Correction: Dielectric metalens for miniaturized imaging systems: progress and challenges

Correction to: Light: Science & Applications

https://doi.org/10.1038/s41377-022-00885-7 published online 28 June 2022

After the publication of this article¹, it is brought to our attention that some mathematical expressions contained errors. Details are listed below.

• 1. In the paragraph below Eq. (1) on p.3, the expression of the root mean square of WAF contains a typo, which should be: ${{{\mathrm{WAF}}}}_{{{{\mathrm{rms}}}}} = \sqrt{\langle{{{{\mathrm{WAF}}}}\rangle^2 - \langle{{{\mathrm{WAF}}^{{2}}}}\rangle}}$.

• 2. In the paragraph at the end of p.12, the expression illustrating the relation between time delay and group delay needs to be changed as: ${{\Delta }}T\left( r \right) = GD\left( r \right) - GD(R)$.

• 3. The correct expression related to the Bode–Fano limit (at the end of p.13) should be: $\Delta \omega _{{{{\mathrm{max}}}}} = - 2\pi c{{{\mathrm{/}}}}[ {{{{\mathrm{log}}}}\left| \Gamma \right|H( {n_{eff}^2 - n_b^2} )}]$.

• 4. We are correcting Eq. (5) on p. 8, Eq. (7) on p. 12, and Eq. (9) on p. 13, where the refractive index of background (n_b) was missing. According to Eq. (1) in the article¹, the correct form of these equations should be:

$$\varphi \left( {r,\lambda ,\theta _i} \right) = - \frac{{2\pi n_b}}{\lambda }\left( {r\,\sin \theta _i + \sqrt {\left( {r - f\tan \theta _i} \right)^2 + f^2} - \frac{f}{{\cos \theta _i}}} \right)$$

(5)

$$GD\left( r \right) = \frac{{\partial {\upvarphi}\left( {r,\omega } \right)}}{{\partial \omega }} = \frac{{n_b}}{c}\left( {f - \sqrt {r^2 + f^2} } \right)$$

(7)

$$\Delta \omega \le \Delta \omega _{{{{\mathrm{max}}}}} = \frac{{\kappa c}}{{n_b\left( {\sqrt {f^2 + R^2} - f} \right)}} = \frac{{\kappa c\sqrt {1 - \left( {NA{{{\mathrm{/}}}}n_b} \right)^2} }}{{n_bf\left[ {1 - \sqrt {1 - \left( {NA{{{\mathrm{/}}}}n_b} \right)^2} } \right]}}$$

(9)

We would like to apologize for any inconvenience these errors may have caused.

The original article has been updated.