A spectrometer is an optical instrument used to measure the intensity of light by wavelength, or wavenumber (k). A conventional spectrometer has intrinsic nonlinearity in k over the pixels due to the nonlinear angular dispersion in k corresponding to the grating or prism used. For spectrometers used in spectral domain optical coherence tomography (SD-OCT), this nonlinearity requires computationally expensive and slow post-processing of linear interpolation prior to the fast Fourier transform (FFT), which hinders real-time applications. It also importantly adds noise into each SD-OCT axial scan by the inaccuracy imposed by the numerical interpolation, the level of which is approximately proportional to the square of depth. Prior mitigation attempts to this problem have involved a hardware solution involving a grism or custom prism separated from the grating. However, despite these approaches achieving a reduction in nonlinearity of k over the camera pixels and a signal-to-noise ratio (SNR) gain compared to the software interpolation approach, there is still residual nonlinearity of k, which remains a problem in the degradation of the axial point spread function (PSF) full width at half maximum (FWHM) through depth.
This absolute linear-in-k spectrometer uses a single transmissive or reflective freeform optic to radically minimize the residual nonlinearity in k (< 10E-4%) after k-linearization by a prism. A freeform optic is one with a surface geometry that has translational and/or rotational variance about the optical axis, and its advantages have been shown in terms of optimal aberration correction in an all-reflective five-mirror electronic viewfinder and a three-mirror imager, and increased compactness in a mirror-based spectrometer. Simulations of the invention showed 29.5 dB SNR gain at the maximum imaging depth of 5.8 mm in air and about 4-micron FWHM axial PSF throughout the depth in comparison to the performance of a conventional benchmark spectrometer adopting a post k-interpolation.
Use of the freeform field lens spectrometer corrected residual aberrations—specifically field-dependent astigmatism and field-dependent coma that is caused by the prism—and dramatically minimized residual k-nonlinearity to the level where it eliminated degradation in the axial PSF FWHM with depth. Removing the need for k-linearization in post processing significantly reduces imaging and signal processing time and improves the sensitivity of SD-OCT, enabling real-time applications.
Spectral domain optical coherence tomography