## Construction and demonstration of a multispectral tomographic scanning imager (TOSCA) |

Optics Express, Vol. 21, Issue 4, pp. 4688-4702 (2013)

http://dx.doi.org/10.1364/OE.21.004688

Acrobat PDF (3892 KB)

### Abstract

This work presents the first experimental demonstrator of an imager based on a tomographic scanning (TOSCA) principle. The device described generates a stream of multispectral images of a scene or target using simple conical scan optics and a simple patterned reticle, followed by collecting optics and one or several single pixel detectors. Tomographic processing techniques are then applied to the one-dimensional signals to reproduce two-dimensional images. Various aspects of the design and construction are described, and resulting images and movies are shown.

© 2013 OSA

## 1. Introduction

1. H. Hovland, “Tomographic scanning imager,” Opt. Express **17**(14), 11371–11387 (2009). [CrossRef] [PubMed]

## 2. TOSCA design

### 2.1 Basic principle

1. H. Hovland, “Tomographic scanning imager,” Opt. Express **17**(14), 11371–11387 (2009). [CrossRef] [PubMed]

2. H. Hovland, “Specialized tomographic scanning imaging seeker,” Proc. SPIE **5778**, 725–731 (2005). [CrossRef]

2. H. Hovland, “Specialized tomographic scanning imaging seeker,” Proc. SPIE **5778**, 725–731 (2005). [CrossRef]

### 2.2 Optics, optoelectronics and A/D conversion

- 1. Focusing optics, consisting of a 25.4 mm diameter, 75 mm focal length (FL) lens.
- 2. First rotating periscope, consisting of a 35.4 mm × 25.0 mm elliptical enhanced aluminum coated flat mirror, and a 12.7 mm diameter protected silver flat mirror.
- 3. Circular field stop. This 4.0 mm diameter circular aperture is made out of 0.2 mm thick Nickel/Teflon coated stainless steel.
- 4. The reticle is a metal coated 2.3 mm thick glass substrate (photolithography master mask) with 65 thin line segments each 6.0 mm long and 70 µm in a circular pattern. The distance from the center to each slit center is 43.0 mm. An odd number of slits avoids redundant information from parallel line pairs [1].
**17**(14), 11371–11387 (2009). [CrossRef] [PubMed] - 5. Second periscope, similar to the first, to realign the optical and rotational axis.
- 6. Collimating/collecting optics, consisting of a 30 mm diameter, 80 mm FL lens, and a 25.0 mm diameter, 20 mm FL aspheric lens.
- 7. Detector. The unit chosen was a Hamamatsu C5460-01 Si avalanche photodetector module, with a 3 mm diameter active area, and a 100 kHz detector bandwidth.

3. A. C. Kak and M. Slaney, *Principles of Computerized Tomographic Imaging* (IEEE Press, 1988). http://www.slaney.org/pct/pct-toc.html.

**17**(14), 11371–11387 (2009). [CrossRef] [PubMed]

## 3. Experimental set-up

## 4. Experimental imaging results

### 4.1 Single point reconstruction

^{3}pixels within the FOV. The detector responsivity at 543 nm being 0.2 A/W (without the avalanche gain), each pixel receives 1.34 × 10

^{−13}C, or 2.1 × 10

^{5}photoelectrons per pixel, resulting in 4.6 × 10

^{2}center pixel photon noise. This noise is incoherently added to the 1.2 × 10

^{3}photoelectrons of detector noise calculated in section 5.2, giving a total noise of 1.3 × 10

^{3}photoelectrons. The resulting relative noise level then becomes 6.2 × 10

^{−3}, in good agreement with Fig. 5(d). The theory presented in section 5.2 indicates a 20% reduction in photon noise at the border relative to the center noise. The relative rim noise level would then be 6.0 × 10

^{−3}if the FOV border effect is ignored. This is consistent with the trend of Fig. 5(d), but the results are inconclusive, given the data uncertainty.

### 4.2 Mono- and multispectral TOSCA imaging

5. P. Mouroulis, R. O. Green, and T. G. Chrien, “Design of pushbroom imaging spectrometers for optimum recovery of spectroscopic and spatial information,” Appl. Opt. **39**(13), 2210–2220 (2000). [CrossRef] [PubMed]

## 5. Design considerations

### 5.1 Sources of noise and systematic error

3. A. C. Kak and M. Slaney, *Principles of Computerized Tomographic Imaging* (IEEE Press, 1988). http://www.slaney.org/pct/pct-toc.html.

