Selection of convolution kernel in non-uniform fast Fourier transform for Fourier domain optical coherence tomography

Accelerated near-field algorithm of sparse apertures by non-uniform fast Fourier transform

We present an accelerated algorithm for calculating the near-field of non-uniform sparse apertures with non-uniform fast Fourier transform (NUFFT). The distances of the adjacent units in non-uniform sparse apertures are unequal and larger than half a wavelength. The near-field of apertures can be calculated by the angular spectrum method and the convolution methods, and according to the different convolution kernels, the convolution methods can be divided as the Fresnel kernel convolution and the Rayleigh-Sommerfeld kernel convolution. The Fresnel kernel is the approximation of the Rayleigh-Sommerfeld kernel in the far regions of the near-field zone. In uniform apertures, the three methods can be accelerated by fast Fourier transform (FFT). However, FFT should be replaced by NUFFT for non-uniform sparse apertures. The simulation results reveal that the Rayleigh-Sommerfeld convolution with NUFFT (RS-NUFFT) can be applied to all aperture sizes, distributions and near-field distances. After investigating the error sources in RS-NUFFT, the techniques (padding zeros for apertures, increasing sampling rate for the convolution kernel) are developed for increasing the calculation accuracy of RS-NUFFT.

Numerical far field simulations with the fast Fourier transformation and Fourier space interpolation

As more complicated microscope systems are engineered, the amount of effects taken into account rises steadily. In this context we experienced the need for a simulation approach, that will deliver the intensity distribution in space and time for scanning laser microscopes. To achieve this goal, the frequency space representation of microscope objectives was used and adapted to determine their solution of the electromagnetic wave equation. We describe the steps necessary to efficiently implement an approach to simulate multidimensional solutions of the wave equation. This includes the connection between the back focal plane and the Fourier space representation as well as a proper interpolation method for the latter. The error-potential of our least erroneous interpolation, the power of hann (POH) interpolation, is compared to other common interpolation methods. Finally we demonstrate the current potential of the approach by simulating an "expanding" optical vortex focus.

GPU-accelerated non-uniform fast Fourier transform-based compressive sensing spectral domain optical coherence tomography

We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial) × 1,000(lateral).

Efficient holoscopy image reconstruction

Holoscopy is a tomographic imaging technique that combines digital holography and Fourier-domain optical coherence tomography (OCT) to gain tomograms with diffraction limited resolution and uniform sensitivity over several Rayleigh lengths. The lateral image information is calculated from the spatial interference pattern formed by light scattered from the sample and a reference beam. The depth information is obtained from the spectral dependence of the recorded digital holograms. Numerous digital holograms are acquired at different wavelengths and then reconstructed for a common plane in the sample. Afterwards standard Fourier-domain OCT signal processing achieves depth discrimination. Here we describe and demonstrate an optimized data reconstruction algorithm for holoscopy which is related to the inverse scattering reconstruction of wavelength-scanned full-field optical coherence tomography data. Instead of calculating a regularized pseudoinverse of the forward operator, the recorded optical fields are propagated back into the sample volume. In one processing step the high frequency components of the scattering potential are reconstructed on a non-equidistant grid in three-dimensional spatial frequency space. A Fourier transform yields an OCT equivalent image of the object structure. In contrast to the original holoscopy reconstruction with backpropagation and Fourier transform with respect to the wavenumber, the required processing time does neither depend on the confocal parameter nor on the depth of the volume. For an imaging NA of 0.14, the processing time was decreased by a factor of 15, at higher NA the gain in reconstruction speed may reach two orders of magnitude.