image reduction programs for non-circular core fiber scrambler

PHY 486: Image Reduction Programs for Non-Circular Core Fiber Scrambler

Joseph M. ReganDepartment of Physics, Astronomy, and Materials Science

Missouri State UniversityDr. Peter Plavchan, Advisor

AbstractOver four months in 2012, data was obtained of several exoplanet candidates using the CSHELL spectrograph at the peak of Mauna Kea in Hawaii, along with Dr. Peter Plavchan’s Non-Circular Core Fiber Scrambler. Images and spectra were obtained in near-infrared wavelengths using different shaped (non-circular) core fibers for the purpose of detecting exoplanets using the radial velocity method. Since then, code has been developed in order to reduce the images using dark images, flat images, and bias images taken at the same time. Code has also been developed to plot a line-spread function of the pixel intensity of sets of images taken using the different fibers with respect to their position. These two programs, used in tandem on Missouri State University’s high performance computing cluster (also known as Exo), have been used to determine which fiber, between a 200 micron diameter square fiber, 50 and 200 micron diameter variants of octagonal fibers, and a 50x100 micron rectangular fiber, most evenly and consistently scrambles the light from the target stars when shone through one end of the fiber.

1 – IntroductionIn the field of Astronomy, the search for extrasolar planets, or Exoplanets, has boomed in the last decade or so, due to increasingly efficient methods of detecting them around other stars. At the time of this writing, we have discovered a total of more than 1800 exoplanets, with over 4000 more waiting to be confirmed3. There are many ways of detecting these planets, but the two most successful methods of planet detection are the transit method, watching a star’s light dim periodically as the planet passes in front of it, and the radial velocity method, observing the red- and blue-shifting of a star as it and a planet orbit a common center of mass. The former method has been more successful overall, with the Kepler space telescope discovering and confirming over a thousand of the total confirmed exoplanets using the transit method. This method is tricky, since it requires a planet and its parent star to be lined up with our field of vision. Using this method, usually we can find short-period large-radius planets2.In any planetary system, it appears due to the vast difference in mass that the planet orbits the star, but instead, the star and the planet orbit a common barycenter, obeying Kepler’s laws of planetary motion. Due to the planet’s gravitational effect, the star will move ever so slightly around this barycenter, causing a slight shift in the spectrum of the star. If this slight movement can be isolated in the spectrum, we can determine the exact radial velocity of the star, and the orbital period and mass of the planet can be measured. These measurements have been taken in optical wavelengths, and at the time of this writing, 533 planets have been confirmed using this method3. However, no measurements have yet been made in the near-infrared, which may allow us to locate far more exoplanets than are currently confirmed.

2 – Non-Circular Core Fiber Scrambler

Dr. Plavchan’s non-circular core fiber scrambler takes precision spectroscopic radial velocity measurements in the near-infrared H band. Tests using the fibers were collected in the near-infrared at H and K bands using the CSHELL spectrograph at the NASA InfraRed Telescope Facility (IRTF) at the peak of Mauna Kea in Hawaii. CSHELL, a near-20-year-old spectrograph, covers wavelengths from 1 to 5.5 µm. Parts of CSHELL were modified to accommodate the prototype fiber scrambler. One added part is an absorption gas cell between two of the mirrors, used for a common optical path relative wavelength calibration. The gas cell is filled with isotopic methane (13CH4) at 275mb of pressure, which in both the H and K bands, leaves a sharp set of absorption lines in the near-infrared. These lines help calibrate the spectrograph, accounting for isotopic methane in the atmosphere that may interfere with the stellar spectra. The fiber scrambler operates, in principle, by running the starlight from the telescope through the fiber input, then relaying the output to the spectrograph slit input. Fibers used for the scrambler were octagonal and square core fibers 200µm in diameter and 1 and 10m in length, rectangular core fibers 50x100µm in diameter and 1 and 10m in length, and octagonal core fibers 50 microns in diameter 1 and 10m in length1.

Figure 1. Images of starlight through fiber tips in near-infrared. From left to right: 200µm octagonal core, 1 and 10 m length, 50µm square core fiber, 50x100µm rectangular core fiber, 50µm octagonal core fiber.

