Fiber positioning in microlens-fiber coupled integral field unit

2020 
A generic fiber positioning strategy and a fabrication path are presented for microlens-fiber-coupled integral field units (IFUs). It is assumed that microlens-produced microimages are carried to the spectrograph input through a step-index, multimode fiber, but our results apply to micropupil reimaging applications as well. Considered are the performance trades between the filling percentage of the fiber core with the microimage versus throughput and observing efficiency. A merit function is defined as the product of the transmission efficiency and the etendue loss. For a hexagonal packing of spatial elements, the merit function has been found to be maximized to 94% of an ideal fiber IFU merit value (which has zero transmission loss and does not increase the etendue) with a microlens-fiber alignment (centering) tolerance of 1-μm RMS. The maximum acceptable relative tilt between the fiber and the microlens face has been analyzed through optical modeling and found to be 0.3 deg RMS for input f-ratio slower than f  /  3.5, but it is much more relaxed for faster beams. From the acceptable tilt, we have deduced a minimum thickness of the fiber holder to be 3 mm for 5  μm clearance in hole diameter relative to the fiber outer diameter. Several options of fabricating fiber holders have been compared to identify cost-effective solutions that deliver the desired fiber positioning accuracy. Femto-second laser-drilling methods from commercial vendors deliver holes arrayed on plates with a relative position accuracy of ±1.5-μm RMS, similar diameter accuracy, and with an aspect ratio of 1:10 (diameter:thickness). One commercial vendor combines femtosecond laser-drilling with photolithographic etching to produce plates with thickness of 5 mm, but with similar (±1-μm RMS) positioning accuracy and conical entry ports. Both of these techniques are found to be moderately expensive. A purely photolithographic technique performed at Wisconsin Center for Advanced Microelectronics (a facility at the University of Wisconsin, Madison), in tandem with deep reactive ion etching, has been used to produce a repeatable recipe with 100% yield. Photolithography is more precise (0.5-μm RMS) in terms of hole positioning and similar diameter accuracy (1-μm RMS) but the plate can only have a thickness of 250  μm.
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