Center Finding Algorithm for Point Source Observation of Slit - - PowerPoint PPT Presentation

Center Finding Algorithm for Point Source Observation of Slit Spectrometer (IGRINS)

Hye-In Lee1, Soojong Pak1, Gregory Mace2, Jae-Joon Lee3

1School of Space Research, Kyung Hee University 2The University of Texas at Austin 3Korea Astronomy & Space Science institute

IGRINS User workshop Kyung Hee University 7/27-28, 2017

Contents

• 1. Introduction
• 2. About IGRINS
• 3. Observation Requirement

for Slit Spectrometer - Algorithms

• 4. Performance Test
• 5. Result & Discussion
• 6. Summary

• 1. Introduction

① Identifying: Are we observing the correct target? ② Centering: Are the maximum number of photons going through the slit? ③ Guiding: Can we take long spectral exposures while guiding?

• 2. About Control Software for IGIRNS
• IGRINS (Immersion GRating INfrared Spectro-graph) is

a high spectral resolution R=45,000 near-infrared slit spectrograph.

• IGRINS consists of House Keeping Package (HKP),

Finding Chart Package (FCP), Slit Camera Package (SCP), Data Taking Package (DTP), Quick Look Package (QLP), Pipe Line Package (PLP). Instrument parts are HKP, SCP, DTP.

• Slit Camera Package (SCP) points the target and guides

the guide star through controlling the Telescope Control System (TCS).

Optical Design of IGRINS

Package Hierarchy for IGRINS

• 3. Observation Requirement for

Slit Spectrometer

• Target Centering
• Reference position

(Yellow dashed line)

• Sending a target in the defined box (Red, Blue box)
• Auto-Guiding
• On-Slit Guiding: No point source besides the target
• Off-Slit Guiding: General guiding method

We need a “Center Fitting Algorithm” on the slit.

Target on the off-slit Target on the on-slit

SCP Observer Storage TCS SDCS

Save Image pyfits.open(Image Path…)

Sequence for pointing

Find Target Select Target Calculate offset GO:MoveTelescope Show Value(RA, Dec) Show Value(RA, Dec) Image Taking mode Setting(Single or Continuous) self.scd.send("SETFSMODE(1)") Start Single Taking self.scd.send(" SETFSPARAM (…)") self.scd.send("ACQUIRERAMP") Return value = self.scd.recv(1024) Return value = self.scd.recv(1024) Return value = self.scd.recv(1024) Load & Display Image If Continuous mode, continue

SCP : Slit Camera Package DTP : Data Taking Package TCS : Telescope Control System HKP : House Keeping Package SDCS : Science Detector control Computer for Slit Camera Request : Red / Data : Green / Image Data : Orange

Get Value(RA, Dec …) recvfrom(1024) CalcOffset(Rotator -> RA, Dec) RaDecOffset(RA, Dec) recvfrom(1024) Get Value(RA, Dec …)

SCP Observer Storage TCS SDCS

Select A or B Position (On-slit guiding) self.scd.send("SETFSMODE(…)") Start Auto-guiding self.scd.send(" SETRAMPPARAM(…)") self.scd.send("ACQUIRERAMP") Return value = self.scd.recv(1024) Return value = self.scd.recv(1024) Return value = self.scd.recv(1024) ImageTakingProgress (road Image) Save Image pyfits.open(Image Path…) Load & Display Image continue Show A or B Position(x, y) calc_offset(…), CalcOffset(…) => Get Value(RA, Dec …) MoveTelescope RaDecOffset(RA, Dec) Stop Auto-guiding

SCP : Slit Camera Package DTP : Data Taking Package TCS : Telescope Control System HKP : House Keeping Package SDCS : Science Detector control Computer for Slit Camera Request : Red / Data : Green / Image Data : Orange

Sequence for auto-guiding

Center Finding Algorithms

• 1. 2D-Gaussian PSF Fitting Algorithm: 2DGA
• 2. Center Balancing Algorithm: CBA

2D-Gaussian PSF Fitting Algorithm

• Considering X line and Y line at the same time.

   

Background 2 y y 2 x x exp Height y) f(x,

2 2 center 2 2 center

                                 

Center Balancing Algorithm

• Making Balance Table (B.T):
• Calculating the offset from centroid of virtual slit to centroid
• f reference PSF.
• Dividing up and down position from slit and calculate the

flux ratio of up to down wings.

