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.

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References

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  1. H. Hovland, “Tomographic scanning imager,” Opt. Express17(14), 11371–11387 (2009).
    [CrossRef] [PubMed]
  2. H. Hovland, “Specialized tomographic scanning imaging seeker,” Proc. SPIE5778, 725–731 (2005).
    [CrossRef]
  3. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, 1988). http://www.slaney.org/pct/pct-toc.html .
  4. P. C. D. Hobbs, Building Electro-Optical Systems (John Wiley & Sons, 2000).
  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]
  6. R. D. Hudson, Infrared System Engineering (John Wiley & Sons, 2006).
  7. J. Hsieh, Computed Tomography Principles, Design, Artefacts, and Recent Advances (SPIE Optical Engineering Press, 2003).
  8. E. Hecht, Optics (Addison-Wesley, 2001).
  9. J. S. Accetta and D. L. Shumaker, The Infrared and Electro-optical Systems Handbook, Vol. 1 (Infrared Information Analysis Centre, 1993).
  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.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. Theory52(2), 489–509 (2006).
    [CrossRef]

2009 (1)

2006 (2)

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]

2005 (1)

H. Hovland, “Specialized tomographic scanning imaging seeker,” Proc. SPIE5778, 725–731 (2005).
[CrossRef]

2000 (1)

Candès, E. J.

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]

Chrien, T. G.

Green, R. O.

Hovland, H.

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]

Mouroulis, P.

Press, W. H.

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]

Romberg, J.

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]

Tao, T.

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]

Appl. Opt. (1)

IEEE Trans. Inf. Theory (1)

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]

Opt. Express (1)

Proc. Natl. Acad. Sci. U.S.A. (1)

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]

Proc. SPIE (1)

H. Hovland, “Specialized tomographic scanning imaging seeker,” Proc. SPIE5778, 725–731 (2005).
[CrossRef]

Other (8)

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).

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 .

Supplementary Material (1)

» Media 1: MOV (1124 KB)     

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Figures (13)

Fig. 1
Fig. 1

(a) Schematic image of a line scan: A thin line detector (yellow line) scans across the image of the scene. (b) Realization chosen in this work. The mirrors (green) and the moving circular aperture (red) rotate together as a unit around the optical axis of the incoming light. The use of a mirror pair to decenter the image on the reticle keeps the image orientation fixed relative to the reticle, making the thin slits scan the image at regular angular intervals. (c) Reticle pattern and moving aperture layout. The interior of the aperture (in red) defines the field of view, moving in a circular pattern indicated by the dashed circle. The use of an aperture enables the use of a single detector element to make all the angular scans.

Fig. 2
Fig. 2

(a) Semi-transparent view of the rotating optics, reticle and detector unit. (b) Experimental TOSCA setup. The motor (top) drives the scan unit (centre) using a belt drive. The lens/ detector/amplifier assembly (left) is mounted on a post holder. The scan head and detector was enclosed to avoid stray light. (c) Laser based tachometer. A laser (top left, connected by red/ blue leads) was pointed at a mirror, mounted on top of the rotating unit. At each turn, the reflected light hit a photodiode, creating a sharp flank pulse used as an absolute angular reference.

Fig. 3
Fig. 3

(a) Signal recorded from the Hamamatsu detector module (inverted). Minimum signal occurs when reticle slit and aperture do not overlap. (b) Rotation frequency components, measured by intervals between detector signal minima. The 25 Hz peak is the optics spin frequency.

Fig. 4
Fig. 4

(a) Laser spot (green) and background illumination (red) contributions in a measured scan signal. The ratio of these areas is 0.009, close to the predicted 1%. Reconstruction of (b) centered and (c) de-centered laser spot reflected off a homogeneous background.

Fig. 5
Fig. 5

Temporal statistics of 101 subsequent reconstructed frames: (a) Mean value. (b) Temporal standard deviation. (c) Histogram. Only pixels within a 50 pixel radius are accounted for to minimize the effect of the field stop. (d) Relative noise level (red curve) as a function of distance to the reconstructed image center, in reconstruction pixel units.

