After publication we became aware of a few typographical errors in the manuscript [1].

In the second paragraph of page 3, the binary phase plate conversion loss is stated as 1.3 ± 0.1 dB, it should read 1.7 ± 0.1 dB. The value appears correctly in the abstract of the document, and in Fig. 7 (page 12).

In the third paragraph of page 11, the loss at the “qualitatively Gaussian point” for axicon reconversion is stated as “0.85 ± 0.1 dB (74% transmission).” The loss in decibels is correct, but there is an error in the quoted percentage value, which should read 82% transmission. The loss appears correctly in the rest of the document.

In the second paragraph of page 15, binary phase plate conversion loss is stated as 1.75 ± 0.1 dB, it should read 1.7 ± 0.1 dB. The number is stated correctly in the abstract as well as in Fig. 7.