Design of a k-space spectrometer for ultra-broad waveband spectral domain optical coherence tomography

Nonlinear sampling of the interferograms in wavenumber (k) space degrades the depth-dependent signal sensitivity in conventional spectral domain optical coherence tomography (SD-OCT). Here we report a linear-in-wavenumber (k-space) spectrometer for an ultra-broad bandwidth (760 nm-920 nm) SD-OCT, whereby a combination of a grating and a prism serves as the dispersion group. Quantitative ray tracing is applied to optimize the linearity and minimize the optical path differences for the dispersed wavenumbers. Zemax simulation is used to fit the point spread functions to the rectangular shape of the pixels of the line-scan camera and to improve the pixel sampling rates. An experimental SD-OCT is built to test and compare the performance of the k-space spectrometer with that of a conventional one. Design results demonstrate that this k-space spectrometer can reduce the nonlinearity error in k-space from 14.86% to 0.47% (by approximately 30 times) compared to the conventional spectrometer. The 95% confidence interval for RMS diameters is 5.48 ± 1.76 μm-significantly smaller than both the pixel size (14 μm × 28 μm) and the Airy disc (25.82 μm in diameter, calculated at the wavenumber of 7.548 μm^-1). Test results demonstrate that the fall-off curve from the k-space spectrometer exhibits much less decay (maximum as -5.20 dB) than the conventional spectrometer (maximum as -16.84 dB) over the whole imaging depth (2.2 mm).