Table 1 Summary of the approximations required to derive the UFT expression.
From: A metalens-based analog computing system for ultrasonic Fourier transform calculations
No | Approximation | Validity |
|---|---|---|
1 | \(\left|{\varvec{r}}-{{\varvec{r}}}_{0}\right|\approx f\left[1+\frac{1}{2}{\left(\frac{x-\xi }{f}\right)}^{2}+\frac{1}{2}{\left(\frac{y-\eta }{f}\right)}^{2}\right]\) | Fresnel |
2 | \(\left|{\varvec{r}}-{{\varvec{r}}}_{0}\right|\approx f\) | Paraxial |
3 | \(\mathrm{cos}\left({\varvec{n}},{\varvec{r}}-{{\varvec{r}}}_{0}\right)\approx 1\) | Paraxial |
4 | \(\frac{1}{\left|{\varvec{r}}-{{\varvec{r}}}_{0}\right|}+jk\approx jk\) | Distances much larger than \(\lambda\) |
