## Improvement of the edge method for on-orbit MTF measurement

Optics Express, Vol. 18, Issue 4, pp. 3531-3545 (2010)

http://dx.doi.org/10.1364/OE.18.003531

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### 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.

© 2010 OSA

## 1. Introduction

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]

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]

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]

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. The edge method

_{x},f

_{y}) stands for the Fourier Transform of the image,

_{x},f

_{y}) stands for the Fourier Transform of the landscape,

_{x},f

_{y}) is the Transfer Function of the sensor.

_{x}, f

_{y}):

_{x},f

_{y}) is a decreasing function of the frequency and thus the noise term increases along with the frequency, spoiling the transfer function assessment for high frequencies.

_{x},f

_{y})⊗W (f

_{x},f

_{y}) ≠ 0 for all frequencies and not far from L(f

_{x},f

_{y}).

_{y}. Such software has been developed by Onera using Matlab under CNES studies. It has been applied with natural edges for SPOT 4 without success [8

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]

## 3. Changes of the method

## 4. Transfer function parametric model

_{defocus}[Eq. (14)] is taken from [10]. Classically, N is the aperture number and λ the central wavelength. α

_{x}or α

_{y}(depending on the direction of the perpendicular to the edge) and the defocus Δ are the parameters to find. f

_{x}and f

_{y}are the spatial frequencies corresponding to the rows and to the columns. f

_{sx}and f

_{sy}are the sampling frequencies along the directions corresponding respectively to x and y.

## 5. Description of the process

_{model}is computed, according to Eq. (17) in the direction perpendicular to the edge with initial parameter values, α

_{x}or α

_{y}, and Δ, chosen by the user. A Line Spread Function (LSF) [1

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]

_{x}or α

_{y}, and Δ.

## 6. First application: SPOT 1 XS1 and XS2 on-orbit MTF assessment

_{s}, 0.5 f

_{s}being the Nyquist frequency. Figure 8 shows that the resulting point is in full agreement with the measurement corresponding to the h1 edge on the array 1.

## 7. Second application: SPOT 5 HM MTF assessment

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]

## 8. Third application: Pleiades defocus assessment

- • Aperture number N = 19,
- • Ratio of diameter of the occultation to the pupil diameter = 0.3,
- • Perfect square detectors 13 x 13 µm
^{2}wide, - • No moving effect (H
_{moving}= 1), - • Defocus = 0 or 400 µm.

_{x}= α

_{y}= 1.583. For each image, two vertical edges have been extracted, a « large » one with 82 columns and 70 rows, and a « small » one with 42 columns and 11 rows.

- • First directly, that is to say without the use of a model,
- • Then using the transfer function parametric model (an “m” is added at the end of the name).

_{s}for the small edge. In this case, the model is then useful to eliminate the sensor noise. For the large edge, the averaging of the rows having the same phase enables to reduce the noise (Fig. 15 ). The obtained parameters and corresponding row MTF for Nyquist frequency are presented in Table 3 .

_{defocus}and of H

_{optics}are different enough only for high frequencies (typically above Nyquist) or for large defocus. As the noise disturb the MTF curve before Nyquist frequency, it becomes difficult, in this case of fairly small defocus, to make the right distinction between α and the defocus Δ.

_{s}. Beyond this frequency, the “direct” curve is quite noisy. The parameter values obtained are presented in Table 4 .

## 9. Conclusion

## Acknowledgements

## References and links

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. |

2. | W. H. Carnahan and G. Zhou, “Fourier Transform techniques for the evaluation of the Thematic Mapper Line Spread Function,” Photogramm. Eng. Remote Sensing |

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. |

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 |

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 |

7. | C. L. Norton, G. C. Brooks, and R. Welch, “Optical and Modulation Transfer Function,” Photogramm. Eng. Remote Sensing |

8. | P. Kubik, E. Breton, A. Meygret, B. Cabrières, P. Hazane, and D. Léger, “SPOT4 HRVIR first in-flight image quality results,” Proc. SPIE |

9. | D. Léger, F. Viallefont, P. Déliot, and C. Valorge, “On-orbit MTF assessment of satellite cameras”, in |

10. | W. H. Steel, “The defocused image of sinusoidal gratings,” Opt. Acta (Lond.) |

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 |

12. | A. Rosak, C. Latry, V. Pascal, and D. Laubier, “From SPOT5 to Pleiades-HR: evolutions of the instrumental specifications”, in |

**OCIS Codes**

(110.3000) Imaging systems : Image quality assessment

(110.4100) Imaging systems : Modulation transfer function

(280.0280) Remote sensing and sensors : Remote sensing and sensors

**ToC Category:**

Imaging Systems

**History**

Original Manuscript: October 6, 2009

Revised Manuscript: November 12, 2009

Manuscript Accepted: November 30, 2009

Published: February 3, 2010

**Citation**

Françoise Viallefont-Robinet and Dominique Léger, "Improvement of the edge method for on-orbit MTF measurement," Opt. Express **18**, 3531-3545 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-4-3531

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### References

- 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]
- 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).
- 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]
- T. Choi, “IKONOS satellite in orbit, modulation transfer function measurement using edge and pulse methods”, MSc Thesis, South Dakota State University (2002).
- 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).
- 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).
- C. L. Norton, G. C. Brooks, and R. Welch, “Optical and Modulation Transfer Function,” Photogramm. Eng. Remote Sensing 43, 613–636 (1977).
- 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]
- 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).
- W. H. Steel, “The defocused image of sinusoidal gratings,” Opt. Acta (Lond.) 3, 65–74 (1956).
- 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]
- 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.

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