Frequency-domain C2 imaging is implemented using the setup detailed in Fig. 4·3
(a). The light source used for these experiments is a continuous-wave (CW) external cavity diode laser (ECL) (Thorlabs TLK-L1050M) which emits ∼5 mW of power with a ∼100 kHz linewidth. Roughly 1% of the laser power is tapped off and sent directly to a silicon camera (Thorlabs DCC1645C, maximum frame rate = 140 frames per second) at the detection plane. This “monitor” arm (shown in orange) allows for normalization of any power fluctuations of the source during the measurement. Normalization could also be achieved using a power meter rather than the camera; the camera is convenient, however, as it is already interfaced. The majority of the light is incident on a fiber 3-dB coupler, which splits the light into the reference (green) and FUT (red) arms of the interferometer. In order to prevent unwanted back reflections, the second input to the coupler is “optically grounded” by angle cleaving the fiber and immersing it in index-matching gel.
The fundamental mode exiting the coupler in the FUT arm is imaged onto the surface of a spatial light modulator (SLM) (Hamamatsu X10468-07) which uses binary phase plates (BPPs) to excite select HOMs in the FUT (described in detail in the next chapter, Sec. 5.3). The reference arm comprises ∼5 m length of SMF (Corning HI1060) which approximately matches the fiber and free-space optical path length of the FUT arm. The reference mode is imaged onto the camera with an objective lens (Nikon BD Plan Apo 150) with magnification such that the reference beam is larger than the field from the FUT at the detection plane. The reference path in free-space leaves the lens, is transmitted by a free-space beam splitter, is retro-reflected by a mirror on a delay stage, and is finally reflected by the same beam splitter and steered onto the camera. Relative delay (τ ) can be tuned by moving the delay stage back and forth with respect to the beam splitter. The FUT beam in free-space is reflected by one beam splitter (such that half the light can be used for other experiments) and then transmitted through a second beam splitter such that it is collinear with the reference beam.
Each port of the 3-dB coupler has a polarization controller, and a linear polarizer (LP) at the output. The polarization controllers can be used in conjunction with the associated LPs to act as variable attenuators in order to adjust the power ratio between the arms such that interference signal is maximized. The LP in the FUT path ensures horizontal polarization, the preferred orientation of the liquid crystals in the SLM. The polarizer in the reference arm also ensures a linear polarization. The field exiting the FUT is modified by quarter and half-wave plates such that interference between the FUT beam and linearly polarized reference is maximized. This implicitly assumes a high polarization extinction ratio for the field exiting the FUT and that off-polarized components are negligible, given that components of the field orthogonal to the reference polarization will not interfere and thus will not be
measured. Recent improvements to the system allow for measuring both components of the field’s polarization simultaneously, removing this assumption (Sec. 4.7). A sample camera frame showing the interfering reference and FUT beams, as well as the monitor arm is shown in Fig. 4·3(b).
Figure 4·3: (a) Experimental setup for fC2 imaging facilitated by an
ECL split into three arms: monitor (orange), reference (green) and fiber under test (red), all combined on a CMOS camera; (b) Sample camera frame showing the monitor (orange) separated from the interference of the Gaussian reference (green) and FUT (red) beams. Reproduced from Fig. 3 in (Demas and Ramachandran, 2014).
For each measurement, the laser sweeps from 1046 nm to 1040 nm at a constant velocity of 6.3 nm/s. During the first 1 nm of the sweep, no data is collected – this buffer ensures that the motor has reached constant velocity and is not accelerating during the measurement. As the wavelength is swept over the next 5 nm (1045 nm - 1040 nm), 99 camera frames are collected with a 8 ms period such that the wave- length of each exposure is encoded by the acquisition time. The entire measurement, including the buffer, takes 950 ms to complete.
S(t) is calculated using a LabVIEW program which processes the camera frames immediately after the measurement is completed. A 141×141 pixel region of inter-
est is defined around the interfering reference and FUT fields. The reference field is measured by capturing a frame with the FUT arm blocked, and computing the square root of the measured intensity. The interference intensity is normalized by the reference field in keeping with the derivation of the modal weight trace in Sec. 4.2, as well as by the intensity from the monitor arm to ensure variations in the power of the source as it sweeps do not effect the measurement. The normalized intensity is transformed into the time domain using a pixel-by-pixel fast Fourier transform algorithm, the modulus squared is computed, and the result is integrated across all pixels in the region of interest to yield S(t). The software interface allows the user to place a cursor at any peak in the modal weight trace and reconstruct the intensity corresponding to the mode at that particular delay. Computation of S(t) requires ∼2.5 s in addition to the measurement time. The processing time could likely be made negligible in comparison to the measurement time with further optimization, given that far more complicated OCT data sets can be displayed at video rates.