2D-FFT implementation on FPGA for wavefront phase recovery from the CAFADIS camera

An FPGA Architecture for Extracting Real-Time Zernike Coefficients from Measured Phase Gradients

“…Resource utilisation in the proposed method compares favourably with that in [12]. The resources consumed by each 2D-FFT block in [12] are shown in Tables 6 and 7, both taken directly from [12].…”

“…To generate a complete set of Fourier coefficients, two such blocks must be used, doubling the resources reported. In each case the resource utilisation is less in the proposed method, except in the DSP usage for the 8 × 8 and 16 × 16 grid sizes, where the proposed method uses 28 DSP48s and [12] uses 12 DSP (8-bit) or 20 DSP (16-bit).…”

“…The resources consumed by each 2D-FFT block in [12] are shown in Tables 6 and 7, both taken directly from [12]. Table 6 shows utilisation for 8-bit inputs while Table 7 is for 16-bit inputs.…”

“…Rodríguez-Ramos, et. al, utilized a forward and inverse 2D-FFT method for grid sizes from 8 × 8 to 128 × 128 [12], though in this case performing a full phase recovery. In order to make a fair comparison only the time taken to calculate the Fourier coefficients from the forward 2D-FFT portion of the recoverer is considered, which is approximately 1.67µs compared to the proposed method's 0.57µs (both running with a system clock = 100 MHz).…”

An Efficient Pipeline Wavefront Phase Recovery for the CAFADIS Camera for Extremely Large Telescopes

“…The phase gradients at pupil plane are calculated from this plenoptic frame using the partial derivates of the wavefront aberration estimated in [5] and implemented in FPGA in [6]. From these gradient estimation, the wavefront phase ϕ ( u , v ) can be recovered using an expansion over complex exponential polynomials, allowing application of 2D-FFT: $\varphi (u,v)=\sum _{p,q=0}^{N-1}{a}_{\mathit{pq}} Z_{\mathit{pq}} false(u,vfalse)=\sum _{p,q=0}^{N-1}{a}_{\mathit{pq}}\frac{1}{N}{e}^{\frac{2\pi i}{N}(\mathit{pu}+\mathit{qv})}=\mathit{IFFT}(a_{\mathrm{italicpq}})$…”