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

Abstract

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).

Figure 1. Linear-in-k optimization by combining a diffraction grating with an isosceles prism as the dispersion component in the SD-OCT spectrometer.

(a) Chief ray tracing of an arbitrary light with the wavenumber of k_i. ρ is the apex angle of the isosceles prism. θ_B is the Blaze angle (in air), α_i is the diffraction angle by grating (in air), β_i and β_i′ are the incident and the refraction angles at the front surface of the prism, η_i and η_i′ are the incident and refraction angles at the back surface of the prism, ϕ_i is defined as the deviation angle between the exit light and the entrance light. (b) Optical path lengths (OPLs) for the chief rays with the wavenumbers of k_6−j, k₆ and k_6+j. (c) Minimization of the non-linearity error in k-space using root-mean-square deviation function (see eq. (8)) in the dispersion group comprised of a grating and a prism. (d) Demonstration of the significant improvement in linear dispersion angle distribution in k-space, by comparing the absolute increment of Δα_ifor grating only and −Δη_i′ for grating-prism pair respectively.

Figure 2. Optical design for the k-space spectrometer.

(a) The k-space spectrometer is comprised of a collimator, a dispersion group (grating and prism), a focusing group and a linear camera. S0−S12 indicate the surface numbers. (b) Point spread functions (PSFs) for the wavenumbers of k₁−k₁₁ are narrower in the X direction than in the Y direction. The figures at the top show the spot diagrams (95% confidence interval for RMS diameters: 5.48 ± 1.76 μm). The black rectangles demonstrate the pixel shape/pitch (14 μm × 28 μm). The figures at the bottom are the cross section of the PSF profile, where the red lines show the cross section in the X direction and the black lines show the cross section in the Y direction. (c) Theoretical sensitivity fall-off calculation based on the average RMS spot diameter of 5.48 μm. The maximum fall-off is −3.39 dB at the imaging depth of 2.26 mm.

Figure 3. Detection sensitivity comparison between the k-space and the conventional spectrometers.

An experimental SD-OCT set-up with both spectrometers is demonstrated in (a). SLD is a superluminescent diode with the bandwidth of 760 nm – 920 nm. The measurement results demonstrate obvious improvement in detection sensitivity in deeper imaging regions using the k-space spectrometer (b-1) in comparison with the conventional spectrometer (b-2).