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.

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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

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system parameters : systematic bias…..

Origin of ‘Grid pattern’ : Algorithm Shape

1-D Example

1-D pixels

Footprint Intensity

0 1 2-1-2

Xc = I0 * (0)

+ I-2 * (-2) + I-1 * (-1)

+ I+2 * (+2) + I+1* (+1) _____________________

Itotal

I-2 = I+2 & I-1 = I+1

If Photon falls in the centre

Xc = 0 19 / 41

system parameters : systematic bias…..

Origin of ‘Grid pattern’ : Algorithm Shape

1-D pixels

Footprint Intensity

0 1 2-1-2

1-D Example

Xc = I0 * (0)

+ I-2 * (-2) + I-1 * (-1)

+ I+2 * (+2) + I+1* (+1) _____________________

Itotal

I-2 > I+2 & I-1 > I+1

If Photon falls on –ve Side

Xc -ve 20 / 41

system parameters : systematic bias…..

But if profile falls outside the algorithm shape: 3-Square

1-D pixels

Footprint Intensity

0 1 2-1-2

I-2 > I+2 A –ve contribution is not being considered

And as,

Xc will be “shifted” on +ve side

Towards Centre

Xc = I0 * (0)

+ I-2 * (-2) + I-1 * (-1)

+ I+2 * (+2) + I+1* (+1) _____________________

Itotal

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system parameters : systematic bias…..

But if profile falls outside the algorithm shape: 3-Square

1-D pixels

Footprint Intensity

0 1 2-1-2

I-2 < I+2 A +ve contribution is not being considered

And if,

Xc will be “shifted” on -ve side

Towards Centre

Xc = I0 * (0)

+ I-2 * (-2) + I-1 * (-1)

+ I+2 * (+2) + I+1* (+1) _____________________

Itotal

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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

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system parameters : systematic bias…..

Algorithms to correct systematic bias

N (y)

0.0 0.5Pixel Boundary

1.0

Actual Histogram

N (x)

0.0 0.5Pixel Boundary

1.0

Calculated Histogram

P(x).dx = P(y).dy

y = f (x)

Calculated Centroidx

Actual Centroidy

0.00 0.00 …. … 0.10 0.12 …… …… 0.50 0.50 …. …. 0.90 0.88 …. ….

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system parameters : random errors…..

Random Errors : due to random fluctuations in pixel values

Before data corrections

After data corrections

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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

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Photon falls in the

centre

Photon falls at a corner

photometric properties : pixel face…..

Centre Pixel Energy Centre Pixel Energy> Total Event Energy in 3-square / 3-cross

Total Event Energy in 3-square / 3-cross

>

Total Event Energy in 5-square

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

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

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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

ButLead to Fake Event Detection

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

Fake Event Detection due to 3-Cross algorithm

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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

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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

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 threshold33 / 41

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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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. Image Ratio 35 / 41

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….. ????

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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 identified37 / 41

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

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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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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

Thank you

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