2 J. Eur. Opt. Society-Rapid Publ. 21, 1( 2025)
2 Analysis and design
The analysis and design of the SRI wavefront sensor is detailed in the following subsections by way of its optical design and image processing.
2.1 Optical design
The proposed study makes use of our testbed having an AO system matched to the SRI wavefront sensor.
The AO system is shown in Figure 1a. Itisseededbya laser module( TeraXion, PS-LM-1550.12-80-06) having a wavelength of 1550 nm and an output power of 4 mW. The beam is coupled out of the laser and collimated for propagation through five relays. The relays have their entrance and exit pupils coincide with the spatial light modulator( Hamamatsu, LCOS-SLM), tip-tilt mirror( Newport, FSM-300), and deformable mirror( Boston Micromachines Corp., 18W160 # 046). With such a system, the spatial light modulator can compensate for static distortion from the lenses and other elements, via a calibration routine, and apply dynamic distortion to mimic the timevarying effects of turbulence. Wavefront correction is then realized by the tip-tilt mirror, for tip-tilt( low-order) modes, and deformable mirror, for the remaining( high-order) modes. The SRI wavefront sensor is key to this correction as it characterizes the transverse phase profiles of the beam and directs their conjugates to the tip-tilt and deformable mirrors. The remainder of this work focuses on the SRI wavefront sensor, while details on the AO system can be found elsewhere [ 20 ].
The exit pupil of the AO system is matched to the input pupil of the SRI wavefront sensor shown in Figure 1b. The SRI takes the form of a Mach-Zehnder interferometer with its input beamsplitter( Thorlabs, BP108) forming signal and reference arms. There is a primary lens with a focal length of f 1 = 100 mm in each arm at a distance of f 1 beyond the sensor’ s input pupil, and a secondary lens with a focal length of f 2 = 150 mm at a distance of f 1 + f 2 beyond the primary lens in each arm. The SRI also has a pinhole aperture with a diameter d at a distance of f 1 beyond the primary lens in the reference arm. Diameters of d = 15and75lm are considered in our theoretical analyses, while a pinhole aperture( Thorlabs, P75S) with a diameter of d = 75lm isused for the experimental analyses. Beams from the signal and reference arms are overlapped by the output beamsplitter( Thorlabs, CM1-BP3) and resolved by an infrared camera( Xenics, Cheetah F051, CL-2078) with a 20-lm pixel size. The camera’ s image sensor is at a distance of f 2 beyond the secondary lens. Such a system has confocal pairing of primary and secondary lenses in each arm, with an input pupil plane before the input beamsplitter, a focal plane at adistanceoff 1 beyond each primary lens( coplanar with the pinhole aperture in the reference arm), and an output pupil plane at a distance of f 2 beyond the secondary lens( coplanar with the camera’ s image sensor).
There are two key considerations in the SRI. First, the beam in the reference arm must be effectively focused through the pinhole aperture, which acts as a spatial filter and forms a reference beam with flattened wavefronts on the camera’ s image sensor. However, there is a tradeoff here
Fig. 1. Schematic of the( a) AO system and( b) SRI wavefront sensor. In( a), the 1550-nm laser beam( violet) propagates through five relays, for which the spatial light modulator, tip-tilt mirror, deformable mirror, and flat mirror( FM) are within the relays’ pupil planes. In( b), the 1550-nm input beam( violet) propagates into the SRI wavefront sensor and is split by the input beamsplitter( BS) into the signal beam( blue) and reference beam( red). These beams pass through confocal lens pairs, with a pinhole aperture in the focus of the reference beam, and are then overlapped by the output beamsplitter( BS). The output beam( violet) is then resolved on the camera’ s image sensor. The four dotted lines across the beams in the SRI wavefront sensor designate the input pupil plane( violet), focal plane of the signal arm( blue), focal plane of the reference arm( red), and output pupil plane( black).
in that smaller aperture diameters give especially flat wavefronts on the reference beam but larger aperture diameters transmit higher powers for the reference beam. Second, the input beamsplitter must be suitably angled to apply a linear tilt on the wavefronts of the signal beam. When the signal