# Rapid calculation of paraxial wave propagation for cylindrically symmetric optics

## Abstract

When calculating the focusing properties of cylindrically symmetric focusing optics, numerical wave propagation calculations can be carried out using the quasi-discrete Hankel transform (QDHT). We describe here an implementation of the QDHT where a partial transform matrix can be stored to speed up repeated wave propagations over specified distances, with reduced computational memory requirements. The accuracy of the approach is then verified by comparison with analytical results, over propagation distances with both small and large Fresnel numbers. We then demonstrate the utility of this approach for calculating the focusing properties of Fresnel zone plate optics that are commonly used for x-ray imaging applications and point to future applications of this approach.

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1392918

- DOE Contract Number:
- AC02-06CH11357

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of the Optical Society of America. A, Optics, Image Science, and Vision; Journal Volume: 32; Journal Issue: 11

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Paraxial wave optics; Propagation methods; Wave propagation; X-ray optics

### Citation Formats

```
Li, Kenan, and Jacobsen, Chris.
```*Rapid calculation of paraxial wave propagation for cylindrically symmetric optics*. United States: N. p., 2015.
Web. doi:10.1364/JOSAA.32.002074.

```
Li, Kenan, & Jacobsen, Chris.
```*Rapid calculation of paraxial wave propagation for cylindrically symmetric optics*. United States. doi:10.1364/JOSAA.32.002074.

```
Li, Kenan, and Jacobsen, Chris. Thu .
"Rapid calculation of paraxial wave propagation for cylindrically symmetric optics". United States.
doi:10.1364/JOSAA.32.002074.
```

```
@article{osti_1392918,
```

title = {Rapid calculation of paraxial wave propagation for cylindrically symmetric optics},

author = {Li, Kenan and Jacobsen, Chris},

abstractNote = {When calculating the focusing properties of cylindrically symmetric focusing optics, numerical wave propagation calculations can be carried out using the quasi-discrete Hankel transform (QDHT). We describe here an implementation of the QDHT where a partial transform matrix can be stored to speed up repeated wave propagations over specified distances, with reduced computational memory requirements. The accuracy of the approach is then verified by comparison with analytical results, over propagation distances with both small and large Fresnel numbers. We then demonstrate the utility of this approach for calculating the focusing properties of Fresnel zone plate optics that are commonly used for x-ray imaging applications and point to future applications of this approach.},

doi = {10.1364/JOSAA.32.002074},

journal = {Journal of the Optical Society of America. A, Optics, Image Science, and Vision},

number = 11,

volume = 32,

place = {United States},

year = {Thu Jan 01 00:00:00 EST 2015},

month = {Thu Jan 01 00:00:00 EST 2015}

}