Fig. 6
Fig. 6

(a) Frame from the first single channel TOSCA movie (Media 1) recorded using the experimental system. (b) Multispectral TOSCA setup. A spectral interference filter splits the beam in two. Each beam is detected with a lens/detector pair. (b)-(d) Author image with green/white, green/ black and white/black checkerboard patterns in (b) ’non-green’ channel, (c) ’green’ channel and (d) a color-coded combined image. The white/black checkerboard pattern transition color purity is due to perfect alignment between channels, inherent in the TOSCA system.

Fig. 7
Fig. 7

(a) Spectral radiant exitance from a 25% diffusely reflecting, horizontal test target in the 1976 U.S. standard atmosphere [9] with an air mass index ma = 1.0, the sun being in zenith. (b) Optics transmission for light passing through the reticle slit in the proposed system. (c) Spectral responsivity of the Hamamatsu C5460-01 detector, not including the avalanche gain.

Fig. 8
Fig. 8

(a) Filtered back projection function and (b) reconstruction of a 512 × 512 image with a single centred unit pixel. (c) Reconstruction of a 512 × 512 image with a de-centred unit pixel.

Fig. 9
Fig. 9

(a) Original 512 × 512 pixels high resolution ‘Lena’ image. Reconstruction using a 65 slit reticle, with 119 samples/scan, onto a 118 × 118 (b) and 512 × 512 (c) pixel grid.

Fig. 10
Fig. 10

Aperture misalignment: (a) Misaligned (red) aperture is displaced from its ideal location (green). A red vector indicates eccentricity relative to the direction towards the rotat-ional axis (yellow). The misalignment rotates (dashed red circle), the aperture hiding different scene parts during the scan. (b-d): Reconstructions with aperture misalignments corresponding to 10% of the aperture diameter, with the phase angle being 0° (b), 45° (c), and 90° (d).

Fig. 11
Fig. 11

Line shift errors: Effect of a constant difference between assumed and real scan line location. (a) The footprint of scan lines at the time where the reconstruction assumes them to pass through the center. This causes point spread function to essentially become a circle-like structure. This error can be due to a fixed timing error or an angularly misaligned (rotated) reticle. Reconstruction similar to that in Fig. 9(b), but with time shift errors, corresponding to (b) 1 sample, (c) 5 samples and (d) 40 samples, respectively.

Fig. 12
Fig. 12

(a) Rotational speeds variations with once (red curve) and twice (green) the rotational cycle frequency, and a general variation (blue). (b) Reconstruction with sinusoidal scan speed variations with a frequency corresponding to one spin cycle, creating a difference between nominal and actual sampling location varying between ± 5 samples. (c) Same as in (b), but with twice the scan speed variation frequency. (d) Reconstruction similar to that in Fig. 9(b), but with a horizontal reticle offset corresponding to 10% of the aperture diameter.

Fig. 13
Fig. 13

Reconstruction with detector + photon noise in (a) bright, (b) medium, and (c) low light conditions, where the brightest pixel is scaled to have (a) the same spectral radiant exitance as the reference target in Fig. 7(a) (Mλ,max = 350 Wm−2µm−1), (b) 10−2 and (c) 10−4 of the value in (a). (d)-(f): As in (a)-(c), but with the energy spread to 3 spectral channels.

Equations (7)

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k max >N/ ( πD )
P Px,λ = M λ A Ap Ω Px /π
S e,sample = e 1 Δt P Px,λ R λ τ λ dλ = ( πe ) 1 Δt A Ap Ω Px M λ R λ τ λ dλ =9.4× 10 4 ,
S e,frame =N S e,sample =6.2× 10 6
N p,frame = S e,frame =2.5× 10 3
N d,sample = R Max NEP Δt e =1.4× 10 2
N d,frame = N N d,sample =1.2× 10 3

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