# Specification of optical components using the power spectral density function

## Abstract

This paper describes the use of Fourier techniques to characterize the wavefront of optical components, specifically, the use of the power spectral density, (PSD), function. The PSDs of several precision optical components will be shown. Many of the optical components of interest to us have square, rectangular or irregularly shaped apertures with major dimensions up-to 800 mm. The wavefronts of components with non-circular apertures cannot be analyzed with Zernicke polynomials since these functions are an orthogonal set for circular apertures only. Furthermore, Zernicke analysis is limited to treating low frequency wavefront aberrations; mid-spatial scale and high frequency error are expressed only as ``residuals.`` A more complete and powerful representation of the optical wavefront can be obtained by Fourier analysis in 1 or 2 dimensions. The PSD is obtained from the amplitude of frequency components present in the Fourier spectrum. The PSD corresponds to the scattered intensity as a function of scattering angle in the wavefront and can be used to describe the intensity distribution at focus. The shape of a resultant wavefront or the focal spot of a complex multi-component laser system can be calculated and optimized using the PSDs of individual optical components which comprise it.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab., CA (United States)

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 109530

- Report Number(s):
- UCRL-JC-120920; CONF-950793-42

ON: DE96000260

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Conference

- Resource Relation:
- Conference: 40. annual meeting of the Society of Photo-Optical Instrumentation Engineers, San Diego, CA (United States), 9-14 Jul 1995; Other Information: PBD: 20 Jun 1995

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; 70 PLASMA PHYSICS AND FUSION; SOLID STATE LASERS; SPECTRAL DENSITY; BEAM PROFILES; WAVE PROPAGATION; INERTIAL CONFINEMENT; LASER FUSION REACTORS; OPTICAL SYSTEMS; INTERFEROMETRY; FOURIER ANALYSIS

### Citation Formats

```
Lawson, J K, Wolfe, C R, Manes, K R, Trenholme, J B, Aikens, D M, and English, Jr, R E.
```*Specification of optical components using the power spectral density function*. United States: N. p., 1995.
Web.

```
Lawson, J K, Wolfe, C R, Manes, K R, Trenholme, J B, Aikens, D M, & English, Jr, R E.
```*Specification of optical components using the power spectral density function*. United States.

```
Lawson, J K, Wolfe, C R, Manes, K R, Trenholme, J B, Aikens, D M, and English, Jr, R E. Tue .
"Specification of optical components using the power spectral density function". United States. https://www.osti.gov/servlets/purl/109530.
```

```
@article{osti_109530,
```

title = {Specification of optical components using the power spectral density function},

author = {Lawson, J K and Wolfe, C R and Manes, K R and Trenholme, J B and Aikens, D M and English, Jr, R E},

abstractNote = {This paper describes the use of Fourier techniques to characterize the wavefront of optical components, specifically, the use of the power spectral density, (PSD), function. The PSDs of several precision optical components will be shown. Many of the optical components of interest to us have square, rectangular or irregularly shaped apertures with major dimensions up-to 800 mm. The wavefronts of components with non-circular apertures cannot be analyzed with Zernicke polynomials since these functions are an orthogonal set for circular apertures only. Furthermore, Zernicke analysis is limited to treating low frequency wavefront aberrations; mid-spatial scale and high frequency error are expressed only as ``residuals.`` A more complete and powerful representation of the optical wavefront can be obtained by Fourier analysis in 1 or 2 dimensions. The PSD is obtained from the amplitude of frequency components present in the Fourier spectrum. The PSD corresponds to the scattered intensity as a function of scattering angle in the wavefront and can be used to describe the intensity distribution at focus. The shape of a resultant wavefront or the focal spot of a complex multi-component laser system can be calculated and optimized using the PSDs of individual optical components which comprise it.},

doi = {},

url = {https://www.osti.gov/biblio/109530},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1995},

month = {6}

}