*k*supported due to angular scan limitations is given by the number of angular scans

_{max}*N*and the aperture diameter

*D*:In the worst-case, the system presented here supports spatial frequencies corresponding to ~20 line pairs across the aperture diameter due to the limited number of angular scans. If the region of interest is a small structure on a homogeneous background, the spatial frequencies supported will be higher, typically limited to the sampling density, and as a bonus, the artefacts are separated from the target.

**17**(14), 11371–11387 (2009). [CrossRef] [PubMed]

**17**(14), 11371–11387 (2009). [CrossRef] [PubMed]

**17**(14), 11371–11387 (2009). [CrossRef] [PubMed]

### 5.2 Photon budget

*M*from published LOWTRAN 7 data [9]. A short scene-camera-distance is assumed, and the resulting atmospheric effects are ignored. Internal optics transmission/reflection losses are accounted for.

_{λ}10. Thorlabs web pages, http://www.thorlabs.com.

11. Hamamatsu web pages, http://www.hamamatsu.com.

_{Px}= 8,7 × 10

^{−7}sr. A Lambertian target filling the pixel illuminates the entrance aperture with spectral intensity:With a 25 Hz frame rate, 65 slits and 119 samples/scan, the sample interval is

*Δt*= 5.1 µs. The number of photoelectrons 〈

*S*〉 generated by light incident on a pixel-size area of the reticle slit is:with the electron charge

_{e,sample}*e*, the detector spectral responsivity

*R*

_{λ}and the optical spectral transmission τ

_{λ}. The total number of photoelectrons per image pixel is the sum from each angular scan:To determine the actual “photon noise” of the photoelectron signal, some assumptions must be made. Only the FOV contributes to the photon noise. The detector sees an entire line within the circular aperture, meaning “hot spots” can give significant noise contributions to low intensity areas. Even homogeneous scenes produce uneven spatial noise distributions: Central pixels get more noise since the average line segment size, defined by the slit and the circular aperture, decreases away from the center (where the line length is the full diameter for all angles). The center noise level is ~1.25 times that at the rim, with an asymptotic value of (π/2)

^{1/2}in the limit of narrow scan lines relative to the FOV diameter. If the reference target fills the FOV, the center pixel photon noise level 〈

*N*〉, given as the square root of the total number of photoelectrons collected in the central pixel, is therefore a conservative estimate:The Hamamatsu C5460-01 noise equivalent power (

_{p,frame}*NEP*) is 2 × 10

^{−14}W/√Hz, at the peak responsivity

*R*= 0.5 A/W. The detector sample noise level

_{Max}*N*in photoelectrons is:The detector noise can be expressed as an equivalent number of frame pixel photoelectrons by incoherent addition of the 65 angular scans:This is about half of the photon noise and leads to a degradation of the signal-to-noise ratio by about 12%, compared to photon noise alone. The chosen example is thus close to the detector noise floor. However, as can be seen in the simulations in section 5.6, spatial averaging makes image features visible at even lower signal levels.

_{d,sample}^{2}. Exploiting the range beyond the Si spectral band using InGaAs detectors do not affect the Si detector performance, but such detectors are typically noisier.

### 5.3 TOSCA simulation tool

- • Scene generation. An arbitrary image is used as input, and photon shot noise is simulated.
- • Circular aperture generation and superposition on the image. Parameters specify the aperture/scene misalignment, inducing a circular aperture movement relative to the scene.
- • Reticle generation. Specifies the physical reticle shape, including overall offset and misalignment, as well as shape, position and orientation errors of each individual slit.
- • Scan movement generation. Includes rotational errors and individual sample errors.
- • Detection process, including detector/electronics noise generation and timing jitter.
- • Reconstruction process using filtered back projection.

**17**(14), 11371–11387 (2009). [CrossRef] [PubMed]

- • Each angular scan is zero-padded and FFT’ed to replace the discrete Fourier transform.
- • The FFT components are multiplied element by element with a modified ramp filter to enhance high frequency components. This filter multiplies the frequency components by a coefficient proportional to the absolute value of the corresponding frequencies, except the DC coefficient value, set to ¼ the value of the lowest non-zero frequency coefficient.
- • The filtered signal is inverse FFT’ed, giving the filtered back projection function.
- • A matrix is filled with interpolated values of the filtered back projection function using the pixel positions orthogonally projected onto the scan line as input.
- • The angular scan matrices are added together to complete the reconstruction

### 5.4 Simulated reconstruction accuracy

3. A. C. Kak and M. Slaney, *Principles of Computerized Tomographic Imaging* (IEEE Press, 1988). http://www.slaney.org/pct/pct-toc.html.

