Absolute linear-in-k spectrometer designs enabled by freeform optics.

ABSTRACT

Linear-in-wavenumber, k, spectrometers have the merits of saving signal processing time and improving the sensitivity of spectral-domain optical coherence tomography (SD-OCT) by avoiding post-k-interpolation. We report on an approach leveraging freeform optics to linearize spectrometers in k to achieve an extremely low residual k-nonlinearity in design. A freeform lens reduced the k-nonlinearity from 2.47% for a benchmark spectrometer to 2.79 × 10-5% and 3.36 × 10-9% using the Fringe Zernike coefficients up to the 16th term and 37th term, respectively. A simulation model was developed to evaluate the performance of SD-OCT with the designed spectrometers. Without the k-interpolation in software, results show that the two freeform spectrometers achieve a roll-off gain of 5.24 dB over the imaging depth from 0.5 to 5.5 mm, while the maximum imaging depth is 5.8 mm. Finally, a 4.2-µm-FWHM axial PSF was maintained throughout the imaging depth in air.