• Making Balance Table.
• Deriving the relationship between the offset and the ratio by

‘least square function’.

• Applying to on-slit image
• Selecting the real on-slit image.
• Calculating the ratio of up to down.
• Getting an offset through the previous calculated relationship

To get the A, B for calculation of ‘least square’ from the array of ‘offset- ratio’, 𝑧 = 𝐵 + 𝐶𝑦 𝐵 = Σ𝑦2Σ𝑧 − Σ𝑦Σ𝑦𝑧 Δ 𝐶 = 𝑂Σ𝑦𝑧 − Σ𝑦Σ𝑧 Δ (𝑧 : boxsize/2+offset, 𝑦 : log10Ratio) It can just calculate 𝑧 from this formula : 𝑝𝑔𝑔𝑡𝑓𝑢 = 𝐵 + 𝐶log10Ratio

• 4. Performance Test
• Performance Simulation
• Selecting a point target with a guiding star within

the slit camera FOV.

• When the target is on the reference position,

measure the relative distance between the target and the guide star.

• Translation of Reference Frames

• 8
• 6
• 4
• 2

2 4 6 8

• 50
• 40
• 30
• 20
• 10

10 20 30 40 50

2DG CB 𝑴𝒇𝒐𝒉𝒖𝒊𝑭 (𝒒𝒋𝒚𝒇𝒎)

• Expected Position VS (Expected Position – Positions by

each of algorithms)

• 𝑴𝒇𝒐𝒉𝒖𝒊𝑭VS ( 𝑴𝒇𝒐𝒉𝒖𝒊𝑭 - 𝑴𝒇𝒐𝒉𝒖𝒊𝑩𝒎𝒉𝒑𝒔𝒋𝒖𝒊𝒏 )

• 8
• 6
• 4
• 2

2 4 6 8

• 8
• 6
• 4
• 2

2 4 6 8

2DG CB 𝑿𝒋𝒆𝒖𝒊𝑭 (𝒒𝒋𝒚𝒇𝒎)

• Expected Position VS (Expected Position – Positions by

each of algorithms)

• 𝑿𝒋𝒆𝒖𝒊𝑭VS ( 𝑿𝒋𝒆𝒖𝒊𝑭 - 𝑿𝒋𝒆𝒖𝒊𝑩𝒎𝒉𝒑𝒔𝒋𝒖𝒊𝒏 )

• 5. Result & Discussion
• Results of 16 samples analysis – Considering

“Slit Width”

• Full graph of 16 samples for comparison
• Table & Graph: Mag – RMS
• Table & Graph: FWHM - RMS

• Results of 16 samples analysis – Considering “Slit Width”

[ Relationship wT - ∆w 2DG, CB ]

• Date Index / Mag (K) / FWHM
• RMS of Residual
• Green Color Background Graph:

Those match with algorithms.

• Yellow Color Background Graph:

Those do not match with algorithms.

• Purple star and box:

Same Target of different days.

• The blue circles (2DGA) of the

yellow graphs show jumping parts between upper and lower wings (about 5 pixels).

• Results of 16 samples analysis – Considering “Slit Width”

Mag - RMS

No Index Date Target Mag(K) Reference Position RMS of Residual Background Peak FWHM LOG_flux 2DG CB 12 02-Jul 20140708 HIP5131 5.3 208.14 22351.28 14.69