Figure 2. Images of the Fiber Scrambler. On the right, the setup of the lenses inside the scrambler before final construction; on the left, the completed fiber scrambler in its aluminum casing.

3 – Data Acquisition3.1 – Format

The images that have been reduced and analyzed are using the Flexible Image Transport System (FITS) image format, and the programs to reduce and analyze the data have been written in the Interactive Data Language (IDL).

3.2 – ObservingThrough several months of 2012, observations on a number of stars were taken using the fiber scrambler through the CSHELL Spectrograph attached to IRTF on the top of Mauna Kea in Hawaii. The images were labelled by their targets, central wavelength, slit width, exposure time, inclusion of gas cell, and most importantly, type of fiber used.

3.3 – Stars ObservedDue to limits placed on the obtained data, the data sets have been narrowed down based on the fiber type, target star, central wavelength, and exposure time. The data being reduced and analyzed only includes images, data with an open slit, and, coincidentally, data excluding the gas cell. As a result of this narrowing, only data from May and December 2012 has been analyzed. Status of the fiber agitator was also included.

Dec-129-Dec

Image Numbers Fiber Target

Wavelength Exposure Time Agitator

355-467 Rect 10m SVPeg 1.672 0.125 On10-Dec



1801-2403 200um Oct 1m SVPeg 2.3-3 .1251 Off

1585-1695 50um Oct 1m SVPeg 2.312 1 Off11-Dec



2534-3403 200um Oct 1m SVPeg 2-2.4 .1251

3304-3403 On

3404-3826 Rect 1m SVPeg 2-2.4 0.125 Off

3827-4386,4399-4408 Square 1m SVPeg 2-2.4 0.125 3877-3976 On

May-128-May

Image Numbers Fiber Target Wavelength Exposure Time Agitator

6418-6573,6681-66936694-6753,6754-68076845-6963,6979-6988

7013-7051

200µm Oct 1m 102_herVega 2.1325 0.25 6845-6878 On

6982-6988 On

7227-7324,7449-7486 200µm Oct 10m Vega 3.3125 0.25 7449-7486 On9-May


8735-8754,8815-8894 200µm Oct 10m Arcturus 1.6 0.125 Off8202-8529,8570-8589

8655-8694200µm Oct 1m Arcturus

45_Boo1.6

2.31250.125

.25 Off

258-265 Rect 10m Vega 2.3125 0.5 Off

9495-9594,9759-9838 Square 10m Arcturus 1.62.3125 0.125 Off

9035-9114,9195-9394 Square 1m Arcturus 1.62.3126 1.125 Off

10-May


5540-5859 200µm Oct 10m 55Alp_Oph 1.6 0.125 5540-5699 On4410-4729 200µm Oct 1m 55Alp_Oph 1.6 0.125 4410-4569 On4127-4316 50µm Oct 10m 55Alp_Oph 1.6 0.25 4127-4206 On

3620-3779,3844-4003 50µm Oct 1m 55Alp_Oph 1.62.3125 0.25 3700-3779 On

3844-3923 On

2004-2005,2068-22332496-2575,2767-2785 Rect 10m

Vega36Eps_Boo30Zet_Boo49Del_Boo

109_Vir16Alp_Boo65Del_Her55Alp_Oph

33_Cyg5Alp_CrB

1.62.3125

2.6

.125.25.52

Off

3080-3239,3428-3587 Rect 1m 55Alp_Oph 1.62.3125 0.25 3160-3239 On

3428-3507 On

5184-5503 Square 10m 55Alp_Oph 1.6 0.125 Off4823-5142 Square 1m 55Alp_Oph 1.6 0.125 4823-4882 On

4 – Data ReductionThe first program is intended to reduce and process the images taken during the IRTF observing sessions. Many individual dark images, long-exposure closed-shutter images taken of the dark current running through the detector, must be stacked together into one image. Then, flat images, shone at a bright light source to fully illuminate the detector to evenly distribute the light, must be stacked together into one image. The dark image stack must be subtracted from the image in order to correct for bad pixels and the resulting image must be divided by the flat image stack in order to correct for uneven light distribution. In the second program, the line-spread function of the final reduced images is plotted to check the variance and consistency of pixel intensity across the different fiber types.

