Abstract

The edge method is a widely used way to assess the on-orbit Modulation Transfer Function (MTF). Since good quality is required for the edge, the higher the spatial resolution, the better the results are. In this case, an artificial target can be built and used to ensure a good edge quality. For moderate spatial resolutions, only natural targets are available. Hence the edge quality is unknown and generally rather poor. Improvements of the method have been researched in order to compensate for the poor quality of natural edges. This has been done through the use of symmetry and/or a transfer function model, which enables the elimination of noise. This has also been used for artificial target. In this case, the use of the model overcomes the incomplete sampling when the target is too small or gives the opportunity to assess the defocus of the sensor. This paper begins with a recall of the method followed by a presentation of the changes relying on transfer function parametric model. The transfer function model and the process corresponding to the changes are described. Applications of these changes for several satellites of the French spatial agency are presented: for SPOT 1, it enables to assess XS MTF with natural edges, for SPOT 5, it enables to use the Salon-de-Provence artificial target for MTF assessment in the HM mode, and for the foreseen Pleiades, it enables to estimate the defocus.

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References

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  1. M. R. B. Forshaw, A. Haskell, P. F. Miller, D. J. Stanley, and J. R. G. Townshend, “Spatial resolution of remotely sensed imagery - A review paper,” Int. J. Remote Sens. 4(3), 497–520 (1983).
    [CrossRef]
  2. W. H. Carnahan and G. Zhou, “Fourier Transform techniques for the evaluation of the Thematic Mapper Line Spread Function,” Photogramm. Eng. Remote Sensing 52, 639–648 (1986).
  3. K. Maeda, M. Kojima, and Y. Azuma, “Geometric and radiometric performance evaluation methods for marine observation satellite-1 (MOS-1) verification program (MVP),” Acta Astronaut. 15(6-7), 297–304 (1987).
    [CrossRef]
  4. T. Choi, “IKONOS satellite in orbit, modulation transfer function measurement using edge and pulse methods”, MSc Thesis, South Dakota State University (2002).
  5. H. J. Fang Lei, “Tiziani, “A comparison of methods to measure the modulation transfer function of aerial survey lens systems from image structures,” Photogramm. Eng. Remote Sensing 54, 41–46 (1988).
  6. H. Hwang, Y.-W. Choi, S. Kwak, M. Kim, and W. Park, “MTF assessment of high resolution satellite images using ISO 12233 slanted-edge method”, Proc. SPIE 7109, 710905–1-710905–9 (2008).
  7. C. L. Norton, G. C. Brooks, and R. Welch, “Optical and Modulation Transfer Function,” Photogramm. Eng. Remote Sensing 43, 613–636 (1977).
  8. P. Kubik, E. Breton, A. Meygret, B. Cabrières, P. Hazane, and D. Léger, “SPOT4 HRVIR first in-flight image quality results,” Proc. SPIE 3498, 376–389 (1998).
    [CrossRef]
  9. D. Léger, F. Viallefont, P. Déliot, and C. Valorge, “On-orbit MTF assessment of satellite cameras”, in Post-launch calibration of satellite sensors, Morain and Budge, ed. (Taylor and Francis group, London, 2004).
  10. W. H. Steel, “The defocused image of sinusoidal gratings,” Opt. Acta (Lond.) 3, 65–74 (1956).
  11. A. Meygret, C. Fratter, E. Breton, F. Cabot, M. C. Laubiès, and J. N. Hourcastagnou, “In-flight assessment of SPOT 5 image quality,” Proc. SPIE 4881, 179–188 (2003).
    [CrossRef]
  12. A. Rosak, C. Latry, V. Pascal, and D. Laubier, “From SPOT5 to Pleiades-HR: evolutions of the instrumental specifications”, in Proceedings of the 5th international conference on Space Optics, B. Warmbein, ed. (ESA SP-554, Noordwijk, Netherlands, 2004), 141–148.

2003

A. Meygret, C. Fratter, E. Breton, F. Cabot, M. C. Laubiès, and J. N. Hourcastagnou, “In-flight assessment of SPOT 5 image quality,” Proc. SPIE 4881, 179–188 (2003).
[CrossRef]

1998

P. Kubik, E. Breton, A. Meygret, B. Cabrières, P. Hazane, and D. Léger, “SPOT4 HRVIR first in-flight image quality results,” Proc. SPIE 3498, 376–389 (1998).
[CrossRef]

1988

H. J. Fang Lei, “Tiziani, “A comparison of methods to measure the modulation transfer function of aerial survey lens systems from image structures,” Photogramm. Eng. Remote Sensing 54, 41–46 (1988).