• 13.5

1.16 1.09 13 03-Jul 20140709a HIP93580 5.3 195.89 15642.35 18.21

• 13.4

1.86 2.09 7 04-May 20140525b 24 Oph 5.5 207.80 20795.50 15.10

• 13.5

2.53 1.34 14 04-Jul 20140709b HIP95560 5.6 160.69 14340.58 17.85

• 13.3

1.03 1.77 15 05-Jul 20140709c HIP97376 6.0 162.30 14427.29 14.81

• 13.1

1.16 0.85 20 10-Jul 20140713 HD155379 6.5 217.20 20336.74 9.58

• 13.0

2.13 0.74 19 09-Jul 20140712b HD155379 6.5 188.05 20983.42 9.65

• 13.0

3.88 1.90 17 07-Jul 20140711b HD155379 6.5 262.36 18917.52 10.22

• 13.0

3.07 1.31 8 05-May 20140525c 2MASS J18331755 6.8 169.65 17616.99 8.06

• 12.6

2.40 0.55 4 01-May 20140524a Serpens15 7.0 211.59 12697.75 9.24

• 12.4

2.50 0.22 18 08-Jul 20140712a GSS32 7.3 207.20 10709.17 9.74

• 12.3

2.11 1.00 9 06-May 20140526a GSS32 7.3 154.75 5137.68 14.07

• 11.9

2.53 1.80 16 06-Jul 20140711a SR4(V* V2058 Oph) 7.5 229.51 6571.84 9.36

• 11.7

1.81 1.53 6 03-May 20140525a Oph Ttau 7.6 442.84 8050.78 10.78

• 12.1

2.58 0.75 5 02-May 20140524b SS433 8.2 143.47 5608.74 9.59

• 11.6

3.00 0.66 10 07-May 20140526b Serpens2 8.6 137.01 3590.78 8.40

• 10.9

2.95 0.51

[ Relationship Mag (K) – RMS (pixel) ]

• For fainter targets, CBA shows better performance than 2DGA.
• The blue circles (2DGA) and red triangle (CBA) have similar results on the green

circle.

• The stars on the purple box mean same target of different days which show

different RMSs.

• Results of 16 samples analysis – Considering “Slit Width”

FWHM - RMS

No Index Date Target Mag(K) Reference Position RMS of Residual Background Peak FWHM LOG_flux 2DG CB 12 02-Jul 20140708 HIP5131 5.3 208.14 22351.28 14.69

• 13.5

1.16 1.09 13 03-Jul 20140709a HIP93580 5.3 195.89 15642.35 18.21

• 13.4

1.86 2.09 7 04-May 20140525b 24 Oph 5.5 207.80 20795.50 15.10

• 13.5

2.53 1.34 14 04-Jul 20140709b HIP95560 5.6 160.69 14340.58 17.85

• 13.3

1.03 1.77 15 05-Jul 20140709c HIP97376 6.0 162.30 14427.29 14.81

• 13.1

1.16 0.85 20 10-Jul 20140713 HD155379 6.5 217.20 20336.74 9.58

• 13.0

2.13 0.74 19 09-Jul 20140712b HD155379 6.5 188.05 20983.42 9.65

• 13.0

3.88 1.90 17 07-Jul 20140711b HD155379 6.5 262.36 18917.52 10.22

• 13.0

3.07 1.31 8 05-May 20140525c 2MASS J18331755 6.8 169.65 17616.99 8.06

• 12.6

2.40 0.55 4 01-May 20140524a Serpens15 7.0 211.59 12697.75 9.24

• 12.4

2.50 0.22 18 08-Jul 20140712a GSS32 7.3 207.20 10709.17 9.74

• 12.3

2.11 1.00 9 06-May 20140526a GSS32 7.3 154.75 5137.68 14.07

• 11.9

2.53 1.80 16 06-Jul 20140711a SR4(V* V2058 Oph) 7.5 229.51 6571.84 9.36

• 11.7

1.81 1.53 6 03-May 20140525a Oph Ttau 7.6 442.84 8050.78 10.78

• 12.1

2.58 0.75 5 02-May 20140524b SS433 8.2 143.47 5608.74 9.59

• 11.6

3.00 0.66 10 07-May 20140526b Serpens2 8.6 137.01 3590.78 8.40

• 10.9

2.95 0.51

[ Relationship FWHM (pixel) – RMS (pixel) ]

• For better seeing conditions, CBA shows better performance than 2DGA. The stars

are inside of the purple box are the same target of different days. We can recognize the results by each algorithm depend on the seeing at that time.

• The blue circles (2DGA) and red triangle (CBA) have similar results on the green

circle and those do not have different results on the yellow circle.

• The RMS errors using the CBA are always < 2 pixels (about 0.24”) which is enough

for good auto-guiding.

• 6. Summary
• The slit-blocked point spread function cannot be

easily fitted with Gaussian function.

• We developed Center Balancing Algorithm on slit

for Slit Camera Package (SCP) of IGRINS.

• We did performance simulation and got the results
• f 16 samples by 2DGA, CBA for evaluation of CBA.
• It shows the results by each algorithm depend on

the seeing at that time. The RMS errors using the CBA are always < 2 pixels (about 0.24”) which is enough for good auto-guiding.

Thank you:)