Figure 3: Image 5600 from May 10, 2012, showing the raw and reduced image of the 200 micron octagonal fiber, respectively.

Fig. 4: Line Spread Functions of the eight main fibers, full plot and zoomed in. From top to bottom: 200 micron Octagonal 10m fiber, images 5540-5859; 200 Micron Octagonal 1m fiber, images 4410-4729; 50 micron Octagonal 10m fiber, images 4127-4316; 50 micron octagonal 1m

fiber, images 3884-3923; Rectangular 10m fiber, images 2496-2575; Rectangular 1m fiber, images 3080-3239; Square 10m fiber, images 5184-5402; Square 1m fiber, images 4823-4881

4.1 – Fiber Agitator

In all of the images used, while science data was being obtained, the fiber agitator was turned on or off at some point. This was accounted for in the plotting of the data, but in nearly

all cases, the status of the agitator did not seem to have an effect on the shape of the line spread function. In the case of images 4410-4569 and 4570-4729, the shape was affected slightly and the standard deviation rose from 1.6% to 2.1%. This was the most significant change brought on by the fiber agitator.

Fig. 5: On the top, Images 4410-4569 of the 200 micron Octagonal 1m fiber, with agitator on. On the bottom, Images 4570-4729 of the same set, with agitator off. There is a slight change in the shape of the LSF, but nearly no change in the standard deviation of the plots. Upon inspecting the data, this is the set that was changed the most from the changing status of the fiber agitator. Below the images are their

respective zoomed-in plots.

4.2 – Standard Deviation

Also recorded were tables showing the implot commands for each data set in relation to their fiber shape along with the standard deviation of each set. Data sets that included a change in agitator status were split into three sets: one set with the agitator off, one with the agitator on, and both combined, in order to compare standard deviations and shapes of each set when plotted.

December’s data was split up into many individual ten-image data sets excluding a few, notably images 1585-1695 on December 10th, the only images taken with the 50 micron octagonal fiber, having a standard deviation of 16.89%. Upon inspection, none of the remaining data taken on December 10th, all taken using the 200 micron octagonal 1m fiber, had standard deviations of less than 14% ranging up to 26%.

Fig. 6: Typical plot of data using the 200 micron Octagonal 1m fiber on the night of December 10th. This particular data set: images 2344-2353.

On the night of December 11th, the data for the 200 micron octagonal 1m fiber was taken in sets of twenty images rather than ten. The data was much more consistent towards the end of the fiber’s run, eventually narrowing down to 1.8% standard deviation after starting the run at about 14%. The rectangular 1m fiber, back to sets of ten images, showed some consistency over the night, reading in standard deviations of about 2.2% at its best, but despite being relatively consistent with the line spread function, the light was shown to be brighter through the edge of the fiber than the core in most cases.

Fig 7: More stable plot of data using the Rectangular 1m fiber on the night of December 11th. This particular data set: Images 3507-3516.

The Square 1m fiber, also using ten-image sets, had by far the most consistency of the three fibers used on December 11th, with the standard deviation ranging between 2.4% and 4% and rarely stepping outside of that range. Over the course of the run, however, while the light on the right side of the fiber stayed consistently bright, the light on the left side of the fiber started out dim, but was even with the right side in brightness by the end of the run.

Fig. 8: Data using the Square 1m fiber on the night of December 11th. On the left: Images 4227-4236. On the right, images 4337-4346.