1987

K. Maeda, M. Kojima, and Y. Azuma, “Geometric and radiometric performance evaluation methods for marine observation satellite-1 (MOS-1) verification program (MVP),” Acta Astronaut. 15(6-7), 297–304 (1987).
[CrossRef]

1986

W. H. Carnahan and G. Zhou, “Fourier Transform techniques for the evaluation of the Thematic Mapper Line Spread Function,” Photogramm. Eng. Remote Sensing 52, 639–648 (1986).

1983

M. R. B. Forshaw, A. Haskell, P. F. Miller, D. J. Stanley, and J. R. G. Townshend, “Spatial resolution of remotely sensed imagery - A review paper,” Int. J. Remote Sens. 4(3), 497–520 (1983).
[CrossRef]

1977

C. L. Norton, G. C. Brooks, and R. Welch, “Optical and Modulation Transfer Function,” Photogramm. Eng. Remote Sensing 43, 613–636 (1977).

1956

W. H. Steel, “The defocused image of sinusoidal gratings,” Opt. Acta (Lond.) 3, 65–74 (1956).

Azuma, Y.

K. Maeda, M. Kojima, and Y. Azuma, “Geometric and radiometric performance evaluation methods for marine observation satellite-1 (MOS-1) verification program (MVP),” Acta Astronaut. 15(6-7), 297–304 (1987).
[CrossRef]

Breton, E.

A. Meygret, C. Fratter, E. Breton, F. Cabot, M. C. Laubiès, and J. N. Hourcastagnou, “In-flight assessment of SPOT 5 image quality,” Proc. SPIE 4881, 179–188 (2003).
[CrossRef]

P. Kubik, E. Breton, A. Meygret, B. Cabrières, P. Hazane, and D. Léger, “SPOT4 HRVIR first in-flight image quality results,” Proc. SPIE 3498, 376–389 (1998).
[CrossRef]

Brooks, G. C.

C. L. Norton, G. C. Brooks, and R. Welch, “Optical and Modulation Transfer Function,” Photogramm. Eng. Remote Sensing 43, 613–636 (1977).

Cabot, F.

A. Meygret, C. Fratter, E. Breton, F. Cabot, M. C. Laubiès, and J. N. Hourcastagnou, “In-flight assessment of SPOT 5 image quality,” Proc. SPIE 4881, 179–188 (2003).
[CrossRef]

Cabrières, B.

P. Kubik, E. Breton, A. Meygret, B. Cabrières, P. Hazane, and D. Léger, “SPOT4 HRVIR first in-flight image quality results,” Proc. SPIE 3498, 376–389 (1998).
[CrossRef]

Carnahan, W. H.

W. H. Carnahan and G. Zhou, “Fourier Transform techniques for the evaluation of the Thematic Mapper Line Spread Function,” Photogramm. Eng. Remote Sensing 52, 639–648 (1986).

Fang Lei, H. J.

H. J. Fang Lei, “Tiziani, “A comparison of methods to measure the modulation transfer function of aerial survey lens systems from image structures,” Photogramm. Eng. Remote Sensing 54, 41–46 (1988).

Forshaw, M. R. B.

M. R. B. Forshaw, A. Haskell, P. F. Miller, D. J. Stanley, and J. R. G. Townshend, “Spatial resolution of remotely sensed imagery - A review paper,” Int. J. Remote Sens. 4(3), 497–520 (1983).
[CrossRef]

Fratter, C.

A. Meygret, C. Fratter, E. Breton, F. Cabot, M. C. Laubiès, and J. N. Hourcastagnou, “In-flight assessment of SPOT 5 image quality,” Proc. SPIE 4881, 179–188 (2003).
[CrossRef]

Haskell, A.

M. R. B. Forshaw, A. Haskell, P. F. Miller, D. J. Stanley, and J. R. G. Townshend, “Spatial resolution of remotely sensed imagery - A review paper,” Int. J. Remote Sens. 4(3), 497–520 (1983).
[CrossRef]

Hazane, P.

P. Kubik, E. Breton, A. Meygret, B. Cabrières, P. Hazane, and D. Léger, “SPOT4 HRVIR first in-flight image quality results,” Proc. SPIE 3498, 376–389 (1998).
[CrossRef]

Hourcastagnou, J. N.

A. Meygret, C. Fratter, E. Breton, F. Cabot, M. C. Laubiès, and J. N. Hourcastagnou, “In-flight assessment of SPOT 5 image quality,” Proc. SPIE 4881, 179–188 (2003).
[CrossRef]

Kojima, M.

K. Maeda, M. Kojima, and Y. Azuma, “Geometric and radiometric performance evaluation methods for marine observation satellite-1 (MOS-1) verification program (MVP),” Acta Astronaut. 15(6-7), 297–304 (1987).
[CrossRef]

Kubik, P.