12. W. H. Press, “Discrete Radon transform has an exact, fast inverse and generalizes to operations other than sums along lines,” Proc. Natl. Acad. Sci. U.S.A. **103**(51), 19249–19254 (2006). [CrossRef] [PubMed]

13. E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory **52**(2), 489–509 (2006). [CrossRef]

### 5.5 Geometrical and timing errors

### 5.6 Noise simulations for single- and multi-channel TOSCA configurations

## 6. Discussion

*Principles of Computerized Tomographic Imaging* (IEEE Press, 1988). http://www.slaney.org/pct/pct-toc.html.

12. W. H. Press, “Discrete Radon transform has an exact, fast inverse and generalizes to operations other than sums along lines,” Proc. Natl. Acad. Sci. U.S.A. **103**(51), 19249–19254 (2006). [CrossRef] [PubMed]

## 7. Conclusion

## Acknowledgments

## References and links

1. | H. Hovland, “Tomographic scanning imager,” Opt. Express |

2. | H. Hovland, “Specialized tomographic scanning imaging seeker,” Proc. SPIE |

3. | A. C. Kak and M. Slaney, |

4. | P. C. D. Hobbs, |

5. | P. Mouroulis, R. O. Green, and T. G. Chrien, “Design of pushbroom imaging spectrometers for optimum recovery of spectroscopic and spatial information,” Appl. Opt. |

6. | R. D. Hudson, |

7. | J. Hsieh, |

8. | E. Hecht, |

9. | J. S. Accetta and D. L. Shumaker, |

10. | Thorlabs web pages, http://www.thorlabs.com. |

11. | Hamamatsu web pages, http://www.hamamatsu.com. |

12. | W. H. Press, “Discrete Radon transform has an exact, fast inverse and generalizes to operations other than sums along lines,” Proc. Natl. Acad. Sci. U.S.A. |

13. | E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory |

**OCIS Codes**

(070.6020) Fourier optics and signal processing : Continuous optical signal processing

(100.6950) Image processing : Tomographic image processing

(110.0110) Imaging systems : Imaging systems

(110.6960) Imaging systems : Tomography

(110.4234) Imaging systems : Multispectral and hyperspectral imaging

(110.3010) Imaging systems : Image reconstruction techniques

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: November 8, 2012

Revised Manuscript: December 28, 2012

Manuscript Accepted: January 8, 2013

Published: February 19, 2013

**Virtual Issues**

Vol. 8, Iss. 3 *Virtual Journal for Biomedical Optics*

**Citation**

Harald Hovland, "Construction and demonstration of a multispectral tomographic scanning imager (TOSCA)," Opt. Express **21**, 4688-4702 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4688

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### References

- H. Hovland, “Tomographic scanning imager,” Opt. Express17(14), 11371–11387 (2009). [CrossRef] [PubMed]
- H. Hovland, “Specialized tomographic scanning imaging seeker,” Proc. SPIE5778, 725–731 (2005). [CrossRef]
- A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988). http://www.slaney.org/pct/pct-toc.html .
- P. C. D. Hobbs, Building Electro-Optical Systems (John Wiley & Sons, 2000).
- P. Mouroulis, R. O. Green, and T. G. Chrien, “Design of pushbroom imaging spectrometers for optimum recovery of spectroscopic and spatial information,” Appl. Opt.39(13), 2210–2220 (2000). [CrossRef] [PubMed]
- R. D. Hudson, Infrared System Engineering (John Wiley & Sons, 2006).
- J. Hsieh, Computed Tomography Principles, Design, Artefacts, and Recent Advances (SPIE Optical Engineering Press, 2003).
- E. Hecht, Optics (Addison-Wesley, 2001).
- J. S. Accetta and D. L. Shumaker, The Infrared and Electro-optical Systems Handbook, Vol. 1 (Infrared Information Analysis Centre, 1993).
- Thorlabs web pages, http://www.thorlabs.com .
- Hamamatsu web pages, http://www.hamamatsu.com .
- W. H. Press, “Discrete Radon transform has an exact, fast inverse and generalizes to operations other than sums along lines,” Proc. Natl. Acad. Sci. U.S.A.103(51), 19249–19254 (2006). [CrossRef] [PubMed]
- E. J. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory52(2), 489–509 (2006). [CrossRef]

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