# Power spectral density specifications for high-power laser systems

## Abstract

This paper describes the use of Fourier techniques to characterize the transmitted and reflected wavefront of optical components. Specifically, a power spectral density, (PSD), approach is used. High power solid-state lasers exhibit non-linear amplification of specific spatial frequencies. Thus, specifications that limit the amplitude of these spatial frequencies are necessary in the design of these systems. Further, NIF optical components have square, rectangular or irregularly shaped apertures with major dimensions up-to 800 mm. Components with non-circular apertures can not be analyzed correctly with Zernicke polynomials since these functions are an orthogonal set for circular apertures only. 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 shape of a resultant wavefront or the focal spot of a complex multicomponent laser system can be calculated and optimized using PSDs of the individual optical components which comprise the system. Surface roughness can be calculated over a range of spatial scale-lengths by integrating the PSD. Finally, since the optical transfer function (OTF) of the instruments used to measure the wavefront degrades at high spatial frequencies, themore »

- Authors:

- Publication Date:

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

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

- OSTI Identifier:
- 243472

- Report Number(s):
- UCRL-JC-123105; CONF-9605182-1

ON: DE96010402; TRN: 96:003513

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

- Resource Type:
- Conference

- Resource Relation:
- Conference: International symposium on optical systems design and production II, Glasgow (United Kingdom), 12-16 May 1996; Other Information: PBD: 22 Apr 1996

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION; PLASMA DIAGNOSTICS; OPTICAL SYSTEMS; INERTIAL CONFINEMENT; SOLID STATE LASERS; SPECTRAL DENSITY; FOURIER ANALYSIS; TRANSFER FUNCTIONS

### Citation Formats

```
Lawson, J K, Aikens, D A, English, Jr, R E, and Wolfe, C R.
```*Power spectral density specifications for high-power laser systems*. United States: N. p., 1996.
Web.

```
Lawson, J K, Aikens, D A, English, Jr, R E, & Wolfe, C R.
```*Power spectral density specifications for high-power laser systems*. United States.

```
Lawson, J K, Aikens, D A, English, Jr, R E, and Wolfe, C R. Mon .
"Power spectral density specifications for high-power laser systems". United States. https://www.osti.gov/servlets/purl/243472.
```

```
@article{osti_243472,
```

title = {Power spectral density specifications for high-power laser systems},

author = {Lawson, J K and Aikens, D A and English, Jr, R E and Wolfe, C R},

abstractNote = {This paper describes the use of Fourier techniques to characterize the transmitted and reflected wavefront of optical components. Specifically, a power spectral density, (PSD), approach is used. High power solid-state lasers exhibit non-linear amplification of specific spatial frequencies. Thus, specifications that limit the amplitude of these spatial frequencies are necessary in the design of these systems. Further, NIF optical components have square, rectangular or irregularly shaped apertures with major dimensions up-to 800 mm. Components with non-circular apertures can not be analyzed correctly with Zernicke polynomials since these functions are an orthogonal set for circular apertures only. 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 shape of a resultant wavefront or the focal spot of a complex multicomponent laser system can be calculated and optimized using PSDs of the individual optical components which comprise the system. Surface roughness can be calculated over a range of spatial scale-lengths by integrating the PSD. Finally, since the optical transfer function (OTF) of the instruments used to measure the wavefront degrades at high spatial frequencies, the PSD of an optical component is underestimated. We can correct for this error by modifying the PSD function to restore high spatial frequency information. The strengths of PSD analysis are leading us to develop optical specifications incorporating this function for the planned National Ignition Facility (NIF).},

doi = {},

url = {https://www.osti.gov/biblio/243472},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1996},

month = {4}

}