8-MayFiber Command Standard Deviation

200µm Oct 1m

implot,6418,6573 0.0364implot,6681,6693 0.0267implot,6694,6753 0.0888implot,6754,6807 0.0437implot,6845,6878 0.0084implot,6845,6963 0.0446implot,6879,6963 0.0521implot,6979,6988 0.0185implot,7013,7051 0.0446

200µm Oct 10m

implot,7227,7324 0.0875implot,7449,7486 0.0138


200µm Oct 10m

implot,8735,8754 0.007implot,8815,8894 0.319

200µm Oct 1m

implot,8352,8529 0.078implot,8570,8589 0.021implot,8655,8694 0.008

Rect 10m implot,258,265 0.011

Square 10m

implot,9495,9594 0.004implot,9759,9838 0.011

Square 1m implot,9035,911 0.129

4implot,9195,9394 0.041


200µm Oct 10mimplot,5540,5699 0.0099implot,5540,5859 0.0104implot,5700,5859 0.0106



50µm Oct 1m

implot,3620,3699 0.032implot,3620,3779 0.021implot,3700,3779 0.0253implot,3884,3923 0.0262implot,3884,4003 0.119implot,3924,4003 0.144

Rect 10m

implot,2068,2171 0.348implot,2181,2233 0.0793implot,2496,2575 0.01implot,2767,2785 0.028

Rect 1m

implot,3080,3159 0.021implot,3080,3239 0.022implot,3160,3239 0.023implot,3428,3507 0.132implot,3428,3587 0.137implot,3508,3587 0.144

Square 10m implot,5184,5402 0.0112implot,5404,5503 0.0118

Square 1mimplot,4823,4881 0.018implot,4883,5142 0.023

As shown by the chart, the lowest standard deviation in any of the given data sets is the Square 10m fiber, at 0.4% on May 9th, 2012. However, the only other data set with a standard deviation less than 1% seems to be both of the 200 micron Octagonal fibers, with at least one set showing sub-1% standard deviation each night in May between the two of them.

5 – Errors and Odd Data

There were a few notable errors in the plots due to the state of the raw images themselves that caused inconsistency when reduced. It is uncertain what caused the errors, but they were present during the gathering of the data.

Fig. 7: Data taken using the Square 1m fiber on May 10th. The top plot, images 4823-5142, show one plot out of place. The bottom plots, from left to right, show images 4823-4881 and images 4883-5142. Image 4882 was determined to be the error image.

Fig. 8: On the left, image 4881 from May 10th. In the middle, the image in question, image 4882. Between the two images there is a noticeable odd area at both the top and bottom of the second image. On the right, the averaged result of the two images, which would normally be

uniform in the case of two consistent images. It is uncertain what may have caused this error.

6 – Code

Fig. 9: Image reduction code, named impro2.pro. Process explained in section 4, syntax detailed in comment section at start of program.

Fig. 10: Program to plot the line spread function of the reduced images. Process includes summing in both directions, normalization, and calculation of standard deviation.

7 – Conclusion

Code has been written for Missouri State University’s high-performance computing cluster, Exo, to reduce images taken during several months’ time using Dr. Peter Plavchan’s Non-Circular Core Fiber Scrambler at the CSHELL spectrograph on the top of Mauna Kea in

Hawaii. Code has also been written to plot the line spread function of pixel intensity with respect to pixel position, with the purpose of determining the most reliable fiber core shape for detecting exoplanets around M-Dwarf stars in the near-infrared using the radial velocity method. After analyzing the data and determining the standard deviations of different sets of data using different fiber shapes, it seems that all the fiber shapes have varying degrees of reliability. However, by a small margin, it seems that the 200 micron Octagonal fibers, both the 1 and 10 meter variants, may be the most reliable fibers used in this analysis.

These plots and reduced images come from the two finished programs, unedited throughout the process of reducing and plotting, and will require little to no upkeep as long as the image sizes remain consistent using CSHELL. In the future the programs should be able to quickly and efficiently reduce and analyze data taken using the CSHELL spectrograph or other similar instruments that may replace it.

7 – References

1. Plavchan, P., et al., “Precision Near-Infrared Radial Velocity Instrumentation II: Non-Circular Core Fiber Scrambler”, 2013, SPIE, in Optical Engineering + Applications, 8864 1J

2. Plavchan, P., et al., “Radial Velociy Prospects Current and Future,” 2015, ExoPAG Study Analysis Group white paper

3. NASA Exoplanet Archive. 2015. Web. <http://exoplanetarchive.ipac.caltech.edu/docs/counts_detail.html>

image reduction programs for non-circular core fiber scrambler

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