P. Kubik, E. Breton, A. Meygret, B. Cabrières, P. Hazane, and D. Léger, “SPOT4 HRVIR first in-flight image quality results,” Proc. SPIE 3498, 376–389 (1998).
[CrossRef]

Laubiès, M. C.

A. Meygret, C. Fratter, E. Breton, F. Cabot, M. C. Laubiès, and J. N. Hourcastagnou, “In-flight assessment of SPOT 5 image quality,” Proc. SPIE 4881, 179–188 (2003).
[CrossRef]

Léger, D.

P. Kubik, E. Breton, A. Meygret, B. Cabrières, P. Hazane, and D. Léger, “SPOT4 HRVIR first in-flight image quality results,” Proc. SPIE 3498, 376–389 (1998).
[CrossRef]

Maeda, K.

K. Maeda, M. Kojima, and Y. Azuma, “Geometric and radiometric performance evaluation methods for marine observation satellite-1 (MOS-1) verification program (MVP),” Acta Astronaut. 15(6-7), 297–304 (1987).
[CrossRef]

Meygret, A.

A. Meygret, C. Fratter, E. Breton, F. Cabot, M. C. Laubiès, and J. N. Hourcastagnou, “In-flight assessment of SPOT 5 image quality,” Proc. SPIE 4881, 179–188 (2003).
[CrossRef]

P. Kubik, E. Breton, A. Meygret, B. Cabrières, P. Hazane, and D. Léger, “SPOT4 HRVIR first in-flight image quality results,” Proc. SPIE 3498, 376–389 (1998).
[CrossRef]

Miller, P. F.

M. R. B. Forshaw, A. Haskell, P. F. Miller, D. J. Stanley, and J. R. G. Townshend, “Spatial resolution of remotely sensed imagery - A review paper,” Int. J. Remote Sens. 4(3), 497–520 (1983).
[CrossRef]

Norton, C. L.

C. L. Norton, G. C. Brooks, and R. Welch, “Optical and Modulation Transfer Function,” Photogramm. Eng. Remote Sensing 43, 613–636 (1977).

Stanley, D. J.

M. R. B. Forshaw, A. Haskell, P. F. Miller, D. J. Stanley, and J. R. G. Townshend, “Spatial resolution of remotely sensed imagery - A review paper,” Int. J. Remote Sens. 4(3), 497–520 (1983).
[CrossRef]

Steel, W. H.

W. H. Steel, “The defocused image of sinusoidal gratings,” Opt. Acta (Lond.) 3, 65–74 (1956).

Townshend, J. R. G.

M. R. B. Forshaw, A. Haskell, P. F. Miller, D. J. Stanley, and J. R. G. Townshend, “Spatial resolution of remotely sensed imagery - A review paper,” Int. J. Remote Sens. 4(3), 497–520 (1983).
[CrossRef]

Welch, R.

C. L. Norton, G. C. Brooks, and R. Welch, “Optical and Modulation Transfer Function,” Photogramm. Eng. Remote Sensing 43, 613–636 (1977).

Zhou, G.

W. H. Carnahan and G. Zhou, “Fourier Transform techniques for the evaluation of the Thematic Mapper Line Spread Function,” Photogramm. Eng. Remote Sensing 52, 639–648 (1986).

Acta Astronaut.

K. Maeda, M. Kojima, and Y. Azuma, “Geometric and radiometric performance evaluation methods for marine observation satellite-1 (MOS-1) verification program (MVP),” Acta Astronaut. 15(6-7), 297–304 (1987).
[CrossRef]

Int. J. Remote Sens.

M. R. B. Forshaw, A. Haskell, P. F. Miller, D. J. Stanley, and J. R. G. Townshend, “Spatial resolution of remotely sensed imagery - A review paper,” Int. J. Remote Sens. 4(3), 497–520 (1983).
[CrossRef]

Opt. Acta (Lond.)

W. H. Steel, “The defocused image of sinusoidal gratings,” Opt. Acta (Lond.) 3, 65–74 (1956).

Photogramm. Eng. Remote Sensing

W. H. Carnahan and G. Zhou, “Fourier Transform techniques for the evaluation of the Thematic Mapper Line Spread Function,” Photogramm. Eng. Remote Sensing 52, 639–648 (1986).

H. J. Fang Lei, “Tiziani, “A comparison of methods to measure the modulation transfer function of aerial survey lens systems from image structures,” Photogramm. Eng. Remote Sensing 54, 41–46 (1988).

C. L. Norton, G. C. Brooks, and R. Welch, “Optical and Modulation Transfer Function,” Photogramm. Eng. Remote Sensing 43, 613–636 (1977).

