An Innovative Combination of Fiber Scrambling and Pupil Slicing for High Resolution Spectrographs

Z. Kaplan (1), J.F.P. Spronck (1), D. Fischer (1) and C. Schwab (1) (1)Yale University, New Haven, CT

Fiber Scrambling: Fiber optics have been used since the 1980’s to couple telescopes to spectrographs, initially for simpler mechanical design and control. However, fiber optics are also naturally efficient scramblers. Scrambling refers to a fiber’s ability to produce an output beam independent of input. Near-field (NF) is defined as the intensity distribution across the face of the fiber (image plane), while far-field (FF) is defined as the intensity distribution of the light cone coming out of the fiber (pupil plane). Fibers with an octagonal core have been shown to exhibit near-perfect scrambling in the near-field but still display variation in the far-field. This has led to a factor of 5 improvement in SLSF stability over circular fibers, and a factor of 50 improvement over traditional slit-fed spectrographs. Stabilizing the far-field will further improve SLSF stability, as this light distribution illuminates the optics in the spectrograph. Thus, minimizing changes in the far-field will reduce the SLSF contribution from each optical element.

Motivation: The detection of Earth-like exoplanets with the radial velocity method requires extreme Doppler precision and long-term stability in order to measure small reflex velocities in the host star. Recent planet searches have led to the detection of so called “super-Earths” (up to a few Earth masses) that induce radial velocity changes of about 1 m/s. However, the detection of true Earth analogs requires a precision of 10 cm/s. One factor limiting Doppler precision is variation in the instrumental profile or spectral line spread function (SLSF) from observation to observation due to changes in the illumination of the slit and spectrograph optics. This stability has become a focus of instrumentation work.

Pupil Slicing with Rectangular Fibers: Image and pupil slicers increase spectral resolution by “slicing” the star image into a spot of lesser width and greater length. However, this creates a multiple-peak order in the cross-dispersion direction, which complicates data extraction and may reduce radial velocity precision. In our design, we use a modified Bowen-Walraven slicer to re-arrange the pupil after the octagonal fiber into two half-moon slices that are then injected into a rectangular optical fiber. This smoothes the two slices into a uniform rectangular beam. To our knowledge, this is the first time that this combination of optical elements has been used to design a high throughput double scrambler.

Conclusion: Fiber optic spectrographs have much better SLSF stability than slit-fed spectrographs. However, resulting resolution is often reduced due to large fiber core size. Image and pupil slicers increase the resolution of fiber-fed spectrographs. However, the odd slit function has proven difficult to extract. By combining pupil slicing with a slit-like rectangular fiber, we achieve the same resolution as a 100-micron slit (R ~80,000 at Keck’s HIRES) while avoiding slit losses. Using this scrambler, SLSF stability of a slit-fed spectrograph could be improved by a factor of 50 while maintaining resolution. Lab tests indicate a total throughput in the range of 60% (while avoiding typical slit losses). A system of mirrors could divert light into a pick-off system of two fibers and pupil slicer. A prototype double scrambler and pick-off system is currently being built for testing at the Keck HIRES Spectrograph.

Double Scrambling:

A double scrambler injects the far-field of a primary fiber into a secondary fiber, therefore stabilizing both the near-field and far-field. Here, the primary fiber is an octagonal fiber coming from the telescope, and the secondary is a rectangular fiber going to the spectrograph.

Octagonal Fiber

Rectangular Fiber

-75 0 75

Spot position (in µm)

-0.05

0.05

0.15

Asy

mm

etry

nor

mal

ized

by

the

med

ian

SL

SF

Circular (0.0475711 RMS)

Octagonal (0.00591758 RMS)

Double Scrambler - Circ. (0.00327782 RMS)

Double Scrambler - Oct. (0.000794587 RMS)

-75 0 75

Spot position (in µm)

0.85

1.00

1.15

Nor

mal

ized

SL

SF

Wid

th

Circular (0.0410060 RMS)

Octagonal (0.00774837 RMS)

Double Scrambler - Circ. (0.0339668 RMS)

Double Scrambler - Oct. (0.00398161 RMS)

50  

55  

60  

65  

70  

75  

80  

85  

90  

95  

100  

2   2.5   3   3.5   4   4.5   5   5.5   6   6.5  

Enci

rcle

d En

ergy

(%

)

Output F/#

Octagonal Double Scrambler: Encircled Energy vs. Output F/# for Input F/5 Beam

50  

55  

60  

65  

70  

75  

80  

85  

90  

95  

100  

2   2.5   3   3.5   4   4.5   5   5.5   6   6.5  

Enci

rcle

d En

ergy

(%

)

Output F/#

Single Octagonal Fiber: Encircled Energy vs. Output F/# for F/5 Input Beam

We acknowledge the support of the Planetary Society, NSF and NASA

Octagonal Fiber

Rectangular Fiber

NF FF FF NF

Octagonal Fiber Rectangular Fiber

FF with slicer