# Compressed channeled spectropolarimetry

## Abstract

Channeled spectropolarimetry measures the spectrally resolved Stokes parameters. A key aspect of this technique is to accurately reconstruct the Stokes parameters from a modulated measurement of the channeled spectropolarimeter. The state-of-the-art reconstruction algorithm uses the Fourier transform to extract the Stokes parameters from channels in the Fourier domain. While this approach is straightforward, it can be sensitive to noise and channel cross-talk, and it imposes bandwidth limitations that cut off high frequency details. To overcome these drawbacks, we present a reconstruction method called *compressed channeled spectropolarimetry*. In our proposed framework, reconstruction in channeled spectropolarimetry is an underdetermined problem, where we take N measurements and solve for 3N unknown Stokes parameters. We formulate an optimization problem by creating a mathematical model of the channeled spectropolarimeter with inspiration from compressed sensing. We show that our approach offers greater noise robustness and reconstruction accuracy compared with the Fourier transform technique in simulations and experimental measurements. By demonstrating more accurate reconstructions, we push performance to the native resolution of the sensor, allowing more information to be recovered from a single measurement of a channeled spectropolarimeter.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1412005

- Alternate Identifier(s):
- OSTI ID: 1478380

- Report Number(s):
- SAND-2017-7987J

Journal ID: ISSN 1094-4087; OPEXFF

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Published Article

- Journal Name:
- Optics Express

- Additional Journal Information:
- Journal Name: Optics Express Journal Volume: 25 Journal Issue: 25; Journal ID: ISSN 1094-4087

- Publisher:
- Optical Society of America

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 47 OTHER INSTRUMENTATION

### Citation Formats

```
Lee, Dennis J., LaCasse, Charles F., and Craven, Julia M. Compressed channeled spectropolarimetry. United States: N. p., 2017.
Web. doi:10.1364/OE.25.032041.
```

```
Lee, Dennis J., LaCasse, Charles F., & Craven, Julia M. Compressed channeled spectropolarimetry. United States. doi:10.1364/OE.25.032041.
```

```
Lee, Dennis J., LaCasse, Charles F., and Craven, Julia M. Fri .
"Compressed channeled spectropolarimetry". United States. doi:10.1364/OE.25.032041.
```

```
@article{osti_1412005,
```

title = {Compressed channeled spectropolarimetry},

author = {Lee, Dennis J. and LaCasse, Charles F. and Craven, Julia M.},

abstractNote = {Channeled spectropolarimetry measures the spectrally resolved Stokes parameters. A key aspect of this technique is to accurately reconstruct the Stokes parameters from a modulated measurement of the channeled spectropolarimeter. The state-of-the-art reconstruction algorithm uses the Fourier transform to extract the Stokes parameters from channels in the Fourier domain. While this approach is straightforward, it can be sensitive to noise and channel cross-talk, and it imposes bandwidth limitations that cut off high frequency details. To overcome these drawbacks, we present a reconstruction method called compressed channeled spectropolarimetry. In our proposed framework, reconstruction in channeled spectropolarimetry is an underdetermined problem, where we take N measurements and solve for 3N unknown Stokes parameters. We formulate an optimization problem by creating a mathematical model of the channeled spectropolarimeter with inspiration from compressed sensing. We show that our approach offers greater noise robustness and reconstruction accuracy compared with the Fourier transform technique in simulations and experimental measurements. By demonstrating more accurate reconstructions, we push performance to the native resolution of the sensor, allowing more information to be recovered from a single measurement of a channeled spectropolarimeter.},

doi = {10.1364/OE.25.032041},

journal = {Optics Express},

number = 25,

volume = 25,

place = {United States},

year = {2017},

month = {12}

}

DOI: 10.1364/OE.25.032041

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