Proc. SPIE

P. Kubik, E. Breton, A. Meygret, B. Cabrières, P. Hazane, and D. Léger, “SPOT4 HRVIR first in-flight image quality results,” Proc. SPIE 3498, 376–389 (1998).
[CrossRef]

A. Meygret, C. Fratter, E. Breton, F. Cabot, M. C. Laubiès, and J. N. Hourcastagnou, “In-flight assessment of SPOT 5 image quality,” Proc. SPIE 4881, 179–188 (2003).
[CrossRef]

Other

A. Rosak, C. Latry, V. Pascal, and D. Laubier, “From SPOT5 to Pleiades-HR: evolutions of the instrumental specifications”, in Proceedings of the 5th international conference on Space Optics, B. Warmbein, ed. (ESA SP-554, Noordwijk, Netherlands, 2004), 141–148.

D. Léger, F. Viallefont, P. Déliot, and C. Valorge, “On-orbit MTF assessment of satellite cameras”, in Post-launch calibration of satellite sensors, Morain and Budge, ed. (Taylor and Francis group, London, 2004).

H. Hwang, Y.-W. Choi, S. Kwak, M. Kim, and W. Park, “MTF assessment of high resolution satellite images using ISO 12233 slanted-edge method”, Proc. SPIE 7109, 710905–1-710905–9 (2008).

T. Choi, “IKONOS satellite in orbit, modulation transfer function measurement using edge and pulse methods”, MSc Thesis, South Dakota State University (2002).

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Figures (16)

Fig. 1
Fig. 1

Principle of 1-D oversampled edge response

Fig. 2
Fig. 2

Image around h1

Fig. 5
Fig. 5

Image around v3

Fig. 3
Fig. 3

Image around h2 and h3

Fig. 4
Fig. 4

Image around v1 and v2

Fig. 6
Fig. 6

1-D h1 edge

Fig. 8
Fig. 8

Results for horizontal edges

Fig. 7
Fig. 7

Fit of SPOT model for 1-D h2 edge in XS2

Fig. 9
Fig. 9

1-D v2 edge to be modified according to symmetry assumption and model assuming symmetry

Fig. 10
Fig. 10

Results for vertical edges

Fig. 11
Fig. 11

SPOT 5 THR image of Salon-de-Provence target

Fig. 12
Fig. 12

Comparison of along-track results

Fig. 13
Fig. 13

Comparison of across-track results

Fig. 14
Fig. 14

MTF curves for small edge image

Fig. 15
Fig. 15

MTF curves for large edge image

Fig. 16
Fig. 16

Results with and without model for a small edge and a 1200 µm defocus

Tables (4)

Tables Icon

Table 1 Features of the edges

Tables Icon

Table 2 Nomenclature of the edges

Tables Icon

Table 3 Obtained model parameters and MTFx

Tables Icon

Table 4 Obtained parameters values for large defocus

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

i(x,y) = l(x,y) h(x,y)
I(f x ,f y ) = L(f x ,f y ) .H(f x ,f y )
I(f x ,f y )/L(f x ,f y ) = H(f x ,f y )
l(x,y) = a .hea(x) + b
L(f x ,f y ) = a .Hea(f x ) + b .δ ( f x )
i(x,y) = l(x,y) h(x,y) + n(x,y)
I(f x ,f y ) = L(f x ,f y ) .H(f x ,f y ) + N(f x ,f y )
I(f x ,f y )/L(f x ,f y ) = H(f x ,f y ) + N(f x ,f y )/L(f x ,f y )
i(x,y) = [ l(x,y) h(x,y) ] .w(x,y) .comb(x,y)
I(f x ,f y ) = [ L(f x ,f y ) .H(f x ,f y ) ] W(f x ,f y ) comb(f x ,f y )
I(f x )/ [ a .Hea(f x ) + b .δ ( fx ) ] W(f x ) H(f x )
H diffraction = 2 π [ arccos ( (f x 2 + f y 2 ) 1/2 D λF ) (f x 2 + f y 2 ) 1/2 D λF ( 1 ( (f x 2 + f y 2 ) ( D λF ) 2 ) ) 1/2 ]
H optics = exp ( α x 2 f x 2 + α y 2 f y 2 )
H defocus = 2J 1 ( πΔ N (f x 2 + f y 2 ) 1/2 [ 1 λN(f x 2 + f y 2 ) 1/2 ] ) πΔ N (f x 2 + f y 2 ) 1/2 [ 1 λN(f x 2 + f y 2 ) 1/2 ]
H detector = sinc ( π f x f sx ) × sinc ( π f y f sy )
H moving = sinc ( π f y f sy )
H model = H diffraction .H optics .H defocus .H detector .H moving

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